quicksmart numeracy
TRANSCRIPT
QuickSmart Numeracy Resources and Organisation Manual
COPYRIGHT/ISBN:
QuickSmart Numeracy Resources and Organisation Manual Edition 2
© 2019 University of New England
This manual is copyright. Except as permitted under the Copyright Act of 1968 (Cth), no part of this
publication may be reproduced by any process, electronic or otherwise, without the specific written
permission of the copyright owner. Neither may information be stored electronically in any form
whatsoever without such permission.
Inquiries should be addressed to the University of New England.
ISBN: 978-1-921597-13-8
Contents QuickSmart Numeracy Resources
SECTION 1 : OVERVIEW Overview of QuickSmart Numeracy Program 1 How to use this Numeracy Resource and Organisation Folder 3 Numeracy Lesson Format 4 Problem Solving Lesson Format 5
SECTION 2 : TEACHING RESOURCES Hundreds Chart 1 – 100 7 Hundreds Chart 0 – 99 8 Number lines 1 – 20 9 Blank Number Lines 10 Multiplication Chart 11 Operation Facts 12
SECTION 3 : FOCUS FACTS Focus Fact Ideas 17 Addition and Subtraction 23 Multiplication and Division 37 Addition and Subtraction Facts to 10 51 Doubles Facts to 12 52 Square Number Facts to 12 53
SECTION 4 : SPEED SHEETS Addition and Subtraction 55 Multiplication and Division 69 Mixed Operation Speed Sheets 85 Solutions for Speed Sheets for Addition and Subtraction 89 Solutions for Speed Sheets for Multiplication and Division 103 Solutions for Speed Sheets for Mixed Operations 119
SECTION 5 : NUMERACY STRATEGIES Addition, Subtraction, Multiplication and Division 123 Strategy Card Proformas for Addition, Subtraction, Multiplication and Division 131
SECTION 6 : PROBLEM SOLVING The ‘6S’ Strategy for Problem Solving 143 Examples of Word Problems 145 Brain Teasers 155 Word Problem Solutions 157
SECTION 7 : NUMERACY GAMES Same Sums 161 Double O 163 QuickSmart Maths Language Dominoes 164 QuickSmart Maths Word Meaning Games 167 QuickSmart Numeracy Dominoes 169 QuickSmart Numeracy Bingo 170 QuickSmart Three in a Row 172
SECTION 8 : NUMERACY GRAPHS .................................................................... 173 Sample Graph 173 Numeracy Graphs for Individual Students 175
SECTION 9 : PROGRAM ADMINISTRATION RESOURCES ................................... 179 Permission Notes 179 Organisation Templates 181 QuickSmart Certificates 187 QuickSmart Data Collection and Stakeholder Survey Proformas 191
Section 1 - Overview
This section contains:
1. Overview of the QuickSmart Numeracy Program
2. QuickSmart Instructional Cycle
3. How to use the Numeracy Resource and Organisation Folder
4. Numeracy Lesson Format
5. Problem Solving/Strategy Development Lesson Format
1 F a s t a n d A c c u r a t e B a s i c S k i l l s
Overview of QuickSmart Numeracy Program Middle-school students, who have problems with learning, face many difficulties at school. These students often need intensive support to bring them ‘up to speed’ with basic skills such as the recall of number facts.
QuickSmart Numeracy is an educational program designed to support numeracy skill development for students from Years 4 to 9. The program was developed by a research team at the University of New England through the National Centre of Science, Information and Communication Technology, and Mathematics Education for Rural and Regional Australia (SiMERR National Research Centre).
The QuickSmart Numeracy program focuses on basic mathematics content by providing instruction that meets individual student learning needs. The program is called QuickSmart because it encourages students to become quick in their response speed and smart in their strategy use when acquiring basic academic skills. QuickSmart Numeracy emphasises the role of automaticity in learning. Automaticity is the immediate recall of basic information. QuickSmart focuses on developing students’ understanding, quick recall of basic academic facts and accuracy. Students aim to increase their accuracy and decrease response times as a means of demonstrating increasing automaticity. Ultimately, QuickSmart aims to free up student’s working memory so they can engage meaningfully in demanding school activities, such as problem solving and questions involving multiple computations.
The QuickSmart Numeracy program is intensive and requires students to work in pairs with an adult instructor for three thirty-minute lessons each week for thirty weeks. The program follows a structured lesson sequence based around a ‘focus set’ of number facts. Teaching and learning approaches used include explicit strategy instruction, modelling, discussion, questioning, and guided and independent practice. Students are given opportunities to self-monitor and to receive and generate immediate, informative feedback. In addition, the program incorporates the Australian version of the Cognitive Aptitude Assessment System (OZCAAS) computer software that provides information about each student’s accuracy and speed of recall of basic academic skills.
Observations and information gained from questioning students about their basic knowledge of fundamental skills are the basis of instructional decision-making and individualisation of instruction in the QuickSmart program. Assessment information is also collected from many activities in the program such as flash cards, speed sheets, and selected classroom-related worksheets. Assessment and instruction form a continuous cycle in the QuickSmart program.
An integral feature of the program is that much of the assessment information is made accessible and understandable to QuickSmart students. Students are able to evaluate their own learning through recording or graphing information, such as how many flash card number facts they can calculate accurately in one minute. The extensive use of graphing provides students with a motivating visual representation of their progress. Students are encouraged to use this information to set realistic future goals.
The QuickSmart program also emphasises the usefulness and relevance of number facts to regular classroom activities. This feature of the program is important for developing transfer of learning to other potentially higher-order settings. For example, the utility of basic academic understandings and skills can be presented to students by relating basic mathematics facts to money or common fractions, decimals and percentages. In addition, where possible, QuickSmart content is linked to current classroom content.
In summary, QuickSmart is a theory-based instructional intervention designed to improve students’ information retrieval times to levels that free up working memory capacity from an excessive focus on simple routine tasks. Becoming faster and more confident in recalling basic mathematics facts, for example, can mean that students have more time, energy and attention available for tackling more challenging mathematical problems.
2 F a s t a n d A c c u r a t e B a s i c S k i l l s
3 F a s t a n d A c c u r a t e B a s i c S k i l l s
How to use this Numeracy Resource and Organisation Folder
Material in this folder will be used to:
[1] conduct QuickSmart lessons
[2] administer and record QuickSmart lesson results
Sections 1 (Overview) and 2 (Resources) contain general information about the QuickSmart program, the QuickSmart Instructional Cycle and lesson formats. It also contains some proformas that could be useful in teaching number and basic mathematics concepts.
Sections 3 (Focus Facts) and 4 (Speed Sheets) contain the master copies of the Focus Fact Sheets for all four operations and the corresponding Speed Sheets.
Sections 5 (Numeracy Strategies) and 6 (Problem Solving) contain useful strategies for achieving automatic recall and understanding of basic number facts and the scaffold for solving mathematical word problems. A number of sheets of simple problems are also included.
Section 7 (Numeracy Games) contains the instructions for some of the numeracy games that are to be used at the conclusion of a QuickSmart lesson.
Section 8 (Numeracy Graphs) contains sample graphs, plus graph proformas for Flash Card recognition for all four operations.
Section 9 (Program Administration Resources) contains information sheets and organisational templates. Proformas for recording daily information of students’ progress and collating and collecting data are also included. Feel free to choose only that material which will assist you with the implementation of QuickSmart in your school.
All material contained in this two ring folder is removable and photocopiable. An electronic version of this material is available in the Resources section of the QuickSmart Numeracy Private Area.
4 F a s t a n d A c c u r a t e B a s i c S k i l l s
Numeracy Lesson Format
The lessons will generally follow this format:
1) Focus Facts: Knowledge / Understanding Check [5 minutes]
Review and discuss the current set of Focus Number Facts. Review errors and consolidate
understanding. Examine patterns in the number facts and how these make sense. Encourage
students to demonstrate their understandings of the processes. Focus on accurate and efficient
strategy use including developing understanding of number patterns/number sense. Work in
pairs. Provide explicit instruction and explanations targeting the facts that are difficult for
students to master.
2) Flash Cards: Automatic Recall of Focus Number Facts [5 minutes]
Use a pack of Flash Cards of current Focus Number Facts to challenge each student in turn to
correctly answer as many number facts as possible in 1 minute. Graph results in each student’s
folder and discuss improvements and errors.
3) Speed Sheet Challenge [5 minutes]
Students work on Speed Sheets focused on the current set of Focus Facts for 2 minutes. Give
feedback on errors and successes.
4) OZCAAS Assessment [5 minutes : One student]
Complete an OZCAAS assessment task relevant to the operation that is the focus of the lesson.
Discuss speed and accuracy results, and graph in student’s folder.
5) Independent Work Sheet [5 minutes – Student not doing OZCAAS task]
One student practises the current Focus Facts or the strategy being studied on a relevant
work sheet for 5 minutes while their QuickSmart partner completes an OZCAAS assessment.
Correct and give appropriate feedback.
Students swap activities numbered 4) and 5) above after 5 minutes.
6) Game [5 minutes]
Play a mathematics game to help students become quick and smart at automatically
recalling number facts and/or using number facts. Games include Three-in-a-Row, Same
Sums, Double O, Number Dominoes, and Numeracy Bingo.
5 F a s t a n d A c c u r a t e B a s i c S k i l l s
Problem Solving Lesson Format
The lessons will generally follow this format:
1) Mathematics Language Mastery [5 minutes]
Activities supporting the development of Mathematical vocabulary. May include:
• Maths language games such as provided dominoes and word meaning games
• Language based OZCAAS assessments
Establish an environment of success in this lesson. This may include reviewing errors from previous lessons, introducing mathematics language that will be useful and consolidating understanding of the 6S Problem Solving Strategy.
[Remember to include strategy instruction and mathematics language mastery opportunities incidentally throughout all QuickSmart instruction sessions.]
2) Guided Response to simple Mathematics Word Problems [10 minutes]
Use the ‘6S’ STRATEGY FOR PROBLEM SOLVING framework and a relevant sheet of Mathematics Word Problems
1. Search Read the problem and find the question
Clarify any vocabulary/comprehension difficulties.
Model searching to find what the problem is asking.
Underline the question to be solved.
2. Sort Identify what information is needed for solving this problem
Highlight key words that indicate the operations required to solve the problem.
Circle the numbers to be used.
Discuss any information included in the problem not needed to solve the problem (as appropriate).
3. See Visualise, sketch, tabulate, or document information relevant to the problem
Discuss how to 'visualise' the problem. Demonstrate ways of developing effective representations of the information in the problem.
4. Select Decide what operations are necessary for solving this problem
Discuss what actions or operation(s) should be used in solving the problem. Reword the question if it is still not clear.
Discuss how the operation(s) are identified.
5. Solve Solve the problem
Solve the problem, include the working out.
Discuss the need to convert all measurements to the same unit, if necessary.
6. Sense Check the answer makes sense
Reread the problem to check the correct question was answered.
Use estimation and number system understanding to validate the answer.
6 F a s t a n d A c c u r a t e B a s i c S k i l l s
3) Independent Problem Solving [10 minutes]
Encourage students to independently solve mathematics problems using the ‘6S’ Strategy.
4) Correction and Feedback [5 minutes]
It is important to correct all completed problems, give necessary feedback and praise good
thinking and problem solving.
Section 2 – Teaching Resources
This section contains: 1. Hundreds Chart
2. Hundreds Chart and Number Lines
3. Blank Number Lines
4. Multiplication Chart
5. Operation Facts
7 F a s t a n d A c c u r a t e B a s i c S k i l l s
Hundreds Chart 1 – 100
1 2 3 4 5 6 7 8 9 10
11 12 13 14 15 16 17 18 19 20
21 22 23 24 25 26 27 28 29 30
31 32 33 34 35 36 37 38 39 40
41 42 43 44 45 46 47 48 49 50
51 52 53 54 55 56 57 58 59 60
61 62 63 64 65 66 67 68 69 70
71 72 73 74 75 76 77 78 79 80
81 82 83 84 85 86 87 88 89 90
91 92 93 94 95 96 97 98 99 100
8 F a s t a n d A c c u r a t e B a s i c S k i l l s
Hundreds Chart 0 – 99
0 1 2 3 4 5 6 7 8 9
10 11 12 13 14 15 16 17 18 19
20 21 22 23 24 25 26 27 28 29
30 31 32 33 34 35 36 37 38 39
40 41 42 43 44 45 46 47 48 49
50 51 52 53 54 55 56 57 58 59
60 61 62 63 64 65 66 67 68 69
70 71 72 73 74 75 76 77 78 79
80 81 82 83 84 85 86 87 88 89
90 91 92 93 94 95 96 97 98 99
9 F a s t a n d A c c u r a t e B a s i c S k i l l s
Number lines 1 – 20
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20
10 F a s t a n d A c c u r a t e B a s i c S k i l l s
Blank Number Lines
Nu
mb
er li
nes
– t
o b
e ca
libra
ted
fo
r in
div
idu
al
mat
he
mat
ics
situ
atio
ns
11 F a s t a n d A c c u r a t e B a s i c S k i l l s
Multiplication Chart
12 0
12
24
36
48
60
72
84
96
10
8
12
0
13
2
14
4
Shad
ed a
rea
[as
an e
xam
ple
] 9
× 8
= 7
2
11 0
11
22
33
44
55
66
77
88
99
11
0
12
1
13
2
10 0
10
20
30
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50
60
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90
10
0
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0
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0
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27
36
45
54
63
72
81
90
99
10
8
8
0
8
16
24
32
40
48
56
64
72
80
88
96
7
0
7
14
21
28
35
42
49
56
63
70
77
84
6
0
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12
18
24
30
36
42
48
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60
66
72
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0
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× 0
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Operation Facts
Ad
dit
ion
Fac
ts (c
olo
ur
the
fact
s yo
u h
ave
lear
nt)
12
0 +
12
1 +
12
2 +
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3 +
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4 +
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5 +
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+ 1
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+ 1
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+ 1
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+ 1
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+ 1
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+ 1
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10
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10
8 +
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+ 1
0
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+ 1
0
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+ 1
0
9
0 +
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1 +
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9
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+ 9
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+ 9
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+ 9
8
0 +
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+ 8
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+ 8
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+ 8
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+ 7
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+ 7
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+ 6
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+ 6
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+ 6
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0 +
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+ 5
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+ 5
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+ 5
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0 +
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2 +
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+ 4
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+ 4
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+ 4
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+ 3
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+ 3
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+ 3
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+ 2
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+ 2
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+ 2
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+ 1
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+ 1
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+ 1
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+ 0
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+ 0
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+ 0
+ 0 1 2 3 4 5 6 7 8 9 10
11
12
13 F a s t a n d A c c u r a t e B a s i c S k i l l s
Sub
trac
tio
n F
acts
(co
lou
r th
e fa
cts
you
hav
e le
arn
t)
= 0
= 1
= 2
= 3
= 4
= 5
= 6
= 7
= 8
= 9
= 1
0
= 1
1
= 1
2
− 1
2
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− 1
2
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− 1
2
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− 1
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− 1
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− 1
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− 9
9 −
9
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− 8
8 −
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7 −
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− 5
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4 −
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9 −
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− 4
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− 4
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− 4
16
− 4
− 3
3 −
3
4 −
3
5 −
3
6 −
3
7 −
3
8 −
3
9 −
3
10
− 3
11
− 3
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− 3
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− 3
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− 3
15
− 3
− 2
2 −
2
3 −
2
4 −
2
5 −
2
6 −
2
7 −
2
8 −
2
9 −
2
10
− 2
11
− 2
12
− 2
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− 2
14
− 2
− 1
1 −
1
2 −
1
3 −
1
4 −
1
5 −
1
6 −
1
7 −
1
8 −
1
9 −
1
10
− 1
11
− 1
12
− 1
13
− 1
− 0
0 −
0
1 −
0
2 −
0
3 −
0
4 −
0
5 −
0
6 −
0
7 −
0
8 −
0
9 −
0
10
− 0
11
− 0
12
− 0
14 F a s t a n d A c c u r a t e B a s i c S k i l l s
Mu
ltip
licat
ion
Fac
ts (
colo
ur
the
fact
s yo
u h
ave
lear
nt)
12
0 ×
12
1 ×
12
2 ×
12
3 ×
12
4 ×
12
5 ×
12
6 ×
12
7 ×
12
8 ×
12
9 ×
12
10
× 1
2
11
× 1
2
12
× 1
2
11
0 ×
11
1 ×
11
2 ×
11
3 ×
11
4 ×
11
5 ×
11
6 ×
11
7 ×
11
8 ×
11
9 ×
11
10
× 1
1
11
× 1
1
12
× 1
1
10
0 ×
10
1 ×
10
2 ×
10
3 ×
10
4 ×
10
5 ×
10
6 ×
10
7 ×
10
8 ×
10
9 ×
10
10
× 1
0
11
× 1
0
12
× 1
0
9
0 ×
9
1 ×
9
2 ×
9
3 ×
9
4 ×
9
5 ×
9
6 ×
9
7 ×
9
8 ×
9
9 ×
9
10
× 9
11
× 9
12
× 9
8
0 ×
8
1 ×
8
2 ×
8
3 ×
8
4 ×
8
5 ×
8
6 ×
8
7 ×
8
8 ×
8
9 ×
8
10
× 8
11
× 8
12
× 8
7
0 ×
7
1 ×
7
2 ×
7
3 ×
7
4 ×
7
5 ×
7
6 ×
7
7 ×
7
8 ×
7
9 ×
7
10
× 7
11
× 7
12
× 7
6
0 ×
6
1 ×
6
2 ×
6
3 ×
6
4 ×
6
5 ×
6
6 ×
6
7 ×
6
8 ×
6
9 ×
6
10
× 6
11
× 6
12
× 6
5
0 ×
5
1 ×
5
2 ×
5
3 ×
5
4 ×
5
5 ×
5
6 ×
5
7 ×
5
8 ×
5
9 ×
5
10
× 5
11
× 5
12
× 5
4
0 ×
4
1 ×
4
2 ×
4
3 ×
4
4 ×
4
5 ×
4
6 ×
4
7 ×
4
8 ×
4
9 ×
4
10
× 4
11
× 4
12
× 4
3
0 ×
3
1 ×
3
2 ×
3
3 ×
3
4 ×
3
5 ×
3
6 ×
3
7 ×
3
8 ×
3
9 ×
3
10
× 3
11
× 3
12
× 3
2
0 ×
2
1 ×
2
2 ×
2
3 ×
2
4 ×
2
5 ×
2
6 ×
2
7 ×
2
8 ×
2
9 ×
2
10
× 2
11
× 2
12
× 2
1
0 ×
1
1 ×
1
2 ×
1
3 ×
1
4 ×
1
5 ×
1
6 ×
1
7 ×
1
8 ×
1
9 ×
1
10
× 1
11
× 1
12
× 1
0
0 ×
0
1 ×
0
2 ×
0
3 ×
0
4 ×
0
5 ×
0
6 ×
0
7 ×
0
8 ×
0
9 ×
0
10
× 0
11
× 0
12
× 0
× 0 1 2 3 4 5 6 7 8 9 10
11
12
15 F a s t a n d A c c u r a t e B a s i c S k i l l s
Div
isio
n F
acts
(co
lou
r th
e fa
cts
you
hav
e le
arn
t)
= 0
= 1
= 2
= 3
= 4
= 5
= 6
= 7
= 8
= 9
= 1
0
= 1
1
= 1
2
÷ 1
2
0 ÷
12
12
÷ 1
2
24
÷ 1
2
36
÷ 1
2
48
÷ 1
2
60
÷ 1
2
72
÷ 1
2
84
÷ 1
2
96
÷ 1
2
10
8 ÷
12
12
0 ÷
12
13
2 ÷
12
14
4 ÷
12
÷ 1
1
0 ÷
11
11
÷ 1
1
22
÷ 1
1
33
÷ 1
1
44
÷ 1
1
55
÷ 1
1
66
÷ 1
1
77
÷ 1
1
88
÷ 1
1
99
÷ 1
1
11
0 ÷
11
12
1 ÷
11
13
2 ÷
11
÷ 1
0
0 ÷
10
10
÷ 1
0
20
÷ 1
0
30
÷ 1
0
40
÷ 1
0
50
÷ 1
0
60
÷ 1
0
70
÷ 1
0
80
÷ 1
0
90
÷ 1
0
10
0 ÷
10
11
0 ÷
10
12
0 ÷
10
÷ 9
0 ÷
9
9 ÷
9
18
÷ 9
27
÷ 9
36
÷ 9
45
÷ 9
54
÷ 9
63
÷ 9
72
÷ 9
81
÷ 9
90
÷ 9
99
÷ 9
10
8 ÷
9
÷ 8
0 ÷
8
8 ÷
8
16
÷ 8
24
÷ 8
32
÷ 8
40
÷ 8
48
÷ 8
56
÷ 8
64
÷ 8
72
÷ 8
80
÷ 8
88
÷ 8
96
÷ 8
÷ 7
0 ÷
7
7 ÷
7
14
÷ 7
21
÷ 7
28
÷ 7
35
÷ 7
42
÷ 7
49
÷ 7
56
÷ 7
63
÷ 7
70
÷ 7
77
÷ 7
84
÷ 7
÷ 6
0 ÷
6
6 ÷
6
12
÷ 6
18
÷ 6
24
÷ 6
30
÷ 6
36
÷ 6
42
÷ 6
48
÷ 6
54
÷ 6
60
÷ 6
66
÷ 6
72
÷ 6
÷ 5
0 ÷
5
5 ÷
5
10
÷ 5
15
÷ 5
20
÷ 5
25
÷ 5
30
÷ 5
35
÷ 5
40
÷ 5
45
÷ 5
50
÷ 5
55
÷ 5
60
÷ 5
÷ 4
0 ÷
4
4 ÷
4
8 ÷
4
12
÷ 4
16
÷ 4
20
÷ 4
24
÷ 4
28
÷ 4
32
÷ 4
36
÷ 4
40
÷ 4
44
÷ 4
48
÷ 4
÷ 3
0 ÷
3
3 ÷
3
6 ÷
3
9 ÷
3
12
÷ 3
15
÷ 3
18
÷ 3
21
÷ 3
24
÷ 3
27
÷ 3
30
÷ 3
33
÷ 3
36
÷ 3
÷ 2
0 ÷
2
2 ÷
2
4 ÷
2
6 ÷
2
8 ÷
2
10
÷ 2
12
÷ 2
14
÷ 2
16
÷ 2
18
÷ 2
20
÷ 2
22
÷ 2
24
÷ 2
÷ 1
0 ÷
1
1 ÷
1
2 ÷
1
3 ÷
1
4 ÷
1
5 ÷
1
6 ÷
1
7 ÷
1
8 ÷
1
9 ÷
1
10
÷ 1
11
÷ 1
12
÷ 1
16 F a s t a n d A c c u r a t e B a s i c S k i l l s
Section 3 - Focus Facts
This section contains:
1. Ideas to be used to enhance understanding when discussing Focus Fact sets
2. Focus Fact Sheets for Addition and Subtraction
3. Focus Fact Sheets for Multiplication and Division
4. Addition and Subtraction Facts to 10
5. Doubles Facts to 12
6. Square Number Facts to 12
QuickSmart Instructors
The following section Focus Fact Ideas defines, elaborates and gives
examples of ideas that would be useful for QuickSmart students in understanding
their basic number facts.
The information contained at the bottom of each Focus Fact sheet indicates
which strategies are relevant to that set of Focus Facts. Use these ideas in
Section 1 of the QuickSmart lesson and incidentally throughout all
QuickSmart instruction.
17
F a s t a n d A c c u r a t e B a s i c S k i l l s
Focus Fact Ideas These ideas can be useful in establishing understanding throughout the QuickSmart Numeracy Program. QuickSmart encourages students to understand and remember basic number facts and aim for quick and accurate responses.
1. DEVELOPING AUTOMATIC RECALL
The focus of the QuickSmart Numeracy program is to enable students to understand and then
practise in order to automatically provide the answer to all the basic number facts across all four
operations [ + ; – ; × ; ÷ ].
2. ADDITION AND SUBTRACTION ARE OPPOSITE OPERATIONS
If you know one addition fact, you also know one more addition fact and the two subtraction facts
using the same numbers. For example,
If you know that 4 + 6 = 10, you also know that 6 + 4 = 10, and you also know these subtraction facts: 10 – 6 = 4; 10 – 4 = 6
3. CHANGING THE ORDER OF NUMBERS IN ADDITION CALCULATIONS
Changing the order of the addends (the numbers you are adding) gives the same sum. For
example,
2 + 9 is the same as 9 + 2
and
3 + 5 + 7 is the same as 7 + 3 + 5
Often, changing the order in which numbers are added makes it easier to calculate the sum mentally. For example,
96 + 7 + 4 is more easily calculated as 96 + 4 + 7
You cannot change the order of the numbers in subtraction calculations. For example,
6 – 4 is NOT the same as 4 – 6
4. ADDING OR SUBTRACTING ZERO
4.1. Adding Zero
When you add zero to any number your answer is the original number. For example,
5 + 0 = 5 and 0 + 63 = 63 4.2. Subtracting Zero
When you subtract zero from any number your answer is the original number. For example,
12 – 0 = 12
5. COUNTING ON/COUNTING BACK WITH WHOLE NUMBERS
5.1. Counting on for addition
When adding two numbers, if the calculation is not known automatically, students may find it
helpful to count on from the larger number.
5.2. Counting back for subtraction
When doing a subtraction calculation, students may find it helpful to count back from the larger
number.
18
F a s t a n d A c c u r a t e B a s i c S k i l l s
Focus Fact Ideas (continued)
6. BRIDGING 10
Knowledge of pairs of numbers whose sum is 10 is very valuable. Students can use this knowledge
to calculate other facts. For example,
8 + 5 could be thought of as (8 + 2) + 3 = 10 + 3 = 13
and
14 – 5 could be thought of as (14 – 4) – 1 = 10 – 1 = 9
7. PARTITIONING COMBINATIONS OF 10
Automatic knowledge of number facts to 10 can assist with lengthy addition calculations. For
example,
4 + 7 + 6 + 8 + 3 + 2 could be rearranged to read (4 + 6) + (7 + 3) + (8 + 2)
Partitioning larger numbers into combinations including tens can also assist the addition of larger
numbers. For example,
12 + 11 could be partitioned as (10 + 2) + (10 + 1), which is easier to calculate quickly,
adding tens together (to get 10 + 10 = 20) and then units together
(2 + 1 = 3) for the final answer of 23.
8. SPECIFIC ADDITION/SUBTRACTION APPROACHES
8.1. Adding 5
When adding 5 to a number that ends in 0 or 5, remember to use your knowledge of counting on
by 5s. For example,
275 + 5 = 2[75] + 5 = 280
and
360 + 5 = 3[60] + 5 = 365
8.2. Subtracting 5
When subtracting 5 from a number that ends in 0 or 5, remember to use your knowledge of
counting back by 5s. For example,
275 – 5 = 2[75] – 5 = 270
and
360 – 5 = 3[60] – 5 = 355
19
F a s t a n d A c c u r a t e B a s i c S k i l l s
Focus Fact Ideas (continued)
8.3. Adding/Subtracting 9
9 can be added or subtracted more easily if it is first converted to 10. You then add or subtract 1
to compensate. For example,
23 + 9 can be changed to
(23 + 10) − 1
= (33) − 1
= 32
and 32 − 9 can be changed to
(32 − 10) + 1
= (22) + 1
= 23
8.4. Adding 10
When adding 10, add ‘1’ to the tens column. This approach works because in this case the digit ‘1’
represents one ten. For example,
47 + 10 = 57
8.5. Adding 100
When adding 100, add ‘1’ to the hundreds column. This approach works because in this case the
digit ‘1’ represents one hundred. For example,
530 + 100 = 630
8.6. Subtracting 10
When subtracting 10, subtract ‘1’ from the tens column. This approach works because in this case
the digit ‘1’ represents one ten. For example,
47 – 10 = 37
8.7. Subtracting 100
When subtracting 100, subtract ‘1’ from the hundreds column. This approach works because in
this case the digit ‘1’ represents one hundred. For example,
530 – 100 = 430
9. MULTIPLICATION AS REPEATED ADDITION OF WHOLE NUMBERS
Using repeated addition and subtraction of the same number can help in the building of sets of
number facts for all four operations on whole numbers. Refer to the examples below.
4 + 4 = 8 (two lots of 4 is eight)
8 + 4 = 12 (two lots of four plus one lot of four is three lots of four, i.e. 12)
12 + 4 = 16 (three lots of four plus one lot of four is four lots of four, i.e. 16)
So 4 + 4 + 4 + 4 is the same as 4 × 4 = 16
20
F a s t a n d A c c u r a t e B a s i c S k i l l s
Focus Fact Ideas (continued)
10. MULTIPLICATION AND DIVISION ARE RECIPROCAL OPERATIONS
If you know one multiplication fact you also know one more multiplication fact and the two
division facts using the same numbers. For example,
if you know that 2 × 6 = 12 you also know that 6 × 2 = 12 and these division facts are
also known: 12 ÷ 2 = 6; 12 ÷ 6 = 2
11. CHANGING THE ORDER OF NUMBERS IN MULTIPLICATION CALCULATIONS
Changing the order of the numbers you are multiplying gives the same answer. For example,
8 × 3 is the same as 3 × 8 and 7 × 2 × 4 is the same as 2 × 4 × 7
Often, changing the order in which numbers are multiplied makes it easier to do the calculation.
For example,
2 × 37 × 5 is more easily calculated as 2 × 5 × 37
You cannot change the order of the numbers in division calculations. For example,
3 ÷ 1 is NOT the same as 1 ÷ 3
12. MULTIPLYING BY ZERO
Any number multiplied by 0 is always 0. For example,
12 × 0 = 0 and 117 × 0 = 0
13. MULTIPLYING OR DIVIDING BY 1
Multiplying or dividing any number by 1 does not change the number. For example,
16 × 1 = 1 × 16 = 16
and
25 ÷ 1 = 25
14. SKIP COUNTING
Skip counting can help with multiplication. For example,
8 × 2 can be calculated by counting by 2s and keeping a tally, i.e. 2, 4, 6, 8, 10, 12, 14, 16.
8 × 5 can be calculated by counting by 5s: 5, 10, 15, 20, 25, 30, 35, 40.
Notice that when you skip count by 5, your answer will always have 0 or 5 as the last digit.
15. KNOWLEDGE OF DOUBLES AND HALVES
Multiplying by two is the same as doubling. For example,
12 × 2 is the same as 12 + 12 or DOUBLE 12 Dividing by
two is the same as halving. For example,
12 ÷ 2 is the same as ½ of 12
21
F a s t a n d A c c u r a t e B a s i c S k i l l s
Focus Fact Ideas (continued)
16. NEAR DOUBLES
Doubles facts can be used to make other calculations easier. For example,
5 + 6 can be worked out as double 5 (i.e. 5 + 5) and 1 more.
17. RELATING 2× AND 4× NUMBER FACTS [DOUBLES/HALVES]
The 4× number facts are doubles of the 2× number facts. For example,
4 × 2 is double 2 × 2
The 2× number facts are halves of the 4× number facts. For example,
2 × 3 is the same as ½ of (4 × 3)
18. UNDERSTANDING THE RELATIONSHIP BETWEEN 5 AND 10
Because 5 is a half of 10 and 10 is double 5, being able to count by 5s and 10s will help with
multiplication facts when multiplying by either 5 or 10. For example,
7 × 5 is the same as ½ of 7 × 10
19. WHY YOU CAN’T DIVIDE BY ZERO
Think about what it means to divide, for example, 6 by 3. You are asking how many groups of 3 it
takes to make 6. Clearly, it takes 2 groups of 3 to make 6.
This might look like:
The diagram shows how if you put 6 crosses into groups of 3, there
are 2 groups.
Then if we ask you to divide 6 by 0, we are asking how many groups of 0 it takes to make 6. The
problem is that it wouldn’t matter how many groups of zero there were, you would only ever
have zero in total – you just cannot put groups of zero together to make 6 eventually. There is
nothing in each group so the total is always nothing.
Here we see groups of zero crosses. Clearly there
will never be 6 crosses no matter how many groups
of zero you draw.
An interesting case arises when you consider 0 ÷ 0. You could try asking yourself, ‘How many
zeros does it take to make zero?’ The problem here is that you could answer ‘6’, or ‘10’, or ‘3452’
or whatever, and there isn’t a unique answer. So again, you can’t get an answer to the question of
dividing by zero.
× × × × × ×
22
F a s t a n d A c c u r a t e B a s i c S k i l l s
Addition and Subtraction Focus Facts
23
Focus Facts
F a s t a n d A c c u r a t e B a s i c S k i l l s
Student Name: ____________________________________________________________
Addition and Subtraction Facts + 0 and − 0
0 + 0 = 0 0 + 0 = 0 0 − 0 = 0 0 − 0 = 0
1 + 0 = 1 0 + 1 = 1 1 − 0 = 1 1 − 1 = 0
2 + 0 = 2 0 + 2 = 2 2 − 0 = 2 2 − 2 = 0
3 + 0 = 3 0 + 3 = 3 3 − 0 = 3 3 − 3 = 0
4 + 0 = 4 0 + 4 = 4 4 − 0 = 4 4 − 4 = 0
5 + 0 = 5 0 + 5 = 5 5 − 0 = 5 5 − 5 = 0
6 + 0 = 6 0 + 6 = 6 6 − 0 = 6 6 − 6 = 0
7 + 0 = 7 0 + 7 = 7 7 − 0 = 7 7 − 7 = 0
8 + 0 = 8 0 + 8 = 8 8 − 0 = 8 8 − 8 = 0
9 + 0 = 9 0 + 9 = 9 9 − 0 = 9 9 − 9 = 0
10 + 0 = 10 0 + 10 = 10 10 − 0 = 10 10 − 10 = 0
11 + 0 = 11 0 + 11 = 11 11 − 0 = 11 11 − 11 = 0
12 + 0 = 12 0 + 12 = 12 12 − 0 = 12 12 − 12 = 0
APPLICABLE FOCUS FACT IDEAS 1. Developing automatic recall 3. Changing the order of numbers in addition calculations 4. Adding or subtracting zero
INSTRUCTOR: For detailed explanations of the relevant strategies (as numbered above) please refer to the Focus Fact Ideas on pp. 17 - 21 of this document.
24
Focus Facts
F a s t a n d A c c u r a t e B a s i c S k i l l s
Student Name: ____________________________________________________________
Addition and Subtraction Facts + 1 and − 1
0 + 1 = 1 1 + 0 = 1 1 − 1 = 0 1 − 0 = 1
1 + 1 = 2 1 + 1 = 2 2 − 1 = 1 2 − 1 = 1
2 + 1 = 3 1 + 2 = 3 3 − 1 = 2 3 − 2 = 1
3 + 1 = 4 1 + 3 = 4 4 − 1 = 3 4 − 3 = 1
4 + 1 = 5 1 + 4 = 5 5 − 1 = 4 5 − 4 = 1
5 + 1 = 6 1 + 5 = 6 6 − 1 = 5 6 − 5 = 1
6 + 1 = 7 1 + 6 = 7 7 − 1 = 6 7 − 6 = 1
7 + 1 = 8 1 + 7 = 8 8 − 1 = 7 8 − 7 = 1
8 + 1 = 9 1 + 8 = 9 9 − 1 = 8 9 − 8 = 1
9 + 1 = 10 1 + 9 = 10 10 − 1 = 9 10 − 9 = 1
10 + 1 = 11 1 + 10 = 11 11 − 1 = 10 11 − 10 = 1
11 + 1 = 12 1 + 11 = 12 12 − 1 = 11 12 − 11 = 1
12 + 1 = 13 1 + 12 = 13 13 − 1 = 12 13 − 12 = 1
APPLICABLE FOCUS FACT IDEAS 1. Developing automatic recall 2. Addition and subtraction are opposite operations 3. Changing the order of numbers in addition calculations
5. Counting on/counting back with whole numbers
INSTRUCTOR: For detailed explanations of the relevant strategies (as numbered above) please refer to the Focus Fact Ideas on pp. 17 - 21 of this document.
25
Focus Facts
F a s t a n d A c c u r a t e B a s i c S k i l l s
Student Name: _____________________________________________________________
Addition and Subtraction Facts + 2 and − 2
0 + 2 = 2 2 + 0 = 2 2 − 2 = 0 2 − 0 = 2
1 + 2 = 3 2 + 1 = 3 3 − 2 = 1 3 − 1 = 2
2 + 2 = 4 2 + 2 = 4 4 − 2 = 2 4 − 2 = 2
3 + 2 = 5 2 + 3 = 5 5 − 2 = 3 5 − 3 = 2
4 + 2 = 6 2 + 4 = 6 6 − 2 = 4 6 − 4 = 2
5 + 2 = 7 2 + 5 = 7 7 − 2 = 5 7 − 5 = 2
6 + 2 = 8 2 + 6 = 8 8 − 2 = 6 8 − 6 = 2
7 + 2 = 9 2 + 7 = 9 9 − 2 = 7 9 − 7 = 2
8 + 2 = 10 2 + 8 = 10 10 − 2 = 8 10 − 8 = 2
9 + 2 = 11 2 + 9 = 11 11 − 2 = 9 11 − 9 = 2
10 + 2 = 12 2 + 10 = 12 12 − 2 = 10 12 − 10 = 2
11 + 2 = 13 2 + 11 = 13 13 − 2 = 11 13 − 11 = 2
12 + 2 = 14 2 + 12 = 14 14 − 2 = 12 14 − 12 = 2
APPLICABLE FOCUS FACT IDEAS 1. Developing automatic recall 6. Bridging 10 2. Addition and subtraction are opposite operations 16. Near doubles 3. Changing the order of numbers in addition calculations 5. Counting on/counting back with whole numbers
INSTRUCTOR: For detailed explanations of the relevant strategies (as numbered above) please refer to the Focus Fact Ideas on pp. 17 - 21 of this document.
26
Focus Facts
F a s t a n d A c c u r a t e B a s i c S k i l l s
Student Name: ____________________________________________________________
Addition and Subtraction Facts + 3 and − 3
0 + 3 = 3 3 + 0 = 3 3 − 3 = 0 3 − 0 = 3
1 + 3 = 4 3 + 1 = 4 4 − 3 = 1 4 − 1 = 3
2 + 3 = 5 3 + 2 = 5 5 − 3 = 2 5 − 2 = 3
3 + 3 = 6 3 + 3 = 6 6 − 3 = 3 6 − 3 = 3
4 + 3 = 7 3 + 4 = 7 7 − 3 = 4 7 − 4 = 3
5 + 3 = 8 3 + 5 = 8 8 − 3 = 5 8 − 5 = 3
6 + 3 = 9 3 + 6 = 9 9 − 3 = 6 9 − 6 = 3
7 + 3 = 10 3 + 7 = 10 10 − 3 = 7 10 − 7 = 3
8 + 3 = 11 3 + 8 = 11 11 − 3 = 8 11 − 8 = 3
9 + 3 = 12 3 + 9 = 12 12 − 3 = 9 12 − 9 = 3
10 + 3 = 13 3 + 10 = 13 13 − 3 = 10 13 − 10 = 3
11 + 3 = 14 3 + 11 = 14 14 − 3 = 11 14 − 11 = 3
12 + 3 = 15 3 + 12 = 15 15 − 3 = 12 15 − 12 = 3
APPLICABLE FOCUS FACT IDEAS 1. Developing automatic recall 6. Bridging 10 2. Addition and subtraction are opposite operations 16. Near doubles 3. Changing the order of numbers in addition calculations 5. Counting on/counting back with whole numbers
INSTRUCTOR: For detailed explanations of the relevant strategies (as numbered above) please refer to the Focus Fact Ideas on pp. 17 - 21 of this document.
27
Focus Facts
F a s t a n d A c c u r a t e B a s i c S k i l l s
Student Name: ____________________________________________________________
Addition and Subtraction Facts + 4 and − 4
0 + 4 = 4 4 + 0 = 4 4 − 4 = 0 4 − 0 = 4
1 + 4 = 5 4 + 1 = 5 5 − 4 = 1 5 − 1 = 4
2 + 4 = 6 4 + 2 = 6 6 − 4 = 2 6 − 2 = 4
3 + 4 = 7 4 + 3 = 7 7 − 4 = 3 7 − 3 = 4
4 + 4 = 8 4 + 4 = 8 8 − 4 = 4 8 − 4 = 4
5 + 4 = 9 4 + 5 = 9 9 − 4 = 5 9 − 5 = 4
6 + 4 = 10 4 + 6 = 10 10 − 4 = 6 10 − 6 = 4
7 + 4 = 11 4 + 7 = 11 11 − 4 = 7 11 − 7 = 4
8 + 4 = 12 4 + 8 = 12 12 − 4 = 8 12 − 8 = 4
9 + 4 = 13 4 + 9 = 13 13 − 4 = 9 13 − 9 = 4
10 + 4 = 14 4 + 10 = 14 14 − 4 = 10 14 − 10 = 4
11 + 4 = 15 4 + 11 = 15 15 − 4 = 11 15 − 11 = 4
12 + 4 = 16 4 + 12 = 16 16 − 4 = 12 16 − 12 = 4
APPLICABLE FOCUS FACT IDEAS 1. Developing automatic recall 6. Bridging 10 2. Addition and subtraction are opposite operations 16. Near doubles 3. Changing the order of numbers in addition calculations 5. Counting on/counting back with whole numbers
INSTRUCTOR: For detailed explanations of the relevant strategies (as numbered above) please refer to the Focus Fact Ideas on pp. 17 - 21 of this document.
28
Focus Facts
F a s t a n d A c c u r a t e B a s i c S k i l l s
Student Name: ____________________________________________________________
Addition and Subtraction Facts + 5 and − 5
0 + 5 = 5 5 + 0 = 5 5 − 5 = 0 5 − 0 = 5
1 + 5 = 6 5 + 1 = 6 6 − 5 = 1 6 − 1 = 5
2 + 5 = 7 5 + 2 = 7 7 − 5 = 2 7 − 2 = 5
3 + 5 = 8 5 + 3 = 8 8 − 5 = 3 8 − 3 = 5
4 + 5 = 9 5 + 4 = 9 9 − 5 = 4 9 − 4 = 5
5 + 5 = 10 5 + 5 = 10 10 − 5 = 5 10 − 5 = 5
6 + 5 = 11 5 + 6 = 11 11 − 5 = 6 11 − 6 = 5
7 + 5 = 12 5 + 7 = 12 12 − 5 = 7 12 − 7 = 5
8 + 5 = 13 5 + 8 = 13 13 − 5 = 8 13 − 8 = 5
9 + 5 = 14 5 + 9 = 14 14 − 5 = 9 14 − 9 = 5
10 + 5 = 15 5 + 10 = 15 15 − 5 = 10 15 − 10 = 5
11 + 5 = 16 5 + 11 = 16 16 − 5 = 11 16 − 11 = 5
12 + 5 = 17 5 + 12 = 17 17 − 5 = 12 17 − 12 = 5
APPLICABLE FOCUS FACT IDEAS 1. Developing automatic recall 6. Bridging 10 2. Addition and subtraction are opposite operations 8.1. Adding 5 3. Changing the order of numbers in addition calculations 8.2. Subtracting 5 5. Counting on/counting back with whole numbers 16. Near doubles
INSTRUCTOR: For detailed explanations of the relevant strategies (as numbered above) please refer to the Focus Fact Ideas on pp. 17 - 21 of this document.
29
Focus Facts
F a s t a n d A c c u r a t e B a s i c S k i l l s
Student Name: ____________________________________________________________
Addition and Subtraction Facts + 6 and − 6
0 + 6 = 6 6 + 0 = 6 6 − 6 = 0 6 − 0 = 6
1 + 6 = 7 6 + 1 = 7 7 − 6 = 1 7 − 1 = 6
2 + 6 = 8 6 + 2 = 8 8 − 6 = 2 8 − 2 = 6
3 + 6 = 9 6 + 3 = 9 9 − 6 = 3 9 − 3 = 6
4 + 6 = 10 6 + 4 = 10 10 − 6 = 4 10 − 4 = 6
5 + 6 = 11 6 + 5 = 11 11 − 6 = 5 11 − 5 = 6
6 + 6 = 12 6 + 6 = 12 12 − 6 = 6 12 − 6 = 6
7 + 6 = 13 6 + 7 = 13 13 − 6 = 7 13 − 7 = 6
8 + 6 = 14 6 + 8 = 14 14 − 6 = 8 14 − 8 = 6
9 + 6 = 15 6 + 9 = 15 15 − 6 = 9 15 − 9 = 6
10 + 6 = 16 6 + 10 = 16 16 − 6 = 10 16 − 10 = 6
11 + 6 = 17 6 + 11 = 17 17 − 6 = 11 17 − 11 = 6
12 + 6 = 18 6 + 12 = 18 18 − 6 = 12 18 − 12 = 6
APPLICABLE FOCUS FACT IDEAS 1. Developing automatic recall 6. Bridging 10 2. Addition and subtraction are opposite operations 16. Near doubles 3. Changing the order of numbers in addition calculations 5. Counting on/counting back with whole numbers
INSTRUCTOR: For detailed explanations of the relevant strategies (as numbered above) please refer to the Focus Fact Ideas on pp. 17 - 21 of this document.
30
Focus Facts
F a s t a n d A c c u r a t e B a s i c S k i l l s
Student Name: ____________________________________________________________
Addition and Subtraction Facts + 7 and − 7
0 + 7 = 7 7 + 0 = 7 7 − 7 = 0 7 − 0 = 7
1 + 7 = 8 7 + 1 = 8 8 − 7 = 1 8 − 1 = 7
2 + 7 = 9 7 + 2 = 9 9 − 7 = 2 9 − 2 = 7
3 + 7 = 10 7 + 3 = 10 10 − 7 = 3 10 − 3 = 7
4 + 7 = 11 7 + 4 = 11 11 − 7 = 4 11 − 4 = 7
5 + 7 = 12 7 + 5 = 12 12 − 7 = 5 12 − 5 = 7
6 + 7 = 13 7 + 6 = 13 13 − 7 = 6 13 − 6 = 7
7 + 7 = 14 7 + 7 = 14 14 − 7 = 7 14 − 7 = 7
8 + 7 = 15 7 + 8 = 15 15 − 7 = 8 15 − 8 = 7
9 + 7 = 16 7 + 9 = 16 16 − 7 = 9 16 − 9 = 7
10 + 7 = 17 7 + 10 = 17 17 − 7 = 10 17 − 10 = 7
11 + 7 = 18 7 + 11 = 18 18 − 7 = 11 18 − 11 = 7
12 + 7 = 19 7 + 12 = 19 19 − 7 = 12 19 − 12 = 7
APPLICABLE FOCUS FACT IDEAS 1. Developing automatic recall 6. Bridging 10 2. Addition and subtraction are opposite operations 16. Near doubles 3. Changing the order of numbers in addition calculations 5. Counting on/counting back with whole numbers
INSTRUCTOR: For detailed explanations of the relevant strategies (as numbered above) please refer to the Focus Fact Ideas on pp. 17 - 21 of this document.
31
Focus Facts
F a s t a n d A c c u r a t e B a s i c S k i l l s
Student Name: ____________________________________________________________
Addition and Subtraction Facts + 8 and − 8
0 + 8 = 8 8 + 0 = 8 8 − 8 = 0 8 − 0 = 8
1 + 8 = 9 8 + 1 = 9 9 − 8 = 1 9 − 1 = 8
2 + 8 = 10 8 + 2 = 10 10 − 8 = 2 10 − 2 = 8
3 + 8 = 11 8 + 3 = 11 11 − 8 = 3 11 − 3 = 8
4 + 8 = 12 8 + 4 = 12 12 − 8 = 4 12 − 4 = 8
5 + 8 = 13 8 + 5 = 13 13 − 8 = 5 13 − 5 = 8
6 + 8 = 14 8 + 6 = 14 14 − 8 = 6 14 − 6 = 8
7 + 8 = 15 8 + 7 = 15 15 − 8 = 7 15 − 7 = 8
8 + 8 = 16 8 + 8 = 16 16 − 8 = 8 16 − 8 = 8
9 + 8 = 17 8 + 9 = 17 17 − 8 = 9 17 − 9 = 8
10 + 8 = 18 8 + 10 = 18 18 − 8 = 10 18 − 10 = 8
11 + 8 = 19 8 + 11 = 19 19 − 8 = 11 19 − 11 = 8
12 + 8 = 20 8 + 12 = 20 20 − 8 = 12 20 − 12 = 8
APPLICABLE FOCUS FACT IDEAS 1. Developing automatic recall 6. Bridging 10 2. Addition and subtraction are opposite operations 16. Near doubles 3. Changing the order of numbers in addition calculations 5. Counting on/counting back with whole numbers
INSTRUCTOR: For detailed explanations of the relevant strategies (as numbered above) please refer to the Focus Fact Ideas on pp. 17 - 21 of this document.
32
Focus Facts
F a s t a n d A c c u r a t e B a s i c S k i l l s
Student Name: ____________________________________________________________
Addition and Subtraction Facts + 9 and − 9
0 + 9 = 9 9 + 0 = 9 9 − 9 = 0 9 − 0 = 9
1 + 9 = 10 9 + 1 = 10 10 − 9 = 1 10 − 1 = 9
2 + 9 = 11 9 + 2 = 11 11 − 9 = 2 11 − 2 = 9
3 + 9 = 12 9 + 3 = 12 12 − 9 = 3 12 − 3 = 9
4 + 9 = 13 9 + 4 = 13 13 − 9 = 4 13 − 4 = 9
5 + 9 = 14 9 + 5 = 14 14 − 9 = 5 14 − 5 = 9
6 + 9 = 15 9 + 6 = 15 15 − 9 = 6 15 − 6 = 9
7 + 9 = 16 9 + 7 = 16 16 − 9 = 7 16 − 7 = 9
8 + 9 = 17 9 + 8 = 17 17 − 9 = 8 17 − 8 = 9
9 + 9 = 18 9 + 9 = 18 18 − 9 = 9 18 − 9 = 9
10 + 9 = 19 9 + 10 = 19 19 − 9 = 10 19 − 10 = 9
11 + 9 = 20 9 + 11 = 20 20 − 9 = 11 20 − 11 = 9
12 + 9 = 21 9 + 12 = 21 21 − 9 = 12 21 − 12 = 9
APPLICABLE FOCUS FACT IDEAS 1. Developing automatic recall 6. Bridging 10 2. Addition and subtraction are opposite operations 8.3. Adding/Subtracting 9 3. Changing the order of numbers in addition calculations 16. Near doubles 5. Counting on/counting back with whole numbers
INSTRUCTOR: For detailed explanations of the relevant strategies (as numbered above) please refer to the Focus Fact Ideas on pp. 17 - 21 of this document.
33
Focus Facts
F a s t a n d A c c u r a t e B a s i c S k i l l s
Student Name: ____________________________________________________________
Addition and Subtraction Facts + 10 and − 10
0 + 10 = 10 10 + 0 = 10 10 − 10 = 0 10 − 0 = 10
1 + 10 = 11 10 + 1 = 11 11 − 10 = 1 11 − 1 = 10
2 + 10 = 12 10 + 2 = 12 12 − 10 = 2 12 − 2 = 10
3 + 10 = 13 10 + 3 = 13 13 − 10 = 3 13 − 3 = 10
4 + 10 = 14 10 + 4 = 14 14 − 10 = 4 14 − 4 = 10
5 + 10 = 15 10 + 5 = 15 15 − 10 = 5 15 − 5 = 10
6 + 10 = 16 10 + 6 = 16 16 − 10 = 6 16 − 6 = 10
7 + 10 = 17 10 + 7 = 17 17 − 10 = 7 17 − 7 = 10
8 + 10 = 18 10 + 8 = 18 18 − 10 = 8 18 − 8 = 10
9 + 10 = 19 10 + 9 = 19 19 − 10 = 9 19 − 9 = 10
10 + 10 = 20 10 + 10 = 20 20 − 10 = 10 20 − 10 = 10
11 + 10 = 21 10 + 11 = 21 21 − 10 = 11 21 − 11 = 10
12 + 10 = 22 10 + 12 = 22 22 − 10 = 12 22 − 12 = 10
APPLICABLE FOCUS FACT IDEAS 1. Developing automatic recall 6. Bridging 10 2. Addition and subtraction are opposite operations 8.4. Adding 10 3. Changing the order of numbers in addition calculations 8.6. Subtracting 10 5. Counting on/counting back with whole numbers 16. Near doubles
INSTRUCTOR: For detailed explanations of the relevant strategies (as numbered above) please refer to the Focus Fact Ideas on pp. 17 - 21 of this document.
34
Focus Facts
F a s t a n d A c c u r a t e B a s i c S k i l l s
Student Name: ____________________________________________________________
Addition and Subtraction Facts + 11 and − 11
0 + 11 = 11 11 + 0 = 11 11 − 11 = 0 11 − 0 = 11
1 + 11 = 12 11 + 1 = 12 12 − 11 = 1 12 − 1 = 11
2 + 11 = 13 11 + 2 = 13 13 − 11 = 2 13 − 2 = 11
3 + 11 = 14 11 + 3 = 14 14 − 11 = 3 14 − 3 = 11
4 + 11 = 15 11 + 4 = 15 15 − 11 = 4 15 − 4 = 11
5 + 11 = 16 11 + 5 = 16 16 − 11 = 5 16 − 5 = 11
6 + 11 = 17 11 + 6 = 17 17 − 11 = 6 17 − 6 = 11
7 + 11 = 18 11 + 7 = 18 18 − 11 = 7 18 − 7 = 11
8 + 11 = 19 11 + 8 = 19 19 − 11 = 8 19 − 8 = 11
9 + 11 = 20 11 + 9 = 20 20 − 11 = 9 20 − 9 = 11
10 + 11 = 21 11 + 10 = 21 21 − 11 = 10 21 − 10 = 11
11 + 11 = 22 11 + 11 = 22 22 − 11 = 11 22 − 11 = 11
12 + 11 = 23 11 + 12 = 23 23 − 11 = 12 23 − 12 = 11
APPLICABLE FOCUS FACT IDEAS 1. Developing automatic recall 6. Bridging 10 2. Addition and subtraction are opposite operations 7. Partitioning combinations of 10 3. Changing the order of numbers in addition calculations 16. Near doubles 5. Counting on/counting back with whole numbers
INSTRUCTOR: For detailed explanations of the relevant strategies (as numbered above) please refer to the Focus Fact Ideas on pp. 17 - 21 of this document.
35
Focus Facts
F a s t a n d A c c u r a t e B a s i c S k i l l s
Student Name: ____________________________________________________________
Addition and Subtraction Facts + 12 and − 12
0 + 12 = 12 12 + 0 = 12 12 − 12 = 0 12 − 0 = 12
1 + 12 = 13 12 + 1 = 13 13 − 12 = 1 13 − 1 = 12
2 + 12 = 14 12 + 2 = 14 14 − 12 = 2 14 − 2 = 12
3 + 12 = 15 12 + 3 = 15 15 − 12 = 3 15 − 3 = 12
4 + 12 = 16 12 + 4 = 16 16 − 12 = 4 16 − 4 = 12
5 + 12 = 17 12 + 5 = 17 17 − 12 = 5 17 − 5 = 12
6 + 12 = 18 12 + 6 = 18 18 − 12 = 6 18 − 6 = 12
7 + 12 = 19 12 + 7 = 19 19 − 12 = 7 19 − 7 = 12
8 + 12 = 20 12 + 8 = 20 20 − 12 = 8 20 − 8 = 12
9 + 12 = 21 12 + 9 = 21 21 − 12 = 9 21 − 9 = 12
10 + 12 = 22 12 + 10 = 22 22 − 12 = 10 22 − 10 = 12
11 + 12 = 23 12 + 11 = 23 23 − 12 = 11 23 − 11 = 12
12 + 12 = 24 12 + 12 = 24 24 − 12 = 12 24 − 12 = 12
APPLICABLE FOCUS FACT IDEAS 1. Developing automatic recall 6. Bridging 10 2. Addition and subtraction are opposite operations 7. Partitioning combinations of 10 3. Changing the order of numbers in addition calculations 16. Near doubles 5. Counting on/counting back with whole numbers
INSTRUCTOR: For detailed explanations of the relevant strategies (as numbered above) please refer to the Focus Fact Ideas on pp. 17 - 21 of this document.
36
Focus Facts
F a s t a n d A c c u r a t e B a s i c S k i l l s
Multiplication and Division Focus Facts
37
Focus Facts
F a s t a n d A c c u r a t e B a s i c S k i l l s
Student Name: ____________________________________________________________
Multiplication and Division Facts × 0 and 0 ÷
0 × 0 = 0 0 × 0 = 0
1 × 0 = 0 0 × 1 = 0 0 ÷ 1 = 0
2 × 0 = 0 0 × 2 = 0 0 ÷ 2 = 0
3 × 0 = 0 0 × 3 = 0 0 ÷ 3 = 0
4 × 0 = 0 0 × 4 = 0 0 ÷ 4 = 0
5 × 0 = 0 0 × 5 = 0 0 ÷ 5 = 0
6 × 0 = 0 0 × 6 = 0 0 ÷ 6 = 0
7 × 0 = 0 0 × 7 = 0 0 ÷ 7 = 0
8 × 0 = 0 0 × 8 = 0 0 ÷ 8 = 0
9 × 0 = 0 0 × 9 = 0 0 ÷ 9 = 0
10 × 0 = 0 0 × 10 = 0 0 ÷ 10 = 0
11 × 0 = 0 0 × 11 = 0 0 ÷ 11 = 0
12 × 0 = 0 0 × 12 = 0 0 ÷ 12 = 0
APPLICABLE FOCUS FACT IDEAS 1. Developing automatic recall 19. Why you can’t divide by zero 11. Changing the order of numbers in multiplication
calculations
12. Multiplying by 0
INSTRUCTOR: For detailed explanations of the relevant strategies (as numbered above) please refer to the Focus Fact Ideas on pp. 17 - 21 of this document.
38
Focus Facts
F a s t a n d A c c u r a t e B a s i c S k i l l s
Student Name: ____________________________________________________________
Multiplication and Division Facts × 1 and ÷ 1
0 × 1 = 0 1 × 0 = 0 0 ÷ 1 = 0
1 × 1 = 1 1 × 1 = 1 1 ÷ 1 = 1 1 ÷ 1 = 1
2 × 1 = 2 1 × 2 = 2 2 ÷ 1 = 2 2 ÷ 2 = 1
3 × 1 = 3 1 × 3 = 3 3 ÷ 1 = 3 3 ÷ 3 = 1
4 × 1 = 4 1 × 4 = 4 4 ÷ 1 = 4 4 ÷ 4 = 1
5 × 1 = 5 1 × 5 = 5 5 ÷ 1 = 5 5 ÷ 5 = 1
6 × 1 = 6 1 × 6 = 6 6 ÷ 1 = 6 6 ÷ 6 = 1
7 × 1 = 7 1 × 7 = 7 7 ÷ 1 = 7 7 ÷ 7 = 1
8 × 1 = 8 1 × 8 = 8 8 ÷ 1 = 8 8 ÷ 8 = 1
9 × 1 = 9 1 × 9 = 9 9 ÷ 1 = 9 9 ÷ 9 = 1
10 × 1 = 10 1 × 10 = 10 10 ÷ 1 = 10 10 ÷ 10 = 1
11 × 1 = 11 1 × 11 = 11 11 ÷ 1 = 11 11 ÷ 11 = 1
12 × 1 = 12 1 × 12 = 12 12 ÷ 1 = 12 12 ÷ 12 = 1
APPLICABLE FOCUS FACT IDEAS 1. Developing automatic recall 12. Multiplying by 0 10. Multiplication and division are reciprocal operations 13. Multiplying or dividing by 1 11. Changing the order of numbers in multiplication
calculations 19. Why you can’t divide by zero
INSTRUCTOR: For detailed explanations of the relevant strategies (as numbered above) please refer to the Focus Fact Ideas on pp. 17 - 21 of this document.
39
Focus Facts
F a s t a n d A c c u r a t e B a s i c S k i l l s
Student Name: ____________________________________________________________
Multiplication and Division Facts × 2 and ÷ 2
0 × 2 = 0 2 × 0 = 0 0 ÷ 2 = 0
1 × 2 = 2 2 × 1 = 2 2 ÷ 2 = 1 2 ÷ 1 = 2
2 × 2 = 4 2 × 2 = 4 4 ÷ 2 = 2 4 ÷ 2 = 2
3 × 2 = 6 2 × 3 = 6 6 ÷ 2 = 3 6 ÷ 3 = 2
4 × 2 = 8 2 × 4 = 8 8 ÷ 2 = 4 8 ÷ 4 = 2
5 × 2 = 10 2 × 5 = 10 10 ÷ 2 = 5 10 ÷ 5 = 2
6 × 2 = 12 2 × 6 = 12 12 ÷ 2 = 6 12 ÷ 6 = 2
7 × 2 = 14 2 × 7 = 14 14 ÷ 2 = 7 14 ÷ 7 = 2
8 × 2 = 16 2 × 8 = 16 16 ÷ 2 = 8 16 ÷ 8 = 2
9 × 2 = 18 2 × 9 = 18 18 ÷ 2 = 9 18 ÷ 9 = 2
10 × 2 = 20 2 × 10 = 20 20 ÷ 2 = 10 20 ÷ 10 = 2
11 × 2 = 22 2 × 11 = 22 22 ÷ 2 = 11 22 ÷ 11 = 2
12 × 2 = 24 2 × 12 = 24 24 ÷ 2 = 12 24 ÷ 12 = 2
APPLICABLE FOCUS FACT IDEAS 1. Developing automatic recall 12. Multiplying by 0 10. Multiplication and division are reciprocal operations 14. Skip counting 11. Changing the order of numbers in multiplication
calculations 15. Knowledge of doubles and halves 19. Why you can’t divide by zero
INSTRUCTOR: For detailed explanations of the relevant strategies (as numbered above) please refer to the Focus Fact Ideas on pp. 17 - 21 of this document.
40
Focus Facts
F a s t a n d A c c u r a t e B a s i c S k i l l s
Student Name: ____________________________________________________________
Multiplication and Division Facts × 3 and ÷ 3
0 × 3 = 0 3 × 0 = 0 0 ÷ 3 = 0
1 × 3 = 3 3 × 1 = 3 3 ÷ 3 = 1 3 ÷ 1 = 3
2 × 3 = 6 3 × 2 = 6 6 ÷ 3 = 2 6 ÷ 2 = 3
3 × 3 = 9 3 × 3 = 9 9 ÷ 3 = 3 9 ÷ 3 = 3
4 × 3 = 12 3 × 4 = 12 12 ÷ 3 = 4 12 ÷ 4 = 3
5 × 3 = 15 3 × 5 = 15 15 ÷ 3 = 5 15 ÷ 5 = 3
6 × 3 = 18 3 × 6 = 18 18 ÷ 3 = 6 18 ÷ 6 = 3
7 × 3 = 21 3 × 7 = 21 21 ÷ 3 = 7 21 ÷ 7 = 3
8 × 3 = 24 3 × 8 = 24 24 ÷ 3 = 8 24 ÷ 8 = 3
9 × 3 = 27 3 × 9 = 27 27 ÷ 3 = 9 27 ÷ 9 = 3
10 × 3 = 30 3 × 10 = 30 30 ÷ 3 = 10 30 ÷ 10 = 3
11 × 3 = 33 3 × 11 = 33 33 ÷ 3 = 11 33 ÷ 11 = 3
12 × 3 = 36 3 × 12 = 36 36 ÷ 3 = 12 36 ÷ 12 = 3
APPLICABLE FOCUS FACT IDEAS 1. Developing automatic recall 12. Multiplying by 0 9. Multiplication as repeated addition of whole numbers 14. Skip counting 10. Multiplication and division are reciprocal operations 19. Why you can’t divide by zero 11. Changing the order of numbers in multiplication
calculations
INSTRUCTOR: For detailed explanations of the relevant strategies (as numbered above) please refer to the Focus Fact Ideas on pp. 17 - 21 of this document.
41
Focus Facts
F a s t a n d A c c u r a t e B a s i c S k i l l s
Student Name: ____________________________________________________________
Multiplication and Division Facts × 4 and ÷ 4
0 × 4 = 0 4 × 0 = 0 0 ÷ 4 = 0
1 × 4 = 4 4 × 1 = 4 4 ÷ 4 = 1 4 ÷ 1 = 4
2 × 4 = 8 4 × 2 = 8 8 ÷ 4 = 2 8 ÷ 2 = 4
3 × 4 = 12 4 × 3 = 12 12 ÷ 4 = 3 12 ÷ 3 = 4
4 × 4 = 16 4 × 4 = 16 16 ÷ 4 = 4 16 ÷ 4 = 4
5 × 4 = 20 4 × 5 = 20 20 ÷ 4 = 5 20 ÷ 5 = 4
6 × 4 = 24 4 × 6 = 24 24 ÷ 4 = 6 24 ÷ 6 = 4
7 × 4 = 28 4 × 7 = 28 28 ÷ 4 = 7 28 ÷ 7 = 4
8 × 4 = 32 4 × 8 = 32 32 ÷ 4 = 8 32 ÷ 8 = 4
9 × 4 = 36 4 × 9 = 36 36 ÷ 4 = 9 36 ÷ 9 = 4
10 × 4 = 40 4 × 10 = 40 40 ÷ 4 = 10 40 ÷ 10 = 4
11 × 4 = 44 4 × 11 = 44 44 ÷ 4 = 11 44 ÷ 11 = 4
12 × 4 = 48 4 × 12 = 48 48 ÷ 4 = 12 48 ÷ 12 = 4
APPLICABLE FOCUS FACT IDEAS 1. Developing automatic recall 12. Multiplying by 0 9. Multiplication as repeated addition of whole numbers 14. Skip counting 10. Multiplication and division are reciprocal operations 11. Changing the order of numbers in multiplication
calculations
17. Relating 2× and 4× number facts
(doubles/halves) 19. Why you can’t divide by zero
INSTRUCTOR: For detailed explanations of the relevant strategies (as numbered above) please refer to the Focus Fact Ideas on pp. 17 - 21 of this document.
42
Focus Facts
F a s t a n d A c c u r a t e B a s i c S k i l l s
Student Name: ____________________________________________________________
Multiplication and Division Facts × 5 and ÷ 5
0 × 5 = 0 5 × 0 = 0 0 ÷ 5 = 0
1 × 5 = 5 5 × 1 = 5 5 ÷ 5 = 1 5 ÷ 1 = 5
2 × 5 = 10 5 × 2 = 10 10 ÷ 5 = 2 10 ÷ 2 = 5
3 × 5 = 15 5 × 3 = 15 15 ÷ 5 = 3 15 ÷ 3 = 5
4 × 5 = 20 5 × 4 = 20 20 ÷ 5 = 4 20 ÷ 4 = 5
5 × 5 = 25 5 × 5 = 25 25 ÷ 5 = 5 25 ÷ 5 = 5
6 × 5 = 30 5 × 6 = 30 30 ÷ 5 = 6 30 ÷ 6 = 5
7 × 5 = 35 5 × 7 = 35 35 ÷ 5 = 7 35 ÷ 7 = 5
8 × 5 = 40 5 × 8 = 40 40 ÷ 5 = 8 40 ÷ 8 = 5
9 × 5 = 45 5 × 9 = 45 45 ÷ 5 = 9 45 ÷ 9 = 5
10 × 5 = 50 5 × 10 = 50 50 ÷ 5 = 10 50 ÷ 10 = 5
11 × 5 = 55 5 × 11 = 55 55 ÷ 5 = 11 55 ÷ 11 = 5
12 × 5 = 60 5 × 12 = 60 60 ÷ 5 = 12 60 ÷ 12 = 5
APPLICABLE FOCUS FACT IDEAS 1. Developing automatic recall 12. Multiplying by 0 9. Multiplication as repeated addition of whole numbers 14. Skip counting 10. Multiplication and division are reciprocal operations 11. Changing the order of numbers in multiplication
calculations
18. Understanding the relationship between 5 and 10
19. Why you can’t divide by zero
INSTRUCTOR: For detailed explanations of the relevant strategies (as numbered above) please refer to the Focus Fact Ideas on pp. 17 - 21 of this document.
43
Focus Facts
F a s t a n d A c c u r a t e B a s i c S k i l l s
Student Name: ____________________________________________________________
Multiplication and Division Facts × 6 and ÷ 6
0 × 6 = 0 6 × 0 = 0 0 ÷ 6 = 0
1 × 6 = 6 6 × 1 = 6 6 ÷ 6 = 1 6 ÷ 1 = 6
2 × 6 = 12 6 × 2 = 12 12 ÷ 6 = 2 12 ÷ 2 = 6
3 × 6 = 18 6 × 3 = 18 18 ÷ 6 = 3 18 ÷ 3 = 6
4 × 6 = 24 6 × 4 = 24 24 ÷ 6 = 4 24 ÷ 4 = 6
5 × 6 = 30 6 × 5 = 30 30 ÷ 6 = 5 30 ÷ 5 = 6
6 × 6 = 36 6 × 6 = 36 36 ÷ 6 = 6 36 ÷ 6 = 6
7 × 6 = 42 6 × 7 = 42 42 ÷ 6 = 7 42 ÷ 7 = 6
8 × 6 = 48 6 × 8 = 48 48 ÷ 6 = 8 48 ÷ 8 = 6
9 × 6 = 54 6 × 9 = 54 54 ÷ 6 = 9 54 ÷ 9 = 6
10 × 6 = 60 6 × 10 = 60 60 ÷ 6 = 10 60 ÷ 10 = 6
11 × 6 = 66 6 × 11 = 66 66 ÷ 6 = 11 66 ÷ 11 = 6
12 × 6 = 72 6 × 12 = 72 72 ÷ 6 = 12 72 ÷ 12 = 6
APPLICABLE FOCUS FACT IDEAS 1. Developing automatic recall 12. Multiplying by 0 9. Multiplication as repeated addition of whole numbers 14. Skip counting 10. Multiplication and division are reciprocal operations 19. Why you can’t divide by zero 11. Changing the order of numbers in multiplication
calculations
INSTRUCTOR: For detailed explanations of the relevant strategies (as numbered above) please refer to the Focus Fact Ideas on pp. 17 - 21 of this document.
44
Focus Facts
F a s t a n d A c c u r a t e B a s i c S k i l l s
Student Name: ____________________________________________________________
Multiplication and Division Facts × 7 and ÷ 7
0 × 7 = 0 7 × 0 = 0 0 ÷ 7 = 0
1 × 7 = 7 7 × 1 = 7 7 ÷ 7 = 1 7 ÷ 1 = 7
2 × 7 = 14 7 × 2 = 14 14 ÷ 7 = 2 14 ÷ 2 = 7
3 × 7 = 21 7 × 3 = 21 21 ÷ 7 = 3 21 ÷ 3 = 7
4 × 7 = 28 7 × 4 = 28 28 ÷ 7 = 4 28 ÷ 4 = 7
5 × 7 = 35 7 × 5 = 35 35 ÷ 7 = 5 35 ÷ 5 = 7
6 × 7 = 42 7 × 6 = 42 42 ÷ 7 = 6 42 ÷ 6 = 7
7 × 7 = 49 7 × 7 = 49 49 ÷ 7 = 7 49 ÷ 7 = 7
8 × 7 = 56 7 × 8 = 56 56 ÷ 7 = 8 56 ÷ 8 = 7
9 × 7 = 63 7 × 9 = 63 63 ÷ 7 = 9 63 ÷ 9 = 7
10 × 7 = 70 7 × 10 = 70 70 ÷ 7 = 10 70 ÷ 10 = 7
11 × 7 = 77 7 × 11 = 77 77 ÷ 7 = 11 77 ÷ 11 = 7
12 × 7 = 84 7 × 12 = 84 84 ÷ 7 = 12 84 ÷ 12 = 7
APPLICABLE FOCUS FACT IDEAS 1. Developing automatic recall 12. Multiplying by 0 9. Multiplication as repeated addition of whole numbers 14. Skip counting 10. Multiplication and division are reciprocal operations 19. Why you can’t divide by zero 11. Changing the order of numbers in multiplication
calculations
INSTRUCTOR: For detailed explanations of the relevant strategies (as numbered above) please refer to the Focus Fact Ideas on pp. 17 - 21 of this document.
45
Focus Facts
F a s t a n d A c c u r a t e B a s i c S k i l l s
Student Name: ____________________________________________________________
Multiplication and Division Facts × 8 and ÷ 8
0 × 8 = 0 8 × 0 = 0 0 ÷ 8 = 0
1 × 8 = 8 8 × 1 = 8 8 ÷ 8 = 1 8 ÷ 1 = 8
2 × 8 = 16 8 × 2 = 16 16 ÷ 8 = 2 16 ÷ 2 = 8
3 × 8 = 24 8 × 3 = 24 24 ÷ 8 = 3 24 ÷ 3 = 8
4 × 8 = 32 8 × 4 = 32 32 ÷ 8 = 4 32 ÷ 4 = 8
5 × 8 = 40 8 × 5 = 40 40 ÷ 8 = 5 40 ÷ 5 = 8
6 × 8 = 48 8 × 6 = 48 48 ÷ 8 = 6 48 ÷ 6 = 8
7 × 8 = 56 8 × 7 = 56 56 ÷ 8 = 7 56 ÷ 7 = 8
8 × 8 = 64 8 × 8 = 64 64 ÷ 8 = 8 64 ÷ 8 = 8
9 × 8 = 72 8 × 9 = 72 72 ÷ 8 = 9 72 ÷ 9 = 8
10 × 8 = 80 8 × 10 = 80 80 ÷ 8 = 10 80 ÷ 10 = 8
11 × 8 = 88 8 × 11 = 88 88 ÷ 8 = 11 88 ÷ 11 = 8
12 × 8 = 96 8 × 12 = 96 96 ÷ 8 = 12 96 ÷ 12 = 8
APPLICABLE FOCUS FACT IDEAS 1. Developing automatic recall 12. Multiplying by 0 9. Multiplication as repeated addition of whole numbers 14. Skip counting 10. Multiplication and division are reciprocal operations 19. Why you can’t divide by zero 11. Changing the order of numbers in multiplication
calculations
INSTRUCTOR: For detailed explanations of the relevant strategies (as numbered above) please refer to the Focus Fact Ideas on pp. 17 - 21 of this document.
46
Focus Facts
F a s t a n d A c c u r a t e B a s i c S k i l l s
Student Name: ____________________________________________________________
Multiplication and Division Facts × 9 and ÷ 9
0 × 9 = 0 9 × 0 = 0 0 ÷ 9 = 0
1 × 9 = 9 9 × 1 = 9 9 ÷ 9 = 1 9 ÷ 1 = 9
2 × 9 = 18 9 × 2 = 18 18 ÷ 9 = 2 18 ÷ 2 = 9
3 × 9 = 27 9 × 3 = 27 27 ÷ 9 = 3 27 ÷ 3 = 9
4 × 9 = 36 9 × 4 = 36 36 ÷ 9 = 4 36 ÷ 4 = 9
5 × 9 = 45 9 × 5 = 45 45 ÷ 9 = 5 45 ÷ 5 = 9
6 × 9 = 54 9 × 6 = 54 54 ÷ 9 = 6 54 ÷ 6 = 9
7 × 9 = 63 9 × 7 = 63 63 ÷ 9 = 7 63 ÷ 7 = 9
8 × 9 = 72 9 × 8 = 72 72 ÷ 9 = 8 72 ÷ 8 = 9
9 × 9 = 81 9 × 9 = 81 81 ÷ 9 = 9 81 ÷ 9 = 9
10 × 9 = 90 9 × 10 = 90 90 ÷ 9 = 10 90 ÷ 10 = 9
11 × 9 = 99 9 × 11 = 99 99 ÷ 9 = 11 99 ÷ 11 = 9
12 × 9 = 108 9 × 12 = 108 108 ÷ 9 = 12 108 ÷ 12 = 9
APPLICABLE FOCUS FACT IDEAS 1. Developing automatic recall 12. Multiplying by 0 9. Multiplication as repeated addition of whole numbers 14. Skip counting 10. Multiplication and division are reciprocal operations 19. Why you can’t divide by zero 11. Changing the order of numbers in multiplication
calculations
INSTRUCTOR: For detailed explanations of the relevant strategies (as numbered above) please refer to the Focus Fact Ideas on pp. 17 - 21 of this document.
47
Focus Facts
F a s t a n d A c c u r a t e B a s i c S k i l l s
Student Name: ____________________________________________________________
Multiplication and Division Facts × 10 and ÷ 10
0 × 10 = 0 10 × 0 = 0 0 ÷ 10 = 0
1 × 10 = 10 10 × 1 = 10 10 ÷ 10 = 1 10 ÷ 1 = 10
2 × 10 = 20 10 × 2 = 20 20 ÷ 10 = 2 20 ÷ 2 = 10
3 × 10 = 30 10 × 3 = 30 30 ÷ 10 = 3 30 ÷ 3 = 10
4 × 10 = 40 10 × 4 = 40 40 ÷ 10 = 4 40 ÷ 4 = 10
5 × 10 = 50 10 × 5 = 50 50 ÷ 10 = 5 50 ÷ 5 = 10
6 × 10 = 60 10 × 6 = 60 60 ÷ 10 = 6 60 ÷ 6 = 10
7 × 10 = 70 10 × 7 = 70 70 ÷ 10 = 7 70 ÷ 7 = 10
8 × 10 = 80 10 × 8 = 80 80 ÷ 10 = 8 80 ÷ 8 = 10
9 × 10 = 90 10 × 9 = 90 90 ÷ 10 = 9 90 ÷ 9 = 10
10 × 10 = 100 10 × 10 = 100 100 ÷ 10 = 10 100 ÷ 10 = 10
11 × 10 = 110 10 × 11 = 110 110 ÷ 10 = 11 110 ÷ 11 = 10
12 × 10 = 120 10 × 12 = 120 120 ÷ 10 = 12 120 ÷ 12 = 10
APPLICABLE FOCUS FACT IDEAS 1. Developing automatic recall 12. Multiplying by 0 9. Multiplication as repeated addition of whole numbers 14. Skip counting 10. Multiplication and division are reciprocal operations 19. Why you can’t divide by zero 11. Changing the order of numbers in multiplication
calculations
INSTRUCTOR: For detailed explanations of the relevant strategies (as numbered above) please refer to the Focus Fact Ideas on pp. 17 - 21 of this document.
48
Focus Facts
F a s t a n d A c c u r a t e B a s i c S k i l l s
Student Name: ____________________________________________________________
Multiplication and Division Facts × 11 and ÷ 11
0 × 11 = 0 11 × 0 = 0 0 ÷ 11 = 0
1 × 11 = 11 11 × 1 = 11 11 ÷ 11 = 1 11 ÷ 1 = 11
2 × 11 = 22 11 × 2 = 22 22 ÷ 11 = 2 22 ÷ 2 = 11
3 × 11 = 33 11 × 3 = 33 33 ÷ 11 = 3 33 ÷ 3 = 11
4 × 11 = 44 11 × 4 = 44 44 ÷ 11 = 4 44 ÷ 4 = 11
5 × 11 = 55 11 × 5 = 55 55 ÷ 11 = 5 55 ÷ 5 = 11
6 × 11 = 66 11 × 6 = 66 66 ÷ 11 = 6 66 ÷ 6 = 11
7 × 11 = 77 11 × 7 = 77 77 ÷ 11 = 7 77 ÷ 7 = 11
8 × 11 = 88 11 × 8 = 88 88 ÷ 11 = 8 88 ÷ 8 = 11
9 × 11 = 99 11 × 9 = 99 99 ÷ 11 = 9 99 ÷ 9 = 11
10 × 11 = 110 11 × 10 = 110 110 ÷ 11 = 10 110 ÷ 10 = 11
11 × 11 = 121 11 × 11 = 121 121 ÷ 11 = 11 121 ÷ 11 = 11
12 × 11 = 132 11 × 12 = 132 132 ÷ 11 = 12 132 ÷ 12 = 11
APPLICABLE FOCUS FACT IDEAS 1. Developing automatic recall 12. Multiplying by 0 9. Multiplication as repeated addition of whole numbers 14. Skip counting 10. Multiplication and division are reciprocal operations 19. Why you can’t divide by zero
INSTRUCTOR: For detailed explanations of the relevant strategies (as numbered above) please refer to the Focus Fact Ideas on pp. 17 - 21 of this document.
49
Focus Facts
F a s t a n d A c c u r a t e B a s i c S k i l l s
Student Name: ____________________________________________________________
Multiplication and Division Facts × 12 and ÷ 12
0 × 12 = 0 12 × 0 = 0 0 ÷ 12 = 0
1 × 12 = 12 12 × 1 = 12 12 ÷ 12 = 1 12 ÷ 1 = 12
2 × 12 = 24 12 × 2 = 24 24 ÷ 12 = 2 24 ÷ 2 = 12
3 × 12 = 36 12 × 3 = 36 36 ÷ 12 = 3 36 ÷ 3 = 12
4 × 12 = 48 12 × 4 = 48 48 ÷ 12 = 4 48 ÷ 4 = 12
5 × 12 = 60 12 × 5 = 60 60 ÷ 12 = 5 60 ÷ 5 = 12
6 × 12 = 72 12 × 6 = 72 72 ÷ 12 = 6 72 ÷ 6 = 12
7 × 12 = 84 12 × 7 = 84 84 ÷ 12 = 7 84 ÷ 7 = 12
8 × 12 = 96 12 × 8 = 96 96 ÷ 12 = 8 96 ÷ 8 = 12
9 × 12 = 108 12 × 9 = 108 108 ÷ 12 = 9 108 ÷ 9 = 12
10 × 12 = 120 12 × 10 = 120 120 ÷ 12 = 10 120 ÷ 10 = 12
11 × 12 = 132 12 × 11 = 132 132 ÷ 12 = 11 132 ÷ 11 = 12
12 × 12 = 144 12 × 12 = 144 144 ÷ 12 = 12 144 ÷ 12 = 12
APPLICABLE FOCUS FACT IDEAS 1. Developing automatic recall 12. Multiplying by 0 9. Multiplication as repeated addition of whole numbers 14. Skip counting 10. Multiplication and division are reciprocal operations 19. Why you can’t divide by zero
INSTRUCTOR: For detailed explanations of the relevant strategies (as numbered above) please refer to the Focus Fact Ideas on pp. 17 - 21 of this document.
50
Focus Facts
F a s t a n d A c c u r a t e B a s i c S k i l l s
Addition and Subtraction Facts to 10
Doubles Facts to 12
and
Squared Number Facts
51
F a s t a n d A c c u r a t e B a s i c S k i l l s
Addition and Subtraction Facts to 10
Student Name: ____________________________________________________________
Addition Subtraction
0 + 10 = 10 10 + 0 = 10 10 − 0 = 10 10 − 10 = 0
1 + 9 = 10 9 + 1 = 10 10 − 1 = 9 10 − 9 = 1
2 + 8 = 10 8 + 2 = 10 10 − 2 = 8 10 − 8 = 2
3 + 7 = 10 7 + 3 = 10 10 − 3 = 7 10 − 7 = 3
4 + 6 = 10 6 + 4 = 10 10 − 4 = 6 10 − 6 = 4
5 + 5 = 10 5 + 5 = 10 10 − 5 = 5 10 − 5 = 5
6 + 4 = 10 4 + 6 = 10 10 − 6 = 4 10 − 4 = 6
7 + 3 = 10 3 + 7 = 10 10 − 7 = 3 10 − 3 = 7
8 + 2 = 10 2 + 8 = 10 10 − 8 = 2 10 − 2 = 8
9 + 1 = 10 1 + 9 = 10 10 − 9 = 1 10 − 1 = 9
10 + 0 = 10 0 + 10 = 10 10 − 10 = 0 10 − 0 = 10
APPLICABLE FOCUS FACT IDEAS
1. Developing automatic recall 2. Addition and subtraction are opposite operations 3. Changing the order of numbers in addition calculations 4. Adding or subtracting zero 5. Counting on/counting back with whole numbers
INSTRUCTOR: For detailed explanations of the relevant strategies (as numbered above) please refer to the Focus Fact Ideas on pp. 17 - 21 of this document.
52
F a s t a n d A c c u r a t e B a s i c S k i l l s
Doubles Facts to 12
Student Name: ____________________________________________________________
Addition Multiplication Division Fractions
1 + 1 = 2 2 × 1 = 2 2 ÷ 2 = 1 ½ × 2 = 1
2 + 2 = 4 2 × 2 = 4 4 ÷ 2 = 2 ½ × 4 = 2
3 + 3 = 6 2 × 3 = 6 6 ÷ 2 = 3 ½ × 6 = 3
4 + 4 = 8 2 × 4 = 8 8 ÷ 2 = 4 ½ × 8 = 4
5 + 5 = 10 2 × 5 = 10 10 ÷ 2 = 5 ½ × 10 = 5
6 + 6 = 12 2 × 6 = 12 12 ÷ 2 = 6 ½ × 12 = 6
7 + 7 = 14 2 × 7 = 14 14 ÷ 2 = 7 ½ × 14 = 7
8 + 8 = 16 2 × 8 = 16 16 ÷ 2 = 8 ½ × 16 = 8
9 + 9 = 18 2 × 9 = 18 18 ÷ 2 = 9 ½ × 18 = 9
10 + 10 = 20 2 × 10 = 20 20 ÷ 2 = 10 ½ × 20 = 10
11 + 11 = 22 2 × 11 = 22 22 ÷ 2 = 11 ½ × 22 = 11
12 + 12 = 24 2 × 12 = 24 24 ÷ 2 = 12 ½ × 24 = 12
APPLICABLE FOCUS FACT IDEAS 1. Developing automatic recall
14. Skip counting
15. Knowledge of doubles and halves
17. Relating 2× and 4× number facts (doubles/ halves)
INSTRUCTOR: For detailed explanations of the relevant strategies (as numbered above) please refer to the Focus Fact Ideas on pp. 17 - 21 of this document.
53
F a s t a n d A c c u r a t e B a s i c S k i l l s
Square Number Facts to 12
Student Name: __________________________________________________________
Multiplication Squares Division Square Roots
1 × 1 = 1 12 = 1 1 ÷ 1 = 1 √1 = 1
2 × 2 = 4 22 = 4 4 ÷ 2 = 2 √4 = 2
3 × 3 = 9 32 = 9 9 ÷ 3 = 3 √9 = 3
4 × 4 = 16 42 = 16 16 ÷ 4 = 4 √16 = 4
5 × 5 = 25 52 = 25 25 ÷ 5 = 5 √25 = 5
6 × 6 = 36 62 = 36 36 ÷ 6 = 6 √36 = 6
7 × 7 = 49 72 = 49 49 ÷ 7 = 7 √49 = 7
8 × 8 = 64 82 = 64 64 ÷ 8 = 8 √64 = 8
9 × 9 = 81 92 = 81 81 ÷ 9 = 9 √81 = 9
10 × 10 = 100 102 = 100 100 ÷ 10 = 10 √100 = 10
11 × 11 = 121 112 = 121 121 ÷ 11 = 11 √121 = 11
12 × 12 = 144 122 = 144 144 ÷ 12 = 12 √144 = 12
54
F a s t a n d A c c u r a t e B a s i c S k i l l s
Section 4 - Speed Sheets
This section contains:
1. Speed Sheets for Addition and Subtraction
2. Speed Sheets for Multiplication and Division
3. Mixed operation Speed Sheets
4. Solutions for Speed Sheets for Addition and Subtraction
5. Solutions for Speed Sheets for Multiplication and Division
6. Solutions for mixed operation Speed Sheets
Speed Sheet Generator Instructions
Please consult the User Guide for instructions about accessing the QuickSmart Speed
Sheet Generator. The Speed Sheet Generator allows you to develop more Speed Sheets
and their answers to suit the needs of QuickSmart students.
Speed Sheets
Addition and Subtraction
55
Speed Sheet
F a s t a n d A c c u r a t e B a s i c S k i l l s
Student Name: ____________________________________________________________
How many facts can you complete in 2 minutes?
Addition and Subtraction Facts to 10
10 − ___ = 7 10 − ___ = 4 4 + ___ = 10 10 − ___ = 8
10 − ___ = 1 5 + ___ = 10 10 − ___ = 8 8 + ___ = 10
3 + ___ = 10 7 + ___ = 10 10 − ___ = 2 20 − ___ = 18
8 + ___ = 10 18 + ___ = 20 27 + ___ = 30 10 − ___ = 7
5 + ___ = 10 10 − ___ = 6 20 − ___ = 18 10 − ___ = 1
10 − ___ = 3 4 + ___ = 10 50 − ___ = 2 3 + ___ = 10
2 + ___ = 10 10 + ___ = 10 10 − ___ = 7 10 − ___ = 2
10 − ___ = 5 4 + ___ = 10 10 − ___ = 1 10 − ___ = 10
7 + ___ = 10 3 + ___ = 10 10 − ___ = 9 27 + ___ = 30
50 − ___ = 2 10 − ___ = 7 10 − ___ = 8 50 − ___ = 2
48 + ___ = 50 10 − ___ = 10 10 − ___ = 4 3 + ___ = 10
3 + ___ = 10 50 − ___ = 2 20 − ___ = 2 10 − ___ = 9
10 − ___ = 9 10 − ___ = 8 3 + ___ = 10 7 + ___ = 10
10 − ___ = 4 10 − ___ = 2 6 + ___ = 10 2 + ___ = 10
10 − ___ = 6 20 − ___ = 18 8 + ___ = 10 3 + ___ = 10
6 + ___ = 10 2 + ___ = 10 18 + ___ = 20 10 − ___ = 4
10 + ___ = 10 3 + ___ = 10 10 − ___ = 1 10 + ___ = 10
20 − ___ = 2 10 − ___ = 3 10 − ___ = 10 10 − ___ = 7
8 + ___ = 10 10 − ___ = 8 7 + ___ = 10 20 − ___ = 2
18 + ___ = 20 10 − ___ = 5 10 − ___ = 6 10 − ___ = 6
Instructions: Rule off after each attempt and date. Record results below.
Date
Number Correct
Number Errors
56
Speed Sheet
F a s t a n d A c c u r a t e B a s i c S k i l l s
Student Name: ____________________________________________________________
How many facts can you complete in 2 minutes?
Addition and Subtraction Facts + 0 and − 0
0 + 0 = 5 + ___ = 5 1 − 0 = 0 + 910 =
1 + 0 = 17 − 0 = 11 + ___ = 11 12 − 0 =
0 + 2 = 13 − 0 = 13 − 0 = 7 + 0 =
3 + 0 = 12 + 0 = 0 + 9 = __ − 0 = 9
11 + 0 = 60 + 0 = __ − 0 = 6 15 − 0 =
5 + 0 = 0 + ___ = 9 211 − 0 = 90 − 0 =
4 + 0 = 14 − 0 = 0 + 11 = 10 + ___ = 10
7 + 0 = 13 − 0 = 88 − 0 = 6 + 0 =
0 + 8 = 7 + 0 = 12 − ___ = 12 80 + 0 =
0 + 9 = 1 + 0 = 0 + 0 = 16 − 0 =
12 + 0 = __ − 0 = 18 5 − 0 = __ − 0 = 42
0 + 6 = 7 + 0 = 2 + 0 = 18 + 0 =
10 + 0 = 0 + 12 = 1 − 0 = 0 + 6 =
12 − ___ = 12 21 − ___ = 21 3 + 0 = 15 − 0 =
21 − 0 = 0 + 8 = 0 + 77 = 12 − 0 =
13 − 0 = 112 − 0 = 5 + 0 = 40 + ___ = 40
__ − 0 = 0 12 + 0 = 131 − 0 = 0 + 2 =
17 − 0 = __ − 0 = 16 4 + 0 = 412 − 0 =
8 − 0 = 10 + 0 = 32 − 0 = 3 + 0 =
12 − 0 = 15 − 0 = __ + 90 = 90 14 − 0 =
Instructions: Rule off after each attempt and date. Record results below.
Date
Number Correct
Number Errors
57
Speed Sheet
F a s t a n d A c c u r a t e B a s i c S k i l l s
Student Name: ____________________________________________________________
How many facts can you complete in 2 minutes?
Addition and Subtraction Facts + 1 and − 1
1 + 0 = 5 + ___ = 6 1 − 1 = __ + 910 = 911
1 + 12 = 17 − 1 = 11 + 1 = 12 − 1 =
1 + 2 = 13 − 1 = __ − 1 = 12 7 + 1 =
3 + 1 = 12 + 1 = 1 + 9 = 9 − 1 =
11 + 1 = 60 + 1 = 6 − 1 = 15 − 1 =
5 + 1 = 1 + ___ = 10 211 − 1 = 90 − 1 =
4 + 1 = 14 − 1 = 1 + ___ = 12 10 + 1 =
7 + 1 = 13 − 1 = 88 − 1 = 6 + 1 =
1 + 8 = 7 + 1 = 12 − 1 = 80 + ___ = 81
1 + 9 = __ + 1 = 2 1 + 0 = 16 − 1 =
12 + 1 = 18 − 1 = 5 − 1 = 42 − 1 =
1 + 11 = 7 + 1 = 2 + ___ = 3 18 + 1 =
9 + 1 = 1 + 12 = 1 − 0 = 1 + 6 =
12 − 1 = 21 − ___ = 20 3 + 1 = __ − 1 = 14
21 − ___ = 20 1 + 8 = 1 + 70 = 12 − 1 =
13 − 1 = 112 − 1 = __ + 1 = 6 40 + 1 =
1 − 0 = 12 + 1 = 131 − 1 = 1 + 2 =
17 − 1 = 16 − ___ = 15 4 + 1 = 412 − 100 =
__ − 1 = 7 10 + 1 = 32 − 1 = 3 + 1 =
12 − 1 = 15 − 1 = 1 + ___ = 91 14 − 1 =
Instructions: Rule off after each attempt and date. Record results below.
Date
Number Correct
Number Errors
58
Speed Sheet
F a s t a n d A c c u r a t e B a s i c S k i l l s
Student Name: ____________________________________________________________
How many facts can you complete in 2 minutes?
Addition and Subtraction Facts + 2 and − 2
2 + 0 = 3 + ___ = 5 2 − 2 = 5 + 2 =
1 + 2 = 7 − 2 = 2 + 4 = 10 − ___ = 8
2 + 2 = 7 + 2 = 9 − 2 = 4 − 2 =
3 + 2 = 10 − 2 = __ − 2 = 1 8 − 2 =
2 + 4 = 11 − 2 = 9 + 2 = 2 + 0 =
5 + 2 = __ + 0 = 2 7 − 2 = 60 + ___ = 80
2 + 6 = 60 + 20 = 5 + 2 = 12 − 2 =
7 + 2 = 9 + 2 = 1 + 2 = 3 + 2 =
2 + 8 = 8 − 2 = __ − 2 = 8 66 + 22 =
9 + 2 = 2 − ___ = 0 7 + ___ = 9 2 + 6 =
2 + 10 = 66 + 22 = 60 + 20 = __ − 2 = 7
2 − 2 = 2 + 2 = 2 + ___ = 8 6 − 2 =
3 − 2 = 88 + 20 = 6 − 2 = 2 + ___ = 4
9 − 2 = 4 − 2 = 2 + 0 = 7 − 2 =
5 − 2 = __ − 2 = 106 66 + 22 = 5 − 2 =
6 − 2 = 12 − 2 = __ + 10 = 12 2 + 4 =
__ − 2 = 5 __ − 20 = 30 8 − 2 = 88 + 20 =
8 − 2 = 1 + 2 = 88 + 20 = 9 + 2 =
9 − 2 = 2 + 8 = 3 + 2 = 200 − 20 =
10 − ___ = 8 5 + 2 = 4 − 2 = 2 + 10 =
Instructions: Rule off after each attempt and date. Record results below.
Date
Number Correct
Number Errors
59
Speed Sheet
F a s t a n d A c c u r a t e B a s i c S k i l l s
Student Name: ____________________________________________________________
How many facts can you complete in 2 minutes?
Addition and Subtraction Facts + 3 and − 3
3 + 0 = 3 + 3 = 4 − 3 = 5 − ___ = 2
1 + 3 = 10 − ___ = 7 12 − 3 = 11 − 3 =
3 + 2 = 3 + 4 = __ + 12 = 15 7 + 3 =
3 + 3 = 6 − 3 = 13 − 3 = 10 − ___ = 7
3 + 4 = 9 + ___ = 12 1 + 3 = 3 + 2 =
5 + 3 = 30 + 80 = 33 + 22 = 88 − 30 =
3 + 6 = 3 + 10 = 3 + 4 = 5 + 3 =
7 + 3 = 3 − 3 = __ − 3 = 12 300 − ___ = 270
8 + 3 = __ + 0 = 3 3 + 10 = 8 + 3 =
9 + 3 = 13 − 3 = 6 − 3 = 15 − 3 =
3 + 10 = 3 + 4 = 78 + 30 = 3 + 0 =
11 + 3 = 11 − ___ = 8 7 − 3 = 30 + 80 =
3 + 12 = 11 + 3 = 9 + ___ = 12 3 + 4 =
3 − 3 = 9 − 3 = 10 − 3 = 8 − ___ = 5
4 − 3 = __ + 3 = 4 3 − 3 = 9 + 3 =
5 − 3 = 33 + 22 = 8 + 3 = __ − 3 = 9
6 − 3 = 7 + ___ = 10 8 − 3 = 3 + 10 =
__ − 3 = 4 15 − 3 = 11 + 3 = 13 − 3 =
8 − 3 = 3 + 12 = 300 − ___ = 270 6 − 3 =
9 − 3 = 88 − ___ = 58 7 + 3 = 3 + 12 =
Instructions: Rule off after each attempt and date. Record results below.
Date
Number Correct
Number Errors
60
Speed Sheet
F a s t a n d A c c u r a t e B a s i c S k i l l s
Student Name: ____________________________________________________________
How many facts can you complete in 2 minutes?
Addition and Subtraction Facts + 4 and − 4
4 + 0 = 5 + 4 = 9 − 4 = 4 + 4 =
1 + 4 = 4 − ___ = 0 11 + 4 = 12 − 4 =
4 + 2 = 12 − 4 = 13 − 4 = 25 − ___ = 21
3 + 4 = 4 + 2 = __ + 4 = 13 15 − 4 =
4 + 4 = 60 + 40 = 7 − 4 = 4 − 4 =
5 + 4 = __ + 6 = 10 300 − 40 = 8 − 4 =
4 + 6 = 14 − 4 = 1 + 4 = 4 + ___ = 14
7 + 4 = 6 − 4 = 50 − ___ = 10 44 + 33 =
4 + 8 = 7 + 4 = 5 − 4 = 7 + ___ = 11
9 + 4 = 44 + 33 = 4 + 0 = 16 − 4 =
4 + 10 = 7 − ___ = 3 11 − 4 = __ − 4 = 1
11 + 4 = 4 + 4 = __ + 2 = 6 58 + 40 =
4 + 12 = 58 + 40 = 4 − 4 = 4 + 6 =
4 − 4 = 10 − ___ = 6 3 + 4 = 7 − 4 =
5 − 4 = 9 + 4 = 60 + ___ = 100 6 − 4 =
6 − 4 = 112 − 4 = 5 + 4 = 9 + 4 =
7 − 4 = 4 + ___ = 4 112 − 4 = 4 + 12 =
__ − 4 = 4 16 − 4 = __ + 6 = 10 300 − 40 =
9 − 4 = 4 + 10 = 8 − 4 = 3 + 4 =
10 − 4 = 15 − ___ = 11 58 + 40 = 14 − 4 =
Instructions: Rule off after each attempt and date. Record results below.
Date
Number Correct
Number Errors
61
Speed Sheet
F a s t a n d A c c u r a t e B a s i c S k i l l s
Student Name: ____________________________________________________________
How many facts can you complete in 2 minutes?
Addition and Subtraction Facts + 5 and − 5
5 + 0 = 3 + 5 = 5 − 5 = 5 + ___ = 10
1 + 5 = 7 − ___ = 2 + 4 = 9 10 − 5 =
5 + 5 = 7 + 5 = 12 − 5 = 7 − 5 =
3 + 5 = 10 − 5 = 6 − 5 = 11 − 5 =
5 + 2 = __ − 5 = 6 9 + ___ = 14 5 + 0 =
5 + 5 = 5 + 0 = 7 − 5 = 10 + ___ = 60
5 + 6 = 50 + 20 = 5 − ___ = 0 15 − 5 =
7 + 5 = 9 + 5 = 1 + 5 = 3 + 5 =
5 + 8 = 8 − ___ = 3 10 − 5 = 22 + 55 =
9 + 5 = 5 − 5 = 7 + 5 = 2 + ___ = 7
5 + 10 = 33 + 55 = 40 + ___ = 90 12 − 5 =
11 − 5 = 5 + 5 = 5 + 6 = __ − 5 = 4
6 − 5 = __ + 20 = 70 6 − 5 = 5 + 5 =
9 − 5 = 7 − 5 = 5 + 0 = 7 − 5 =
5 − ___ = 0 108 − 5 = 23 + 55 = 8 − 5 =
9 − 5 = 12 − 5 = __ + 10 = 15 5 + 4 =
7 − 5 = __ − 50 = 30 8 − 5 = 11 + ___ = 61
8 − 5 = 1 + 5 = 28 + 50 = 9 + 5 =
__ − 5 = 7 5 + 8 = 3 + 5 = 100 − 50 =
10 − 5 = 5 + 5 = 8 − 5 = 5 + 10 =
Instructions: Rule off after each attempt and date. Record results below.
Date
Number Correct
Number Errors
62
Speed Sheet
F a s t a n d A c c u r a t e B a s i c S k i l l s
Student Name: ____________________________________________________________
How many facts can you complete in 2 minutes?
Addition and Subtraction Facts + 6 and − 6
6 + 0 = 6 + ___ = 12 7 − 6 = 9 − 6 =
1 + 6 = 10 − 6 = 12 − 6 = 11 − ___ = 5
6 + 2 = 6 + 4 = __ + 12 = 18 7 + 6 =
6 + 6 = __ − 6 = 0 13 − 6 = 10 − 6 =
6 + 4 = 9 + 6 = 1 + ___ = 7 __ + 2 = 8
5 + 6 = 60 + 80 = 66 + 22 = 98 − 60 =
6 + 6 = 6 + ___ = 16 6 + 4 = 5 + 6 =
7 + 6 = 6 − 6 = 15 − 6 = __ − 60 = 540
8 + 6 = __ + 0 = 6 6 + 10 = 8 + 6 =
9 + 6 = 13 − 6 = 9 − ___ = 3 15 − 6 =
6 + 10 = 6 + 4 = 28 + 60 = 6 + 0 =
11 + 6 = 11 − ___ = 5 7 − 6 = 60 + 80 =
6 + 12 = 11 + 6 = 9 + 6 = __ + 4 = 10
6 − 6 = 9 − 6 = 10 − 6 = 8 − ___ = 2
__ − 6 = 1 __ + 6 = 7 6 − ___ = 0 9 + 6 =
8 − 6 = 66 + 22 = 8 + 6 = 12 − 6 =
6 − 6 = 7 + ___ = 13 8 − 6 = __ + 10 = 16
7 − 6 = 15 − 6 = 11 + ___ = 17 13 − 6 =
8 − 6 = 6 + 12 = 300 − 60 = 6 − 6 =
9 − ___ = 3 88 − 60 = 7 + 6 = 6 + 12 =
Instructions: Rule off after each attempt and date. Record results below.
Date
Number Correct
Number Errors
63
Speed Sheet
F a s t a n d A c c u r a t e B a s i c S k i l l s
Student Name: ____________________________________________________________
How many facts can you complete in 2 minutes?
Addition and Subtraction Facts + 7 and − 7
7 + 0 = 5 + 7 = 9 − 7 = 7 + 7 =
1 + 7 = __ − 7 = 0 11 + 7 = 12 − 7 =
7 + 2 = 12 − 7 = 13 − 7 = __ + 8 = 15
3 + 7 = 7 + 2 = 9 + ___ = 16 15 − 7 =
7 + 7 = 60 + 70 = 7 − 7 = 7 − 7 =
5 + 7 = 7 + 6 = 300 − 70 = 8 − 7 =
4 + 7 = 14 − ___ = 7 1 + 7 = __ + 10 = 17
7 + 7 = 7 − 4 = 90 − 70 = 77 + 22 =
7 + 8 = 7 + 7 = 8 − ___ = 1 7 + 7 =
9 + 7 = 77 + 22 = 7 + 0 = 16 − 7 =
7 + 10 = 7 − 7 = 11 − 7 = 8 − ___ = 1
11 + 7 = __ + 7 = 14 7 + 2 = 38 + 70 =
7 + 12 = 18 + 70 = 7 − 7 = 7 + 6 =
7 − 7 = 10 − 7 = 3 + ___ = 10 7 − 7 =
8 − 7 = 9 + 7 = 60 + 70 = 9 − 7 =
9 − ___ = 2 112 − ___ = 105 5 + 7 = 9 + ___ = 16
10 − 7 = 7 + 0 = 112 − 7 = __ + 12 = 19
8 − 7 = 16 − ___ = 9 4 + 7 = 300 − 70 =
9 − 7 = 7 + 10 = 8 − ___ = 1 3 + 7 =
10 − 7 = 15 − 7 = 58 + 70 = 14 − 7 =
Instructions: Rule off after each attempt and date. Record results below.
Date
Number Correct
Number Errors
64
Speed Sheet
F a s t a n d A c c u r a t e B a s i c S k i l l s
Student Name: ____________________________________________________________
How many facts can you complete in 2 minutes?
Addition and Subtraction Facts + 8 and − 8
8 + 0 = 5 + ___ = 13 9 − 8 = 8 + ___ = 16
1 + 8 = 17 − 8 = 11 + 8 = 12 − 8 =
8 + 2 = 13 − 8 = 13 − ___ = 5 7 + 8 =
3 + 8 = 8 + 2 = 9 + 8 = 19 − 8 =
8 + 8 = 60 + 80 = __ − 8 = 8 15 − 8 =
5 + 8 = 7 + 8 = 200 − 80 = 8 − 8 =
4 + 8 = 14 − 8 = 1 + ___ = 9 __ + 10 = 18
7 + 8 = 12 − ___ = 4 100 − 80 = 88 + 2 =
8 + 8 = 7 + 8 = 9 − 8 = 8 + 8 =
9 + 8 = 88 + 11 = __ + 0 = 8 16 − 8 =
8 + 10 = 18 − ___ = 10 11 − 8 = 9 − ___ = 1
11 + 8 = 7 + 8 = 8 + 2 = 18 + 80 =
8 + 12 = 18 + 80 = 8 − 0 = 8 + 6 =
8 − 8 = 10 − 8 = 3 + ___ = 11 15 − 8 =
11 − 8 = 9 + ___ = 17 30 + ___ = 110 9 − 8 =
9 − 8 = 112 − 8 = 5 + 8 = 9 + ___ = 17
10 − 8 = 8 + 0 = 112 − ___ = 104 __ + 12 = 20
8 − 8 = 16 − ___ = 8 4 + 8 = 400 − 80 =
9 − 8 = __ + 10 = 18 10 − 8 = 3 + 8 =
10 − ___ = 2 15 − 8 = 18 + 80 = 14 − ___ = 6
Instructions: Rule off after each attempt and date. Record results below.
Date
Number Correct
Number Errors
65
Speed Sheet
F a s t a n d A c c u r a t e B a s i c S k i l l s
Student Name: ____________________________________________________________
How many facts can you complete in 2 minutes?
Addition and Subtraction Facts + 9 and − 9
9 + 0 = 5 + 9 = 11 − 9 = 9 + 9 =
1 + 9 = 17 − ___ = 8 11 + ___ = 20 12 − 9 =
9 + 2 = 13 − 9 = 13 − 9 = 7 + ___ = 16
3 + 9 = 9 + 2 = 9 + 9 = 19 − 9 =
9 + 9 = 60 + ___ = 150 16 − 9 = 15 − 9 =
5 + 9 = 7 + 9 = 200 − 90 = 9 − 9 =
4 + 9 = 14 − 9 = 1 + ___ = 10 9 + 10 =
7 + 9 = 12 − ___ = 3 100 − 90 = 99 + ___ = 99
9 + 8 = 7 + 9 = 9 − 9 = 8 + 9 =
9 + 9 = 99 + ___ = 100 9 + 0 = 16 − 9 =
__ + 10 = 19 18 − 9 = 11 − ___ = 2 9 − ___ = 0
11 + 9 = 7 + 9 = 9 + 2 = 19 + 80 =
9 + 12 = 18 + 90 = 9 − 0 = 9 + 6 =
9 − ___ = 0 10 − 9 = 3 + 9 = 15 − ___ = 6
11 − 9 = __ + 8 = 17 30 + 90 = 9 − 9 =
9 − 9 = 112 − 9 = __ + 8 = 17 9 + 9 =
10 − 9 = 9 + 0 = 112 − 9 = __ + 12 = 21
9 + ___ = 9 16 − 9 = 4 + 9 = 400 − 90 =
18 − 9 = __ + 10 = 19 10 − 9 = 3 + 9 =
10 − 9 = 15 − 9 = 8 + 90 = 14 − ___ = 5
Instructions: Rule off after each attempt and date. Record results below.
Date
Number Correct
Number Errors
66
Speed Sheet
F a s t a n d A c c u r a t e B a s i c S k i l l s
Student Name: ____________________________________________________________
How many facts can you complete in 2 minutes?
Addition and Subtraction Facts + 10 and − 10
10 + 0 = 5 + 10 = 11 − 10 = 9 + 910 =
1 + 10 = 17 − ___ = 7 11 + 10 = 12 − ___ = 2
10 + 2 = 13 − 10 = 13 − 10 = 7 + 10 =
3 + 10 = 10 + 2 = 10 + ___ = 19 19 − 10 =
10 + 10 = 60 + ___ = 70 16 − 10 = 15 − 10 =
5 + 10 = 10 + 9 = 200 − 10 = 90 − 10 =
4 + 10 = __ − 10 = 4 1 + ___ = 11 __ + 10 = 20
7 + 10 = 12 − 10 = 80 − ___ = 70 69 + 100 =
10 + 8 = 7 + 10 = 10 − 10 = 80 + ___ = 90
10 + 9 = 10 + 1 = 10 + 0 = 16 − 10 =
11 + ___ = 21 18 − ___ = 8 __ − 10 = 1 40 − 10 =
12 + 10 = 7 + 10 = 10 + 2 = 19 + 10 =
9 + 10 = 18 + 10 = 10 − 0 = 10 + 6 =
10 − 0 = __ − 10 = 0 3 + 10 = 15 − 10 =
11 − 10 = 10 + 8 = __ + 90 = 100 10 − 10 =
13 − ___ = 3 112 − ___ = 102 5 + 10 = 40 + 10 =
10 − 10 = 10 + 0 = 112 − 10 = 10 + 12 =
17 − 10 = 16 − 10 = 4 + 10 = 400 − ___ = 300
18 − 10 = __ + 10 = 20 33 − 10 = 3 + 10 =
10 − 0 = 15 − 10 = 10 + 90 = 14 − 10 =
Instructions: Rule off after each attempt and date. Record results below.
Date
Number Correct
Number Errors
67
Speed Sheet
F a s t a n d A c c u r a t e B a s i c S k i l l s
Student Name: ____________________________________________________________
How many facts can you complete in 2 minutes?
Addition and Subtraction Facts + 11 and − 11
11 + 0 = 5 + ___ = 16 11 − 11 = 11 + 910 =
1 + 11 = 17 − 11 = 11 + 1 = 12 − ___ = 1
11 + 2 = 13 − 11 = 13 − ___ = 2 7 + 11 =
3 + 11 = 11 + 2 = 11 + 9 = 19 − 11 =
11 + 11 = 60 + 11 = 16 − 11 = 15 − ___ = 4
5 + 11 = 11 + 9 = 211 − 11 = 91 − 11 =
4 + 11 = 14 − ___ = 3 1 + ___ = 12 __ + 10 = 21
7 + 11 = 12 − 11 = 88 − 11 = 66 + 11 =
11 + 8 = 7 + 11 = __ − 11 = 0 80 + 11 =
11 + 9 = __ + 1 = 12 11 + 0 = 16 − ___ = 5
11 + 11 = 18 − 11 = 15 − ___ = 4 41 − 11 =
12 + 11 = 7 + ___ = 18 11 + 2 = 18 + 11 =
8 + ___ = 19 18 + 11 = 11 − 0 = __ + 6 = 17
11 − 11 = 11 − ___ = 0 3 + ___ = 14 15 − 11 =
__ − 11 = 0 11 + 8 = 11 + 90 = 11 − 0 =
13 − 11 = 112 − ___ = 101 5 + ___ = 16 40 + 11 =
12 − 11 = 11 + 0 = 112 − 11 = __ + 12 = 23
17 − 11 = 16 − 11 = 4 + 11 = 411 − 111 =
18 − 11 = 10 + ___ = 21 33 − 11 = 3 + ___ = 14
__ − 0 = 11 15 − 11 = 11 + 90 = 14 − 11 =
Instructions: Rule off after each attempt and date. Record results below.
Date
Number Correct
Number Errors
68
Speed Sheet
F a s t a n d A c c u r a t e B a s i c S k i l l s
Student Name: ____________________________________________________________
How many facts can you complete in 2 minutes?
Addition and Subtraction Facts + 12 and − 12
12 + 0 = 5 + 12 = 12 − 12 = 12 + 900 =
1 + 12 = 17 − ___ = 5 12 + 1 = __ − 10 = 2
12 + 2 = 13 − 12 = 13 − ___ = 1 7 + 12 =
3 + 12 = 12 + 2 = 12 + 9 = 19 − ___ = 7
11 + 12 = 60 + 12 = 16 − 12 = 15 − 12 =
5 + 12 = 12 + 9 = 212 − 12 = 80 + 12 =
4 + 12 = 14 − 12 = 1 + ___ = 13 __ + 12 = 24
7 + 12 = 13 − ___ = 1 88 − 11 = 66 + 11 =
12 + 8 = 7 + 12 = 12 − 12 = 80 + ___ = 92
12 + 9 = __ + 1 = 13 12 + 0 = 16 − 12 =
12 + ___ = 24 18 − 12 = 15 − ___ = 3 42 − 12 =
12 + 11 = 7 + 12 = 12 + 2 = 18 + 12 =
9 + 12 = 18 + 12 = 12 − 0 = 12 + 6 =
12 − 12 = 21 − 12 = 3 + ___ = 15 15 − 12 =
12 − ___ = 0 __ + 8 = 20 12 + 70 = __ − 0 = 12
13 − 12 = 112 − ___ = 100 5 + 12 = 40 + ___ = 52
12 − 0 = 12 + 0 = 132 − 12 = 11 + 12 =
17 − 12 = 16 − 12 = 4 + ___ = 16 412 − 112 =
18 − 12 = 10 + 12 = 32 − 12 = 3 + 12 =
__ − 0 = 12 15 − ___ = 3 12 + 90 = 14 − 12 =
Instructions: Rule off after each attempt and date. Record results below.
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Speed Sheets
Multiplication and Division
69
Speed Sheet
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Doubles and × 2 speed sheet
1 × 2 = 4 × ___ = 8 ___ × 2 = 12 9 × 2 =
2 × ___ = 4 9 × 2 = 7 × 2 = 3 + 3 =
3 × 2 = ___ × 2 = 24 2 + 2 = 7 + 7 =
4 × ___ = 8 1 × 2 = 10 + 10 = 10 + 10 =
5 × 2 = 5 + 5 = 3 + 3 = 1 × 2 =
___ × 2 = 12 2 + 2 = ___ × 2 = 16 9 × 2 =
7 × 2 = 6 + 6 = 9 × 2 = 7 × 2 =
___ × 2 = 16 4 + 4 = ___ × 2 = 24 12 + 12 =
9 × 2 = 10 + 10 = 4 × ___ = 8 ½ × 60 =
___ × 2 = 20 2 × ___ = 4 7 + 7 = ___ × 2 = 24
11 × 2 = 7 + 7 = ___ × 2 = 20 3 × 2 =
___ × 2 = 24 11 × 2 = 3 × 2 = 8 + 8 =
3 + 3 = 12 + 12 = 1 × 2 = 1000 ÷ 2 =
4 + 4 = 9 + 9 = 8 + 8 = ___ × 2 = 16
5 + 5 = 7 × 2 = 1000 ÷ 2 = 6 + 6 =
6 + 6 = ½ × 50 = 100 ÷ 2 = 5 × 2 =
7 + 7 = 3 + 3 = 5 × 2 = ___ × 2 = 16
8 + 8 = ½ × 60 = ½ × 60 = ½ × 50 =
9 + 9 = 3 × 2 = 11 × 2 = 4 + 4 =
10 + 10 = 1000 ÷ 2 = 6 + 6 = 9 + 9 =
Instructions: Rule off after each attempt and date. Record results below.
Date
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70
Speed Sheet
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Multiplication and Division 2's - Double and Half
2 × ___ = 0 2 × 5 = 2 × 10 = 2 × 1 =
2 × 1 = 6 ÷ ___ = 3 16 ÷ 2 = 12 ÷ 2 =
2 × ___ = 4 2 × 9 = Double 7 = 2 × 90 =
2 × 3 = 16 ÷ 2 = 2 × 9 = 20 ÷ 2 =
2 × ___ = 8 12 ÷ 2 = 10 ÷ ___ = 5 2 × ___ = 8
2 × 5 = 2 × ___ = 0 2 × 3 = Double 7 =
2 × ___ = 12 14 ÷ ___ = 7 8 ÷ 2 = 2 × ___ = 0
2 × 7 = 2 × ___ = 16 2 × ___ = 4 Double 9 =
2 × ___ = 16 Half of 24 = 6 ÷ ___ = 3 2 × ___ = 12
2 × 9 = 2 × ___ = 22 2 × ___ = 24 4 ÷ 2 =
2 × 10 = 2 ÷ ___ = 1 2 × 5 = Half of 24 =
2 × ___ = 22 2 × 1 = Half of 24 = 6 ÷ ___ = 3
2 × ___ = 24 Double 9 = 2 ÷ ___ = 1 160 ÷ 2 =
2 ÷ ___ = 1 2 × 10 = 160 ÷ 2 = Double 8 =
4 ÷ 2 = Double 8 = 12 ÷ 2 = 2 × ___ = 22
6 ÷ ___ = 3 2 × ___ = 8 Double 9 = Half of 30 =
8 ÷ 2 = 20 ÷ 2 = 24 ÷ 2 = 18 ÷ ___ = 9
10 ÷ ___ = 5 2 × 90 = 4 ÷ 2 = 2 × ___ = 24
12 ÷ 2 = 18 ÷ ___ = 9 2 × ___ = 8 2 × ___ = 4
14 ÷ ___ = 7 8 ÷ 2 = 2 × 90 = 16 ÷ 2 =
Instructions: Rule off after each attempt and date. Record results below.
Date
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71
Speed Sheet
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Multiplication and Division Facts × 0 and 0 ÷
0 × ___ = 0 3 × 0 = 37 × ___ = 0 36 × ___ = 0
3 × 0 = 0 × 10 = 18 × 0 = 0 × 31 =
4 × ___ = 0 36 × ___ = 0 30 × 0 = 3 × ___ = 0
0 × 0 = 13 × 0 = 3 × ___ = 0 33 × ___ = 0
3 × ___ = 0 15 × ___ = 0 27 × ___ = 0 9 × ___ = 0
0 × 5 = 330 × ___ = 0 126 × ___ = 0 27 × ___ = 0
8 × ___ = 0 27 × ___ = 0 43 × ___ = 0 ÷ 23 = 0
0 × 7 = 7 × ___ = 0 0 × 10 = 12 × 0 =
10 × ___ = 0 46 × ___ = 0 0 × 18 = 273 × ___ = 0
0 × 9 = 12 × 0 = 540 × ___ = 0 0 × 310 =
0 × 10 = 0 × 10 = 62 × 0 = 25 × ___ = 0
11 × ___ = 0 0 × 90 = 0 × 9 = 73 × ___ = 0
12 × ___ = 0 243 × ___ = 0 0 × 76 = 0 × 90 =
6 × ___ = 0 12 × 0 = 68 × ___ = 0 40 × 0 =
0 ÷ 3 = 7 × ___ = 0 248 × ___ = 0 18 × 0 =
1 × ___ = 0 36 × 0 = 21 × ___ = 0 254 × ___ = 0
0 × 9 = 24 × 0 = 36 × 0 = 360 × 0 =
2 × ___ = 0 21 × ___ = 0 12 × 0 = 30 × 0 =
10 × 0 = 9 × ___ = 0 15 × ___ = 0 181 × 0 =
9 × ___ = 0 0 ÷ 5 = 91 × 0 = 77 × ___ = 0
Instructions: Rule off after each attempt and date. Record results below.
Date
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72
Speed Sheet
F a s t a n d A c c u r a t e B a s i c S k i l l s
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Multiplication and Division Facts × 1 and ÷ 1
1 × ___ = 0 1 × 3 = 1 × ___ = 6 1 × ___ = 36
1 × 1 = 1 × 10 = 18 ÷ 1 = 36 ÷ 1 =
1 × ___ = 6 36 × ___ = 36 30 ÷ 1 = 3 × ___ = 3
3 × 1 = 18 ÷ 1 = 1 × ___ = 12 33 × ___ = 33
1 × ___ = 12 15 ÷ ___ = 15 27 ÷ ___ = 27 9 ÷ ___ = 9
5 × 1 = 1 × ___ = 330 1 × ___ = 36 273 ÷ ___ = 273
1 × ___ = 18 27 ÷ ___ = 27 1 × ___ = 330 6 ÷ 1 =
1 × 7 = 40 × ___ = 40 1 × 108 = 12 ÷ 1 =
1 × ___ = 24 33 ÷ ___ = 33 3 × 1 = 330 × ___ = 330
9 × 1 = 12 ÷ 1 = 1 × ___ = 18 1 × 65 =
1 × 10 = 1 × 170 = 6 ÷ 1 = 24 × ___ = 24
13 × ___ = 13 1 × 90 = 1 × 9 = 1 × ___ = 56
8 × ___ = 8 1 × ___ = 240 1 × 67 = 1 × 90 =
1 ÷ ___ = 1 12 ÷ 1 = 1 × ___ = 33 1 × 9 =
6 ÷ 1 = 73 × ___ = 73 1 × ___ = 240 18 ÷ 1 =
9 ÷ ___ = 9 36 ÷ 1 = 210 ÷ ___ = 210 1 × ___ = 97
1 × 90 = 24 ÷ 1 = 36 ÷ 1 = 360 ÷ 1 =
1 × ___ = 330 21 ÷ ___ = 21 12 ÷ 1 = 38 ÷ 1 =
180 ÷ 1 = 9 ÷ ___ = 9 15 ÷ ___ = 15 180 ÷ 1 =
1 × ___ = 240 1 × 5 = 9 ÷ ___ = 9 246 ÷ ___ = 246
Instructions: Rule off after each attempt and date. Record results below.
Date
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73
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Multiplication and Division Facts × 2 and ÷ 2
2 × ___ = 0 3 × 2 = 3 × ___ = 6 2 × ___ = 16
2 × 2 = 2 × 10 = 18 ÷ 2 = 26 ÷ 2 =
3 × ___ = 6 2 × ___ = 14 60 ÷ 2 = 2 × ___ = 0
2 × 5 = 18 ÷ 2 = 2 × ___ = 12 48 ÷ ___ = 24
2 × ___ = 12 16 ÷ ___ = 8 28 ÷ ___ = 14 16 ÷ ___ = 8
3 × 2 = 2 × ___ = 220 2 × ___ = 24 28 ÷ ___ = 14
2 × ___ = 18 240 ÷ ___ = 120 2 × ___ = 68 6 ÷ 2 =
2 × 7 = 2 × ___ = 0 2 × 10 = 22 ÷ 2 =
2 × ___ = 24 22 ÷ ___ = 11 2 × 1 = 2 × ___ = 48
2 × 9 = 12 ÷ 2 = 2 × ___ = 18 2 × 3 =
2 × 10 = 2 × 104 = 6 ÷ 2 = 2 × ___ = 24
2 × ___ = 22 2 × 90 = 2 × 90 = 2 × ___ = 240
2 × ___ = 24 2 × ___ = 240 2 × 7 = 2 × 90 =
2 ÷ ___ = 1 12 ÷ 2 = 11 × ___ = 22 2 × 9 =
6 ÷ 2 = 3 × ___ = 6 2 × ___ = 240 18 ÷ 2 =
10 ÷ ___ = 5 46 ÷ 2 = 220 ÷ ___ = 2 2 × ___ = 180
2 × 90 = 24 ÷ 2 = 24 ÷ 2 = 660 ÷ 2 =
2 × ___ = 220 14 ÷ ___ = 7 12 ÷ 2 = 80 ÷ 2 =
180 ÷ 2 = 8 ÷ ___ = 4 16 ÷ ___ = 8 180 ÷ 2 =
2 × ___ = 240 2 × 5 = 48 ÷ ___ = 24 2 ÷ ___ = 1
Instructions: Rule off after each attempt and date. Record results below.
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74
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Multiplication and Division Facts × 3 and ÷ 3
3 × ___ = 0 3 × 3 = 3 × ___ = 6 3 × ___ = 36
3 × 1 = 3 × 10 = 18 ÷ 3 = 36 ÷ 3 =
3 × ___ = 6 3 × ___ = 36 30 ÷ 3 = 3 × ___ = 0
3 × 3 = 18 ÷ 3 = 3 × ___ = 12 33 ÷ ___ = 11
3 × ___ = 12 15 ÷ ___ = 5 27 ÷ ___ = 9 9 ÷ ___ = 3
3 × 5 = 3 × ___ = 330 3 × ___ = 36 27 ÷ ___ = 9
3 × ___ = 18 27 ÷ ___ = 9 3 × ___ = 330 6 ÷ 3 =
3 × 7 = 3 × ___ = 0 3 × 10 = 12 ÷ 3 =
3 × ___ = 24 33 ÷ ___ = 11 3 × 1 = 3 × ___ = 330
3 × 9 = 12 ÷ 3 = 3 × ___ = 18 3 × 3 =
3 × 10 = 3 × 10 = 6 ÷ 3 = 3 × ___ = 24
3 × ___ = 33 3 × 90 = 3 × 9 = 3 × ___ = 240
3 × ___ = 36 3 × ___ = 240 3 × 7 = 3 × 90 =
3 ÷ ___ = 1 12 ÷ 3 = 11 × ___ = 33 3 × 9 =
6 ÷ 3 = 3 × ___ = 6 3 × ___ = 240 18 ÷ 3 =
9 ÷ ___ = 3 36 ÷ 3 = 210 ÷ ___ = 7 3 × ___ = 18
3 × 90 = 24 ÷ 3 = 36 ÷ 3 = 360 ÷ 30 =
3 × ___ = 330 21 ÷ ___ = 7 12 ÷ 3 = 30 ÷ 3 =
180 ÷ 3 = 9 ÷ ___ = 3 15 ÷ ___ = 5 180 ÷ 3 =
3 × ___ = 240 3 × 5 = 9 ÷ ___ = 3 3 ÷ ___ = 1
Instructions: Rule off after each attempt and date. Record results below.
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75
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Multiplication and Division Facts × 4 and ÷ 4
4 × ___ = 0 4 × ___ = 16 16 ÷ 4 = 8 ÷ 4 =
4 × 1 = 4 ÷ ___ = 1 48 ÷ 4 = 4 × 70 =
4 × ___ = 8 4 × ___ = 44 4 × 1 = 360 ÷ ___ = 9
4 × 3 = 36 ÷ ___ = 9 32 ÷ 4 = 40 ÷ 4 =
4 × ___ = 16 16 ÷ 4 = 28 ÷ ___ = 7 4 × ___ = 0
4 × 5 = 4 × ___ = 0 160 ÷ 4 = 24 ÷ 4 =
4 × ___ = 24 44 ÷ ___ = 11 20 ÷ ___ = 5 4 × 3 =
4 × 7 = 160 ÷ 4 = 4 × 9 = 4 ÷ ___ = 1
4 × ___ = 32 4 × 10 = 48 ÷ 4 = 4 × ___ = 240
4 × 9 = 4 × ___ = 48 4 × ___ = 0 12 ÷ ___ = 3
4 × 10 = 4 × 70 = 8 ÷ 4 = 4 × ___ = 8
4 × ___ = 44 4 × 3 = 4 ÷ ___ = 1 4 × ___ = 16
4 × ___ = 48 28 ÷ ___ = 7 80 ÷ 4 = 28 ÷ ___ = 7
4 ÷ ___ = 1 80 ÷ 4 = 4 × ___ = 44 20 ÷ ___ = 5
8 ÷ 4 = 4 × ___ = 24 4 × ___ = 240 4 × 50 =
12 ÷ ___ = 3 32 ÷ 4 = 4 × ___ = 8 32 ÷ 4 =
16 ÷ 4 = 4 × 50 = 36 ÷ ___ = 9 80 ÷ 4 =
20 ÷ ___ = 5 8 ÷ 4 = 4 × ___ = 32 44 ÷ ___ = 11
24 ÷ 4 = 4 × 5 = 12 ÷ ___ = 3 4 × ___ = 44
28 ÷ ___ = 7 4 × 7 = 24 ÷ 4 = 4 × 1 =
Instructions: Rule off after each attempt and date. Record results below.
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76
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Multiplication and Division Facts × 5 and ÷ 5
5 × ___ = 0 5 ÷ ___ = 1 5 × ___ = 10 350 ÷ ___ = 7
5 × 1 = 5 × 7 = 35 ÷ ___ = 7 5 × 10 =
5 × ___ = 10 250 ÷ ___ = 5 5 × 5 = 40 ÷ 5 =
5 × 3 = 20 ÷ 5 = 400 ÷ 5 = 45 ÷ ___ = 9
5 × ___ = 20 5 × ___ = 200 5 × ___ = 30 5 × ___ = 0
5 × 5 = 30 ÷ 5 = 50 ÷ 5 = 5 × 9 =
5 × ___ = 30 5 × ___ = 55 5 × 30 = 15 ÷ ___ = 3
5 × 7 = 35 ÷ ___ = 7 55 ÷ ___ = 11 50 × 1 =
5 × 8 = 5 × 8 = 5 ÷ ___ = 1 10 ÷ 5 =
5 × 9 = 400 ÷ 5 = 5 × 1 = 5 × 7 =
5 × 10 = 10 ÷ 5 = 5 × 90 = 5 × ___ = 20
5 × ___ = 55 5 × ___ = 100 30 ÷ 5 = 20 ÷ 5 =
5 × ___ = 60 5 × ___ = 20 5 × 7 = 5 × ___ = 10
5 ÷ ___ = 1 50 ÷ 5 = 15 ÷ ___ = 3 50 ÷ ___ = 1
10 ÷ 5 = 450 ÷ ___ = 9 5 × ___ = 550 5 × 8 =
15 ÷ ___ = 3 55 ÷ ___ = 11 5 × ___ = 0 5 × 7 =
20 ÷ 5 = 5 × 9 = 45 ÷ ___ = 9 5 × 50 =
25 ÷ ___ = 5 5 × ___ = 30 200 ÷ 5 = 25 ÷ ___ = 5
30 ÷ 5 = 5 × 50 = 5 × 10 = 30 ÷ 5 =
35 ÷ ___ = 7 60 ÷ 5 = 10 ÷ 5 = 50 × 3 =
Instructions: Rule off after each attempt and date. Record results below.
Date
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77
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Multiplication and Division Facts × 6 and ÷ 6
6 × ___ = 0 6 × ___ = 12 36 ÷ 6 = 30 ÷ ___ = 5
6 × 1 = 48 ÷ 6 = 180 ÷ ___ = 3 6 × 5 =
6 × ___ = 12 18 ÷ ___ = 3 6 × ___ = 36 18 ÷ ___ = 3
6 × 3 = 6 × ___ = 72 6 ÷ ___ = 1 12 ÷ 6 =
6 × ___ = 24 6 × 50 = 6 × 1 = 6 × ___ = 12
6 × 5 = 6 × ___ = 0 72 ÷ 6 = 360 ÷ 6 =
6 × ___ = 36 36 ÷ 6 = 6 × 9 = 6 × ___ = 36
6 × 7 = 12 ÷ 6 = 18 ÷ ___ = 3 180 ÷ ___ = 3
6 × ___ = 48 6 × 10 = 6 × 3 = 6 × 1 =
6 × 9 = 180 ÷ ___ = 3 48 ÷ 6 = 6 ÷ ___ = 1
6 × 10 = 6 × ___ = 24 6 × 7 = 6 × ___ = 72
6 × ___ = 66 42 ÷ ___ = 7 66 ÷ ___ = 11 6 × 9 =
6 × ___ = 72 24 ÷ 6 = 6 × ___ = 0 36 ÷ 6 =
6 ÷ ___ = 1 72 ÷ 6 = 30 ÷ ___ = 5 6 × ___ = 24
12 ÷ 6 = 6 × ___ = 36 54 ÷ ___ = 9 24 ÷ 6 =
18 ÷ ___ = 3 360 ÷ 6 = 6 × ___ = 48 6 × ___ = 66
24 ÷ 6 = 6 × 1 = 60 ÷ 6 = 6 × ___ = 48
30 ÷ ___ = 5 60 ÷ 6 = 6 × ___ = 24 72 ÷ 6 =
36 ÷ 6 = 6 × 9 = 42 ÷ ___ = 7 6 × ___ = 0
42 ÷ ___ = 7 6 × ___ = 660 6 × ___ = 12 66 ÷ ___ = 11
Instructions: Rule off after each attempt and date. Record results below.
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78
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Multiplication and Division Facts × 7 and ÷ 7
7 × ___ = 0 7 × 7 = 21 ÷ ___ = 3 7 ÷ ___ = 1
7 × 1 = 56 ÷ 7 = 7 × ___ = 14 7 × ___ = 0
7 × ___ = 14 7 × 50 = 7 × 1 = 49 ÷ ___ = 7
7 × 3 = 7 × 9 = 49 ÷ ___ = 7 7 × 50 =
7 × ___ = 28 14 ÷ 7 = 84 ÷ 7 = 7 × ___ = 42
7 × 5 = 7 × ___ = 0 7 × 7 = 7 × ___ = 84
7 × ___ = 42 7 × ___ = 140 7 × 50 = 21 ÷ ___ = 3
7 × 7 = 42 ÷ 7 = 63 ÷ ___ = 9 7 × 3 =
7 × ___ = 56 84 ÷ 7 = 7 × 10 = 77 ÷ ___ = 11
7 × 9 = 7 × ___ = 84 56 ÷ 7 = 7 × ___ = 56
7 × 10 = 7 × ___ = 42 7 × ___ = 77 7 × 1 =
7 × ___ = 77 77 ÷ ___ = 11 7 × ___ = 28 7 × ___ = 140
7 × ___ = 84 700 ÷ 7 = 42 ÷ 7 = 7 × 5 =
7 ÷ ___ = 1 7 × 5 = 7 ÷ ___ = 1 84 ÷ 7 =
14 ÷ 7 = 63 ÷ ___ = 9 7 × ___ = 42 7 × 7 =
21 ÷ ___ = 3 7 × 70 = 7 × ___ = 0 70 ÷ 7 =
28 ÷ 7 = 7 × 1 = 14 ÷ 7 = 28 ÷ 7 =
35 ÷ ___ = 5 49 ÷ ___ = 7 7 × 5 = 7 × ___ = 14
42 ÷ 7 = 21 ÷ ___ = 3 70 ÷ 7 = 56 ÷ 7 =
49 ÷ ___ = 7 70 ÷ 7 = 7 × 3 = 7 × 9 =
Instructions: Rule off after each attempt and date. Record results below.
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79
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Multiplication and Division Facts × 8 and ÷ 8
8 × ___ = 0 8 ÷ ___ = 1 40 ÷ ___ = 5 8 ÷ ___ = 1
8 × 1 = 8 × ___ = 96 640 ÷ 8 = 96 ÷ 8 =
8 × ___ = 16 8 × 3 = 8 × ___ = 16 8 × 9 =
8 × 3 = 16 ÷ 8 = 160 ÷ 8 = 8 × ___ = 32
8 × ___ = 32 8 × 7 = 8 ÷ ___ = 1 56 ÷ ___ = 7
8 × 5 = 640 ÷ 8 = 80 × 5 = 8 × 10 =
8 × ___ = 48 8 × 9 = 8 × ___ = 0 40 ÷ ___ = 5
8 × 7 = 160 ÷ 8 = 96 ÷ 8 = 8 × 1 =
8 × ___ = 64 8 × ___ = 0 8 × 7 = 72 ÷ ___ = 9
8 × 9 = 80 ÷ 8 = 24 ÷ ___ = 3 8 × 7 =
8 × 10 = 8 × 5 = 8 × ___ = 32 64 ÷ 8 =
8 × ___ = 88 40 ÷ ___ = 5 16 ÷ 8 = 8 × 3 =
8 × ___ = 96 8 × ___ = 64 8 × 10 = 88 ÷ ___ = 11
8 ÷ ___ = 1 88 ÷ ___ = 11 32 ÷ 8 = 8 × ___ = 48
16 ÷ 8 = 8 × ___ = 16 8 × 1 = 80 ÷ 8 =
24 ÷ ___ = 3 64 ÷ 8 = 72 ÷ ___ = 9 16 ÷ 8 =
32 ÷ 8 = 8 × ___ = 32 8 × ___ = 88 8 × 3 =
40 ÷ ___ = 5 24 ÷ ___ = 3 8 × 70 = 48 ÷ 8 =
48 ÷ 8 = 8 × 50 = 8 × ___ = 48 8 × 50 =
56 ÷ ___ = 7 8 × 1 = 56 ÷ ___ = 7 8 × 5 =
Instructions: Rule off after each attempt and date. Record results below.
Date
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80
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Multiplication and Division Facts × 9 and ÷ 9
9 × ___ = 0 90 × 1 = 99 ÷ ___ = 11 9 × ___ = 360
9 × 1 = 9 ÷ ___ = 1 9 × ___ = 99 9 × ___ = 72
9 × ___ = 18 9 × ___ = 36 9 × 7 = 54 ÷ 9 =
9 × 3 = 36 ÷ 9 = 45 ÷ ___ = 5 81 ÷ ___ = 9
9 × ___ = 36 54 ÷ 9 = 9 × 1 = 9 × 3 =
9 × 5 = 9 × ___ = 54 81 ÷ ___ = 9 9 ÷ ___ = 1
9 × ___ = 54 81 ÷ ___ = 9 9 × 10 = 90 ÷ 9 =
9 × 7 = 9 × 9 = 36 ÷ 9 = 9 × ___ = 108
9 × ___ = 72 90 ÷ 9 = 9 × 3 = 45 ÷ ___ = 5
9 × 9 = 63 ÷ ___ = 7 990 ÷ ___ = 11 9 × 5 =
9 × 10 = 9 × 1 = 9 ÷ ___ = 1 9 × 9 =
9 × ___ = 99 99 ÷ ___ = 11 9 × ___ = 72 36 ÷ 9 =
9 × ___ = 108 18 ÷ 9 = 54 ÷ 9 = 9 × ___ = 99
9 ÷ ___ = 1 72 ÷ 9 = 9 × ___ = 18 99 ÷ ___ = 11
18 ÷ 9 = 9 × 7 = 90 ÷ 9 = 9 × ___ = 36
27 ÷ ___ = 3 360 ÷ 9 = 27 ÷ ___ = 3 63 ÷ ___ = 7
36 ÷ 9 = 27 ÷ ___ = 3 9 × 9 = 18 ÷ 9 =
45 ÷ ___ = 5 9 × ___ = 720 9 × 50 = 108 ÷ 9 =
54 ÷ 9 = 9 × ___ = 18 9 × ___ = 108 9 × ___ = 54
63 ÷ ___ = 7 630 ÷ ___ = 7 360 ÷ 9 = 72 ÷ 9 =
Instructions: Rule off after each attempt and date. Record results below.
Date
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81
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Multiplication and Division Facts × 10 and ÷ 10
10 × ___ = 0 40 ÷ 10 = 20 ÷ 10 = 500 ÷ ___ = 50
10 × 1 = 10 × 1 = 30 ÷ ___ = 3 120 × 10 =
10 × ___ = 20 200 ÷ 10 = 10 × 50 = 70 ÷ ___ = 7
10 × 3 = 10 × 9 = 60 ÷ ___ = 6 10 × 3 =
10 × ___ = 40 70 ÷ 10 = 10 × ___ = 0 800 ÷ 10 =
10 × 5 = 10 × ___ = 700 700 ÷ ___ = 70 10 × ___ = 120
10 × ___ = 60 10 × ___ = 110 10 × 12 = 10 × ___ = 40
10 × 7 = 10 ÷ ___ = 1 10 × 3 = 400 ÷ 10 =
10 × ___ = 80 10 × ___ = 400 10 × ___ = 70 10 × ___ = 80
10 × 9 = 80 ÷ ___ = 8 90 ÷ 10 = 10 ÷ ___ = 1
10 × 10 = 50 ÷ ___ = 5 10 × 1 = 10 × ___ = 0
10 × ___ = 110 10 × ___ = 0 90 ÷ ___ = 9 30 ÷ ___ = 3
10 × ___ = 120 90 ÷ 10 = 10 × ___ = 110 10 × ___ = 70
10 ÷ ___ = 1 10 × 100 = 10 × 70 = 60 ÷ 10 =
20 ÷ 10 = 110 ÷ ___ = 11 40 ÷ 10 = 90 ÷ ___ = 9
30 ÷ ___ = 3 10 × 5 = 10 ÷ ___ = 1 10 × ___ = 20
40 ÷ 10 = 10 × 3 = 10 × ___ = 400 1200 ÷ 10 =
60 ÷ ___ = 6 1200 ÷ 10 = 120 ÷ 10 = 10 × 100 =
70 ÷ 10 = 10 × 7 = 10 × 9 = 10 × 5 =
80 ÷ ___ = 8 120 ÷ 10 = 120 ÷ 12 = 110 ÷ ___ = 11
Instructions: Rule off after each attempt and date. Record results below.
Date
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Multiplication and Division Facts × 11 and ÷ 11
11 × ___ = 0 44 ÷ 11 = 22 ÷ 11 = 55 ÷ ___ = 5
11 × 1 = 11 × 1 = 33 ÷ ___ = 3 11 × 7 =
11 × ___ = 22 22 ÷ 11 = 11 × 50 = 77 ÷ ___ = 7
11 × 3 = 11 × 9 = 66 ÷ ___ = 6 11 × 3 =
11 × ___ = 44 77 ÷ 11 = 11 × ___ = 0 880 ÷ 11 =
11 × 5 = 11 × ___ = 770 77 ÷ ___ = 7 11 × ___ = 110
11 × ___ = 66 11 × ___ = 110 11 × 12 = 11 × ___ = 44
11 × 7 = 11 ÷ ___ = 1 11 × 3 = 44 ÷ 11 =
11 × ___ = 88 11 × ___ = 44 11 × ___ = 770 11 × ___ = 88
11 × 9 = 77 ÷ ___ = 7 99 ÷ 11 = 11 ÷ ___ = 1
11 × 10 = 550 ÷ ___ = 50 11 × 1 = 11 × ___ = 0
11 × ___ = 121 11 × ___ = 0 99 ÷ ___ = 9 33 ÷ ___ = 3
11 × ___ = 132 990 ÷ 11 = 11 × ___ = 110 11 × ___ = 770
11 ÷ ___ = 1 11 × 10 = 11 × 7 = 66 ÷ 11 =
22 ÷ 11 = 110 ÷ ___ = 10 440 ÷ 11 = 99 ÷ ___ = 9
33 ÷ ___ = 3 11 × 5 = 11 ÷ ___ = 1 11 × ___ = 220
44 ÷ 11 = 11 × 30 = 11 × ___ = 44 132 ÷ 11 =
55 ÷ ___ = 5 110 ÷ 11 = 132 ÷ 11 = 11 × 10 =
66 ÷ 11 = 11 × 7 = 11 × 9 = 11 × 5 =
77 ÷ ___ = 7 132 ÷ 11 = 110 ÷ 11 = 110 ÷ ___ = 10
Instructions: Rule off after each attempt and date. Record results below.
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Multiplication and Division Facts × 12 and ÷ 12
12 × ___ = 0 480 ÷ 12 = 24 ÷ 12 = 60 ÷ ___ = 5
12 × 1 = 12 × 1 = 360 ÷ ___ = 3 12 × 70 =
12 × ___ = 24 24 ÷ 12 = 12 × 5 = 84 ÷ ___ = 7
12 × 3 = 12 × 9 = 60 ÷ ___ = 5 12 × 3 =
12 × ___ = 48 72 ÷ 12 = 12 × ___ = 0 960 ÷ 12 =
12 × 5 = 12 × ___ = 72 84 ÷ ___ = 7 12 × ___ = 132
12 × ___ = 72 12 × ___ = 132 12 × 10 = 12 × ___ = 48
12 × 7 = 12 ÷ ___ = 1 12 × 3 = 48 ÷ 12 =
12 × ___ = 96 12 × ___ = 480 12 × ___ = 720 12 × ___ = 96
12 × 9 = 84 ÷ ___ = 7 96 ÷ 12 = 12 ÷ ___ = 1
12 × 10 = 60 ÷ ___ = 5 12 × 1 = 12 × ___ = 0
12 × ___ = 132 12 × ___ = 0 108 ÷ ___ = 9 360 ÷ ___ = 3
12 × ___ = 144 96 ÷ 12 = 12 × ___ = 132 12 × ___ = 72
12 ÷ ___ = 1 12 × 10 = 12 × 7 = 72 ÷ 12 =
24 ÷ 12 = 132 ÷ ___ = 11 48 ÷ 12 = 108 ÷ ___ = 9
36 ÷ ___ = 3 120 × 5 = 12 ÷ ___ = 1 12 × ___ = 24
48 ÷ 12 = 12 × 3 = 12 × ___ = 480 120 ÷ 12 =
60 ÷ ___ = 5 144 ÷ 12 = 120 ÷ 12 = 120 × 10 =
72 ÷ 12 = 12 × 7 = 12 × 9 = 12 × 5 =
84 ÷ ___ = 7 120 ÷ 12 = 144 ÷ 12 = 132 ÷ ___ = 11
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Multiplication and Division - Square Numbers
1 × ___ = 1 10 × 10 = 9 × ___ = 81 5 × ___ = 25
2 × 2 = 25 ÷ ___ = 5 2 × 2 = √36 =
3 × ___ = 9 7 × ___ = 49 √4 = 11 × 11 =
4 × 4 = 36 ÷ 6 = 9 ÷ ___ = 3 3 × ___ = 9
5 × ___ = 25 82 = 25 ÷ ___ = 5 9 ÷ ___ = 3
6 × 6 = 16 ÷ 4 = 1 × ___ = 1 12 × ___ = 144
7 × ___ = 49 1 ÷ ___ = 1 4 × 4 = 7 × ___ = 49
8 × ___ = 64 4 × 4 = 8 × 8 = 49 ÷ ___ = 7
9 × ___ = 81 49 ÷ ___ = 7 64 ÷ 8 = 8 × 8 =
10 × 10 = 12 × ___ = 144 3 × ___ = 9 √64 =
11 × 11 = 9 ÷ ___ = 3 16 ÷ 4 = 2 × 2 =
12 × ___ = 144 1 × ___ = 1 112 = 16 ÷ 4 =
1 ÷ ___ = 1 100 ÷ 10 = 5 × ___ = 25 4 × 4 =
4 ÷ 2 = 42 = 81 ÷ ___ = 9 62 =
9 ÷ 3 = 3 × ___ = 9 102 = 81 ÷ ___ = 9
16 ÷ 4 = 11 × 11 = 121 ÷ ___ = 11 1 ÷ ___ = 1
25 ÷ ___ = 5 121 ÷ ___ = 11 6 × 6 = 1 × ___ = 1
36 ÷ 6 = √64 = √100 = 10 × 10 =
49 ÷ ___ = 7 5 × ___ = 25 42 = 100 ÷ 10 =
64 ÷ 8 = 81 ÷ ___ = 9 49 ÷ ___ = 7 9 × ___ = 81
Instructions: Rule off after each attempt and date. Record results below.
Date
Number Correct
Number Errors
Mixed Operation Speed Sheets
85
Speed Sheet
F a s t a n d A c c u r a t e B a s i c S k i l l s
Student Name: ____________________________________________________________
How many facts can you complete in 2 minutes?
Mixed Operations – Sheet 1
0 + 8 = 120 – 80 = ___ × 8 = 8 80 ÷ 10 =
3 – ___ = 0 ___ ÷ 1 = 0 ___ – 0 = 1 ___ ÷ 110 = 10
4 × ___ = 12 500 – ___ = 300 1 × ___ = 110 ___ – 20 = 60
1200 – ___ = 200 12 × ___ = 0 3 – 3 = ___ × 6 = 0
___ + 2 = 6 11 × ___ = 99 12 + 1 = 70 × ___ = 42000
5 × 12 = 5 + 2 = 3 × ___ = 36 2 – 0 =
12 + 7 = ___ ÷ 3 = 8 6 – 4 = ___ ÷ 1 = 12
5 × ___ = 55 11 – 6 = ___ ÷ 1 = 4 ___ + 11 = 19
6 + 3 = 0 ÷ 4 = ___ + 8 = 10 400 × 11 =
___ – 0 = 11 12 × ___ = 60 10 – 6 = 700 × ___ = 350000
1 + ___ = 8 40 ÷ ___ = 4 7 + 4 = 20 × 30 =
5 + 3 = 1 × ___ = 6 ___ – 0 = 60 10 ÷ 10 =
___ ÷ 9 = 3 6 + ___ = 7 8 – ___ = 4 ___ × 10 = 60
3 × 5 = ___ – 2 = 2 40 ÷ ___ = 8 ___ – 0 = 1100
___ – 4 = 6 ___ ÷ 4 = 0 7 – ___ = 1 ___ × 2 = 10
6 + 3 = 48 ÷ 6 = 7 – 7 = ___ ÷ 2 = 1
___ + 3 = 11 9 × ___ = 54 10 + ___ = 130 ___ × 7 = 84
10 × 9 = 9 + ___ = 14 12 × ___ = 120 ___ – 0 = 11
8 + 1 = ___ ÷ 12 = 0 11 + 11 = 55 ÷ ___ = 5
10 + 8 = ___ ÷ 100 = 1 120 – 80 = 0 × 5 =
Instructions: Rule off after each attempt and date. Record results below.
Date
Number Correct
Number Errors
86
Speed Sheet
F a s t a n d A c c u r a t e B a s i c S k i l l s
Student Name: ____________________________________________________________
How many facts can you complete in 2 minutes?
Mixed Operations – Sheet 2
7 – 3 = 12 – ___ = 5 11 × 9 = 1 × 12 =
3 × ___ = 36 ___ – 6 = 1 10 + 0 = ___ × 2 = 16
___ – 1 = 4 4 ÷ ___ = 1 4 – 3 = ___ ÷ 3 = 12
___ × 3 = 27 ___ – 2 = 5 1 × 7 = 2 + 12 =
7 + 6 = 1 × ___ = 5 ___ + 80 = 180 4 × ___ = 24
7 × ___ = 350 7 – 0 = 63 ÷ ___ = 7 12 – ___ = 2
___ + 4 = 10 3 ÷ 3 = 8 – ___ = 2 ___ ÷ 8 = 12
___ + 12 = 18 ___ ÷ 10 = 40 11 + 6 = ___ × 12 = 132
5 × 8 = ___ – 2 = 7 24 ÷ 4 = 9 + ___ = 18
___ – 8 = 3 ___ × 10 = 120 8 + ___ = 10 5 × ___ = 30
___ + 4 = 12 70 ÷ ___ = 10 6 – 5 = 9 × ___ = 0
4 ÷ ___ = 1 11 + 3 = 27 ÷ ___ = 9 10 – 5 =
3 + ___ = 14 3 × 9 = ___ – 10 = 1 3 × ___ = 21
___ – 6 = 4 1 × 1 = 12 – 2 = 4 × 3 =
4 – ___ = 0 4 × 4 = 3 + ___ = 12 ___ × 4 = 44
21 ÷ 3 = 11 – 2 = 9 × ___ = 99 ___ + 5 = 15
0 + ___ = 110 10 × 3 = ___ – 30 = 90 10 × ___ = 10
12 – 5 = ___ ÷ 12 = 12 ___ – 40 = 70 0 × 3 =
10 – 2 = 30 ÷ ___ = 6 ___ + 1 = 2 6 × 10 =
5 × ___ = 25 8 + 2 = ___ ÷ 60 = 2 12 + 10 =
Instructions: Rule off after each attempt and date. Record results below.
Date
Number Correct
Number Errors
87
Speed Sheet
F a s t a n d A c c u r a t e B a s i c S k i l l s
Student Name: ____________________________________________________________
How many facts can you complete in 2 minutes?
Mixed Operations – Sheet 3
7 – ___ = 2 15 ÷ 3 = 2 – ___ = 1 48 ÷ 8 =
___ × 10 = 60 ___ + 600 = 1800 0 × 8 = 11 – ___ = 10
4 – 3 = 10 × 10 = ___ – 2 = 1 2 × ___ = 8
30 ÷ ___ = 10 1 + ___ = 12 0 ÷ 9 = 0 + ___ = 800
30 ÷ 3 = ___ – 1 = 1 700 ÷ 70 = 5 + 7 =
6 + 7 = 1 × ___ = 3 9 + 3 = 7 × ___ = 70
11 + 9 = 120 × ___ = 1200 3 + 1 = 200 ÷ 2 =
48 ÷ 6 = ___ + 8 = 11 30 ÷ ___ = 3 3 – 2 =
11 × ___ = 0 3 – 3 = 2 × ___ = 22 200 + 400 =
5 ÷ 1 = 5 – ___ = 5 ___ × 10 = 80 3 + ___ = 14
10 + ___ = 19 11 × 0 = ___ + 8 = 18 90 ÷ 10 =
900 – ___ = 600 4 × 9 = ___ + 10 = 21 ___ ÷ 3 = 12
10 – 8 = 6 ÷ ___ = 1 ___ – 5 = 3 ___ ÷ 8 = 4
___ ÷ 6 = 11 ___ + 700 = 1800 6 × ___ = 60 11 + 9 =
___ ÷ 4 = 9 9 – ___ = 2 ___ ÷ 6 = 0 7 + 0 =
49 ÷ ___ = 7 9 + ___ = 10 ___ ÷ 1 = 10 ___ + 200 = 700
110 + 50 = 4 × ___ = 40 1000 – 500 = 0 ÷ 3 =
5 + ___ = 9 22 ÷ 2 = 12 – ___ = 9 12 × 8 =
___ – 2 = 3 ___ ÷ 11 = 8 1 + ___ = 2 9 ÷ ___ = 9
7 × ___ = 21 8 + 4 = 400 ÷ 80 = 11 – 3 =
Instructions: Rule off after each attempt and date. Record results below.
Date
Number Correct
Number Errors
88
Speed Sheet
F a s t a n d A c c u r a t e B a s i c S k i l l s
Student Name: ____________________________________________________________
How many facts can you complete in 2 minutes?
Mixed Operations – Sheet 4
1 + ___ = 5 2 × ___ = 18 ___ × 10 = 100 ___ + 1000 = 1600
27 ÷ ___ = 9 ___ – 6 = 5 0 ÷ 12 = 8 + ___ = 8
___ × 100 = 8000 8 – 3 = 1 × ___ = 2 ___ – 1 = 8
___ + 6 = 6 ___ ÷ 10 = 8 ___ + 4 = 13 ___ ÷ 1 = 0
10 – ___ = 2 18 ÷ ___ = 6 ___ + 50 = 160 2 × ___ = 16
28 ÷ ___ = 4 8 + 9 = 270 ÷ ___ = 3 7 – 4 =
0 ÷ 3 = ___ + 1 = 5 36 ÷ ___ = 6 5 + 8 =
2 × 8 = 5 + ___ = 17 ___ × 11 = 121 7 – ___ = 6
___ + 8 = 12 6 ÷ 3 = 3 + 2 = 6 × ___ = 240
11 – 4 = 6 × ___ = 6 1200 – 500 = ___ ÷ 6 = 7
7 + 3 = 22 ÷ 2 = 2 + ___ = 10 ___ × 2 = 10
___ + 90 = 110 108 ÷ ___ = 12 ___ – 5 = 7 42 ÷ ___ = 7
0 × 70 = 3 + ___ = 11 ___ ÷ 6 = 5 200 + ___ = 800
0 ÷ 100 = ___ – 1 = 10 ___ ÷ 5 = 2 4 + ___ = 5
49 ÷ ___ = 7 9 + 1 = 1 × ___ = 9 30 + ___ = 50
500 – 300 = 11 × 6 = ___ + 10 = 18 ___ × 12 = 0
9 – 2 = 56 ÷ 7 = ___ – 4 = 1 8 × ___ = 40
100 × 60 = 0 + ___ = 6 8 ÷ ___ = 8 ___ + 30 = 110
10 × 6 = ___ + 8 = 16 11 × 4 = 1200 – ___ = 600
___ × 5 = 10 ___ – 0 = 12 48 ÷ ___ = 8 ___ – 100 = 600
Instructions: Rule off after each attempt and date. Record results below.
Date
Number Correct
Number Errors
Solutions for Speed Sheets for
Addition and Subtraction
89
F a s t a n d A c c u r a t e B a s i c S k i l l s
Speed Sheet - Solutions
Answers are provided below and typed in bold.
Addition and Subtraction Facts to 10
10 − 3 = 7 10 − 6 = 4 4 + 6 = 10 10 − 2 = 8
10 − 9 = 1 5 + 5 = 10 10 − 2 = 8 8 + 2 = 10
3 + 7 = 10 7 + 3 = 10 10 − 8 = 2 20 − 2 = 18
8 + 2 = 10 18 + 2 = 20 27 + 3 = 30 10 − 3 = 7
5 + 5 = 10 10 − 4 = 6 20 − 2 = 18 10 − 9 = 1
10 − 7 = 3 4 + 6 = 10 50 − 48 = 2 3 + 7 = 10
2 + 8 = 10 10 + 0 = 10 10 − 3 = 7 10 − 8 = 2
10 − 5 = 5 4 + 6 = 10 10 − 9 = 1 10 − 0 = 10
7 + 3 = 10 3 + 7 = 10 10 − 1 = 9 27 + 3 = 30
50 − 48 = 2 10 − 3 = 7 10 − 2 = 8 50 − 48 = 2
48 + 2 = 50 10 − 0 = 10 10 − 6 = 4 3 + 7 = 10
3 + 7 = 10 50 − 48 = 2 20 − 18 = 2 10 − 1 = 9
10 − 1 = 9 10 − 2 = 8 3 + 7 = 10 7 + 3 = 10
10 − 6 = 4 10 − 8 = 2 6 + 4 = 10 2 + 8 = 10
10 − 4 = 6 20 − 2 = 18 8 + 2 = 10 3 + 7 = 10
6 + 4 = 10 2 + 8 = 10 18 + 2 = 20 10 − 6 = 4
10 + 0 = 10 3 + 7 = 10 10 − 9 = 1 10 + 0 = 10
20 − 18 = 2 10 − 7 = 3 10 − 0 = 10 10 − 3 = 7
8 + 2 = 10 10 − 2 = 8 7 + 3 = 10 20 − 18 = 2
18 + 2 = 20 10 − 5 = 5 10 − 4 = 6 10 − 4 = 6
90
F a s t a n d A c c u r a t e B a s i c S k i l l s
Speed Sheet - Solutions
Answers are provided below and typed in bold.
Addition and Subtraction Facts + 0 and − 0
0 + 0 = 0 5 + 0 = 5 1 − 0 = 1 0 + 910 = 910
1 + 0 = 1 17 − 0 = 17 11 + 0 = 11 12 − 0 = 12
0 + 2 = 2 13 − 0 = 13 13 − 0 = 13 7 + 0 = 7
3 + 0 = 3 12 + 0 = 12 0 + 9 = 9 9 − 0 = 9
11 + 0 = 11 60 + 0 = 60 6 − 0 = 6 15 − 0 = 15
5 + 0 = 5 0 + 9 = 9 211 − 0 = 211 90 − 0 = 90
4 + 0 = 4 14 − 0 = 14 0 + 11 = 11 10 + 0 = 10
7 + 0 = 7 13 − 0 = 13 88 − 0 = 88 6 + 0 = 6
0 + 8 = 8 7 + 0 = 7 12 − 0 = 12 80 + 0 = 80
0 + 9 = 9 1 + 0 = 1 0 + 0 = 0 16 − 0 = 16
12 + 0 = 12 18 − 0 = 18 5 − 0 = 5 42 − 0 = 42
0 + 6 = 6 7 + 0 = 7 2 + 0 = 2 18 + 0 = 18
10 + 0 = 10 0 + 12 = 12 1 − 0 = 1 0 + 6 = 6
12 − 0 = 12 21 − 0 = 21 3 + 0 = 3 15 − 0 = 15
21 − 0 = 21 0 + 8 = 8 0 + 77 = 77 12 − 0 = 12
13 − 0 = 13 112 − 0 = 112 5 + 0 = 5 40 + 0 = 40
0 − 0 = 0 12 + 0 = 12 131 − 0 = 131 0 + 2 = 2
17 − 0 = 17 16 − 0 = 16 4 + 0 = 4 412 − 0 = 412
8 − 0 = 8 10 + 0 = 10 32 − 0 = 32 3 + 0 = 3
12 − 0 = 12 15 − 0 = 15 0 + 90 = 90 14 − 0 = 14
91
F a s t a n d A c c u r a t e B a s i c S k i l l s
Speed Sheet - Solutions
Answers are provided below and typed in bold.
Addition and Subtraction Facts + 1 and − 1
1 + 0 = 1 5 + 1 = 6 1 − 1 = 0 1 + 910 = 911
1 + 12 = 13 17 − 1 = 16 11 + 1 = 12 12 − 1 = 11
1 + 2 = 3 13 − 1 = 12 13 − 1 = 12 7 + 1 = 8
3 + 1 = 4 12 + 1 = 13 1 + 9 = 10 9 − 1 = 8
11 + 1 = 12 60 + 1 = 61 6 − 1 = 5 15 − 1 = 14
5 + 1 = 6 1 + 9 = 10 211 − 1 = 210 90 − 1 = 89
4 + 1 = 5 14 − 1 = 13 1 + 11 = 12 10 + 1 = 11
7 + 1 = 8 13 − 1 = 12 88 − 1 = 87 6 + 1 = 7
1 + 8 = 9 7 + 1 = 8 12 − 1 = 11 80 + 1 = 81
1 + 9 = 10 1 + 1 = 2 1 + 0 = 1 16 − 1 = 15
12 + 1 = 13 18 − 1 = 17 5 − 1 = 4 42 − 1 = 41
1 + 11 = 12 7 + 1 = 8 2 + 1 = 3 18 + 1 = 19
9 + 1 = 10 1 + 12 = 13 1 − 0 = 1 1 + 6 = 7
12 − 1 = 11 21 − 1 = 20 3 + 1 = 4 15 − 1 = 14
21 − 1 = 20 1 + 8 = 9 1 + 70 = 71 12 − 1 = 11
13 − 1 = 12 112 − 1 = 111 5 + 1 = 6 40 + 1 = 41
1 − 0 = 1 12 + 1 = 13 131 − 1 = 130 1 + 2 = 3
17 − 1 = 16 16 − 1 = 15 4 + 1 = 5 412 − 100 = 312
8 − 1 = 7 10 + 1 = 11 32 − 1 = 31 3 + 1 = 4
12 − 1 = 11 15 − 1 = 14 1 + 90 = 91 14 − 1 = 13
92
F a s t a n d A c c u r a t e B a s i c S k i l l s
Speed Sheet - Solutions
Answers are provided below and typed in bold.
Addition and Subtraction Facts + 2 and − 2
2 + 0 = 2 3 + 2 = 5 2 − 2 = 0 5 + 2 = 7
1 + 2 = 3 7 − 2 = 5 2 + 4 = 6 10 − 2 = 8
2 + 2 = 4 7 + 2 = 9 9 − 2 = 7 4 − 2 = 2
3 + 2 = 5 10 − 2 = 8 3 − 2 = 1 8 − 2 = 6
2 + 4 = 6 11 − 2 = 9 9 + 2 = 11 2 + 0 = 2
5 + 2 = 7 2 + 0 = 2 7 − 2 = 5 60 + 20 = 80
2 + 6 = 8 60 + 20 = 80 5 + 2 = 7 12 − 2 = 10
7 + 2 = 9 9 + 2 = 11 1 + 2 = 3 3 + 2 = 5
2 + 8 = 10 8 − 2 = 6 10 − 2 = 8 66 + 22 = 88
9 + 2 = 11 2 − 2 = 0 7 + 2 = 9 2 + 6 = 8
2 + 10 = 12 66 + 22 = 88 60 + 20 = 80 9 − 2 = 7
2 − 2 = 0 2 + 2 = 4 2 + 6 = 8 6 − 2 = 4
3 − 2 = 1 88 + 20 = 108 6 − 2 = 4 2 + 2 = 4
9 − 2 = 7 4 − 2 = 2 2 + 0 = 2 7 − 2 = 5
5 − 2 = 3 108 − 2 = 106 66 + 22 = 88 5 − 2 = 3
6 − 2 = 4 12 − 2 = 10 2 + 10 = 12 2 + 4 = 6
7 − 2 = 5 50 − 20 = 30 8 − 2 = 6 88 + 20 = 108
8 − 2 = 6 1 + 2 = 3 88 + 20 = 108 9 + 2 = 11
9 − 2 = 7 2 + 8 = 10 3 + 2 = 5 200 − 20 = 180
10 − 2 = 8 5 + 2 = 7 4 − 2 = 2 2 + 10 = 12
93
F a s t a n d A c c u r a t e B a s i c S k i l l s
Speed Sheet - Solutions
Answers are provided below and typed in bold.
Addition and Subtraction Facts + 3 and − 3
3 + 0 = 3 3 + 3 = 6 4 − 3 = 1 5 − 3 = 2
1 + 3 = 4 10 − 3 = 7 12 − 3 = 9 11 − 3 = 8
3 + 2 = 5 3 + 4 = 7 3 + 12 = 15 7 + 3 = 10
3 + 3 = 6 6 − 3 = 3 13 − 3 = 10 10 − 3 = 7
3 + 4 = 7 9 + 3 = 12 1 + 3 = 4 3 + 2 = 5
5 + 3 = 8 30 + 80 = 110 33 + 22 = 55 88 − 30 = 58
3 + 6 = 9 3 + 10 = 13 3 + 4 = 7 5 + 3 = 8
7 + 3 = 10 3 − 3 = 0 15 − 3 = 12 300 − 30 = 270
8 + 3 = 11 3 + 0 = 3 3 + 10 = 13 8 + 3 = 11
9 + 3 = 12 13 − 3 = 10 6 − 3 = 3 15 − 3 = 12
3 + 10 = 13 3 + 4 = 7 78 + 30 = 108 3 + 0 = 3
11 + 3 = 14 11 − 3 = 8 7 − 3 = 4 30 + 80 = 110
3 + 12 = 15 11 + 3 = 14 9 + 3 = 12 3 + 4 = 7
3 − 3 = 0 9 − 3 = 6 10 − 3 = 7 8 − 3 = 5
4 − 3 = 1 1 + 3 = 4 3 − 3 = 0 9 + 3 = 12
5 − 3 = 2 33 + 22 = 55 8 + 3 = 11 12 − 3 = 9
6 − 3 = 3 7 + 3 = 10 8 − 3 = 5 3 + 10 = 13
7 − 3 = 4 15 − 3 = 12 11 + 3 = 14 13 − 3 = 10
8 − 3 = 5 3 + 12 = 15 300 − 30 = 270 6 − 3 = 3
9 − 3 = 6 88 − 30 = 58 7 + 3 = 10 3 + 12 = 15
94
F a s t a n d A c c u r a t e B a s i c S k i l l s
Speed Sheet - Solutions
Answers are provided below and typed in bold.
Addition and Subtraction Facts + 4 and − 4
4 + 0 = 4 5 + 4 = 9 9 − 4 = 5 4 + 4 = 8
1 + 4 = 5 4 − 4 = 0 11 + 4 = 15 12 − 4 = 8
4 + 2 = 6 12 − 4 = 8 13 − 4 = 9 25 − 4 = 21
3 + 4 = 7 4 + 2 = 6 9 + 4 = 13 15 − 4 = 11
4 + 4 = 8 60 + 40 = 100 7 − 4 = 3 4 − 4 = 0
5 + 4 = 9 4 + 6 = 10 300 − 40 = 260 8 − 4 = 4
4 + 6 = 10 14 − 4 = 10 1 + 4 = 5 4 + 10 = 14
7 + 4 = 11 6 − 4 = 2 50 − 40 = 10 44 + 33 = 77
4 + 8 = 12 7 + 4 = 11 5 − 4 = 1 7 + 4 = 11
9 + 4 = 13 44 + 33 = 77 4 + 0 = 4 16 − 4 = 12
4 + 10 = 14 7 − 4 = 3 11 − 4 = 7 5 − 4 = 1
11 + 4 = 15 4 + 4 = 8 4 + 2 = 6 58 + 40 = 98
4 + 12 = 16 58 + 40 = 98 4 − 4 = 0 4 + 6 = 10
4 − 4 = 0 10 − 4 = 6 3 + 4 = 7 7 − 4 = 3
5 − 4 = 1 9 + 4 = 13 60 + 40 = 100 6 − 4 = 2
6 − 4 = 2 112 − 4 = 108 5 + 4 = 9 9 + 4 = 13
7 − 4 = 3 4 + 0 = 4 112 − 4 = 108 4 + 12 = 16
8 − 4 = 4 16 − 4 = 12 4 + 6 = 10 300 − 40 = 260
9 − 4 = 5 4 + 10 = 14 8 − 4 = 4 3 + 4 = 7
10 − 4 = 6 15 − 4 = 11 58 + 40 = 98 14 − 4 = 10
95
F a s t a n d A c c u r a t e B a s i c S k i l l s
Speed Sheet - Solutions
Answers are provided below and typed in bold.
Addition and Subtraction Facts + 5 and − 5
5 + 0 = 5 3 + 5 = 8 5 − 5 = 0 5 + 5 = 10
1 + 5 = 6 7 − 5 = 2 5 + 4 = 9 10 − 5 = 5
5 + 5 = 10 7 + 5 = 12 12 − 5 = 7 7 − 5 = 2
3 + 5 = 8 10 − 5 = 5 6 − 5 = 1 11 − 5 = 6
5 + 2 = 7 11 − 5 = 6 9 + 5 = 14 5 + 0 = 5
5 + 5 = 10 5 + 0 = 5 7 − 5 = 2 10 + 50 = 60
5 + 6 = 11 50 + 20 = 70 5 − 5 = 0 15 − 5 = 10
7 + 5 = 12 9 + 5 = 14 1 + 5 = 6 3 + 5 = 8
5 + 8 = 13 8 − 5 = 3 10 − 5 = 5 22 + 55 = 77
9 + 5 = 14 5 − 5 = 0 7 + 5 = 12 2 + 5 = 7
5 + 10 = 15 33 + 55 = 88 40 + 50 = 90 12 − 5 = 7
11 − 5 = 6 5 + 5 = 10 5 + 6 = 11 9 − 5 = 4
6 − 5 = 1 50 + 20 = 70 6 − 5 = 1 5 + 5 = 10
9 − 5 = 4 7 − 5 = 2 5 + 0 = 5 7 − 5 = 2
5 − 5 = 0 108 − 5 = 103 23 + 55 = 78 8 − 5 = 3
9 − 5 = 4 12 − 5 = 7 5 + 10 = 15 5 + 4 = 9
7 − 5 = 2 80 − 50 = 30 8 − 5 = 3 11 + 50 = 61
8 − 5 = 3 1 + 5 = 6 28 + 50 = 78 9 + 5 = 14
12 − 5 = 7 5 + 8 = 13 3 + 5 = 8 100 − 50 = 50
10 − 5 = 5 5 + 5 = 10 8 − 5 = 3 5 + 10 = 15
96
F a s t a n d A c c u r a t e B a s i c S k i l l s
Speed Sheet - Solutions
Answers are provided below and typed in bold.
Addition and Subtraction Facts + 6 and − 6
6 + 0 = 6 6 + 6 = 12 7 − 6 = 1 9 − 6 = 3
1 + 6 = 7 10 − 6 = 4 12 − 6 = 6 11 − 6 = 5
6 + 2 = 8 6 + 4 = 10 6 + 12 = 18 7 + 6 = 13
6 + 6 = 12 6 − 6 = 0 13 − 6 = 7 10 − 6 = 4
6 + 4 = 10 9 + 6 = 15 1 + 6 = 7 6 + 2 = 8
5 + 6 = 11 60 + 80 = 140 66 + 22 = 88 98 − 60 = 38
6 + 6 = 12 6 + 10 = 16 6 + 4 = 10 5 + 6 = 11
7 + 6 = 13 6 − 6 = 0 15 − 6 = 9 600 − 60 = 540
8 + 6 = 14 6 + 0 = 6 6 + 10 = 16 8 + 6 = 14
9 + 6 = 15 13 − 6 = 7 9 − 6 = 3 15 − 6 = 9
6 + 10 = 16 6 + 4 = 10 28 + 60 = 88 6 + 0 = 6
11 + 6 = 17 11 − 6 = 5 7 − 6 = 1 60 + 80 = 140
6 + 12 = 18 11 + 6 = 17 9 + 6 = 15 6 + 4 = 10
6 − 6 = 0 9 − 6 = 3 10 − 6 = 4 8 − 6 = 2
7 − 6 = 1 1 + 6 = 7 6 − 6 = 0 9 + 6 = 15
8 − 6 = 2 66 + 22 = 88 8 + 6 = 14 12 − 6 = 6
6 − 6 = 0 7 + 6 = 13 8 − 6 = 2 6 + 10 = 16
7 − 6 = 1 15 − 6 = 9 11 + 6 = 17 13 − 6 = 7
8 − 6 = 2 6 + 12 = 18 300 − 60 = 240 6 − 6 = 0
9 − 6 = 3 88 − 60 = 28 7 + 6 = 13 6 + 12 = 18
97
F a s t a n d A c c u r a t e B a s i c S k i l l s
Speed Sheet - Solutions
Answers are provided below and typed in bold.
Addition and Subtraction Facts + 7 and − 7
7 + 0 = 7 5 + 7 = 12 9 − 7 = 2 7 + 7 = 14
1 + 7 = 8 7 − 7 = 0 11 + 7 = 18 12 − 7 = 5
7 + 2 = 9 12 − 7 = 5 13 − 7 = 6 7 + 8 = 15
3 + 7 = 10 7 + 2 = 9 9 + 7 = 16 15 − 7 = 8
7 + 7 = 14 60 + 70 = 130 7 − 7 = 0 7 − 7 = 0
5 + 7 = 12 7 + 6 = 13 300 − 70 = 230 8 − 7 = 1
4 + 7 = 11 14 − 7 = 7 1 + 7 = 8 7 + 10 = 17
7 + 7 = 14 7 − 4 = 3 90 − 70 = 20 77 + 22 = 99
7 + 8 = 15 7 + 7 = 14 8 − 7 = 1 7 + 7 = 14
9 + 7 = 16 77 + 22 = 99 7 + 0 = 7 16 − 7 = 9
7 + 10 = 17 7 − 7 = 0 11 − 7 = 4 8 − 7 = 1
11 + 7 = 18 7 + 7 = 14 7 + 2 = 9 38 + 70 = 108
7 + 12 = 19 18 + 70 = 88 7 − 7 = 0 7 + 6 = 13
7 − 7 = 0 10 − 7 = 3 3 + 7 = 10 7 − 7 = 0
8 − 7 = 1 9 + 7 = 16 60 + 70 = 130 9 − 7 = 2
9 − 7 = 2 112 − 7 = 105 5 + 7 = 12 9 + 7 = 16
10 − 7 = 3 7 + 0 = 7 112 − 7 = 105 7 + 12 = 19
8 − 7 = 1 16 − 7 = 9 4 + 7 = 11 300 − 70 = 230
9 − 7 = 2 7 + 10 = 17 8 − 7 = 1 3 + 7 = 10
10 − 7 = 3 15 − 7 = 8 58 + 70 = 128 14 − 7 = 7
98
F a s t a n d A c c u r a t e B a s i c S k i l l s
Speed Sheet - Solutions
Answers are provided below and typed in bold.
Addition and Subtraction Facts + 8 and − 8
8 + 0 = 8 5 + 8 = 13 9 − 8 = 1 8 + 8 = 16
1 + 8 = 9 17 − 8 = 9 11 + 8 = 19 12 − 8 = 4
8 + 2 = 10 13 − 8 = 5 13 − 8 = 5 7 + 8 = 15
3 + 8 = 11 8 + 2 = 10 9 + 8 = 17 19 − 8 = 11
8 + 8 = 16 60 + 80 = 140 16 − 8 = 8 15 − 8 = 7
5 + 8 = 13 7 + 8 = 15 200 − 80 = 120 8 − 8 = 0
4 + 8 = 12 14 − 8 = 6 1 + 8 = 9 8 + 10 = 18
7 + 8 = 15 12 − 8 = 4 100 − 80 = 20 88 + 2 = 90
8 + 8 = 16 7 + 8 = 15 9 − 8 = 1 8 + 8 = 16
9 + 8 = 17 88 + 11 = 99 8 + 0 = 8 16 − 8 = 8
8 + 10 = 18 18 − 8 = 10 11 − 8 = 3 9 − 8 = 1
11 + 8 = 19 7 + 8 = 15 8 + 2 = 10 18 + 80 = 98
8 + 12 = 20 18 + 80 = 98 8 − 0 = 8 8 + 6 = 14
8 − 8 = 0 10 − 8 = 2 3 + 8 = 11 15 − 8 = 7
11 − 8 = 3 9 + 8 = 17 30 + 80 = 110 9 − 8 = 1
9 − 8 = 1 112 − 8 = 104 5 + 8 = 13 9 + 8 = 17
10 − 8 = 2 8 + 0 = 8 112 − 8 = 104 8 + 12 = 20
8 − 8 = 0 16 − 8 = 8 4 + 8 = 12 400 − 80 = 320
9 − 8 = 1 8 + 10 = 18 10 − 8 = 2 3 + 8 = 11
10 − 8 = 2 15 − 8 = 7 18 + 80 = 98 14 − 8 = 6
99
F a s t a n d A c c u r a t e B a s i c S k i l l s
Speed Sheet - Solutions
Answers are provided below and typed in bold.
Addition and Subtraction Facts + 9 and − 9
9 + 0 = 9 5 + 9 = 14 11 − 9 = 2 9 + 9 = 18
1 + 9 = 10 17 − 9 = 8 11 + 9 = 20 12 − 9 = 3
9 + 2 = 11 13 − 9 = 4 13 − 9 = 4 7 + 9 = 16
3 + 9 = 12 9 + 2 = 11 9 + 9 = 18 19 − 9 = 10
9 + 9 = 18 60 + 90 = 150 16 − 9 = 7 15 − 9 = 6
5 + 9 = 14 7 + 9 = 16 200 − 90 = 110 9 − 9 = 0
4 + 9 = 13 14 − 9 = 5 1 + 9 = 10 9 + 10 = 19
7 + 9 = 16 12 − 9 = 3 100 − 90 = 10 99 + 0 = 99
9 + 8 = 17 7 + 9 = 16 9 − 9 = 0 8 + 9 = 17
9 + 9 = 18 99 + 1 = 100 9 + 0 = 9 16 − 9 = 7
9 + 10 = 19 18 − 9 = 9 11 − 9 = 2 9 − 9 = 0
11 + 9 = 20 7 + 9 = 16 9 + 2 = 11 19 + 80 = 99
9 + 12 = 21 18 + 90 = 108 9 − 0 = 9 9 + 6 = 15
9 − 9 = 0 10 − 9 = 1 3 + 9 = 12 15 − 9 = 6
11 − 9 = 2 9 + 8 = 17 30 + 90 = 120 9 − 9 = 0
9 − 9 = 0 112 − 9 = 103 9 + 8 = 17 9 + 9 = 18
10 − 9 = 1 9 + 0 = 9 112 − 9 = 103 9 + 12 = 21
9 + 0 = 9 16 − 9 = 7 4 + 9 = 13 400 − 90 = 310
18 − 9 = 9 9 + 10 = 19 10 − 9 = 1 3 + 9 = 12
10 − 9 = 1 15 − 9 = 6 8 + 90 = 98 14 − 9 = 5
100
F a s t a n d A c c u r a t e B a s i c S k i l l s
Speed Sheet - Solutions
Answers are provided below and typed in bold.
Addition and Subtraction Facts + 10 and − 10
10 + 0 = 10 5 + 10 = 15 11 − 10 = 1 9 + 910 = 919
1 + 10 = 11 17 − 10 = 7 11 + 10 = 21 12 − 10 = 2
10 + 2 = 12 13 − 10 = 3 13 − 10 = 3 7 + 10 = 17
3 + 10 = 13 10 + 2 = 12 10 + 9 = 19 19 − 10 = 9
10 + 10 = 20 60 + 10 = 70 16 − 10 = 6 15 − 10 = 5
5 + 10 = 15 10 + 9 = 19 200 − 10 = 190 90 − 10 = 80
4 + 10 = 14 14 − 10 = 4 1 + 10 = 11 10 + 10 = 20
7 + 10 = 17 12 − 10 = 2 80 − 10 = 70 69 + 100 = 169
10 + 8 = 18 7 + 10 = 17 10 − 10 = 0 80 + 10 = 90
10 + 9 = 19 10 + 1 = 11 10 + 0 = 10 16 − 10 = 6
11 + 10 = 21 18 − 10 = 8 11 − 10 = 1 40 − 10 = 30
12 + 10 = 22 7 + 10 = 17 10 + 2 = 12 19 + 10 = 29
9 + 10 = 19 18 + 10 = 28 10 − 0 = 10 10 + 6 = 16
10 − 0 = 10 10 − 10 = 0 3 + 10 = 13 15 − 10 = 5
11 − 10 = 1 10 + 8 = 18 10 + 90 = 100 10 − 10 = 0
13 − 10 = 3 112 − 10 = 102 5 + 10 = 15 40 + 10 = 50
10 − 10 = 0 10 + 0 = 10 112 − 10 = 102 10 + 12 = 22
17 − 10 = 7 16 − 10 = 6 4 + 10 = 14 400 − 100 = 300
18 − 10 = 8 10 + 10 = 20 33 − 10 = 23 3 + 10 = 13
10 − 0 = 10 15 − 10 = 5 10 + 90 = 100 14 − 10 = 4
101
F a s t a n d A c c u r a t e B a s i c S k i l l s
Speed Sheet - Solutions
Answers are provided below and typed in bold.
Addition and Subtraction Facts + 11 and − 11
11 + 0 = 11 5 + 11 = 16 11 − 11 = 0 11 + 910 = 921
1 + 11 = 12 17 − 11 = 6 11 + 1 = 12 12 − 11 = 1
11 + 2 = 13 13 − 11 = 2 13 − 11 = 2 7 + 11 = 18
3 + 11 = 14 11 + 2 = 13 11 + 9 = 20 19 − 11 = 8
11 + 11 = 22 60 + 11 = 71 16 − 11 = 5 15 − 11 = 4
5 + 11 = 16 11 + 9 = 20 211 − 11 = 200 91 − 11 = 80
4 + 11 = 15 14 − 11 = 3 1 + 11 = 12 11 + 10 = 21
7 + 11 = 18 12 − 11 = 1 88 − 11 = 77 66 + 11 = 77
11 + 8 = 19 7 + 11 = 18 11 − 11 = 0 80 + 11 = 91
11 + 9 = 20 11 + 1 = 12 11 + 0 = 11 16 − 11 = 5
11 + 11 = 22 18 − 11 = 7 15 − 11 = 4 41 − 11 = 30
12 + 11 = 23 7 + 11 = 18 11 + 2 = 13 18 + 11 = 29
8 + 11 = 19 18 + 11 = 29 11 − 0 = 11 11 + 6 = 17
11 − 11 = 0 11 − 11 = 0 3 + 11 = 14 15 − 11 = 4
11 − 11 = 0 11 + 8 = 19 11 + 90 = 101 11 − 0 = 11
13 − 11 = 2 112 − 11 = 101 5 + 11 = 16 40 + 11 = 51
12 − 11 = 1 11 + 0 = 11 112 − 11 = 101 11 + 12 = 23
17 − 11 = 6 16 − 11 = 5 4 + 11 = 15 411 − 111 = 300
18 − 11 = 7 10 + 11 = 21 33 − 11 = 22 3 + 11 = 14
11 − 0 = 11 15 − 11 = 4 11 + 90 = 101 14 − 11 = 3
102
F a s t a n d A c c u r a t e B a s i c S k i l l s
Speed Sheet - Solutions
Answers are provided below and typed in bold.
Addition and Subtraction Facts + 12 and − 12
12 + 0 = 12 5 + 12 = 17 12 − 12 = 0 12 + 900 = 912
1 + 12 = 13 17 − 12 = 5 12 + 1 = 13 12 − 10 = 2
12 + 2 = 14 13 − 12 = 1 13 − 12 = 1 7 + 12 = 19
3 + 12 = 15 12 + 2 = 14 12 + 9 = 21 19 − 12 = 7
11 + 12 = 23 60 + 12 = 72 16 − 12 = 4 15 − 12 = 3
5 + 12 = 17 12 + 9 = 21 212 − 12 = 200 80 + 12 = 92
4 + 12 = 16 14 − 12 = 2 1 + 12 = 13 12 + 12 = 24
7 + 12 = 19 13 − 12 = 1 88 − 11 = 77 66 + 11 = 77
12 + 8 = 20 7 + 12 = 19 12 − 12 = 0 80 + 12 = 92
12 + 9 = 21 12 + 1 = 13 12 + 0 = 12 16 − 12 = 4
12 + 12 = 24 18 − 12 = 6 15 − 12 = 3 42 − 12 = 30
12 + 11 = 23 7 + 12 = 19 12 + 2 = 14 18 + 12 = 30
9 + 12 = 21 18 + 12 = 30 12 − 0 = 12 12 + 6 = 18
12 − 12 = 0 21 − 12 = 9 3 + 12 = 15 15 − 12 = 3
12 − 12 = 0 12 + 8 = 20 12 + 70 = 82 12 − 0 = 12
13 − 12 = 1 112 − 12 = 100 5 + 12 = 17 40 + 12 = 52
12 − 0 = 12 12 + 0 = 12 132 − 12 = 120 11 + 12 = 23
17 − 12 = 5 16 − 12 = 4 4 + 12 = 16 412 − 112 = 300
18 − 12 = 6 10 + 12 = 22 32 − 12 = 20 3 + 12 = 15
12 − 0 = 12 15 − 12 = 3 12 + 90 = 102 14 − 12 = 2
Solutions for Speed Sheets for
Multiplication and Division
103
F a s t a n d A c c u r a t e B a s i c S k i l l s
Speed Sheet - Solutions
Answers are provided below and typed in bold.
Doubles and × 2 speed sheet
1 × 2 = 2 4 × 2 = 8 6 × 2 = 12 9 × 2 = 18
2 × 2 = 4 9 × 2 = 18 7 × 2 = 14 3 + 3 = 6
3 × 2 = 6 12 × 2 = 24 2 + 2 = 4 7 + 7 = 14
4 × 2 = 8 1 × 2 = 2 10 + 10 = 20 10 + 10 = 20
5 × 2 = 10 5 + 5 = 10 3 + 3 = 6 1 × 2 = 2
6 × 2 = 12 2 + 2 = 4 8 × 2 = 16 9 × 2 = 18
7 × 2 = 14 6 + 6 = 12 9 × 2 = 18 7 × 2 = 14
8 × 2 = 16 4 + 4 = 8 12 × 2 = 24 12 + 12 = 24
9 × 2 = 18 10 + 10 = 20 4 × 2 = 8 ½ × 60 = 30
10 × 2 = 20 2 × 2 = 4 7 + 7 = 14 12 × 2 = 24
11 × 2 = 22 7 + 7 = 14 10 × 2 = 20 3 × 2 = 6
12 × 2 = 24 11 × 2 = 22 3 × 2 = 6 8 + 8 = 16
3 + 3 = 6 12 + 12 = 24 1 × 2 = 2 1000 ÷ 2 = 500
4 + 4 = 8 9 + 9 = 18 8 + 8 = 16 8 × 2 = 16
5 + 5 = 10 7 × 2 = 14 1000 ÷ 2 = 500 6 + 6 = 12
6 + 6 = 12 ½ × 50 = 25 100 ÷ 2 = 50 5 × 2 = 10
7 + 7 = 14 3 + 3 = 6 5 × 2 = 10 8 × 2 = 16
8 + 8 = 16 ½ × 60 = 30 ½ × 60 = 30 ½ × 50 = 25
9 + 9 = 18 3 × 2 = 6 11 × 2 = 22 4 + 4 = 8
10 + 10 = 20 1000 ÷ 2 = 500 6 + 6 = 12 9 + 9 = 18
104
F a s t a n d A c c u r a t e B a s i c S k i l l s
Speed Sheet - Solutions
Answers are provided below and typed in bold.
Multiplication and Division 2's - Double and Half
2 × 0 = 0 2 × 5 = 10 2 × 10 = 20 2 × 1 = 2
2 × 1 = 2 6 ÷ 2 = 3 16 ÷ 2 = 8 12 ÷ 2 = 6
2 × 2 = 4 2 × 9 = 18 Double 7 = 14 2 × 90 = 180
2 × 3 = 6 16 ÷ 2 = 8 2 × 9 = 18 20 ÷ 2 = 10
2 × 4 = 8 12 ÷ 2 = 6 10 ÷ 2 = 5 2 × 4 = 8
2 × 5 = 10 2 × 0 = 0 2 × 3 = 6 Double 7 = 14
2 × 6 = 12 14 ÷ 2 = 7 8 ÷ 2 = 4 2 × 0 = 0
2 × 7 = 14 2 × 8 = 16 2 × 2 = 4 Double 9 = 18
2 × 8 = 16 Half of 24 = 12 6 ÷ 2 = 3 2 × 6 = 12
2 × 9 = 18 2 × 11 = 22 2 × 12 = 24 4 ÷ 2 = 2
2 × 10 = 20 2 ÷ 2 = 1 2 × 5 = 10 Half of 24 = 12
2 × 11 = 22 2 × 1 = 2 Half of 24 = 12 6 ÷ 2 = 3
2 × 12 = 24 Double 9 = 18 2 ÷ 2 = 1 160 ÷ 2 = 80
2 ÷ 2 = 1 2 × 10 = 20 160 ÷ 2 = 80 Double 8 = 16
4 ÷ 2 = 2 Double 8 = 16 12 ÷ 2 = 6 2 × 11 = 22
6 ÷ 2 = 3 2 × 4 = 8 Double 9 = 18 Half of 30 = 15
8 ÷ 2 = 4 20 ÷ 2 = 10 24 ÷ 2 = 12 18 ÷ 2 = 9
10 ÷ 2 = 5 2 × 90 = 180 4 ÷ 2 = 2 2 × 12 = 24
12 ÷ 2 = 6 18 ÷ 2 = 9 2 × 4 = 8 2 × 2 = 4
14 ÷ 2 = 7 8 ÷ 2 = 4 2 × 90 = 180 16 ÷ 2 = 8
105
F a s t a n d A c c u r a t e B a s i c S k i l l s
Speed Sheet - Solutions
Answers are provided below and typed in bold.
Multiplication and Division Facts × 0 and 0 ÷
0 × 0 = 0 3 × 0 = 0 37 × 0 = 0 36 × 0 = 0
3 × 0 = 0 0 × 10 = 0 18 × 0 = 0 0 × 31 = 0
4 × 0 = 0 36 × 0 = 0 30 × 0 = 0 3 × 0 = 0
0 × 0 = 0 13 × 0 = 0 3 × 0 = 0 33 × 0 = 0
3 × 0 = 0 15 × 0 = 0 27 × 0 = 0 9 × 0 = 0
0 × 5 = 0 330 × 0 = 0 126 × 0 = 0 27 × 0 = 0
8 × 0 = 0 27 × 0 = 0 43 × 0 = 0 0 ÷ 23 = 0
0 × 7 = 0 7 × 0 = 0 0 × 10 = 0 12 × 0 = 0
10 × 0 = 0 46 × 0 = 0 0 × 18 = 0 273 × 0 = 0
0 × 9 = 0 12 × 0 = 0 540 × 0 = 0 0 × 310 = 0
0 × 10 = 0 0 × 10 = 0 62 × 0 = 0 25 × 0 = 0
11 × 0 = 0 0 × 90 = 0 0 × 9 = 0 73 × 0 = 0
12 × 0 = 0 243 × 0 = 0 0 × 76 = 0 0 × 90 = 0
6 × 0 = 0 12 × 0 = 0 68 × 0 = 0 40 × 0 = 0
0 ÷ 3 = 0 7 × 0 = 0 248 × 0 = 0 18 × 0 = 0
1 × 0 = 0 36 × 0 = 0 21 × 0 = 0 254 × 0 = 0
0 × 9 = 0 24 × 0 = 0 36 × 0 = 0 360 × 0 = 0
2 × 0 = 0 21 × 0 = 0 12 × 0 = 0 30 × 0 = 0
10 × 0 = 0 9 × 0 = 0 15 × 0 = 0 181 × 0 = 0
9 × 0 = 0 0 ÷ 5 = 0 91 × 0 = 0 77 × 0 = 0
106
F a s t a n d A c c u r a t e B a s i c S k i l l s
Speed Sheet - Solutions
Answers are provided below and typed in bold.
Multiplication and Division Facts × 1 and ÷ 1
1 × 0 = 0 1 × 3 = 3 1 × 6 = 6 1 × 36 = 36
1 × 1 = 1 1 × 10 = 10 18 ÷ 1 = 18 36 ÷ 1 = 36
1 × 6 = 6 36 × 1 = 36 30 ÷ 1 = 30 3 × 1 = 3
3 × 1 = 3 18 ÷ 1 = 18 1 × 12 = 12 33 × 1 = 33
1 × 12 = 12 15 ÷ 1 = 15 27 ÷ 1 = 27 9 ÷ 1 = 9
5 × 1 = 5 1 × 330 = 330 1 × 36 = 36 273 ÷ 1 = 273
1 × 18 = 18 27 ÷ 1 = 27 1 × 330 = 330 6 ÷ 1 = 6
1 × 7 = 7 40 × 1 = 40 1 × 108 = 108 12 ÷ 1 = 12
1 × 24 = 24 33 ÷ 1 = 33 3 × 1 = 3 330 × 1 = 330
9 × 1 = 9 12 ÷ 1 = 12 1 × 18 = 18 1 × 65 = 65
1 × 10 = 10 1 × 170 = 170 6 ÷ 1 = 6 24 × 1 = 24
13 × 1 = 13 1 × 90 = 90 1 × 9 = 9 1 × 56 = 56
8 × 1 = 8 1 × 240 = 240 1 × 67 = 67 1 × 90 = 90
1 ÷ 1 = 1 12 ÷ 1 = 12 1 × 33 = 33 1 × 9 = 9
6 ÷ 1 = 6 73 × 1 = 73 1 × 240 = 240 18 ÷ 1 = 18
9 ÷ 1 = 9 36 ÷ 1 = 36 210 ÷ 1 = 210 1 × 97 = 97
1 × 90 = 90 24 ÷ 1 = 24 36 ÷ 1 = 36 360 ÷ 1 = 360
1 × 330 = 330 21 ÷ 1 = 21 12 ÷ 1 = 12 38 ÷ 1 = 38
180 ÷ 1 = 180 9 ÷ 1 = 9 15 ÷ 1 = 15 180 ÷ 1 = 180
1 × 240 = 240 1 × 5 = 5 9 ÷ 1 = 9 246 ÷ 1 = 246
107
F a s t a n d A c c u r a t e B a s i c S k i l l s
Speed Sheet - Solutions
Answers are provided below and typed in bold.
Multiplication and Division Facts × 2 and ÷ 2
2 × 0 = 0 3 × 2 = 6 3 × 2 = 6 2 × 8 = 16
2 × 2 = 4 2 × 10 = 20 18 ÷ 2 = 9 26 ÷ 2 = 13
3 × 2 = 6 2 × 7 = 14 60 ÷ 2 = 30 2 × 0 = 0
2 × 5 = 10 18 ÷ 2 = 9 2 × 6 = 12 48 ÷ 2 = 24
2 × 6 = 12 16 ÷ 2 = 8 28 ÷ 2 = 14 16 ÷ 2 = 8
3 × 2 = 6 2 × 110 = 220 2 × 12 = 24 28 ÷ 2 = 14
2 × 9 = 18 240 ÷ 2 = 120 2 × 34 = 68 6 ÷ 2 = 3
2 × 7 = 14 2 × 0 = 0 2 × 10 = 20 22 ÷ 2 = 11
2 × 12 = 24 22 ÷ 2 = 11 2 × 1 = 2 2 × 24 = 48
2 × 9 = 18 12 ÷ 2 = 6 2 × 9 = 18 2 × 3 = 6
2 × 10 = 20 2 × 104 = 208 6 ÷ 2 = 3 2 × 12 = 24
2 × 11 = 22 2 × 90 = 180 2 × 90 = 180 2 × 120 = 240
2 × 12 = 24 2 × 120 = 240 2 × 7 = 14 2 × 90 = 180
2 ÷ 2 = 1 12 ÷ 2 = 6 11 × 2 = 22 2 × 9 = 18
6 ÷ 2 = 3 3 × 2 = 6 2 × 120 = 240 18 ÷ 2 = 9
10 ÷ 2 = 5 46 ÷ 2 = 23 220 ÷ 110 = 2 2 × 90 = 180
2 × 90 = 180 24 ÷ 2 = 12 24 ÷ 2 = 12 660 ÷ 2 = 330
2 × 110 = 220 14 ÷ 2 = 7 12 ÷ 2 = 6 80 ÷ 2 = 40
180 ÷ 2 = 90 8 ÷ 2 = 4 16 ÷ 2 = 8 180 ÷ 2 = 90
2 × 120 = 240 2 × 5 = 10 48 ÷ 2 = 24 2 ÷ 2 = 1
108
F a s t a n d A c c u r a t e B a s i c S k i l l s
Speed Sheet - Solutions
Answers are provided below and typed in bold.
Multiplication and Division Facts × 3 and ÷ 3
3 × 0 = 0 3 × 3 = 9 3 × 2 = 6 3 × 12 = 36
3 × 1 = 3 3 × 10 = 30 18 ÷ 3 = 6 36 ÷ 3 = 12
3 × 2 = 6 3 × 12 = 36 30 ÷ 3 = 10 3 × 0 = 0
3 × 3 = 9 18 ÷ 3 = 6 3 × 4 = 12 33 ÷ 3 = 11
3 × 4 = 12 15 ÷ 3 = 5 27 ÷ 3 = 9 9 ÷ 3 = 3
3 × 5 = 15 3 × 110 = 330 3 × 12 = 36 27 ÷ 3 = 9
3 × 6 = 18 27 ÷ 3 = 9 3 × 110 = 330 6 ÷ 3 = 2
3 × 7 = 21 3 × 0 = 0 3 × 10 = 30 12 ÷ 3 = 4
3 × 8 = 24 33 ÷ 3 = 11 3 × 1 = 3 3 × 110 = 330
3 × 9 = 27 12 ÷ 3 = 4 3 × 6 = 18 3 × 3 = 9
3 × 10 = 30 3 × 10 = 30 6 ÷ 3 = 2 3 × 8 = 24
3 × 11 = 33 3 × 90 = 270 3 × 9 = 27 3 × 80 = 240
3 × 12 = 36 3 × 80 = 240 3 × 7 = 21 3 × 90 = 270
3 ÷ 3 = 1 12 ÷ 3 = 4 11 × 3 = 33 3 × 9 = 27
6 ÷ 3 = 2 3 × 2 = 6 3 × 80 = 240 18 ÷ 3 = 6
9 ÷ 3 = 3 36 ÷ 3 = 12 210 ÷ 30 = 7 3 × 6 = 18
3 × 90 = 270 24 ÷ 3 = 8 36 ÷ 3 = 12 360 ÷ 30 = 12
3 × 110 = 330 21 ÷ 3 = 7 12 ÷ 3 = 4 30 ÷ 3 = 10
180 ÷ 3 = 60 9 ÷ 3 = 3 15 ÷ 3 = 5 180 ÷ 3 = 60
3 × 80 = 240 3 × 5 = 15 9 ÷ 3 = 3 3 ÷ 3 = 1
109
F a s t a n d A c c u r a t e B a s i c S k i l l s
Speed Sheet - Solutions
Answers are provided below and typed in bold.
Multiplication and Division Facts × 4 and ÷ 4
4 × 0 = 0 4 × 4 = 16 16 ÷ 4 = 4 8 ÷ 4 = 2
4 × 1 = 4 4 ÷ 4 = 1 48 ÷ 4 = 12 4 × 70 = 280
4 × 2 = 8 4 × 11 = 44 4 × 1 = 4 360 ÷ 40 = 9
4 × 3 = 12 36 ÷ 4 = 9 32 ÷ 4 = 8 40 ÷ 4 = 10
4 × 4 = 16 16 ÷ 4 = 4 28 ÷ 4 = 7 4 × 0 = 0
4 × 5 = 20 4 × 0 = 0 160 ÷ 4 = 40 24 ÷ 4 = 6
4 × 6 = 24 44 ÷ 4 = 11 20 ÷ 4 = 5 4 × 3 = 12
4 × 7 = 28 160 ÷ 4 = 40 4 × 9 = 36 4 ÷ 4 = 1
4 × 8 = 32 4 × 10 = 40 48 ÷ 4 = 12 4 × 60 = 240
4 × 9 = 36 4 × 12 = 48 4 × 0 = 0 12 ÷ 4 = 3
4 × 10 = 40 4 × 70 = 280 8 ÷ 4 = 2 4 × 2 = 8
4 × 11 = 44 4 × 3 = 12 4 ÷ 4 = 1 4 × 4 = 16
4 × 12 = 48 28 ÷ 4 = 7 80 ÷ 4 = 20 28 ÷ 4 = 7
4 ÷ 4 = 1 80 ÷ 4 = 20 4 × 11 = 44 20 ÷ 4 = 5
8 ÷ 4 = 2 4 × 6 = 24 4 × 60 = 240 4 × 50 = 200
12 ÷ 4 = 3 32 ÷ 4 = 8 4 × 2 = 8 32 ÷ 4 = 8
16 ÷ 4 = 4 4 × 50 = 200 36 ÷ 4 = 9 80 ÷ 4 = 20
20 ÷ 4 = 5 8 ÷ 4 = 2 4 × 8 = 32 44 ÷ 4 = 11
24 ÷ 4 = 6 4 × 5 = 20 12 ÷ 4 = 3 4 × 11 = 44
28 ÷ 4 = 7 4 × 7 = 28 24 ÷ 4 = 6 4 × 1 = 4
110
F a s t a n d A c c u r a t e B a s i c S k i l l s
Speed Sheet - Solutions
Answers are provided below and typed in bold.
Multiplication and Division Facts × 5 and ÷ 5
5 × 0 = 0 5 ÷ 5 = 1 5 × 2 = 10 350 ÷ 50 = 7
5 × 1 = 5 5 × 7 = 35 35 ÷ 5 = 7 5 × 10 = 50
5 × 2 = 10 250 ÷ 50 = 5 5 × 5 = 25 40 ÷ 5 = 8
5 × 3 = 15 20 ÷ 5 = 4 400 ÷ 5 = 80 45 ÷ 5 = 9
5 × 4 = 20 5 × 40 = 200 5 × 6 = 30 5 × 0 = 0
5 × 5 = 25 30 ÷ 5 = 6 50 ÷ 5 = 10 5 × 9 = 45
5 × 6 = 30 5 × 11 = 55 5 × 30 = 150 15 ÷ 5 = 3
5 × 7 = 35 35 ÷ 5 = 7 55 ÷ 5 = 11 50 × 1 = 50
5 × 8 = 40 5 × 8 = 40 5 ÷ 5 = 1 10 ÷ 5 = 2
5 × 9 = 45 400 ÷ 5 = 80 5 × 1 = 5 5 × 7 = 35
5 × 10 = 50 10 ÷ 5 = 2 5 × 90 = 450 5 × 4 = 20
5 × 11 = 55 5 × 20 = 100 30 ÷ 5 = 6 20 ÷ 5 = 4
5 × 12 = 60 5 × 4 = 20 5 × 7 = 35 5 × 2 = 10
5 ÷ 5 = 1 50 ÷ 5 = 10 15 ÷ 5 = 3 50 ÷ 50 = 1
10 ÷ 5 = 2 450 ÷ 50 = 9 5 × 110 = 550 5 × 8 = 40
15 ÷ 5 = 3 55 ÷ 5 = 11 5 × 0 = 0 5 × 7 = 35
20 ÷ 5 = 4 5 × 9 = 45 45 ÷ 5 = 9 5 × 50 = 250
25 ÷ 5 = 5 5 × 6 = 30 200 ÷ 5 = 40 25 ÷ 5 = 5
30 ÷ 5 = 6 5 × 50 = 250 5 × 10 = 50 30 ÷ 5 = 6
35 ÷ 5 = 7 60 ÷ 5 = 12 10 ÷ 5 = 2 50 × 3 = 150
111
F a s t a n d A c c u r a t e B a s i c S k i l l s
Speed Sheet - Solutions
Answers are provided below and typed in bold.
Multiplication and Division Facts × 6 and ÷ 6
6 × 0 = 0 6 × 2 = 12 36 ÷ 6 = 6 30 ÷ 6 = 5
6 × 1 = 6 48 ÷ 6 = 8 180 ÷ 60 = 3 6 × 5 = 30
6 × 2 = 12 18 ÷ 6 = 3 6 × 6 = 36 18 ÷ 6 = 3
6 × 3 = 18 6 × 12 = 72 6 ÷ 6 = 1 12 ÷ 6 = 2
6 × 4 = 24 6 × 50 = 300 6 × 1 = 6 6 × 2 = 12
6 × 5 = 30 6 × 0 = 0 72 ÷ 6 = 12 360 ÷ 6 = 60
6 × 6 = 36 36 ÷ 6 = 6 6 × 9 = 54 6 × 6 = 36
6 × 7 = 42 12 ÷ 6 = 2 18 ÷ 6 = 3 180 ÷ 60 = 3
6 × 8 = 48 6 × 10 = 60 6 × 3 = 18 6 × 1 = 6
6 × 9 = 54 180 ÷ 60 = 3 48 ÷ 6 = 8 6 ÷ 6 = 1
6 × 10 = 60 6 × 4 = 24 6 × 7 = 42 6 × 12 = 72
6 × 11 = 66 42 ÷ 6 = 7 66 ÷ 6 = 11 6 × 9 = 54
6 × 12 = 72 24 ÷ 6 = 4 6 × 0 = 0 36 ÷ 6 = 6
6 ÷ 6 = 1 72 ÷ 6 = 12 30 ÷ 6 = 5 6 × 4 = 24
12 ÷ 6 = 2 6 × 6 = 36 54 ÷ 6 = 9 24 ÷ 6 = 4
18 ÷ 6 = 3 360 ÷ 6 = 60 6 × 8 = 48 6 × 11 = 66
24 ÷ 6 = 4 6 × 1 = 6 60 ÷ 6 = 10 6 × 8 = 48
30 ÷ 6 = 5 60 ÷ 6 = 10 6 × 4 = 24 72 ÷ 6 = 12
36 ÷ 6 = 6 6 × 9 = 54 42 ÷ 6 = 7 6 × 0 = 0
42 ÷ 6 = 7 6 × 110 = 660 6 × 2 = 12 66 ÷ 6 = 11
112
F a s t a n d A c c u r a t e B a s i c S k i l l s
Speed Sheet - Solutions
Answers are provided below and typed in bold.
Multiplication and Division Facts × 7 and ÷ 7
7 × 0 = 0 7 × 7 = 49 21 ÷ 7 = 3 7 ÷ 7 = 1
7 × 1 = 7 56 ÷ 7 = 8 7 × 2 = 14 7 × 0 = 0
7 × 2 = 14 7 × 50 = 350 7 × 1 = 7 49 ÷ 7 = 7
7 × 3 = 21 7 × 9 = 63 49 ÷ 7 = 7 7 × 50 = 350
7 × 4 = 28 14 ÷ 7 = 2 84 ÷ 7 = 12 7 × 6 = 42
7 × 5 = 35 7 × 0 = 0 7 × 7 = 49 7 × 12 = 84
7 × 6 = 42 7 × 20 = 140 7 × 50 = 350 21 ÷ 7 = 3
7 × 7 = 49 42 ÷ 7 = 6 63 ÷ 7 = 9 7 × 3 = 21
7 × 8 = 56 84 ÷ 7 = 12 7 × 10 = 70 77 ÷ 7 = 11
7 × 9 = 63 7 × 12 = 84 56 ÷ 7 = 8 7 × 8 = 56
7 × 10 = 70 7 × 6 = 42 7 × 11 = 77 7 × 1 = 7
7 × 11 = 77 77 ÷ 7 = 11 7 × 4 = 28 7 × 20 = 140
7 × 12 = 84 700 ÷ 7 = 100 42 ÷ 7 = 6 7 × 5 = 35
7 ÷ 7 = 1 7 × 5 = 35 7 ÷ 7 = 1 84 ÷ 7 = 12
14 ÷ 7 = 2 63 ÷ 7 = 9 7 × 6 = 42 7 × 7 = 49
21 ÷ 7 = 3 7 × 70 = 490 7 × 0 = 0 70 ÷ 7 = 10
28 ÷ 7 = 4 7 × 1 = 7 14 ÷ 7 = 2 28 ÷ 7 = 4
35 ÷ 7 = 5 49 ÷ 7 = 7 7 × 5 = 35 7 × 2 = 14
42 ÷ 7 = 6 21 ÷ 7 = 3 70 ÷ 7 = 10 56 ÷ 7 = 8
49 ÷ 7 = 7 70 ÷ 7 = 10 7 × 3 = 21 7 × 9 = 63
113
F a s t a n d A c c u r a t e B a s i c S k i l l s
Speed Sheet - Solutions
Answers are provided below and typed in bold.
Multiplication and Division Facts × 8 and ÷ 8
8 × 0 = 0 8 ÷ 8 = 1 40 ÷ 8 = 5 8 ÷ 8 = 1
8 × 1 = 8 8 × 12 = 96 640 ÷ 8 = 80 96 ÷ 8 = 12
8 × 2 = 16 8 × 3 = 24 8 × 2 = 16 8 × 9 = 72
8 × 3 = 24 16 ÷ 8 = 2 160 ÷ 8 = 20 8 × 4 = 32
8 × 4 = 32 8 × 7 = 56 8 ÷ 8 = 1 56 ÷ 8 = 7
8 × 5 = 40 640 ÷ 8 = 80 80 × 5 = 400 8 × 10 = 80
8 × 6 = 48 8 × 9 = 72 8 × 0 = 0 40 ÷ 8 = 5
8 × 7 = 56 160 ÷ 8 = 20 96 ÷ 8 = 12 8 × 1 = 8
8 × 8 = 64 8 × 0 = 0 8 × 7 = 56 72 ÷ 8 = 9
8 × 9 = 72 80 ÷ 8 = 10 24 ÷ 8 = 3 8 × 7 = 56
8 × 10 = 80 8 × 5 = 40 8 × 4 = 32 64 ÷ 8 = 8
8 × 11 = 88 40 ÷ 8 = 5 16 ÷ 8 = 2 8 × 3 = 24
8 × 12 = 96 8 × 8 = 64 8 × 10 = 80 88 ÷ 8 = 11
8 ÷ 8 = 1 88 ÷ 8 = 11 32 ÷ 8 = 4 8 × 6 = 48
16 ÷ 8 = 2 8 × 2 = 16 8 × 1 = 8 80 ÷ 8 = 10
24 ÷ 8 = 3 64 ÷ 8 = 8 72 ÷ 8 = 9 16 ÷ 8 = 2
32 ÷ 8 = 4 8 × 4 = 32 8 × 11 = 88 8 × 3 = 24
40 ÷ 8 = 5 24 ÷ 8 = 3 8 × 70 = 560 48 ÷ 8 = 6
48 ÷ 8 = 6 8 × 50 = 400 8 × 6 = 48 8 × 50 = 400
56 ÷ 8 = 7 8 × 1 = 8 56 ÷ 8 = 7 8 × 5 = 40
114
F a s t a n d A c c u r a t e B a s i c S k i l l s
Speed Sheet - Solutions
Answers are provided below and typed in bold.
Multiplication and Division Facts × 9 and ÷ 9
9 × 0 = 0 90 × 1 = 90 99 ÷ 9 = 11 9 × 40 = 360
9 × 1 = 9 9 ÷ 9 = 1 9 × 11 = 99 9 × 8 = 72
9 × 2 = 18 9 × 4 = 36 9 × 7 = 63 54 ÷ 9 = 6
9 × 3 = 27 36 ÷ 9 = 4 45 ÷ 9 = 5 81 ÷ 9 = 9
9 × 4 = 36 54 ÷ 9 = 6 9 × 1 = 9 9 × 3 = 27
9 × 5 = 45 9 × 6 = 54 81 ÷ 9 = 9 9 ÷ 9 = 1
9 × 6 = 54 81 ÷ 9 = 9 9 × 10 = 90 90 ÷ 9 = 10
9 × 7 = 63 9 × 9 = 81 36 ÷ 9 = 4 9 × 12 = 108
9 × 8 = 72 90 ÷ 9 = 10 9 × 3 = 27 45 ÷ 9 = 5
9 × 9 = 81 63 ÷ 9 = 7 990 ÷ 90 = 11 9 × 5 = 45
9 × 10 = 90 9 × 1 = 9 9 ÷ 9 = 1 9 × 9 = 81
9 × 11 = 99 99 ÷ 9 = 11 9 × 8 = 72 36 ÷ 9 = 4
9 × 12 = 108 18 ÷ 9 = 2 54 ÷ 9 = 6 9 × 11 = 99
9 ÷ 9 = 1 72 ÷ 9 = 8 9 × 2 = 18 99 ÷ 9 = 11
18 ÷ 9 = 2 9 × 7 = 63 90 ÷ 9 = 10 9 × 4 = 36
27 ÷ 9 = 3 360 ÷ 9 = 40 27 ÷ 9 = 3 63 ÷ 9 = 7
36 ÷ 9 = 4 27 ÷ 9 = 3 9 × 9 = 81 18 ÷ 9 = 2
45 ÷ 9 = 5 9 × 80 = 720 9 × 50 = 450 108 ÷ 9 = 12
54 ÷ 9 = 6 9 × 2 = 18 9 × 12 = 108 9 × 6 = 54
63 ÷ 9 = 7 630 ÷ 90 = 7 360 ÷ 9 = 40 72 ÷ 9 = 8
115
F a s t a n d A c c u r a t e B a s i c S k i l l s
Speed Sheet - Solutions
Answers are provided below and typed in bold.
Multiplication and Division Facts × 10 and ÷ 10
10 × 0 = 0 40 ÷ 10 = 4 20 ÷ 10 = 2 500 ÷ 10 = 50
10 × 1 = 10 10 × 1 = 10 30 ÷ 10 = 3 120 × 10 = 1200
10 × 2 = 20 200 ÷ 10 = 20 10 × 50 = 500 70 ÷ 10 = 7
10 × 3 = 30 10 × 9 = 90 60 ÷ 10 = 6 10 × 3 = 30
10 × 4 = 40 70 ÷ 10 = 7 10 × 0 = 0 800 ÷ 10 = 80
10 × 5 = 50 10 × 70 = 700 700 ÷ 10 = 70 10 × 12 = 120
10 × 6 = 60 10 × 11 = 110 10 × 12 = 120 10 × 4 = 40
10 × 7 = 70 10 ÷ 10 = 1 10 × 3 = 30 400 ÷ 10 = 40
10 × 8 = 80 10 × 40 = 400 10 × 7 = 70 10 × 8 = 80
10 × 9 = 90 80 ÷ 10 = 8 90 ÷ 10 = 9 10 ÷ 10 = 1
10 × 10 = 100 50 ÷ 10 = 5 10 × 1 = 10 10 × 0 = 0
10 × 11 = 110 10 × 0 = 0 90 ÷ 10 = 9 30 ÷ 10 = 3
10 × 12 = 120 90 ÷ 10 = 9 10 × 11 = 110 10 × 7 = 70
10 ÷ 10 = 1 10 × 100 = 1000 10 × 70 = 700 60 ÷ 10 = 6
20 ÷ 10 = 2 110 ÷ 10 = 11 40 ÷ 10 = 4 90 ÷ 10 = 9
30 ÷ 10 = 3 10 × 5 = 50 10 ÷ 10 = 1 10 × 2 = 20
40 ÷ 10 = 4 10 × 3 = 30 10 × 40 = 400 1200 ÷ 10 = 120
60 ÷ 10 = 6 1200 ÷ 10 = 120 120 ÷ 10 = 12 10 × 100 = 1000
70 ÷ 10 = 7 10 × 7 = 70 10 × 9 = 90 10 × 5 = 50
80 ÷ 10 = 8 120 ÷ 10 = 12 120 ÷ 12 = 10 110 ÷ 10 = 11
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Speed Sheet - Solutions
Answers are provided below and typed in bold.
Multiplication and Division Facts × 11 and ÷ 11
11 × 0 = 0 44 ÷ 11 = 4 22 ÷ 11 = 2 55 ÷ 11 = 5
11 × 1 = 11 11 × 1 = 11 33 ÷ 11 = 3 11 × 7 = 77
11 × 2 = 22 22 ÷ 11 = 2 11 × 50 = 550 77 ÷ 11 = 7
11 × 3 = 33 11 × 9 = 99 66 ÷ 11 = 6 11 × 3 = 33
11 × 4 = 44 77 ÷ 11 = 7 11 × 0 = 0 880 ÷ 11 = 80
11 × 5 = 55 11 × 70 = 770 77 ÷ 11 = 7 11 × 10 = 110
11 × 6 = 66 11 × 10 = 110 11 × 12 = 132 11 × 4 = 44
11 × 7 = 77 11 ÷ 11 = 1 11 × 3 = 33 44 ÷ 11 = 4
11 × 8 = 88 11 × 4 = 44 11 × 70 = 770 11 × 8 = 88
11 × 9 = 99 77 ÷ 11 = 7 99 ÷ 11 = 9 11 ÷ 11 = 1
11 × 10 = 110 550 ÷ 11 = 50 11 × 1 = 11 11 × 0 = 0
11 × 11 = 121 11 × 0 = 0 99 ÷ 11 = 9 33 ÷ 11 = 3
11 × 12 = 132 990 ÷ 11 = 90 11 × 10 = 110 11 × 70 = 770
11 ÷ 11 = 1 11 × 10 = 110 11 × 7 = 77 66 ÷ 11 = 6
22 ÷ 11 = 2 110 ÷ 11 = 10 440 ÷ 11 = 40 99 ÷ 11 = 9
33 ÷ 11 = 3 11 × 5 = 55 11 ÷ 11 = 1 11 × 20 = 220
44 ÷ 11 = 4 11 × 30 = 330 11 × 4 = 44 132 ÷ 11 = 12
55 ÷ 11 = 5 110 ÷ 11 = 10 132 ÷ 11 = 12 11 × 10 = 110
66 ÷ 11 = 6 11 × 7 = 77 11 × 9 = 99 11 × 5 = 55
77 ÷ 11 = 7 132 ÷ 11 = 12 110 ÷ 11 = 10 110 ÷ 11 = 10
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Speed Sheet - Solutions
Answers are provided below and typed in bold.
Multiplication and Division Facts × 12 and ÷ 12
12 × 0 = 0 480 ÷ 12 = 40 24 ÷ 12 = 2 60 ÷ 12 = 5
12 × 1 = 12 12 × 1 = 12 360 ÷ 120 = 3 12 × 70 = 840
12 × 2 = 24 24 ÷ 12 = 2 12 × 5 = 60 84 ÷ 12 = 7
12 × 3 = 36 12 × 9 = 108 60 ÷ 12 = 5 12 × 3 = 36
12 × 4 = 48 72 ÷ 12 = 6 12 × 0 = 0 960 ÷ 12 = 80
12 × 5 = 60 12 × 6 = 72 84 ÷ 12 = 7 12 × 11 = 132
12 × 6 = 72 12 × 11 = 132 12 × 10 = 120 12 × 4 = 48
12 × 7 = 84 12 ÷ 12 = 1 12 × 3 = 36 48 ÷ 12 = 4
12 × 8 = 96 12 × 40 = 480 12 × 60 = 720 12 × 8 = 96
12 × 9 = 108 84 ÷ 12 = 7 96 ÷ 12 = 8 12 ÷ 12 = 1
12 × 10 = 120 60 ÷ 12 = 5 12 × 1 = 12 12 × 0 = 0
12 × 11 = 132 12 × 0 = 0 108 ÷ 12 = 9 360 ÷ 120 = 3
12 × 12 = 144 96 ÷ 12 = 8 12 × 11 = 132 12 × 6 = 72
12 ÷ 12 = 1 12 × 10 = 120 12 × 7 = 84 72 ÷ 12 = 6
24 ÷ 12 = 2 132 ÷ 12 = 11 48 ÷ 12 = 4 108 ÷ 12 = 9
36 ÷ 12 = 3 120 × 5 = 600 12 ÷ 12 = 1 12 × 2 = 24
48 ÷ 12 = 4 12 × 3 = 36 12 × 40 = 480 120 ÷ 12 = 10
60 ÷ 12 = 5 144 ÷ 12 = 12 120 ÷ 12 = 10 120 × 10 = 1200
72 ÷ 12 = 6 12 × 7 = 84 12 × 9 = 108 12 × 5 = 60
84 ÷ 12 = 7 120 ÷ 12 = 10 144 ÷ 12 = 12 132 ÷ 12 = 11
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Speed Sheet - Solutions
Answers are provided below and typed in bold.
Multiplication and Division - Square Numbers
1 × 1 = 1 10 × 10 = 100 9 × 9 = 81 5 × 5 = 25
2 × 2 = 2 25 ÷ 5 = 5 2 × 2 = 4 √36 = 6
3 × 3 = 9 7 × 7 = 49 √4 = 2 11 × 11 = 121
4 × 4 = 16 36 ÷ 6 = 6 9 ÷ 3 = 3 3 × 3 = 9
5 × 5 = 25 82 = 64 25 ÷ 5 = 5 9 ÷ 3 = 3
6 × 6 = 36 16 ÷ 4 = 4 1 × 1 = 1 12 × 12 = 144
7 × 7 = 49 1 ÷ 1 = 1 4 × 4 = 16 7 × 7 = 49
8 × 8 = 64 4 × 4 = 16 8 × 8 = 64 49 ÷ 7 = 7
9 × 9 = 81 49 ÷ 7 = 7 64 ÷ 8 = 8 8 × 8 = 64
10 × 10 = 100 12 × 12 = 144 3 × 3 = 9 √64 = 8
11 × 11 = 121 9 ÷ 3 = 3 16 ÷ 4 = 4 2 × 2 = 4
12 × 12 = 144 1 × 1 = 1 112 = 121 16 ÷ 4 = 4
1 ÷ 1 = 1 100 ÷ 10 = 10 5 × 5 = 25 4 × 4 = 16
4 ÷ 2 = 2 42 = 16 81 ÷ 9 = 9 62 = 36
9 ÷ 3 = 3 3 × 3 = 9 102 = 100 81 ÷ 9 = 9
16 ÷ 4 = 4 11 × 11 = 121 121 ÷ 11 = 11 1 ÷ 1 = 1
25 ÷ 5 = 5 121 ÷ 11 = 11 6 × 6 = 36 1 × 1 = 1
36 ÷ 6 = 6 √64 = 8 √100 = 10 10 × 10 = 100
49 ÷ 7 = 7 5 × 5 = 25 42 = 16 100 ÷ 10 = 10
64 ÷ 8 = 8 81 ÷ 9 = 9 49 ÷ 7 = 7 9 × 9 = 81
Solutions for Speed Sheets for
Mixed Operations
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Speed Sheet - Solutions
Answers are provided below and typed in bold.
Mixed Operations speed sheet 1
0 + 8 = 8 120 – 80 = 40 1 × 8 = 8 80 ÷ 10 = 8
3 – 3 = 0 0 ÷ 1 = 0 1 – 0 = 1 110 ÷ 110 = 10
4 × 3 = 12 500 – 200 = 300 1 × 110 = 110 80 – 20 = 60
1200 – 1000 = 200 12 × 0 = 0 3 – 3 = 0 0 × 6 = 0
4 + 2 = 6 11 × 9 = 99 12 + 1 = 13 70 × 600 = 42000
5 × 12 = 60 5 + 2 = 7 3 × 12 = 36 2 – 0 = 2
12 + 7 = 19 24 ÷ 3 = 8 6 – 4 = 2 12 ÷ 1 = 12
5 × 11 = 55 11 – 6 = 5 4 ÷ 1 = 4 8 + 11 = 19
6 + 3 = 9 0 ÷ 4 = 0 2 + 8 = 10 400 × 11 = 4400
11 – 0 = 11 12 × 5 = 60 10 – 6 = 4 700 × 500 = 350000
1 + 7 = 8 40 ÷ 10 = 4 7 + 4 = 11 20 × 30 = 600
5 + 3 = 8 1 × 6 = 6 60 – 0 = 60 10 ÷ 10 = 1
27 ÷ 9 = 3 6 + 1 = 7 8 – 4 = 4 6 × 10 = 60
3 × 5 = 15 4 – 2 = 2 40 ÷ 5 = 8 1100 – 0 = 1100
10 – 4 = 6 0 ÷ 4 = 0 7 – 6 = 1 5 × 2 = 10
6 + 3 = 9 48 ÷ 6 = 8 7 – 7 = 0 2 ÷ 2 = 1
8 + 3 = 11 9 × 6 = 54 10 + 120 = 130 12 × 7 = 84
10 × 9 = 90 9 + 5 = 14 12 × 10 = 120 11 – 0 = 11
8 + 1 = 9 0 ÷ 12 = 0 11 + 11 = 22 55 ÷ 11 = 5
10 + 8 = 18 100 ÷ 100 = 1 120 – 80 = 40 0 × 5 = 0
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Speed Sheet - Solutions
Answers are provided below and typed in bold.
Mixed Operations speed sheet 2
7 – 3 = 4 12 – 7 = 5 11 × 9 = 99 1 × 12 = 12
3 × 12 = 36 7 – 6 = 1 10 + 0 = 10 8 × 2 = 16
5 – 1 = 4 4 ÷ 4 = 1 4 – 3 = 1 36 ÷ 3 = 12
9 × 3 = 27 7 – 2 = 5 1 × 7 = 7 2 + 12 = 14
7 + 6 = 13 1 × 5 = 5 100 + 80 = 180 4 × 6 = 24
7 × 50 = 350 7 – 0 = 7 63 ÷ 9 = 7 12 – 10 = 2
6 + 4 = 10 3 ÷ 3 = 1 8 – 6 = 2 96 ÷ 8 = 12
6 + 12 = 18 400 ÷ 10 = 40 11 + 6 = 17 11 × 12 = 132
5 × 8 = 40 9 – 2 = 7 24 ÷ 4 = 6 9 + 9 = 18
11 – 8 = 3 12 × 10 = 120 8 + 2 = 10 5 × 6 = 30
8 + 4 = 12 70 ÷ 7 = 10 6 – 5 = 1 9 × 0 = 0
4 ÷ 4 = 1 11 + 3 = 14 27 ÷ 3 = 9 10 – 5 = 5
3 + 11 = 14 3 × 9 = 27 11 – 10 = 1 3 × 7 = 21
10 – 6 = 4 1 × 1 = 1 12 – 2 = 10 4 × 3 = 12
4 – 4 = 0 4 × 4 = 16 3 + 9 = 12 11 × 4 = 44
21 ÷ 3 = 7 11 – 2 = 9 9 × 11 = 99 10 + 5 = 15
0 + 110 = 110 10 × 3 = 30 120 – 30 = 90 10 × 1 = 10
12 – 5 = 7 144 ÷ 12 = 12 110 – 40 = 70 0 × 3 = 0
10 – 2 = 8 30 ÷ 5 = 6 1 + 1 = 2 6 × 10 = 60
5 × 5 = 25 8 + 2 = 10 120 ÷ 60 = 2 12 + 10 = 22
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Speed Sheet - Solutions
Answers are provided below and typed in bold.
Mixed Operations speed sheet 3
7 – 5 = 2 15 ÷ 3 = 5 2 – 1 = 1 48 ÷ 8 = 6
6 × 10 = 60 1200 + 600 = 1800 0 × 8 = 0 11 – 1 = 10
4 – 3 = 1 10 × 10 = 100 3 – 2 = 1 2 × 4 = 8
30 ÷ 3 = 10 1 + 11 = 12 0 ÷ 9 = 0 0 + 800 = 800
30 ÷ 3 = 10 2 – 1 = 1 700 ÷ 70 = 10 5 + 7 = 12
6 + 7 = 13 1 × 3 = 3 9 + 3 = 12 7 × 10 = 70
11 + 9 = 20 120 × 10 = 1200 3 + 1 = 4 200 ÷ 2 = 100
48 ÷ 6 = 8 3 + 8 = 11 30 ÷ 10 = 3 3 – 2 = 1
11 × 0 = 0 3 – 3 = 0 2 × 11 = 22 200 + 400 = 600
5 ÷ 1 = 5 5 – 0 = 5 8 × 10 = 80 3 + 11 = 14
10 + 9 = 19 11 × 0 = 0 10 + 8 = 18 90 ÷ 10 = 9
900 – 300 = 600 4 × 9 = 36 11 + 10 = 21 36 ÷ 3 = 12
10 – 8 = 2 6 ÷ 6 = 1 8 – 5 = 3 32 ÷ 8 = 4
66 ÷ 6 = 11 1100 + 700 = 1800 6 × 10 = 60 11 + 9 = 20
36 ÷ 4 = 9 9 – 7 = 2 0 ÷ 6 = 0 7 + 0 = 7
49 ÷ 7 = 7 9 + 1 = 10 10 ÷ 1 = 10 500 + 200 = 700
110 + 50 = 160 4 × 10 = 40 1000 – 500 = 500 0 ÷ 3 = 0
5 + 4 = 9 22 ÷ 2 = 11 12 – 3 = 9 12 × 8 = 96
5 – 2 = 3 88 ÷ 11 = 8 1 + 1 = 2 9 ÷ 1 = 9
7 × 3 = 21 8 + 4 = 12 400 ÷ 80 = 5 11 – 3 = 8
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Speed Sheet - Solutions
Answers are provided below and typed in bold.
Mixed Operations speed sheet 4
1 + 4 = 5 2 × 9 = 18 10 × 10 = 100 600 + 1000 = 1600
27 ÷ 3 = 9 11 – 6 = 5 0 ÷ 12 = 0 8 + 0 = 8
80 × 100 = 8000 8 – 3 = 5 1 × 2 = 2 9 – 1 = 8
0 + 6 = 6 80 ÷ 10 = 8 9 + 4 = 13 0 ÷ 1 = 0
10 – 8 = 2 18 ÷ 3 = 6 110 + 50 = 160 2 × 8 = 16
28 ÷ 7 = 4 8 + 9 = 17 270 ÷ 90 = 3 7 – 4 = 3
0 ÷ 3 = 0 4 + 1 = 5 36 ÷ 6 = 6 5 + 8 = 13
2 × 8 = 16 5 + 12 = 17 11 × 11 = 121 7 – 1 = 6
4 + 8 = 12 6 ÷ 3 = 2 3 + 2 = 5 6 × 40 = 240
11 – 4 = 7 6 × 1 = 6 1200 – 500 = 700 42 ÷ 6 = 7
7 + 3 = 10 22 ÷ 2 = 11 2 + 8 = 10 5 × 2 = 10
20 + 90 = 110 108 ÷ 9 = 12 12 – 5 = 7 42 ÷ 6 = 7
0 × 70 = 0 3 + 8 = 11 30 ÷ 6 = 5 200 + 600 = 800
0 ÷ 100 = 0 11 – 1 = 10 10 ÷ 5 = 2 4 + 1 = 5
49 ÷ 7 = 7 9 + 1 = 10 1 × 9 = 9 30 + 20 = 50
500 – 300 = 200 11 × 6 = 66 8 + 10 = 18 0 × 12 = 0
9 – 2 = 5 56 ÷ 7 = 8 5 – 4 = 1 8 × 5 = 40
100 × 60 = 6000 0 + 6 = 6 8 ÷ 1 = 8 80 + 30 = 110
10 × 6 = 60 8 + 8 = 16 11 × 4 = 44 1200 – 600 = 600
2 × 5 = 10 12 – 0 = 12 48 ÷ 6 = 8 700 – 100 = 600
Section 5 - Numeracy Strategies
This section contains:
1. Numeracy strategies for:
• Addition
• Subtraction
• Multiplication
• Division
2. Strategy Card Proformas
Addition, Subtraction, Multiplication and Division
QuickSmart Instructors
The following section Numeracy Strategies provides useful strategies for
all four operations to assist students to achieve automatic recall and
understanding of basic number facts.
Numeracy strategies are often used to help learners work out facts that they
do not already know. They build on existing knowledge to create new
knowledge. A numeracy strategy is like scaffolding for a building. When it is in
place, it provides a rigid system that allows the building to be constructed.
Eventually, the scaffold comes down and the building is complete.
These strategies can be explained and used throughout the QuickSmart
lessons when applicable. In particular individual strategies could be focused
and applied in Component 1 of the lesson - Focus Fact Understanding and
during the Speed Sheet activity and the regular OZCAAS computer
assessment.
In the following section of this document, there are photocopiable
proformas of the individual strategies that allow the construction of
individual sets of strategy cards for each student. [This mirrors the set of
Strategy Cards that is contained in the Resource Kit].
It is important to remember in QuickSmart that in order for automaticity to be
achieved, students must not rely on strategy use. The goal with automaticity
is to reduce the working memory demands of providing answers to basic
number facts.
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Strategies for Addition [+]
15 + 3 = 18
15 + 7 = 22
What happens to the size of the answer when you add whole numbers?
The answer is always more than the number you started with.
3 + 6 = 9 or 6 + 3 = 9
3 + 7 + 8 = 18 or 8 + 7 + 3 = 18
What do you notice when numbers are added in a different order?
The numbers in addition sums can be added in any order.
3 + 0 = 3
28 + 0 = 28
What is the pattern when you add zero?
Answers to addition facts are always the same number if 0 is added.
264 + 1 = 265
133 + 1 = 134
When adding 1, count on to the next whole number.
275 + 5 = 280 or 360 + 5 = 365
2[75] + 5 = 280 or 3[60] + 5 = 365
What is the pattern?
When adding 5 to a number that ends in 5 or 0, remember to use
your knowledge of counting by 5s.
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Strategies for Addition [+]
When adding 9, add 10 and then take off 1.
8 + 9 changes to 8 + 10 then 18 – 1 = 17
453 + 9 changes to 453 + 10 then 463 – 1 + 462
80 + 10 = 90
130 + 10 = 140
267 + 10 = 277
What is the pattern?
When adding 10, add 1 ten to the tens column.
40 + 20 = 60
740 + 30 = 770
345 + 40 = 385
What is the pattern?
When adding 20 or 30 or 40, add 2 tens, 3 tens or 4 tens
to the tens column.
389 + 100 = 489
1367 + 100 = 1467
What is the pattern?
When adding 100, add 1 hundred to the hundreds column.
432 + 200 = 632
369 + 300 = 669
2376 + 400 = 2776
When adding 200, 300 or 400, add 2 hundreds, 3 hundreds or 4 hundreds
to the hundreds column.
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Strategies for Addition [+]
Knowledge of DOUBLES or NEAR DOUBLES can assist with addition.
4 + 4 is the same as DOUBLE 4
or
4 + 5 can be DOUBLE 4 add 1
or
4 + 3 can be DOUBLE 4 subtract 1
Knowledge of combinations to 10 can be used to work out more complex addition sums.
1 + 9 = 10 can be used to assist in working out 32 + 9
by
30 + 1 + [ 1 + 9 ] = 41
or
2 + 8 = 10 can be used to assist in working out 64 + 8 by
60 + 2 + [ 2 + 8 ] = 72
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Strategies for Subtraction [–]
37 – 3 = 34
26 – 12 = 14
What happens to the size of the answer when you subtract whole numbers?
The answer is always less than the number you started with.
37 – 0 = 37
25 – 0 = 25
What is the pattern when you subtract 0?
Answers to subtraction facts are always going to be the same
number if 0 is subtracted.
26 – 1 = 25
2384 – 1 = 2383
What does it mean to subtract 1?
When subtracting 1, count backwards to the whole number below.
275 – 5 = 270 is the same as 2[75] – 5 = 270
360 – 5 = 355 is the same as 3[60] – 5 = 355
What is the pattern?
When subtracting 5 from a number that ends in 5 or 0,
remember to use your knowledge of counting backwards by 5s.
When subtracting 9, take away 10 and then add on 1.
12 – 9 changes to 12 – 10 then 2 + 1 = 3
453 – 9 changes to 453 – 10 then 443 + 1 = 444
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F a s t a n d A c c u r a t e B a s i c S k i l l s
Strategies for Subtraction [–]
80 – 10 = 70
130 – 10 = 120
267 – 10 = 257
What is the pattern?
When subtracting 10, take away 1 ten from the tens column.
40 – 20 = 20
740 – 30 = 710
345 – 40 = 305
What is the pattern?
When subtracting 20, 30 or 40, take away 2 tens,
3 tens or 4 tens from the tens column.
390 – 100 = 290
824 – 100 = 724
1367 – 100 = 1267
What is the pattern?
When subtracting 100, take away 1 hundred from the hundreds column.
432 – 200 = 232
369 – 300 = 69
2576 – 400 = 2176
What is the pattern?
When subtracting 200, 300 or 400, take away 2 hundreds, 3 hundreds or
4 hundreds from the hundreds column.
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Strategies for Multiplication [×]
9 × 4 = 36 is the same as 4 × 9 = 36
2 × 7 × 5 is the same as 2 × 5 × 7
What do you notice?
The numbers in any multiplication fact can be swapped around to
make the multiplication easier.
8 × 0 = 0
0 × 854 = 0
What is the pattern?
When one of the numbers being multiplied is
0, the answer to the question is zero.
1 × 117 = 117
56 × 1 = 56
When any number is multiplied by 1 the answer is the number itself.
12 × 2 is the same as ?
What are some more doubles?
Multiplying a number by 2 is the same as doubling the number.
Skip counting by fives can help with understanding your five times table
Your answer is always going to end in either 5 or 0.
5, 10, 15, 20, 25, 30, 35, 40, 45, 50, 55, 60
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Strategies for Multiplication [×] 1 × 9 = 9 (0 + 9 = 9) 6 × 9 = 54 (5 + 4 = 9)
2 × 9 = 18 (1 + 8 = 9) 7 × 9 = 63 (6 + 3 = 9)
3 × 9 = 27 (2 + 7 =9) 8 × 9 = 72 (7 + 2 = 9)
4 × 9 = 36 (3 + 6 = 9) 9 × 9 = 81 (8 + 1 = 9)
5 × 9 = 45 (4 + 5 = 9) 10 × 9 = 90 (9 + 0 = 9)
There is a pattern to all the multiples of 9 up to 10 × 9 = 90. All the single digits that
make up the multiples add together to make a total of 9.
This is why the nine finger trick works.
11 × 10 = 110
10 × 678 = 6780
What is the pattern when whole numbers are multiplied by 10?
You add a zero to the ones column and move all other numbers one place to
the left to show the change in place value.
11 × 11 = 121
11 × 12 = 132
What is the pattern?
When multiplying 11 × 11 and 12 × 11 (and other two-digit examples like these),
split the tens and ones columns apart and add them together to find the
number that goes in the tens column.
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Strategies for Division [÷]
63 ÷ 7 = 9
63 ÷ 9 = 7
The order of numbers in division facts is critical. Larger numbers are usually
divided by smaller numbers. Numbers cannot be reversed,
or swapped around, without changing the answer.
117 ÷ 1 = 117
56 ÷ 1 = 56
What is the pattern?
When any number is divided by 1, the answer is the number itself.
Think of the question as, “How many ones are there in this
number?”
What is another way of saying 24 ÷ 2?
Dividing a number by 2 is the same as halving that number.
48 ÷ 2 is the same as “What is half of 48?”
80 ÷ 10 = 8
110 ÷ 10 = 11
6780 ÷ 10 = 678
What is the pattern?
When dividing any number that ends in 0 by 10, there is a pattern to the answers.
Cross off the zero and move all other numbers one place to the
right to show the change in place value.
If you know 6 × 7 = 42
What division facts do you know?
If you know one multiplication fact, then you know two division facts that
belong to the same ‘family’ of number facts. For example, then you know
42 ÷ 6 = 7 and 42 ÷ 7 = 6
Strategy Card Proformas for Addition, Subtraction, Multiplication and
Division
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Strategies for Addition [+]
15 + 3 = 18
15 + 7 = 22
What happens to the size of the answer when you add whole numbers?
The answer is always more than the number you started with.
3 + 6 = 9 or 6 + 3 = 9
3 + 7 + 8 = 18 or 8 + 7 + 3 = 18
What do you notice when numbers are added in a different order?
The numbers in addition sums can be added in any order.
3 + 0 = 3
28 + 0 = 28
What is the pattern when you add zero?
Answers to addition facts are always the same number if 0 is added.
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Strategies for Addition [+]
264 + 1 = 265
133 + 1 = 134
When adding 1, count on to the next whole number.
275 + 5 = 280 or 360 + 5 = 365
2[75] + 5 = 280 or 3[60] + 5 = 365
What is the pattern?
When adding 5 to a number that ends in 5 or 0, remember to use your
knowledge of counting by 5s.
When adding 9, add 10 and then take off 1.
8 + 9 changes to 8 + 10 then 18 – 1 = 17
453 + 9 changes to 453 + 10 then 463 – 1 = 462
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F a s t a n d A c c u r a t e B a s i c S k i l l s
Strategies for Addition [+]
80 + 10 = 90
130 + 10 = 140
267 + 10 = 277
What is the pattern?
When adding 10, add 1 ten to the tens column.
40 + 20 = 60
740 + 30 = 770
345 + 40 = 385
What is the pattern?
When adding 20 or 30 or 40, add 2 tens, 3 tens or 4 tens to the tens column.
389 + 100 = 489
1367 + 100 = 1467
What is the pattern?
When adding 100, add 1 hundred to the hundreds column.
134
F a s t a n d A c c u r a t e B a s i c S k i l l s
Strategies for Addition [+]
432 + 200 = 632
369 + 300 = 669
2376 + 400 = 2776
When adding 200, 300 or 400, add 2 hundreds, 3 hundreds or 4 hundreds to the
hundreds column.
Knowledge of DOUBLES or NEAR DOUBLES can assist with addition.
4 + 4 is the same as DOUBLE 4 or
4 + 5 can be DOUBLE 4 add 1 or
4 + 3 can be DOUBLE 4 subtract 1
Knowledge of combinations to 10 can be used to work out more complex addition sums.
1 + 9 = 10 can be used in working out 32 + 9 by
30 + 1 + [ 1 + 9 ] = 41 or
2 + 8 = 10 can be used in working out 64 + 8 by
60 + 2 + [ 2 + 8 ] = 72
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Strategies for Subtraction [–]
37 – 3 = 34
26 – 12 = 14
What happens to the size of the answer when you subtract whole numbers?
The answer is always less than the number you started with.
37 – 0 = 37
25 – 0 = 25
What is the pattern when you subtract 0?
Answers to subtraction facts are always going to be the same number if 0 is subtracted.
26 – 1 = 25
2384 – 1 = 2383
What does it mean to subtract 1?
When subtracting 1, count backwards to the whole number below.
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Strategies for Subtraction [–]
275 – 5 = 270 is the same as 2[75] – 5 = 270
360 – 5 = 355 is the same as 3[60] – 5 = 355
What is the pattern?
When subtracting 5 from a number that ends in 5 or 0, remember to use your
knowledge of counting backwards by 5s.
When subtracting 9, take away 10 and then add on 1.
12 – 9 changes to 12 – 10 then 2 + 1 = 3
453 – 9 changes to 453 – 10 then 443 + 1 = 444
80 – 10 = 70
130 – 10 = 120
267 – 10 = 257
What is the pattern?
When subtracting 10, take away 1 ten from the tens column.
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F a s t a n d A c c u r a t e B a s i c S k i l l s
Strategies for Subtraction [–]
40 – 20 = 20
740 – 30 = 710
345 – 40 = 305
What is the pattern?
When subtracting 20, 30 or 40, take away 2 tens, 3 tens or 4 tens from the tens column.
390 – 100 = 290
824 – 100 = 724
1367 – 100 = 1267
What is the pattern?
When subtracting 100, take away 1 hundred from the hundreds column.
432 – 200 = 232
369 – 300 = 69
2576 – 400 = 2176
What is the pattern?
When subtracting 200, 300 or 400, take away 2 hundreds, 3 hundreds or 4 hundreds from
the hundreds column.
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F a s t a n d A c c u r a t e B a s i c S k i l l s
Strategies for Multiplication [×]
9 × 4 = 36 is the same as 4 × 9 = 36
2 × 7 × 5 is the same as 2 × 5 × 7
What do you notice?
The numbers in any multiplication fact can be swapped around to make
the multiplication easier.
8 × 0 = 0
0 × 854 = 0
What is the pattern?
When one of the numbers being multiplied is 0, the answer to the question is zero.
1 × 117 = 117
56 × 1 = 56
When any number is multiplied by 1 the answer is the number itself.
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Strategies for Multiplication [×]
12 × 2 is the same as ?
What are some more doubles?
Multiplying a number by 2 is the same as doubling the number.
Skip counting by fives can help with understanding your five times table Your
answer is always going to end in either 5 or 0.
5, 10, 15, 20, 25, 30, 35, 40, 45, 50, 55, 60
1 × 9 = 9 [0 + 9 = 9] 6 × 9 = 54 [5 + 4 = 9]
2 × 9 = 18 [1 + 8 = 9] 7 × 9 = 63 [6 + 3 = 9]
3 × 9 = 27 [2 + 7 =9] 8 × 9 = 72 [7 + 2 = 9]
4 × 9 = 36 [3 + 6 = 9] 9 × 9 = 81 [8 + 1 = 9]
5 × 9 = 45 [4 + 5 = 9] 10 × 9 = 90 [9 + 0 = 9]
There is a pattern to all the multiples of 9 up to 10 × 9 = 90. All the single digits that make up
the multiples add together to make a total of 9. This is why the nine finger trick works.
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Strategies for Multiplication [×]
11 × 10 = 110
10 × 678 = 6780
What is the pattern when whole numbers are multiplied by 10?
You add a zero to the ones column and move all other numbers one place to the left to
show the change in place value.
11 × 11 = 121
11 × 12 = 132
What is the pattern?
When multiplying 11 × 11 and 12 × 11 (and other two-digit examples like these),
split the tens and ones columns apart and add them together to find the number that goes in
the tens column.
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Strategies for Division [÷]
63 ÷ 7 = 9
63 ÷ 9 = 7
The order of numbers in division facts is critical. Larger numbers are usually divided
by smaller numbers. Numbers cannot be reversed, or swapped around, without
changing the answer.
117 ÷ 1 = 117
56 ÷ 1 = 56
What is the pattern?
When any number is divided by 1, the answer is the number itself. Think of the question as, “How many ones are there in this number?”
What is another way of saying 24 ÷ 2?
Dividing a number by 2 is the same as halving that number.
48 ÷ 2 is the same as “What is half of 48?”
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Strategies for Division [÷]
80 ÷ 10 = 8
110 ÷ 10 = 11
6780 ÷ 10 = 678
What is the pattern?
When dividing any number that ends in 0 by 10, there is a pattern to the answers.
Cross off the zero and move all other numbers one place to the right to show the change in
place value.
If you know 6 × 7 = 42
What division facts do you know?
If you know one multiplication fact, then you know two division facts that belong to
the same ‘family’ of number facts. For example, then you know
42 ÷ 6 = 7 and 42 ÷ 7 = 6
Section 6 - Problem Solving
This section contains:
1. The ‘6S’ Strategy for Problem Solving
2. Examples of Word Problems
(Instructors should source other relevant problems to provide variety
and appropriate practice opportunities.)
3. Brain Teasers
4. Solutions
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The ‘6S’ Strategy for Problem Solving
1. Search: Students read the problem and think about what to do, i.e., What is the question?
• QuickSmart Instructor clarifies any vocabulary/comprehension difficulties.
• Students search to find what the problem is asking.
• Have the students underline the question that they are to solve.
2. Sort: Students identify what information seems most important for solving this
problem
• Highlight key words that indicate the operations required to solve the problem.
• Have students circle the numbers to be used.
• Discuss what information is included in the problem but may not be needed to solve the
problem (optional).
3. See: Students visualise, sketch, tabulate, or document information relevant to the
problem
• Discuss how to ‘visualise’ the problem. Demonstrate ways of developing effective
representations of the information in the problem.
• Encourage students to do their own ‘sketches’.
[We interpret the word ‘sketch’ in the broadest possible way. It could mean a simple sketch
on paper or visualising the problem, or it could be some other form of documenting
information such as tabulating or using graphic organisers like tree diagrams or Venn
diagrams.]
4. Select: Students decide what operations are necessary for solving this problem
• Discuss what actions or operation(s) should be used in solving the problem.
5. Solve: Students solve the problem
• Encourage students to provide their working out for calculations that extends beyond basic number facts.
• Discuss the need to convert all measurements to the same unit, if necessary.
• Model how to solve the problem for the students.
6. Sense: Students ask themselves: Does the answer make sense?
a) Request that students reread the problem.
b) Discuss what the problem required, the process used and whether their
solution makes sense.
SUPER PROBLEM SOLVING
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Examples of Word Problems
Word Problem Operation Matrix Set-Question + – Notes
1-1 Y
1-2 Y
1-3 Y
1-4 Y Unnecessary information provided
1-5 Y Unnecessary information provided
1-6 Y
2-1 Y Unnecessary information provided
2-2 Y Unnecessary information provided
2-3 Y Unnecessary information provided
2-4 Y Unnecessary information provided
2-5 Y Unnecessary information provided
2-6 Y Unnecessary information provided
3-1 Y Prior knowledge, unnecessary information provided
3-2 Y Money, knowledge of coins
3-3 Y Unnecessary information provided
3-4 Y Unnecessary information provided
3-5 Y Y Money, 2 part solution, knowledge of coins
3-6 Y Unnecessary information provided
4-1 Y Money, decimals, unnecessary information provided
4-2 Y Money, decimals, unnecessary information provided
4-3 Y Money, decimals, unnecessary information provided
4-4 Y Money, decimals, unnecessary information provided
4-5 Y Money, decimals, unnecessary information provided
4-6 Y Y Money, 2 part solution, unnecessary information provided
5-1 Y Unnecessary information provided
5-2 Y
5-3 Y
5-4 Y Money, knowledge of coins
5-5 Y Money, decimals, unnecessary information provided
5-6 Y Money, decimals, unnecessary information provided
6-1 Y Unnecessary information provided
6-2 Y Unnecessary information provided
6-3 Y Unnecessary information provided
6-4 Y
6-5 Y Dollar to cent conversion
6-6 Y
7-1 Y Unnecessary information provided
7-2 Y
7-3 Y
7-4 Y Y 2 part solution
7-5 Y Decimals, unnecessary information provided
8-1(a) Y 3 part question, money, decimals
8-1(b) Y Money, decimals
8-2 Y Money, coins to dollar conversion, decimals
8-3 Y Unnecessary information provided
8-4 Y
9-1 Y Y Unnecessary information provided
9-2 Y
9-3 Y Money, decimals
9-4 Y Money, decimals
9-5 Y
9-6 Y Unnecessary information provided
10-1 Y Y 2 part solution
10-2 Y Unnecessary information provided
10-3 Y
10-4 Y Unnecessary information provided
10-5 Y
10-6 Y Y Mixed operation or 2 part solution
BT1-1 Y
BT1-2 Y Y Y 2 part solution, brain teaser
BT1-3 Y 2 part solution, brain teaser
BT1-4 Y Brain teaser
BT1-5 Y Dollar to coin conversion
BT1-6 Required knowledge of analog clocks
BT2-1 Y Y Mixed operations, brain teaser
BT2-2 Y
BT2-3 Y Y 3 part solution, brain teaser
BT2-4 Y
BT2-5 Y 2 part solution, brain teaser
BT2-6 Y Y 2 part solution, brain teaser
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1. There were 30 boys and 27 girls in the cinema. How many were there altogether?
2. I bought 15 apples, 12 kiwifruit, and 4 oranges. How many pieces of fruit did I buy?
3. I saw 29 animals in the Australian section of the zoo. 11 were koalas. All the others were
kangaroos. How many were kangaroos?
4. There were 47 children and 3 teachers in the playground. 27 of the children were boys. How
many girls were in the playground?
5. Jeremy had these coins in his pocket – 50c, 20c, 5c, 5c, 10c, and 10c. He also had a $5 note.
How much money in coins did he have in his pocket?
6. Natasha cut these lengths of ribbon: 45cm, 20cm and 25cm. What was the total length of
ribbon that she cut?
QuickSmart Problems - Set 1
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1. There were 25 children in the classroom. 2 children were working at the back of the room
and 15 students left the room to go to Art in another room. How many children are there left
in the classroom?
2. The canteen had orders for 39 pies. There were 20 pies and 6 sausage rolls in the oven.
How many more pies needed to be heated to fill the order?
3. The school bus can carry 40 children and 50 bags. If 33 children were on the bus, how many
spare seats were there on the bus?
4. There were 90 butterflies and 20 pot plants in the butterfly enclosure. The zoo keeper
released 30 butterflies. How many butterflies were left in the enclosure?
5. The farmer sold 59 eggs to the supermarket. Each egg cost 40c. If he had 99 eggs, how
many eggs does he have left?
6. The ferris wheel has 31 carriages that can carry 62 passengers in total but there were 12
empty seats. How many people were on the ferris wheel?
QuickSmart Problems - Set 2
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1. The zoo keeper fed 34 lizards, 20 goannas, 7 snakes and 5 bats. How many reptiles did he
feed?
2. I had four coins in my pocket and a $5 note that added up to $6.20. What coins were in my
pocket?
3. Use the table to work out how many students were in the school.
SCHOOL NUMBERS
Year Level Students Classes
YEAR 1 25 2
YEAR 2 25 2
YEAR 3 18 1
YEAR 4 20 1
4. The ghost train ride can hold 58 people and goes through 6 rooms. If 48 people were on
the train when it went into the first room, how many spare seats were there?
5. I had these coins in my wallet: 50c, 20c, 20c and 5c. How much more do I need to buy a $2
toy?
6. Marcus had 8 toy cars, 3 trucks and 2 tennis balls. He then gave half of his cars to his brother.
How many cars did his brother get?
QuickSmart Problems - Set 3
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Canteen Prices
Doughnut 95c Sausage Roll $2.90
Icy pole 75c Hamburger $4.80
Pie $3.20 Orange Drink $1.95
Cream Bun $1.85 Chips $1.80
Pizza Slice $2.10 Sandwiches $3.20
Jam Tart $1.70 Chocolate Milk $1.85
1. What would 1 hamburger and 1 orange drink cost?
2. What would be the cost of 1 pizza slice and 1 cream bun?
3. How much would 1 pie and 2 jam tarts cost?
4. How much change would I get from $2 if I bought 1 doughnut?
5. What would be the cost if I bought an icy pole for my friend and myself?
6. What change would I get from $5 if I bought 2 packets of chips at the canteen?
QuickSmart Problems - Set 4
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1. Celia had 10 packets of lifesavers and 12 caramels. She gave 1
2 of the caramels to Liz. How many
caramels did Liz get?
2. Louisa had twenty dollars. She spent half her money at the movies. How much money did she
have left?
3. I had three coins in my pocket that totalled 75c. Which coins were in my pocket?
4. Tony had ten 5c coins and 3 buttons in his pocket. How much money did he have?
5. I bought 3 bags of chips at $1.80 a bag, and 7 bags of licorice at 50c a bag. How much did I
spend on licorice?
6. Hamburgers cost $4.80 each and chips cost $3 each. How much will 5 hamburgers cost?
QuickSmart Problems - Set 5
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The farmer had an equal number of animals in his paddocks.
1. He had 24 cows and 8 goats in 4 paddocks. How many cows were in each paddock?
2. He had 36 goats and 6 alpacas in 3 paddocks. How many goats were in each paddock?
3. He had 42 goats and 12 sheep in 6 paddocks. How many goats were in each paddock?
Joanne had all her money in 5 cent coins.
4. In one piggy bank she had 95 cents. How many 5 cent coins did it contain?
5. In her other piggy bank she had 28 coins. How much money did this piggy bank contain?
6. How many 5 cent coins did she have altogether?
QuickSmart Problems - Set 6
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1. The farmer had four hen coops containing 400 hens. She collected 350 eggs altogether: 120
eggs from Coop One, 70 eggs from Coop Two and 50 eggs from Coop Three. How many eggs did
she collect from Coop Four?
2. In the pet shop I saw dogs, cats and budgies. I counted 50 pets in total. If there were 24 cats and
6 dogs, how many budgies were in the pet shop?
3. The mystery container contained seven boxes with a total mass of 265kg. I took out six boxes
which had a total mass of 145kg. What was the mass of the seventh box?
4. Mum spent $70.25 at the supermarket. She also spent $30.05 at the butcher, $17.70 at the
fruit market and $30 at the clothes store. How much change will she get from $200?
5. Year 4 students walked the following distances at camp:
DAY KILOMETRES WALKED
Monday 3.4
Tuesday 2.1
Wednesday 3.3
Thursday 4.1
Friday 9.0
Saturday 1.4
What distance did the Year 4 students walk before Saturday?
QuickSmart Problems - Set 7
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Pie
$3.20
Orange Drink
$1.95
Sausage Roll $2.90 Milkshake $3.40
Pizza Slice $2.10 Icy pole 75c
Hamburger $1.80 Twisties $1.75
Soup $1.90 Licorice Stick 60c
1. Three friends each had $10. They went into the milk bar together. Kate bought 1 pie, 1
orange drink and 2 licorice sticks. Anna bought 1 cup of soup, 1 pizza slice and 1 packet of
Twisties. Tessa bought 2 sausage rolls, 1 milkshake and 1 licorice stick.
[a] Work out the cost of each person’s order and how much change each girl got back.
[b] How much did the three orders cost altogether?
2. Timothy had these coins in his wallet:
20c , 20c , 5c , 5c , 50c , $1 , $2 , 5c , 5c , 10c , 50c , 20c , 20c
How much money did he have in his wallet?
3. The school librarian put the following items on the shelves: 5 CD’s, 24 adventure books, 10
nature books, 7 fantasy books and 7 cooking books. How many books did he put on the
shelves?
4. Nine Year 5 students threw a ball the following distances:
20m , 7m , 3m , 27m , 5m , 22m , 10m , 6m , 9m
What was the total distance thrown by the students?
QuickSmart Problems - Set 8
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1. Our school had a fundraising day: $67 was made by the children who sold 35 drinks, $20 was
made by washing 6 cars, 20 parents paid $1 each to take part in the "Guess the number of
jellybeans" game and 3 children sold 15 cakes for 20 cents each. How much money was raised
on the fundraising day?
2. Work out the total mass of these five boxes:
Box A 10kg Box B 3kg Box C 40kg
Box D 20kg Box E 2kg
3. Diana had 4 coins in her purse that totaled $3.55. What coins were in her purse?
4. Tom bought five cakes for a total of $15.75. If four cakes cost $13.65, how much did the fifth
cake cost?
5. Five hundred and sixty people were on three rides in the fun park: 130 were on the
ferris wheel and 300 were on the ghost train. How many people were on the
rollercoaster?
6. Chen had 23 marbles, 2 soccer balls and 16 cards. He gave 1
4 of the cards to Wang. How
many cards did he give away?
QuickSmart Problems - Set 9
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1. In a game of cricket against the West Indies, Australia made 230 and 340 runs. The West Indies
made 356 runs in their first innings. How many runs do they need to score in their second
innings to equal Australia’s score?
2. Jason weighs 46 kg, his brother weighs 22 kg and his father weighs 86 kg. How much more
than Jason does his father weigh?
3. A farmer has 168 animals. Half the animals are cows. How many cows does she have on
her farm?
4. In the last basketball match, the Tigers scored 152 points including 10 three pointers and the
Cats scored 132 points. By how many did the Tigers win?
5. To reach our holiday destination we had to travel 712 km. By nightfall we had travelled
512km. How many more kilometres do we need to travel to reach our destination on the
next day?
6. There were 572 students at school in February. During the year 42 children left and 60 new
children came to the school. How many students were enrolled in the school at the end of the
year?
QuickSmart Problems - Set 10
Brain Teasers
QuickSmart Instructors
The following section Brain Teasers contains two sheets of example word
problems to extend your QuickSmart students. These problems require
students to focus on using their visualising and sketching skills to make sense
of the problems.
Encourage students to use the ‘6S’ Problem Solving Strategy as their
procedure in attacking each problem. Other problems of this degree of
difficulty need to be sourced from other school resources, commercially
available mathematics text-books or websites.
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1. One half of the total flowers in a vase are roses. There are six roses. How many flowers are
there in the vase?
2. I’m thinking of a number. Twice the number is 2 fewer than 3 times 4. What is the
number?
3. A hamburger and a milkshake cost $5.50. Two hamburgers and a milkshake cost $7.60. What is
the cost of the milkshake?
4. You have two noses and three hats. How many different nose-hat disguises can you wear?
5. Dave and Linda were paid 1 cent for each weed they pulled. At the end of the day, they had
earned $16.00. How many weeds did they pull?
6. How many complete turns does the hour hand of a clock make in one day?
QuickSmart Brain Teaser -1
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1. John is five years older that Pat. Pat is three years younger that Betsy. John is 15 years old.
How old is Betsy?
2. Rita has 3 kilograms of peanuts. She put 1
2 kilogram of peanuts in each bag. How many
bags did she use?
3. Jack, Susan and Carla went strawberry picking. Jack ate some strawberries. Susan ate four fewer
strawberries than Jack. Carla ate five more strawberries than Susan. Carla ate eight
strawberries. How many strawberries did Jack eat?
4. A Douglas DC9 plane holds 120 passengers. Three-quarters of the seats are taken. How many
seats are still available?
5. If you divide my number by 11, you get 26. What will you get when you multiply my
number by 4?
6. Carlos had one Australian stamp for every eight foreign stamps in his stamp collection. He has
720 stamps in his collection. How many foreign stamps does he have?
QuickSmart Brain Teaser - 2
Word Problem Solutions
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Word problem set 1 worked example
1. There were 30 boys and 27 girls in the cinema. How many were there altogether?
30 + 27 = 57 There were 57 people in the cinema.
2. I bought 15 apples, 12 kiwifruit, and 4 oranges. How many pieces of fruit did I buy?
15 + 12 + 4 = 31 I bought 31 pieces of fruit.
3. I saw 29 animals in the Australian section of the zoo. 11 were koalas. All the others were kangaroos. How many were kangaroos?
29 – 11 = 18 There were 18 kangaroos in the Australian section of the zoo.
4. There were 47 children and 3 teachers in the playground. 27 of the children were boys. How many girls were in the playground?
47 – 27 = 20 There were 20 girls in the playground.
5. Jeremy had these coins in his pocket - 50c, 20c, 5c, 5c, 10c, and 10c. He also had a $5 note. How much money in coins did he have in his pocket?
50 + 20 + 5 + 5 + 10 + 10 = 100 Jeremy had one dollar in coins in his pocket.
6. Natasha cut these lengths of ribbon: 45 cm, 20 cm and 25 cm. What was the total length of ribbon that she cut?
45 + 20 + 25 = 90 Natasha cut a total of 90cms of ribbon.
Word problem set 2 worked example
1. There were 25 children in the classroom. 2 children were working at the back of the room and 15 students left the room to go to Art in another room. How many children were there left in the classroom?
25 – 15 = 10 There were 10 children left in the classroom.
2. The canteen had orders for 39 pies. There were 20 pies and 6 sausage rolls in the oven. How many more pies were needed to be heated to fill the order?
39 – 20 = 19 To fill the order ,19 more pies need to be heated.
3. The school bus can carry 40 passengers and 50 bags. If 33 children were on the bus, how many spare seats were there on the bus?
40 – 33 = 7 There were 7 spare seats on the bus.
4. There were 90 butterflies and 20 pot plants in the butterfly enclosure. The zoo keeper released 30 butterflies. How many butterflies were left in the enclosure?
90 – 30 = 60 There were 60 butterflies left in the enclosure.
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5. The farmer sold 59 eggs to the supermarket. Each egg cost 40c. If he had 99 eggs, how many eggs did he have left?
99 – 59 = 40 The farmer has 40 eggs left.
6. The ferris wheel has 31 carriages that can carry 62 passengers in total but there were 12 empty seats. How many people were on the ferris wheel?
62 – 12 = 50 There were 50 people on the ferris wheel.
Word problem solutions (sets 3 – 10)
Word problem set 3 1. The zoo keeper fed 61 animals.
2. The coins in my pocket could be 50c, 50c, 10c and 10c or $1, 10c, 5c and 5c.
3. There were 88 students in the school.
4. There were 10 spare seats on the ghost train.
5. I need another $1.05 to buy a $2 toy.
6. Marcus’ brother got 4 cars.
Word problem set 4 1. A hamburger and an orange drink would cost $6.75.
2. The slice of pizza and a cream bun would cost $3.95.
3. A pie and 2 jam tarts would cost $6.60.
4. I would get $1.05 change.
5. An icy pole for my friend and myself would cost $1.50.
6. I would get $1.40 change.
Word problem set 5 1. Liz got 6 caramels.
2. Louisa had $10 left.
3. I had 50c, 20c and 5c in my pocket.
4. Tony had 50 cents.
5. I spent $3.50 on licorice.
6. The 5 hamburgers would cost $24.00.
Word problem set 6 1. The farmer had 6 cows in each paddock.
2. The farmer had 12 goats in each paddock.
3. The farmer had 7 goats in each paddock.
4. The piggy bank contained 19 five cent coins.
5. The other piggy bank contained $1.40.
6. Joanne had 47 five cent coins altogether.
Word problem set 7 1. The farmer collected 110 eggs from Coop Four.
2. There were 20 budgies in the pet shop.
3. The mass of the seventh box was 120kg.
4. Mum will get $52 change.
5. The Year 4 students had walked 21.9km before Saturday.
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Word problem set 8 1. [a]
Kate’s order cost $6.35 and she got $3.65 back in change.
Anna’s order cost $5.80 and she got $4.20 back in change.
Tessa’s order cost $9.80 and she got 20c back in change.
[b] The three orders cost $21.95 altogether.
2. Timothy had $5.10 in his wallet.
3. The librarian put 48 books on the shelf.
4. The students threw a total of 109m.
Word problem set 9 1. There was $110 raised on the fundraising day.
2. The total mass of the five boxes is 75kg.
3. The 4 coins in Diana’s purse where $2, $1, 50c and 5c.
4. The fifth cake cost $2.10
5. There were 130 people were on the rollercoaster.
6. Chen gave away 8 cards.
Word problem set 10 1. The West Indies need to score 214 runs in their second innings to equal Australia's score.
2. Jason's father weighs 40kg more.
3. The farmer has 84 cows on her farm.
4. The tigers won by 20 points.
5. We need to travel 200 km to reach our destination on the next day.
6. There were 590 students enrolled in the school at the end of the year.
Brain Teaser Solutions
Brain Teaser - 1 1. There were 12 flowers in the vase.
2. The number I am thinking of is 5.
3. The cost of the milkshake is $3.40.
4. There are 6 different nose-hat disguises you can wear.
5. Dave and Linda pulled 1600 weeds.
6. The hour hand of a clock makes 2 complete turns in one day.
Brain Teaser - 2 1. Betsy is 13 years old.
2. Rita used 6 bags.
3. Jack ate 7 strawberries.
4. There are 30 seats still available.
5. When I multiply my number by 4, I will get 1144.
6. Carlos has 640 foreign stamps.
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Section 7 - Numeracy Games
This section contains the instructions for the following Numeracy Games:
1. Same Sums and Game Board
2. Double O
3. QuickSmart Maths Language Dominoes
4. Maths word meaning games
5. QuickSmart Numeracy Dominoes
6. QuickSmart Numeracy Bingo
7. Three in a Row
What else should I know about the games component? • Don’t hesitate to invent your own games or to use games from other sources,
provided they target appropriate mathematical skills
• There are many quick games you can invent if you don’t have the full 5 minutes available, e.g., take 2 dice from the kit and roll them simultaneously. Players have to be the first to add or to multiply the two numbers or to subtract the smaller number from the larger number. Keep score to see who is the winner.
• There are various dice in the kit for use with other games
• You can change the rules of any of the games to suit your circumstances.
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Same Sums OBJECTIVE: To practise addition GROUP SIZE: Small group; whole class MATERIALS: Dice Pencil Playing Board based on a nine square grid
HOW TO PLAY: 1. The leader rolls the dice and calls out the number.
2. Each player writes the number in one of the small squares on the playing board. Once a number
has been placed, it may not be changed. 3. Repeat this procedure eight more times, until each player has a number in each square of the
grid. 4. Each player then computes the sum of each row, each column and the two diagonals.
5. Each player circles totals that appear more than once.
6. The player’s total score is equal to the sum of these circled scores.
e.g. [ 12 + 12 + 8 + 8 + 8 = 48 ]
7. The winner is the player with the highest total.
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Same Sums Board
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Double O A game suitable for 2 or 3 players - There are 20 cards in the pack
How to Play:
1. Choose a dealer. The dealer places the top card face up on the table and then deals five cards
to each player. The remaining cards are placed face down in a pile in the middle of the table.
2. The person next to the dealer on his/her left side puts down a card which matches one of the
four numerals on the upturned card.
[The cards are played side by side, above or below, with the matching numerals touching each
other domino style]. E.g.
If two 5’s are matched, the player says
‘5 + 5 = 10, doubled is 20’, scoring 20 points.
3. Players take turns. If a player cannot make a match, a card is picked up from the central pile
and immediately played if a match is possible.
4. Cards can be played in any direction. Sometimes a pattern such as the one below allows a
player 2 scores for one move.
E.g. 6 + 6 = 12, doubled is 24 and 3 + 3 = 6, doubled is 12, 24 + 12 = 36
5. The dealer keeps the totals. The player with the highest total wins.
5
4
6
2
8
5
7
1
5
4
6
2
8
5
7
1
3
10
8
6
9
3
4
7
Last card
put down
164
F a s t a n d A c c u r a t e B a s i c S k i l l s
QuickSmart Maths Language Dominoes A game suitable for 2 to 4 players - There are 24 cards in each pack
There are two Maths Language domino packs. The packs can be combined to allow a larger group to play. How to Play:
1. Choose a dealer. The dealer needs to deal six dominoes, one at a time, to each player.
2. Players place their six cards face up in front of themselves.
3. The remaining pile is placed face downwards in the centre of the table. The top card of the pile is then turned over to commence the game.
4. The dealer commences the game. Players in turn attempt to form a correct definition by connecting a domino at either end. Dominoes may not be turned upside down. The connecting ends must not be identical.
5. If unsuccessful, the player selects another domino card from the central pile that can either be used immediately or added to the domino cards in front of the player.
6. The game continues until one player has used up all of his/her cards or 5 minutes is up. Either the first player to use all their cards, or the player with the smallest number of cards left at the end of the time, is declared the winner.
7. If there is time, a new game can be commenced with the winner as the dealer.
8. Individual scores can be kept if a number of games are to be played, by tallying up the number of cards each person has left at the end of each game.
165
F a s t a n d A c c u r a t e B a s i c S k i l l s
QuickSmart Maths Language Dominoes – Pack 1
There are twenty-four dominoes in each pack. Each card can be matched to 2 or 3 cards as defined by the groupings below. Packs can be joined to form a larger set.
LEFT SIDE OF DOMINO RIGHT SIDE OF DOMINO
addition +
plus total
add +
subtraction −
minus take away
subtract difference
multiply ×
times product
lots of ×
divide ÷
division ÷
share evenly ÷
less than <
smaller than <
greater than >
the bigger of >
larger >
equal =
having the same value =
equivalent same as
double multiply by 2
twice as much × 2
half 1
2
divide by 2 1
2
166
F a s t a n d A c c u r a t e B a s i c S k i l l s
QuickSmart Maths Language Dominoes– Pack 2
There are twenty-four dominoes in each pack. Each card can be matched to 2 or 3 cards as defined by the groupings below. Packs can be joined to form a larger set.
LEFT SIDE OF DOMINO RIGHT SIDE OF DOMINO
having the same value =
equivalent same as
percent %
out of 100 %
double multiply by 2
twice as much × 2
half 1
2
divide by 2 1
2
1000g kg
kilogram kg
kilometre km
1000m km
52 weeks year
12 months year
hour a 24th of a day
60 minutes hr
2 weeks fortnight
14 days fortnight
60 seconds minute
a 60th of an hour minute
litre L
1000mL L
millilitre mL
1
1000 of a litre mL
167
F a s t a n d A c c u r a t e B a s i c S k i l l s
QuickSmart Maths Word Meaning Games A game suitable for 2 or 3 players - There are 16 pairs of cards in each pack
There are four word meaning games based on strands of Mathematics and on difficulty. Word meaning games can be played as a memory game or as a matching game. A suggested method is to lay down a number (6 to 10) of word cards and place the matching meaning cards randomly around. The player has to place the correct meaning card beside each word card. To make it more difficult, include more meaning cards than words so they cannot use a process of elimination.
Number, Probability and Statistics Set 1
Word Meaning
ascending arrangement of numbers from smallest to largest
calculate to work out the answer
descending arrangement of numbers from largest to smallest
division how many times one number is contained in another
double twice as much
dozen a set of twelve things
even any number that is divisible by 2
first the one at the beginning
half divided into two equal parts
last the one at the end
less the smaller of two amounts
more the greater of two amounts
odd any number that is not divisible by 2
pair two things that belong together
subtraction the process of taking away one number from another
sum the total obtained from addition
Number, Probability and Statistics Set 2
Word Meaning
certain something that must happen
composite a number with a factor other than itself or 1
divisor the number by which another number is to be divided
equation a statement asserting 2 expressions are equal
equivalent having the same value
expression two or more numbers connected by operators
factor a whole number that divides into another without a remainder
frequency number of times an event or value occurs
maximum the largest quantity or value
minimum the least quantity or value
ordinal a number that shows the position of something in a list (eg, 4th)
palindrome a number that reads the same backwards and forwards
prime a number that is only divisible by itself and 1
probability chance or likelihood of an event happening
product the answer to a multiplication fact
remainder amount left over when a number is divided by another
168
F a s t a n d A c c u r a t e B a s i c S k i l l s
Measurement and Geometry Set 1
Word Meaning
anticlockwise movement in the opposite direction to the clock
area the size of a surface
capacity how much a container will hold
clockwise the direction that the hands of the clock move
diameter a line drawn from one side of a circle to the other which passes through the centre of the circle
distance a kilometre is a measurement of this
dollar 100 cents
fortnight two weeks or fourteen days
hour a unit of time equal to 60 minutes
kg the symbol for a kilogram
length the distance from end to end
parallel two lines that remain the same distance apart
semicircle half a circle
square a regular rectangle
triangle a shape with 3 sides and 3 angles
volume size of a solid shape
Measurement and Geometry Set 2
Word Meaning
acute an angle less than ninety degrees
adjacent being next to something
bisect divide into two equal parts
circumference the distance around a circle
equilateral a triangle with three equal sides
mass the amount of matter in an object
obtuse an angle that measures between 90 degrees and 180 degrees
pentagon a shape with 5 sides
perimeter the distance around the outside of a shape
prism a shape with a uniform cross section
radius the distance from the centre of the circle to its circumference
regular type of shape having equal sides and angles
revolution one complete turn through 360 degrees
right an angle that measures 90 degrees
tessellate repeated use of a single shape, without gaps or overlapping
vertex the corner where two lines meet
169
F a s t a n d A c c u r a t e B a s i c S k i l l s
QuickSmart Numeracy Dominoes A game suitable for 2 to 6 players - There are 44 cards in each pack
There are four dominoes packs using the pairs of operations. How to Play:
1. Choose a dealer. The dealer needs to deal six dominoes, one at a time, to each player.
2. Players place their six cards face up in front of themselves.
3. The remaining pile is placed face downwards in the centre of the table. The top card of the pile is then turned over to commence the game.
4. The dealer commences the game. Players in turn attempt to form a correct definition by connecting a domino at either end. The dominoes may not be turned upside down. The connecting ends must not be identical.
5. If unsuccessful, the player selects another domino card from the central pile that can either be used immediately or added to the domino cards in front of the player.
6. The game continues until one player has used up all of his/her cards or 5 minutes is up. Either the first player to use all their cards, or the player with the smallest number of cards left at the end of the time, is declared the winner.
7. If there is time, a new game can be commenced with the winner as the dealer.
8. Individual scores can be kept if a number of games are to be played, by tallying up the number of cards each person is left with at the end of each game.
170
F a s t a n d A c c u r a t e B a s i c S k i l l s
QuickSmart Numeracy Bingo A game suitable for 2 to 6 players - There are 8 lists of number facts
There are eight lists of number facts and six cards for each list. This allows six children to play at any one time or for students to play more than one card at a time when they become more “automatic” with their number facts.. The cards are individually numbered, e.g., (list : card number) 5:1, 5:2, 5:3, 5:4, 5:5, 5:6. How to Play: 1. To start the game, give a card to each of the players and a pile of counters.
2. Tell the players to hide the QuickSmart logo with a counter. This counts as a free number fact. 3. The teacher or fellow student randomly reads the number facts from the list selected excluding
the answer. 4. Players cover the answer with a counter as they calculate the number fact in their heads. 5. The winner is the player who first has five correct answers in a row and calls out “QuickSmart
Bingo”. The counters must go down or across or diagonally from corner to corner of the card. 6. When a player wins, all players remove their counters and exchange cards. A new game can then
be started.
171
F a s t a n d A c c u r a t e B a s i c S k i l l s
Bin
go N
um
era
cy F
acts
Lis
t
Lis
t 8
21
x 3
= [
63
]
84
÷ 2
= [
42
]
39
÷ 3
= [
13
]
80
÷ 4
= [
20
]
2 x
24 =
[48
]
5 x
20 =
[10
0]
10
x 2
4 =
[2
40
]
21
x 4
= [
84
]
63
÷ 3
= [
21
]
88
÷ 4
= [
22
]
46
÷ 2
= [
23
]
58
x 1
= [
58
]
3 x
22 =
[66
]
4 x
30 =
[12
0]
2 x
34 =
[68
]
86
÷ 2
= [
43
]
99
÷ 3
= [
33
]
78
÷ 1
= [
78
]
4 x
21 =
[84
]
63
x 0
= [
0]
3 x
32 =
[96
]
68
÷ 2
= [
34
]
73
÷ 7
3 =
[1
]
2 x
42 =
[84
]
Lis
t 7
72
÷ 1
2 =
[6
]
10
x 7
= [
70
]
12
x 3
= [
36
]
88
÷ 1
1 =
[8
]
10
8 ÷
12
= [
9]
90
÷ 1
0 =
[9
]
11
x 4
= [
44
]
12
x 7
= [
84
]
10
x 3
= [
30
]
90
÷ 1
0 =
[9
]
72
÷ 1
2 =
[6
]
44
÷ 1
1 =
[4
]
12
x 4
= [
48
]
10
x 1
= [
10
]
12
x 8
= [
96
]
60
÷ 1
2 =
[5
]
10
0 ÷
10
= [
10
]
24
÷ 1
2 =
[2
]
99
÷ 1
1 =
[9
]
11
x 5
= [
55
]
12
x 1
1 =
[1
32
]
10
x 1
2 =
[1
20
]
14
4 ÷
12
= [
12
]
12
x 0
= [
0]
Lis
t 6
6 x
11 =
[66
]
8 x
2 =
[1
6]
10
x 4
= [
40
]
42
÷ 6
= [
7]
32
÷ 8
= [
4]
14
÷ 2
= [
7]
9 x
4 =
[3
6]
7 x
7 =
[4
9]
10
x 8
= [
80
]
72
÷ 9
= [
8]
24
÷ 6
= [
4]
6 x
8 =
[4
8]
8 x
5 =
[4
0]
7 x
9 =
[6
3]
54
÷ 6
= [
9]
10
÷ 1
0 =
[1
]
81
÷ 9
= [
9]
6 x
9 =
[5
4]
10
x 9
= [
90
]
8 x
1 =
[8
]
63
÷ 7
= [
9]
12
÷ 6
= [
2]
60
÷ 1
0 =
[6
]
9 x
3 =
[2
7]
Lis
t 5
4 x
5 =
[2
0]
1 x
2 =
[2
]
27
÷ 3
= [
9]
18
÷ 2
= [
9]
3 x
6 =
[1
8]
5 x
8 =
[4
0]
33
÷ 3
= [
11
]
12
÷ 4
= [
3]
60
÷ 5
= [
12
]
4 x
7 =
[2
8]
2 x
6 =
[1
2]
32
÷ 4
= [
8]
25
÷ 5
= [
5]
12
÷ 1
= [
12
]
4 x
9 =
[3
6]
3 x
5 =
[1
5]
1 x
8 =
[8
]
36
÷ 3
= [
12
]
45
÷ 5
= [
9]
18
÷ 2
= [
9]
3 x
7 =
[2
1]
5 x
7 =
[3
5]
60
÷ 5
= [
12
]
44
÷ 4
= [
11
]
Lis
t 4
34
+ 2
1 =
[55
]
68
– 1
4 =
[5
4]
25
– 1
1 =
[1
4]
42
+ 3
5 =
[77
]
81
+ 1
6 =
[97
]
29
– 1
4 =
[1
5]
55
– 2
3 =
[3
2]
17
+ 3
2 =
[49
]
76
– 3
3 =
[4
3]
89
– 1
7 =
[7
2]
33
+ 2
2 =
[55
]
74
+ 1
5 =
[89
]
37
– 2
1 =
[1
6]
62
+ 2
4 =
[86
]
48
– 1
7 =
[3
1]
96
– 3
3 =
[6
3]
42
+ 4
2 =
[84
]
72
+ 1
5 =
[87
]
39
– 1
7 =
[2
2]
96
– 4
3 =
[5
3]
42
+ 3
6 =
[78
]
61
+ 3
5 =
[96
]
58
– 2
4 =
[3
4]
75
– 4
1 =
[3
4]
Lis
t 3
22
+ 4
= [
26]
81
+ 7
= [
88]
58
– 4
= [
54
]
39
– 6
= [
33
]
43
+ 4
= [
47]
6 +
61 =
[6
7]
27
– 5
= [
22
]
1 +
39 =
[4
0]
85
– 3
= [
82
]
78
– 7
= [
71
]
4 +
63 =
[6
7]
96
– 4
= [
92
]
68
– 8
= [
60
]
72
+ 0
= [
72]
5 +
44 =
[4
9]
92
+ 5
= [
97]
48
– 3
= [
45
]
65
– 1
= [
64
]
37
– 0
= [
37
]
4 +
73 =
[7
7]
53
+ 6
= [
59]
24
– 2
= [
22
]
88
– 3
= [
85
]
0 +
57 =
[5
7]
Lis
t 2
8 +
4 =
[1
2]
15
– 1
1 =
[4
]
7 +
7 =
[1
4]
6 +
9 =
[1
5]
11
– 5
= [
6]
3 +
9 =
[1
2]
18
– 9
= [
9]
6 +
10 =
[1
6]
12
+ 5
= [
17]
18
– 1
1 =
[7
]
4 +
13 =
[1
7]
19
– 6
= [
13
]
11
– 3
= [
8]
10
+ 5
= [
15]
12
– 8
= [
4]
16
– 6
= [
10
]
3 +
12 =
[1
5]
7 +
9 =
[1
6]
14
– 6
= [
8]
15
+ 0
= [
15]
19
– 7
= [
12
]
13
– 0
= [
13
]
11
+ 8
= [
19]
5 +
8 =
[1
3]
Lis
t 1
3 +
4 =
[7
]
8 –
3 =
[5
]
2 +
7 =
[9
]
3 +
5 =
[8
]
10
– 4
= [
6]
2 +
5 =
[7
]
7 –
5 =
[2
]
5 +
5 =
[1
0]
9 –
6 =
[3
]
1 +
4 =
[5
]
7 –
6 =
[1
]
9 –
5 =
[4
]
2 +
6 =
[8
]
10
– 3
= [
7]
8 –
8 =
[0
]
1 +
2 =
[3
]
3 +
7 =
[1
0]
10
– 1
= [
9]
3 +
3 =
[6
]
9 –
9 =
[0
]
10
– 8
= [
2]
3 +
1 =
[4
]
7 –
4 =
[3
]
4 +
5 =
[9
]
172
F a s t a n d A c c u r a t e B a s i c S k i l l s
QuickSmart Three in a Row A game suitable for 2 to 4 players –There are 30 cards and 1 game board in each pack
There are 25 individual game packs that make up this set. Each game targets either addition and subtraction or multiplication and division for a particular number. These games support players very specifically as they progress through the sets of Flash Cards. The players will learn to become strategic about the placement of their counters. How to Play:
1. Each player needs 5 – 10 counters of one colour.
2. Turn all the Number Fact cards face down.
3. Players take turns choosing a card then turning it over and saying the answer as quickly as possible. If their answer is correct, the player places their counter on the corresponding answer on the game board. If their answer is incorrect, the next player takes their turn.
4. The winner is the first person to have three of their markers in a row, up, down, across or diagonal.
5. Concentrate on the game and say the answers as quickly as possible.
Section 8 - Numeracy Graphs
This section contains:
1. Sample Flash Cards Graph
2. The Numeracy Graphs for Individual Students
• Flash Card Recognition for Four Operations
Sample Graph
173
F a s t a n d A c c u r a t e B a s i c S k i l l s
Sample Graph Flash Cards - Addition
How many ADDITION FACTS can I calculate in ONE MINUTE?
Student name:
Nu
mb
er o
f A
dd
itio
n F
acts
Co
rrec
t
70
Students are to enter their results on the graph after the Flash Card recognition
activity is completed. The use of a different coloured pencil or pen for each set
will enhance this graph. Feedback should be given on results and errors should be
discussed.
60
50
40
30
20
10
0
No. cards correct 24 31 34 25 28 32 31 24 31 30
Flash card set +2 +2 +2 +4 +4 +4 +4 +3 +3 +3
Nu
mb
er o
f er
rors
10
5
0
2 0 0 3 0 0 0 3 2 1 No. errors
Date
23
/3
24
/3
26
/3
28
/3
29
/3
31
/3
3/4
6/4
7/4
9/4
174
F a s t a n d A c c u r a t e B a s i c S k i l l s
Numeracy Graphs for Individual Students
175
F a s t a n d A c c u r a t e B a s i c S k i l l s
Flash Cards - Addition
How many ADDITION FACTS can I calculate in ONE MINUTE?
Student name:
Nu
mb
er o
f A
dd
itio
n F
acts
Co
rrec
t
70
60
50
40
30
20
10
0
No. cards correct
Flash card set
Nu
mb
er o
f er
rors
10
5
0
No. errors
Date
176
F a s t a n d A c c u r a t e B a s i c S k i l l s
Flash Cards - Subtraction
How many SUBTRACTION FACTS can I calculate in ONE MINUTE?
Student name:
Nu
mb
er o
f Su
btr
acti
on
Fac
ts C
orr
ect
70
60
50
40
30
20
10
0
No. cards correct
Flash card set
Nu
mb
er o
f er
rors
10
5
0
No. errors
Date
177
F a s t a n d A c c u r a t e B a s i c S k i l l s
Flash Cards - Multiplication
How many MULTIPLICATION FACTS can I calculate in ONE MINUTE?
Student name:
Nu
mb
er o
f M
ult
iplic
atio
n F
acts
Co
rre
ct
70
60
50
40
30
20
10
0
No. cards correct
Flash card set
Nu
mb
er o
f er
rors
10
5
0
No. errors
Date
178
F a s t a n d A c c u r a t e B a s i c S k i l l s
Flash Cards - Division
How many DIVISION FACTS can I calculate in ONE MINUTE?
Student name:
Nu
mb
er o
f D
ivis
ion
Fac
ts C
orr
ect
70
60
50
40
30
20
10
0
No. cards correct
Flash card set
Nu
mb
er o
f er
rors
10
5
0
No. errors
Date
Section 9 - Program Administration Resources
This section contains:
1. Permission Notes
2. Organisation templates
3. QuickSmart Certificates
4. QuickSmart Data Collection and Stakeholder Survey Proformas
This collection of support materials contains information sheets and organisational templates that have
been developed to facilitate the implementation of the QuickSmart Numeracy program. Some of the
material will be useful in recording daily information of students’ progress and in collating and
collecting critical data for your school, your education system and for SiMERR National Research Centre
at the University of New England.
Feel free to choose only those materials that will assist with the implementation of the QuickSmart program in your school. Electronic copies are available on the QuickSmart Resources page of the Private area.
Schools often develop different templates that work well for them. Shared versions of these may be found on the QuickSmart Numeracy Private Area in the “Shared Resources from QuickSmart Schools” section.
179 F a s t a n d A c c u r a t e B a s i c S k i l l s
Permission Notes
Before data for any student can be provided to the University of New England, the permission of the parent/care giver must be obtained by the school. These permission notes must be held within the school.
Permission notes for QuickSmart and Comparison students, as well as information sheets for parents and students, are available on the private area of the QuickSmart website. Importantly, no student should be excluded from QuickSmart because they have not returned a permission note. You will just not be able to share their data with us.
Organisation Templates
• Sample Intervention planner
• Sample Timetable showing rotation of groups
• Attendance sheet
• Sample title page for student Numeracy folder
• Individual student Numeracy summary sheet
181
F a s t a n d A c c u r a t e B a s i c S k i l l s
Sample QuickSmart Intervention Planner
School: Year
WEEK DATES PROGRAM FOCUS
1 Testing - Targeted & Comparison Students Standardised Tests
2 Testing - Targeted & Comparison Students - OZCAAS
3 Testing - Targeted & Comparison Students - OZCAAS
4 Week 1 - Intervention
5 Week 2 - Intervention
6 Week 3 - Intervention
7 Week 4 - Intervention
8 Week 5 - Intervention
9 Week 6 - Intervention
10 Week 7 - Intervention - Parent Meetings
11 Week 8 - Intervention - Parent Meetings
12 Week 9 - Intervention
13 Week 10 - Intervention
14 Week 11 - Intervention
15 Week 12 - Intervention
16 Week 13 - Intervention
17 Week 14 - Intervention
18 Week 15 - Intervention
19 Testing - Targeted Students - OZCAAS [optional]
20 Testing - Targeted Students - OZCAAS [optional]
21 Week 16 - Intervention
22 Week 17 - Intervention
23 Week 18 - Intervention
24 Week 19 - Intervention
25 Week 20 - Intervention
26 Week 21 - Intervention
27 Week 22 - Intervention
28 Week 23 - Intervention
29 Week 24 - Intervention
30 Week 25 - Intervention
31 Week 26 - Intervention
32 Week 27 - Intervention
33 Week 28 - Intervention
34 Week 29 - Intervention
35 Week 30 - Intervention
36 Testing - Targeted & Comparison Students - OZCAAS
37 Testing - Targeted & Comparison Students - OZCAAS
38 Testing - Targeted & Comparison Students – Standardised Tests
39 and Submit all data to website and administer Stakeholder Surveys
40 send Completed Stakeholder Surveys
182
F a s t a n d A c c u r a t e B a s i c S k i l l s
THU
RSD
AY
12
AU
G
Gro
up
2 [
Lit
erac
y]
Gro
up
3 [
Nu
mer
acy]
Gro
up
4 [
Nu
mer
acy]
Gro
up
5 [
Lit
/ N
um
]
Gro
up
6 [
Lit
/ N
um
]
Gro
up
1 [
Lite
racy
]
TH
UR
SDA
Y 2
6 A
UG
Gro
up
2 [
Lite
racy
]
Gro
up
3 [
Nu
mer
acy]
Gro
up
4 [
Nu
mer
acy]
Gro
up
5 [
Lit
/ N
um
]
Gro
up
6 [
Lit
/ N
um
]
Gro
up
1 [
Lit
erac
y]
THU
R 9
SEP
T
Gro
up
2 [
Lit
erac
y]
Gro
up
3 [
Nu
mer
acy]
Gro
up
4 [
Nu
mer
acy]
Gro
up
5 [
Lit
/ N
um
]
Gro
up
6 [
Lit
/ N
um
]
Gro
up
1 [
Lit
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y]
THU
R 2
3 S
EPT
Gro
up
2 [
Lit
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Gro
up
3 [
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mer
acy]
Gro
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4 [
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Gro
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5 [
Lit
/ N
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]
Gro
up
6 [
Lit
/ N
um
]
Gro
up
1 [
Lit
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y]
Sa
mp
le t
ime
tab
le s
ho
win
g ro
tati
on
of
pai
rs o
f Q
uic
kSm
art
stu
den
ts
WED
NES
DA
Y 1
1 A
UG
Gro
up
3 [
Nu
mer
acy]
Gro
up
4 [
Nu
mer
acy]
Gro
up
5 [
Lit
/ N
um
]
Gro
up
6 [
Lit
/ N
um
]
Gro
up
1 [
Lit
erac
y]
Gro
up
2 [
Lit
erac
y]
W
EDN
ESD
AY
25
AU
G
Gro
up
3 [
Nu
mer
acy]
Gro
up
4 [
Nu
mer
acy]
Gro
up
5 [
Lit
/ N
um
]
Gro
up
6 [
Lit
/ N
um
]
Gro
up
1 [
Lit
erac
y]
Gro
up
2 [
Lit
erac
y]
WED
8 S
EPT
Gro
up
3 [
Nu
mer
acy]
Gro
up
4 [
Nu
mer
acy]
Gro
up
5 [
Lit
/ N
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]
Gro
up
6 [
Lit
/ N
um
]
Gro
up
1 [
Lit
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y]
Gro
up
2 [
Lit
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y]
WED
22
SEP
T
Gro
up
3 [
Nu
mer
acy]
Gro
up
4 [
Nu
mer
acy]
Gro
up
5 [
Lit
/ N
um
]
Gro
up
6 [
Lit
/ N
um
]
Gro
up
1 [
Lit
erac
y]
Gro
up
2 [
Lit
erac
y]
Qu
ickS
ma
rt T
imet
able
Year
: ___
___
___
___
Sch
oo
l: __
___
____
___
___
___
___
___
____
__
____
•
G
rou
p 1
– L
iter
acy/
Nu
mer
acy
•
Gro
up
2 –
Lit
erac
y/N
um
erac
y
TUES
DA
Y 1
0 A
UG
Gro
up
4 [
Nu
mer
acy]
Gro
up
5 [
Lit
/ N
um
]
Gro
up
6 [
Lit
/ N
um
]
Gro
up
1 [
Lit
erac
y]
Gro
up
2 [
Lit
erac
y]
Gro
up
3 [
Nu
mer
acy]
TUES
DA
Y 2
4 A
UG
Gro
up
4 [
Nu
mer
acy]
Gro
up
5 [
Lit
/ N
um
]
Gro
up
6 [
Lit
/ N
um
]
Gro
up
1 [
Lit
erac
y]
Gro
up
2 [
Lit
erac
y]
Gro
up
3 [
Nu
mer
acy]
TU
ES 7
SEP
T
Gro
up
4 [
Nu
mer
acy]
Gro
up
5 [
Lit
/ N
um
]
Gro
up
6 [
Lit
/ N
um
]
Gro
up
1 [
Lit
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y]
Gro
up
2 [
Lit
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y]
Gro
up
3 [
Nu
mer
acy]
TUES
21
SEP
T
Gro
up
4 [
Nu
mer
acy]
Gro
up
5 [
Lit
/ N
um
]
Gro
up
6 [
Lit
/ N
um
]
Gro
up
1 [
Lit
erac
y]
Gro
up
2 [
Lit
erac
y]
Gro
up
3 [
Nu
mer
acy]
THU
RSD
AY
5 A
UG
Gro
up
5 [
Lit
/ N
um
]
Gro
up
6 [
Lit
/ N
um
]
Gro
up
1 [
Lit
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y]
Gro
up
2 [
Lit
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y]
Gro
up
3 [
Nu
mer
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Gro
up
4 [
Nu
mer
acy]
THU
RSD
AY
19
AU
G
Gro
up
5 [
Lit
/ N
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]
Gro
up
6 [
Lit
/ N
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]
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up
1 [
Lit
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y]
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2 [
Lit
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y]
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up
3 [
Nu
mer
acy]
Gro
up
4 [
Nu
mer
acy]
THU
R 2
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T
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up
5 [
Lit
/ N
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]
Gro
up
6 [
Lit
/ N
um
]
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up
1 [
Lit
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y]
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up
2 [
Lit
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up
3 [
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mer
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Gro
up
4 [
Nu
mer
acy]
THU
R 1
6 S
EPT
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5 [
Lit
/ N
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]
Gro
up
6 [
Lit
/ N
um
]
Gro
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1 [
Lit
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2 [
Lit
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Gro
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4 [
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1 –
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acy
•
Gro
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2 –
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WED
NES
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Y 4
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G
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up
6 [
Lit
/ N
um
]
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up
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Lit
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up
2 [
Lit
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y]
Gro
up
3 [
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acy]
Gro
up
4 [
Nu
mer
acy]
Gro
up
5 [
Lit
/ N
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]
WED
NES
DA
Y 1
8 A
UG
Gro
up
6 [
Lit
/ N
um
]
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up
1 [
Lit
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y]
Gro
up
2 [
Lit
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y]
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up
3 [
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mer
acy]
Gro
up
4 [
Nu
mer
acy]
Gro
up
5 [
Lit
/ N
um
]
WED
1 S
EPT
Gro
up
6 [
Lit
/ N
um
]
Gro
up
1 [
Lit
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y]
Gro
up
2 [
Lit
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y]
Gro
up
3 [
Nu
mer
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Gro
up
4 [
Nu
mer
acy]
Gro
up
5 [
Lit
/ N
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]
WED
15
SEP
T
Gro
up
6 [
Lit
/ N
um
]
Gro
up
1 [
Lit
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y]
Gro
up
2 [
Lit
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y]
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up
3 [
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mer
acy]
Gro
up
4 [
Nu
mer
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Gro
up
5 [
Lit
/ N
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]
•
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up
1 –
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erac
y
•
Gro
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2 -
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TUES
DA
Y 3
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G
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up
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Lit
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up
2 [
Lit
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3 [
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up
4 [
Nu
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5 [
Lit
/ N
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up
6 [
Lit
/ N
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]
TUES
DA
Y 1
7 A
UG
Gro
up
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Lit
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Gro
up
2 [
Lit
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Gro
up
3 [
Nu
mer
acy]
Gro
up
4 [
Nu
mer
acy]
Gro
up
5 [
Lit
/ N
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]
Gro
up
6 [
Lit
/ N
um
]
TUES
31
AU
G
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up
1 [
Lit
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up
2 [
Lit
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up
3 [
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mer
acy]
Gro
up
4 [
Nu
mer
acy]
Gro
up
5 [
Lit
/ N
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]
Gro
up
6 [
Lit
/ N
um
]
TUES
14
SEP
T
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up
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Lit
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up
2 [
Lit
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y ]
Gro
up
3 [
Nu
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acy]
Gro
up
4 [
Nu
mer
acy]
Gro
up
5 [
Lit
/ N
um
]
Gro
up
6 [
Lit
/ N
um
]
TIM
E
9:0
0am
- 9
:30
am
9:3
0am
- 1
0:0
0am
10
:00
am -
10
:30
am
10
:30
am -
11
:00
am
11
:30
am -
12
:00
am
12
:00
am -
12
:30
pm
TIM
E
9:0
0am
- 9
:30
am
9:3
0am
- 1
0:0
0am
10
:00
am -
10
:30
am
10
:30
am -
11
:00
am
11
:30
am -
12
:00
am
12
:00
am -
12
:30
pm
TIM
E
9:0
0am
- 9
:30
am
9:3
0am
- 1
0:0
0am
10
:00
am -
10
:30
am
10
:30
am -
11
:00
am
11
:30
am -
12
:00
am
12
:00
am -
12
:30
pm
TIM
E
9:0
0am
- 9
:30
am
9:3
0am
- 1
0:0
0am
10
:00
am -
10
:30
am
10
:30
am -
11
:00
am
11
:30
am -
12
:00
am
12
:00
am -
12
:30
pm
183
F a s t a n d A c c u r a t e B a s i c S k i l l s
She
et N
o:_
___
_
Sch
oo
l: __
___
___
___
___
___
___
____
___
___
___
___
____
____
___
___
___
Tick
fo
r at
ten
dan
ce, C
ross
fo
r ab
sen
ce.
Less
on
s
atte
nd
ed
/
Less
on
s o
ffer
ed
/ / / / / / / / / / / / / /
Qu
ickS
ma
rt N
um
era
cy L
esso
n A
tten
dan
ce S
hee
t 2
0_
___
_
Less
on
Dat
e
Att
en
dan
ce
fro
m
pre
vio
us
shee
t
/ / / / / / / / / / / / / /
Stu
den
t N
ame
184
F a s t a n d A c c u r a t e B a s i c S k i l l s
Numeracy (YEAR)
Student photo
(STUDENT NAME)
Sample title page for Student Numeracy Folder
A coloured copy of this is available on the private area of the QuickSmart website
Place a photo of QuickSmart student in blank area
185
F a s t a n d A c c u r a t e B a s i c S k i l l s
Ind
ivid
ual
Stu
den
t N
um
erac
y Su
mm
ary
Shee
t
Nam
e: _
____
___
___
___
___
___
____
___
___
__
Year
: __
___
___
___
___
____
___
___
___
___
_
Teac
her
: __
___
___
___
___
____
____
___
___
__
I
nst
ruct
or:
__
___
___
____
___
___
___
____
__
Co
mm
ence
d: _
___
___
____
____
____
___
___
_
C
om
ple
ted
: ___
____
____
___
___
___
____
__
Co
mm
ent
Ind
epen
den
t W
ork
shee
t Fo
cus
Are
a/P
age
OZC
AA
S
Inco
rre
ct
Fact
s
Acc
ura
cy
%
Ave
rage
Re
spo
nse
Tim
e
Op
era
tio
n
Spe
ed
Sh
ee
t
No
.
Co
rre
ct/
Inco
rre
ct
Focu
s
Are
a/P
age
Flas
h C
ard
s
Inco
rre
ct
Fact
s
No
.
Inco
rre
ct
No
.
Co
rre
ct
(pe
r m
in)
Focu
s Fa
cts
Dat
e
186
F a s t a n d A c c u r a t e B a s i c S k i l l s
QuickSmart Certificates
• Merit Certificate
• Completion of Program Certificate
Digital copies of these certificates can be found on the QuickSmart Numeracy Private Area in the “Certificates for QuickSmart Participants” Section
189
F a s t a n d A c c u r a t e B a s i c S k i l l s
Cer
tifi
cate
of
Mer
it
Pre
sen
ted
to
__
____
___
___
___
___
____
___
___
___
___
___
____
__
____
___
___
For
___
___
___
___
___
____
___
__
____
___
____
___
___
___
___
___
___
____
___
_
____
___
____
___
___
___
___
___
____
___
___
___
___
___
__
Qu
ickS
ma
rt In
stru
cto
r
P
rin
cip
al
____
___
____
___
___
___
___
___
____
___
___
___
___
___
__
Dat
e
S
cho
ol
Cer
tifi
cate
of
Mer
it
Pre
sen
ted
to
__
____
___
___
___
___
____
___
___
___
___
___
____
__
____
___
___
For
___
___
___
___
___
____
___
__
____
___
____
___
___
___
___
___
___
____
___
_
____
___
____
___
___
___
___
___
____
___
___
___
___
___
__
Qu
ickS
ma
rt In
stru
cto
r
P
rin
cip
al
____
___
____
___
___
___
___
___
____
___
___
___
___
___
__
Dat
e
S
cho
ol
Cer
tifi
cate
of
Mer
it
Pre
sen
ted
to
__
____
___
___
___
___
____
___
___
___
___
___
____
__
____
___
___
For
___
___
___
___
___
____
___
__
____
___
____
___
___
___
___
___
___
____
___
_
____
___
____
___
___
___
___
___
____
___
___
___
___
___
__
Qu
ickS
ma
rt In
stru
cto
r
P
rin
cip
al
____
___
____
___
___
___
___
___
____
___
___
___
___
___
__
Dat
e
S
cho
ol
Cer
tifi
cate
of
Mer
it
Pre
sen
ted
to
__
____
___
___
___
___
____
___
___
___
___
___
____
__
____
___
___
For
___
___
___
___
___
____
___
__
____
___
____
___
___
___
___
___
___
____
___
_
____
___
____
___
___
___
___
___
____
___
___
___
___
___
__
Qu
ickS
ma
rt In
stru
cto
r
P
rin
cip
al
____
___
____
___
___
___
___
___
____
___
___
___
___
___
__
Dat
e
S
cho
ol
This is an example. The proforma is provided on the QuickSmart website.
__________________________________________
is now
having successfully completed the QuickSmart Numeracy program at
_________________________________________ School
resulting in improved recall of number facts.
___________ Year
____________________ ____________________ QuickSmart QuickSmart Co-ordinator Instructor
Co
ng
ratu
lati
on
s
QuickSmart Data Collection and Stakeholder Survey Proformas
• Guidelines to Assist in Completing Data Collection Sheets
• Numeracy Individual Data Sheets:
QuickSmart Students and Comparison Students
• Stakeholder Evaluation Proformas
1) QuickSmart Student
2) Parent/Carer
3) QuickSmart Co-ordinator
4) QuickSmart Instructor
5) Class Teacher
6) Principal
191
F a s t a n d A c c u r a t e B a s i c S k i l l s
Guidelines to Assist in Completing Data Collection Sheets
IMPORTANT: Data collection at your school is of critical importance to the future of the
QuickSmart program. Sharing your data with us allows us to prepare and send to you a school
report based on your own school’s data. As well, we will compile an Annual Numeracy Program
Report (based on all schools each year) to which you will have access. Schools use these
documents for a variety of important purposes, including:
• confirming the learning gains of participating students in comparison to the scores of
their average achieving peers and sharing this information with members of the school
community;
• justifying funding expenditure for funding bodies;
• comparing the learning gains of participating QuickSmart students from one year to the
next;
• gaining insights about the successful implementation of the program over time; and
• promotion of the school and its programs in local media.
There are 2 types of data to collect:
1. Electronic data
These are the results for each student (QuickSmart and Comparison) on the PATMaths and
OZCAAS pre- and post-intervention testing.
Firstly, record each student’s pre-intervention results on a copy of the ‘Summary of Individual
Student Performance for QuickSmart (or Comparison) Students’ page (located in the Resources
and Organisation Folder on pages 193 and 194).
When time permits, but before the end of the program, submit these data electronically via the
secure section of the QuickSmart data upload site. (Refer to the private area of the QuickSmart
website for more detailed instructions.) At the end of the year, after doing the post-intervention
testing, record the results on the hard copy pages you used for the pre-intervention results and
transfer this second set of results electronically to our website. (That allows us to have access to your
two sets of data on which we will perform our analysis.)
2. Data you post to us at:
QuickSmart Evaluations (located beyond page 195 in the Resources and Organisation Folder).
are available for your school to provide feedback to us about the program. These are
optional. Copies of these pages can be found in the Private Area of the website for printing,
alternatively, photocopy the pages from this folder. Any completed evaluations can be
scanned an emailed to [email protected] or posted to:
The QuickSmart Project
SiMERR National Research Centre
University of New England
Armidale, NSW, 2351
192
F a s t a n d A c c u r a t e B a s i c S k i l l s
How to submit data electronically
1. All registered QuickSmart schools will be emailed an Access Code that is used to access the
QuickSmart online sites. From the online site, schools can access the private area of the QuickSmart
website and the Data Upload site.
2. Student pre-intervention data may be uploaded as soon as the data upload site is made available
for the current year.
3. Data can be added or edited, if necessary, at any time during the year.
4. If you have problems using the data upload function, contact [email protected]
5. At the end of the program, follow the same procedure to add each student’s post-intervention
data.
6. Ensure that you have completed the "Pre-Test", "Post-Test" and "Other" sections for each student, before you click "Request a Report" at the end of the QuickSmart Year.
General Information about submitting data electronically
1. The Browser
Problems may arise with some internet browsers. Try a different browser in such circumstances.
2. General Database Correction Information
When completing any page of information, you must provide all mandatory information before you can
save. You can edit this information at a later date.
If you have issues with this process, contact [email protected]
193
F a s t a n d A c c u r a t e B a s i c S k i l l s
Summary of Individual Student Performance
QuickSmart Student
Numeracy _______________ Year
Name ______________________________________ Initials ___________ DOB ____________ M F
Indigenous/N.E.S.B ____________________________________________ Diagnosed Disability Yes No
Type of Disability __________________________________________________________________ [Optional]
School ______________________________________ Year at School ________________________________
No. Lessons Attended _____________________________ Total No. Lessons Offered _______________________
OZCAAS RESULTS
Test Pre-Intervention Post-Intervention
Time Accur Time Accur
Number Naming
Basic addition
Addition
Basic subtraction
Subtraction
Basic Multiplication
Multiplication
Basic Division
Division
Standardised Test Results
Test used: ___________ Mode: ____________ Test Edition: ___________ Level of Test: ______________
[PAT OR ALTERNATE TEST] [Online/Paper] [PAT Ed 3 or 4] [Test number]
Test Pre-Intervention Post-Intervention
Maths Raw Score Raw Score
For online PAT also provide these values
Scale Score Scale Score
Percentile Percentile
Stanine Stanine
DATA FROM THIS FORM NEEDS TO BE UPLOADED AT THE END OF YOUR QUICKSMART YEAR [FOLLOWING PRE-TESTING AND POST-TESTING] SO THAT THE ANALYSIS FOR YOUR SCHOOL CAN BE CONDUCTED. THIS IS DONE VIA THE QUICKSMART DASHBOARD.
For assistance call QuickSmart Help on 02 6773 5061 or email [email protected]
DO NOT SEND See submission instructions below
194
F a s t a n d A c c u r a t e B a s i c S k i l l s
Summary of Individual Student Performance
Comparison Student
Numeracy _______________ Year
Name ______________________________________ Initials ___________ DOB ____________ M F
Indigenous/N.E.S.B ____________________________________________ Diagnosed Disability Yes No
Type of Disability __________________________________________________________________ [Optional]
School ______________________________________ Year at School ________________________________
OZCAAS RESULTS
Test Pre-Intervention Post-Intervention
Time Accur Time Accur
Number Naming
Basic addition
Addition
Basic subtraction
Subtraction
Basic Multiplication
Multiplication
Basic Division
Division
Standardised Test Results
Test used: ___________ Mode: ____________ Test Edition: ___________ Level of Test: ______________
[PAT OR ALTERNATE TEST] [Online/Paper] [PAT Ed 3 or 4] [Test number]
Test Pre-Intervention Post-Intervention
Maths Raw Score Raw Score
For online PAT also provide these values
Scale Score Scale Score
Percentile Percentile
Stanine Stanine
DATA FROM THIS FORM NEEDS TO BE UPLOADED AT THE END OF YOUR QUICKSMART YEAR [FOLLOWING PRE-TESTING AND POST-TESTING] SO THAT THE ANALYSIS FOR YOUR SCHOOL CAN BE CONDUCTED. THIS IS DONE VIA THE QUICKSMART DASHBOARD.
For assistance call QuickSmart Help on 02 6773 5061 or email [email protected]
DO NOT SEND See submission instructions below
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School: Location:
Year level at school: Male/Female:
Year:
QuickSmart Evaluation: QS Students
1. Has QuickSmart helped you? How?
2. Think about all the activities you do in your classroom. How does
QuickSmart help you?
3. Think about your life outside school. How does QuickSmart help you?
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4. What did you enjoy most about the QuickSmart program?
5. What would you change to make the QuickSmart program better?
6. Complete this sentence:
QuickSmart is .
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School: Location:
Year:
QuickSmart Evaluation: Parents/Carers
The purpose of this questionnaire is to gather information to help evaluate the usefulness of the
QuickSmart program in which your child has participated this year.
We appreciate the time you spend in answering these questions.
Please be open with your comments. We are very interested in your insights and feedback about how
the program has worked with your child.
1. What effect has the QuickSmart program had on the performance of your child? Please
comment on the performance of your child in terms of:
academic achievement:
attitude to learning:
self confidence; self-esteem; behaviour:
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2. What effect has the QuickSmart program had on your child at home [e.g. in doing homework,
or in reading for fun, in using maths whilst shopping or cooking and in sporting or other
recreational activities]?
3. What have you heard about the QuickSmart program from your child?
4. We would value any other comments about the QuickSmart program that you would like to make.
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School: Location:
Year:
QuickSmart Evaluation: QS Co-ordinator
The purpose of this questionnaire is to gather information to help evaluate the usefulness of the
QuickSmart program in your school during this year.
We appreciate the time you spend in answering these questions.
Please be open with your comments. We are very interested in your insights and feedback about how
the program has worked with the students this year.
1. Please comment, in general terms, on the QuickSmart program that has been offered in your
school during the year.
2. What effect has the QuickSmart program had on the performance of the QS students? What
feedback have you had about the QuickSmart program from:
Principals:
Teaching Staff:
Parents/Carers:
Students:
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3. Can you comment on any observed “flow-on” effects to other aspects of the students’
learning or personal development?
4. What aspects of the QuickSmart program and its rationale and structure were most effective in
meeting the students’ learning needs and enhancing their learning outcomes?
5. The QuickSmart program is offered as an intense and effective small group intervention. How has
this worked in your school?
6. We would value any other comments about the QuickSmart program and its future in your school.
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School: Location:
Status: [Class Teacher/Support Teacher/Teacher’s Aide or Assistant]
Year:
QuickSmart Evaluation: QS Instructors
The purpose of this questionnaire is to gather information to help evaluate the usefulness of the
QuickSmart program in your school during this year.
We appreciate the time you spend in answering these questions.
Please be open with your comments. We are very interested in your insights and feedback about how
the program has worked with the students this year.
1. What effect has the QuickSmart program had on the performance of the QS students you have
taught? Please comment on these students’ performance in terms of -
academic achievement:
attitude to learning:
self confidence; self-esteem; behaviour:
2. What do you think have been the positive aspects of the QuickSmart program?
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3. What do you think have been the challenging aspects of the QuickSmart program?
4. What has been your experience as a QuickSmart instructor?
5. We would value any other comments from you about the QuickSmart program, including your
professional learning experiences and/or your role as a QuickSmart instructor in your school.
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School: Location:
Year:
QuickSmart Evaluation: Class Teachers
The purpose of this questionnaire is to gather information to help evaluate the usefulness of the
QuickSmart program in your school this year.
We appreciate the time you spend in answering these questions.
Please be open with your comments. We are very interested in your insights and feedback about how
the program has worked with the students this year.
1. What effect has the QuickSmart program had on the performance of the QS students in your class?
Please comment on these students’ performance in terms of:
academic achievement in your classroom:
attitude to learning:
self confidence; self-esteem; behaviour:
attendance at school:
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2. The QuickSmart program has been offered as an intense small group
intervention in your school. How effective has this been for the students in
your class?
3. What effect has the QuickSmart program had on the climate of your
classroom and your teaching? For example:
What perceptions of the program were held by non-participant students?
What was their attitude towards the QuickSmart students?
Were there any whole class benefits as a result of changes in the
QuickSmart students’ attitudes and/or skills?
4. We would value any other comments from you about the QuickSmart program.
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School: Location:
Year:
QuickSmart Evaluation: Principal
The purpose of this questionnaire is to gather information to help evaluate the usefulness of the
QuickSmart program in your school during this year.
We appreciate the time you spend in answering these questions.
Please be open with your comments. We are very interested in your insights and feedback about how
the program has worked with the students this year.
1. Please comment, in general terms, on the QuickSmart program that has been offered in your
school this year.
2. What feedback have you had about the QuickSmart program from your:
Teaching Staff:
Parents/Carers:
QS students:
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3. What effect, if any, has the QuickSmart program had on the performance of the
participating students in your school? Please comment on –
academic achievement:
attitude to learning:
self confidence; self esteem; behaviour:
attendance at school:
4. What aspects of the QuickSmart program were most effective in meeting the students’ learning
needs and enhancing their learning outcomes?
5. The QuickSmart program is offered as an intense small group intervention. How has this worked in
your school?
6. We would value any other comments from you about the QuickSmart program and its future in
your school.