8678 cover.qxd.qxd:tm up operations cover.qxd 5/2/08 … · 120x3 854x5 615x10 13x9 22x8 1x53 914x5...

Operations andNumber Patterns

TargetingMathsUpper Primary

Over90 BLMs

Graded activitiesthat target allMaths topics

8678_cover.qxd.qxd:TM UP Operations Cover.qxd 5/2/08 3:17 PM

41

Formal setting out of multiplication algorithms ispractised with both vertical and horizontal forms.Algorithms extend to multiplying by three-digit numbers.Estimation is encouraged. Patterns are discovered andextended. Multiplication facts are practised throughcompletion of speed grids and finding missing digits.

Problem solving uses multiplication in varied ways. Areasare calculated, money spent, a wedding and the schoolconcert organised and the school doors all repaired.Students are also required to write their own problemsto fit given information.

The activity page explores products in a fun way andthere are two assessment pages.

MULTIPLICATION

42

PrismsPyramidsBuilding 3D SolidsDrawing 3D Solids

MULTIPLICATION

BLM Content

Remember*

*

UPPER PRIMARY

Assessment outcomesA student:

• uses multiplication involving whole numbers tosolve problems.

• recalls and uses multiplication factsup to 10 ¥ 10.

• models and explains patterns related tonumber facts for multiplication.

• selects appropriate strategies to approximateand calculate solutions to problems involvingwhole numbers, money and decimal fractions.

• appreciates how mathematics is used in arange of aspects of society.

• uses understood written methods to multiplywhole numbers to two-digit numbers.

• uses a calculator efficiently for operating onnumbers.

• estimates and calculates mentally.

Languageestimate, calculate, units, ones, tens, hundreds,thousands, columns, decimals, decimal point,trade, contracted form, extended form, multiply,multiplication

Materials/resourcesBase 10 materials, calculator, coloured pencils,TimesTable Poster

* Materials needed for each BLM.

1 Look and see – patterns; codes.* calculator

2 Extended form – calculating the extended2-digit ¥ 1-digit algorithm; using columns;horizontal and vertical calculations.

3 Contracted form – calculating the contractedalgorithm; estimating; calculator usage.* calculator

4 Patterns – multiplying by 1, 10, 100;multiplying decimals; the movement of thedecimal point.* calculator

5 Concert problems – estimating; identifyingnumber sentences; calculation of problems.

6 Calculated effort – finding the path taken;calculator usage; identifying number sentenceswhen problem solving.* calculator, coloured pencils

7 Assessment

8 Activity – Finding products.

Encourage students to:

* seek help when unsure.

* explain their understandings.

* use Times Table Poster if needed.

* use concrete materials if necessary.

UNIT 1Extended formContracted formPatternsProblem solvingEstimation

43

Additional Activities

BLM 31 a 156 b 234 c 512 d 455 e 108

f 1442 a 27 x 6 b 32 x 5 c 81 x 8 d 15 x 9

e 47 x 7 f 13 x 13 a $217.20 b $239.85 c $198.10

d $333.60 e 105.424 a 5 382 b 3 765 c 2 013 d 3 720 e 3645 a F b T c T d F e T f F6 a 3 b 6 c 7 d 6, 1 e 3, 1

BLM 41 Student to check using a calculator.2 a 300 b 950 c 90 d 820

e 4 400 f 6 300 g 580 h 9 900i 670 j 7 500 k 180 l 260

3 Student to check using a calculator.4 3.25 32.5 325

62.06 620.6 6 20697.34 973.4 9 734

582.11 5 821.1 58 211

5 a it didn’t moveb one place to the rightc two places to the right

6 Student to check using a calculator.

BLM 51 72 2 170 3 32 4 3525 $216 6 1 650 7 1 pair

BLM 61 Teacher to check.2 a 87 b 696 c no, 174 d $31.32

e hinges $29.58 f 4 days

BLM 71 a 186 b 128 c 468 d 02 a 170 b 26 700 c 9 840 d 410

e 82.5 f 3763 a correct b incorrect - 665

c correct d incorrect - 17464 a 945 b 1 968 c 2 208 d 1 516

e 2 538 f 1 440 g 1 904 h 5 4905 a 152 b $119.70 c 13.5 metres6 a 2 b 4 c 2, 7 d 9

BLM 8Answers will vary.One solution is:

highest – 63 ¥ 9, 52 ¥ 8, 41 ¥ 7, 1270lowest – 14 ¥ 9, 25 ¥ 8, 36 ¥ 7, 578

� Using supermarket catalogues, explore howmultiplication is used.

� Play board games using 3 dice and calculators.To move forward multiply the 3 dice and addthe numbers in the total, e.g. 3 x 6 x 4 = 72 �

7 + 2 = 9, move forward 9 spaces. If the totalwas 184, add 1, 8 and 4 to get 13 then add 1and 3 to move forward 4 spaces.

� Students design a simple multiplication boardgame for lower grades using 2, 3, 4, 5 or 10times tables.

� Daily multiplication grid – students beat theirown time if using the same grid outline,developing accuracy and confidence.

BLM 11 Teacher to check.

BLM 21 a 98 b 86 c 88 d 96 e 648

f 448 g 963 h 6272 a F b T c F d F e T

f T g T h F i F3 a 260 b 48 c 568 d 168 e 189

f 108 g 170 h 4744 Teacher to check.

ANSWERS

ANSWERSCONT…

44Outcomes • Recalls multiplication facts up to 10 x 10.

• Models and explains patterns related to number facts for multiplication.• Uses multiplication involving whole numbers to solve problems.

LOOK AND SEE

BLM 1

1 a Complete the grid.

b What is the pattern?00000000000000000000000000000000000000000000000000000

000000000000000000000000000000000000000000000000000000000000000000000

2 a Multiply the calculations from A to Z then check using a calculator.

A 2 x 2 = 0000 B 4 x 3 = 0000 C 8 x 5 = 0000 D 7 x 3 = 0000

E 3 x 2 = 0000 F 6 x 9 = 0000 G 9 x 4 = 0000 H 5 x 3 = 0000

I 4 x 2 = 0000 J 3 x 9 = 0000 K 9 x 9 = 0000 L 5 x 4 = 0000

M 10 x 5 = 0000 N 7 x 5 = 0000 O 5 x 2 = 0000 P 4 x 6 = 0000

Q 6 x 7 = 0000 R 7 x 8 = 0000 S 3 x 3 = 0000 T 4 x 8 = 0000

U 6 x 2 = 0000 V 9 x 7 = 0000 W 4 x 4 = 0000 X 10 x 10 = 000

Y 8 x 8 = 0000 Z 9 x 8 = 0000

b Calculate the value of your name. 000000000000000000000000

c Compare this to three friends’ names and rank the four in order from least to most.

0000000000000000 0000000000000000 0000000000000000 0000000000000000

d Repeat with your surnames.

0000000000000000 0000000000000000 0000000000000000 0000000000000000

e With a partner try other comparisons such as: teachers’ names, street names,

football teams, Olympic sports, TV shows etc.

f Represent your findings using as many mathematical explanations as you can

(e.g. graphs, chance and data, numerical comparisons).

Name 0000000000000000000000000000000000Date 00000000

8 10 3 4 1 5 0 9 7 2 6

x 5

x 10

© Blake Education Targeting Maths. This page may be reproduced for classroom use.

45

1 Multiply. Remember to keep numbers in the correct columns.

2 True or false?

a 13 ¥ 3 = 19 0000 b 34 ¥ 2 = 68 0000 c 24 ¥ 4 = 86 0000

d 123 ¥ 3 = 126 0000 e 349 ¥ 0 = 0 0000 f 863 ¥ 1 = 863 0000

g 403 ¥ 2 = 806 0000 h 444 ¥ 2 = 666 0000 i 245 ¥ 3 = 645 0000

3 Complete these algorithms using the extended form.

4 Complete.

Outcomes • Uses understood written methods to multiply whole numbers to two-digit numbers.• Explains patterns related to number facts for multiplication.

Name 0000000000000000000000000000000000Date 00000000

EXTENDED FORM

BLM2

a 6 5

x 4

b 1 6

x 3

c 7 1

x 8

d 8 4

x 2

e 2 7

x 7

f 1 2

x 9

g 3 4

x 5

h 7 9

x 6

e H T U

3 2 4

¥ 2

f H T U

1 1 2

¥ 4

g H T U

3 2 1

¥ 3

h H T U

6 2 7

¥ 1

¥ 7 2 5 9 6 0 4 3 8 10 1

3

6

9

a T U

9 8

¥ 1(8 ¥ 1)

(90 ¥ 1)

b T U

4 3

¥ 2

c T U

2 2

¥ 4

d T U

3 2

¥ 3


46 Outcome • Selects appropriate strategies to calculate solutions to problemsinvolving whole numbers, money and decimal fractions.

CONTRACTED FORM

BLM3Name 0000000000000000000000000000000000Date 00000000

1 Estimate answers first. Then set each one out vertically to solve it.

a 52 x 3 Est. 00000000 b 39 x 6 Est. 00000000

c 64 x 8 Est. 00000000 d 91 x 5 Est. 00000000

e 27 x 4 Est. 00000000 f 18 x 8 Est. 00000000

2 Circle the larger answer.

a 27 x 6 or 18 x 5 b 32 x 5 or 62 x 2

c 56 x 4 or 81 x 8 d 15 x 9 or 96 x 1

e 47 x 7 or 101 x 2 f 13 x 1 or 73 x 0

3 Calculate, then check with a calculator.

4 Try these!

a b c d e f

a $27.15

x 8

b $79.95

x 3

c $39.62

x 5

d $83.40

x 4

e $15.06

x 7

a 8 9 7

x 6

b 7 5 3

x 5

c 6 7 1

x 3

d 4 6 5

x 8

e 1 8 2

x 2

18x 4723

5 True or false? Use a calculator.

a 0.36 x 4 = 144 0000 b 6.27 x 5 = 31.35 0000 c 101.00 x 0 = 0 0000

d 18.03 x 6 = 108.08 0000 e 20.02 x 7 = 140.14 0000 f 42.15 x 10 = 4.215 0000

6 Write the missing digits.

a 2

x 2

4 6

b 1 5

x

9 0

c 3 4

x 5

1 0

d 6 9

x 9

2

e 5 7

x 3

1 07


47Outcomes • Models and explains patterns related to number facts for multiplication.• Uses a calculator efficiently for operating on numbers.

Name 0000000000000000000000000000000000Date 00000000

PATTERNS

BLM4

1 Use a calculator. Look for the patterns.

a 6 x 1 = 0000 b 17 x 1 = 0000 c 22 x 1 = 0000 d 39 x 1 = 0000

6 x 10 = 0000 17 x 10 = 0000 22 x 10 = 0000 39 x 10 = 0000

6 x 100 = 0000 17 x 100 = 0000 22 x 100 = 0000 39 x 100 = 0000

On the back of this page continue this pattern for 43, 85, 103.

2 Now calculate without using a calculator.

a 3 x 100 = 0000 b 95 x 10 = 0000 c 10 x 9 = 0000 d 10 x 82 = 0000

e 44 x 100 = 0000 f 63 x 100 = 0000 g 58 x 10 = 0000 h 99 x 100 = 0000

i 67 x 10 = 0000 j 75 x 100 = 0000 k 10 x 18 = 0000 l 10 x 26 = 0000

3 Now try these.

a 56 x 1 000 = 0000 b 381 x 100 = 0000 c 198 x 100 = 0000 d 80 x 100 = 0000

e 47 x 1 000 = 0000 f 272 x 0 = 0000 g 9 x 1 = 000 h 65 x 100 = 0000

4 Use a calculator and watch the answers carefully.

5 Where did the decimal point move to when you:

a multiplied by 1? 00000000000000000000000000000000

b multiplied by 10? 0000000000000000000000000000000

c multiplied by 100? 000000000000000000000000000000

6 Complete these. NO CALCULATORS!

x 1 x 10 x 100

3.2562.0697.34582.11

x 1 x 10 x 100 x 1000

14.4930.8223.716.43210.54976.58322.44587.90


ELECTRONIC

CALCULATOR

0N A/C MR M− M+

7 8 9

4 5 6 × ÷

1 2 3−

1.

+=

%√

Check using acalculator.


48 Outcomes • Uses understood written methods to multiply whole numbers to two-digit numbers.• Appreciates how mathematics is used in a range of aspects of society.

Name 0000000000000000000000000000000000Date 00000000

CONCERT PROBLEMS

BLM 5

Miss Major-Mayhem is organising the School Concert. Help her finalise the

arrangements. Estimate first, then calculate to see if your estimate makes sense.

1 Three rows of VIP seats are to be set out with 24 seats in

each row. How many VIP reserved signs need to be made?

Estimation 000000000000 Calculation 000000000000

2 Nathan’s mum will make seventeen flower arrangements

required on the night. Each arrangement consists of 10

roses. How many roses must she order?


3 The Consistent Effort Awards are being made. Kindergarten,

Year 1 and Year 2 need four each. Years 3 – 6 need five

each. How many need to be printed?


4 Miss Major-Mayhem said that eight rows of 44 seats would

be needed for the school students. How many students

attend the school?


5 Hall hiring costs $72 per hour. The concert will take 3 hours.

What is the amount written on the cheque Miss Major-

Mayhem sends, prior to the night of the concert?


6 Three A4 pages are used per program. How many pages are

needed for 550 programs?


7 With over 1 000 people expected to fill the Concert Hall,

each wearing one pair of shoes, how many pairs of shoes

will Miss Major-Mayhem wear on the night?


Working Out


49Outcomes • Uses understood written methods to multiply whole numbers to two-digit numbers.• Appreciates how mathematics is used in a range of aspects of society.

Name 0000000000000000000000000000000000Date 00000000

CALCULATEDEFFORT

BLM6

1 Secure the loose pavers by colouring in those which have answers that are even. Write

the largest answer on the glue bucket.

2 Read the problems carefully before calculating.a How many doors are there? 00000000

b Darrel has attached 174 door handles to the doors of a new school.

How many screws does he need if he uses 8 screws per door?

(Hint: Remember that a door has two handles.) 00000000

c Each door has two hinges. He has 164. Is this enough? 00000000

How many does he need in total? 00000000

d Every hinge requires 6 screws.

What will the total cost be if the screws are three cents each? 00000000

e Hinges cost $0.35 each. Which costs more – the hinges or the screws? 00000000

By how much? 00000000

f Darrel and Stan need roughly 20 minutes to complete each door.

How many days will it take them if they work from 9 am to 6 pm with an

hour lunch break? 00000000

789 x 4

17 x 1

103 x 5

83 x 3

459 x 7

170 x 9

60 x 5

37 x 10

Start 224 x 5

120 x 3

854 x 5

615 x 10

13 x 9

22 x 8

1 x 53

914 x 5

251 x 3

369 x 7

35 x 5

98 x 6

45 x 9

47 x 2

783 x 3

88 x 4

753 x 100

46 x 9

258 x 7

139 x 2

29 x 3

86 x 8

155 x 9

66 x 8

39 x 9

717 x 2

410 x 10

68 x 1

8 x 4

10 x 9

963 x 7

14 x 7

59 x 5

99 x 3

33 x 5

101 x 7

77 x 9

678 x 1

345 x 5

9 x 6


50

Name 0000000000000000000000000000000000Date 00000000

MULTIPLICATION

ASSESSMENT BLM7

1

2 a 17 ¥ 10 = 00 00 b 267 ¥ 100 = 0 0 00 c 984 ¥ 10 = 00 00

d 4.1 ¥ 100 = 00 00 e 8.25 ¥ 10 = 00 00 f 3.76 ¥ 100 = 00 00

3 Find and correct the errors by rewriting each one below.

4 Multiply to solve these algorithms. Show your working.

5 a At a local neighbourhood meeting 4 rows of chairs were set up with 38 in each row.

How many people could be seated? 00000000

b Nicole sold six pairs of shoes on sale at $19.95 each.

What was the total amount of her sales? 00000000

c Silvana received an order to cut and sew nine tablecloths 1.5 metres in length.

How much material is needed to complete the order? 00000000

6 Fill in the

missing

digits.

a 6 2

¥ 3

b 3 2

¥ 4

c 2 3 4

¥ 2

d 5 6 7

¥ 0

a 7 2

¥ 6

4 3 2

b 9 5

¥ 7

1 0 2

c 9 1 6

¥ 4

3 6 6 4

d 5 8 2

¥ 3

2 4 5

a 189 ¥ 5 b 246 ¥ 8 c 552 ¥ 4 d 379 ¥ 4

a b c d

a b c d

e 4 2 3

¥ 6

f 7 2 0

¥ 2

g 2 7 2

¥ 7

h 6 1 0

¥ 9

a 7

¥ 5

3 6 0

b 3 6 0

¥

1 4 4 0

c 1 5 9

¥ 8

1 2

d 4

¥ 3

2 8 2

51

Your aim is to make the highest or lowest total possible.

• Place the digits 1–6 in the six boxes. Each digit may only be used once.

• Work out the products.

• Find the sum of the products.

• Try this several times until you have the highest/lowest total you can find.

HIGHEST TOTAL

Product

¥ 9 00000000

¥ 8 00000000

¥ 7 00000000

¥ 9 00000000 Total

LOWEST TOTAL

Product

¥ 9 00000000

¥ 8 00000000

¥ 7 00000000

¥ 9 00000000 Total

Variation: Make the task more interesting by having 9 boxes and usingthe digits 1–9.

NameDate

PRODUCTS

BLM8ACTIVITY PAGE

Targeting Maths

Measurement


Over90 BLMs


Measurement

TargetingMathsLower Primary

Over90 BLMs


TargetingMathsMiddle PrimaryGraded activities

that target allMaths topics

Over90 BLMs

Measurement

Numeration and Fractions


Over90 BLMs



Over90 BLMsGraded activities



TargetingMathsMiddle Primary


Over90 BLMs




Over90 BLMs










Space and Chance and Data


Over90 BLMs


Space






Space

Over90 BLMs

ISBN 978-1-86509-867-8

9 7 8 1 8 6 5 0 9 8 6 7 8

The Targeting Maths Series is a comprehensive resource for primary schools. It has beendesigned to provide busy teachers with all the additional material they need when teaching mathe-matics. All aspects of the primary mathematics curriculum are covered in this twelve book series. WithTargeting Maths, teachers can easily find student activities, reproducible pages and assessment ideasfor every mathematical topic or concept.

Each topic is covered by one or more units of work which are progressive in level. Each unit startswith two teaching pages that include outcomes, language and materials needed. This is followed by adescription of the six blackline masters and all their answers. There are activities and exercises forextension as well as reinforcement and practice, plus high interest activities and games. Each unitends with an assessment page, which is a valuable teaching resource in itself. They can be used toassess specific outcomes or as a pre-test to discover levels of student understanding.

There are four books at each level—Lower, Middle and Upper Primary.

8678_cover.qxd.qxd:TM UP Operations Cover.qxd 5/2/08 3:17 PM Page 2

8678 cover.qxd.qxd:tm up operations cover.qxd 5/2/08 … · 120x3 854x5 615x10 13x9 22x8 1x53 914x5...

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