maths program proforma yr 5 t2

8/12/2019 Maths Program Proforma Yr 5 T2

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MATHS PROGRAM : STAGE THREE

YEAR FIVE

WEEKLY ROUTINE

Monday Tuesday Wednesday Thursday Friday

Whole Number 1

Terms 1-4

Number & Algebra

Terms 1-4: Addition and Subtraction 1

Terms 1-4 : Multiplication & Division 1

Terms 1 & 3: Patterns and Algebra 1

Terms 2 & 4: Fractions and Decimals 1

Statistics & Probability

Terms 1 & 3: Data 1

Terms 2 & 4: Chance 1

Measurement & Geometry

Term 1: Length 1 / Time 1 / 2D 1 / Position 1

Term 2: Mass 1 / 3D 1 / Angles 1

Term 3: Volume and Capacity 1 / Time 1 / 2D 1 / Position 1

Term 4: Area 1 / 3D1 / Angles 1


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K-6 MATHEMATICS SCOPE AND SEQUENCE

NUMBER AND ALGEBRA MEASUREMENT AND GEOMETRY STATISTICS &

PROBABILITY TERM

Whole

Number

Addition &

Subtraction

Multiplication

& Division

Fractions &

Decimals

Patterns

& Algebra

Length Area Volume &

Capacity

Mass Time 3D 2D Angles Position Data Chance

K 1

2

3 4

Yr 1 1

2

3

4

Yr 2 1

2

3

4

Yr 3 1

2

3

4

Yr 4 1

2

3

4

Yr 5 1

2

3

4

Yr 6 1

2

3

4

NB: Where a content strand has a level 1 & 2, the 1 refers to the lower grade within the stage, eg. Whole Number 1 in S1 is for Yr 1, Whole Number 2 is for Yr 2.


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CONTENT WEEK TEACHING, LEARNING and ASSESSMENT ADJUSTMENTS RESOURCES REG

Recognise,

represent and

order numbers

to at least tens

of millions

Identify and

describe factors

and multiples of

whole numbers

and use them to

solve problems

1

Highest Common Factor

Revise students understanding of HCF from previous term to gauge retention and

understanding of key concepts.

Provide exercises on HCF for students to complete, such as:

Find the highest common factor of the following numbers:

(1) HCF of 12 and 15 ________ (2) HCF of 10 and 8 ________(3) HCF of 20 and 15 ________ (4) HCF of 25 and 10_______

(5) HCF of 16 and 24 ________ (6) HCF of 12 and 18_______


(9) HCF of 18 and 30 ________ (10) HCF of 12 and 24______

(11) HCF of 15 and 75 _______ (12) HCF of 25 and 50______


(15) HCF of 12and 50 _______ (16) HCF of 8 and 100______



(21) HCF of 10 and 30_______ (22) HCF of 24 and 32______

(23) HCF of 48 and 12_______ (24) HCF of 13 and 15______

In pairs have students compare their answers and discuss any d ifferences, resolving which isthe correct answer and why.

Report back to class and discuss any difficulties that arose.

Support:peer tutor

grouping strategies

Whiteboard and

markers, paper and

pencils

2

Lowest Common Multiple

The smallest number that is a multiple of two or more numbers.

Example: the Least Common Multiple of 3 and 5 is 15, because 15 is a multiple of 3 and also

a multiple of 5. Other common multiples include 30 and 45, etc, but they are not the

smallest (least).

Provide exercises on LCM for students to complete, such as:

Find the lowest common multiple of the following numbers:

(1) LCM of 3 and 4 _________ (2) LCM of 2 and 5 _________

(3) LCM of 2 and 6 _________ (4) LCM of 3 and 5_________

(5) LCM of 10 and 4 ________ (6) LCM of 3 and 9_________

(7) LCM of 5 and 6_________ (8) LCM of 2 and 7_________

(9) LCM of 8 and 6 _________ (10) LCM of 3 and 7________

(11) LCM of 6 and 7________ (12) LCM of 4 and 9________

(13) LCM of 8 and 10 _______ (14) LCM of 3 and 2________

Support:peer tutor

grouping strategies

Whiteboard and

markers, paper and

pencils
http://www.google.com.au/url?q=http://www.etsy.com/market/educational_clipart&sa=U&ei=S34iU4KBD4aDlQWqsYGICA&ved=0CHkQ9QEwJg&sig2=zJONnAm1qaoM9402Kfbtwg&usg=AFQjCNHIHsLSqq8flcJMiNT0QZlR5Z0rxA


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(15) LCM of 4 and 5________ (16) LCM of 8 and 10_______

(17) LCM of 9 and 6 ________ (18) LCM of 2 and 9________

(19) LCM of 3 and 8________ (20) LCM of 5 and 7________

(21) LCM of 10 and 5_______ (22) LCM of 5 and 9________

(23) LCM of 8 and 12_______ (24) LCM of 10 and 2_______

In pairs have students compare their answers and discuss any d ifferences, resolving which is

the correct answer and why.

Report back to class and discuss any difficulties that arose.

3

Prime Numbers

A Prime Number can be divided evenly only by 1, or itself and it must be a whole number

greater than 1.

Example: 5 can only be divided evenly by 1 or 5, so it is a prime number.

But 6 can be divided evenly by 1, 2, 3 and 6 so it is NOT a prime number (it is a composite

number).

Provide students with a hundreds chart and have them colour all of the prime numbers.

Before starting ask students to predict how many prime numbers they think there is

between 1-100.

In pairs have students compare their answers and discuss any d ifferences, resolving which isthe correct answer and why.

As a class check predictions and discuss.

Support:peer tutor

grouping strategies

Whiteboard and

markers, paper and

pencils, 100s charts

4

Ascending Order and Descending Order

In pairs provide students with six d ice. Each student takes turns at rolling all of the dice at

once and then the two students use the numbers rolled to create the smallest number

possible and record this. After three turns each, the students must then p lace their six

numbers in ascending order.

Repeat the above activity, but this time students must make the largest number possible

with the numbers on the dice. When they once again have size numbers, the students

should place these in descending order.

Still in pairs, have students each roll the six dice and make their own largest number. Each

time that the pair have created a number, they must make a statement about the numbersthat they have created in relation to their partners, ie:

My number of 643221 is greater than __________ number of 554321, etc

Support:peer tutor

grouping strategies,

decrease number of dice

used.

Extension: use multi-sided

dice and/or increase

number of dice

Dice, paper and

pencils

5

Millionaire Place Value

Students draw 4 joined boxes in a horizontal line. Squared paper will help. The teacher has

a standard pack of playing cards with the picture cards removed. The teacher shuffles them,

turns the top card and calls out the number. The students must choose a box to write this

number in. The teacher also does this in secret. The cards are turned and called until all four

boxes are filled.

Support: provide prepared

box sheets

Playing cards,

squared paper and

pencils


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Students and teacher then display their number. Students who get a higher number than

the teacher get 5 points. Equal to the teacher gets 3 points. Lower than the teacher 1 point.

The teacher gets 10 points if he / she beats all the students!

Note - a ten playing card is called as a zero.

This game can be adapted to higher numbers by increasing the number of boxes or a

decimal point can be added to change the numbers into pounds and pence.

A further twist with 5/6 figure numbers is to offer pupils the option of switching round two

of the numbers to increase their total.

6

Partitioning and Place Value

Discuss place value with the students and have them explain the place value of a given

number from an example written on the board. Eg in the number 2367, what is the place

value of 3?

Explain to the students how the next step on from this is to partition numbers, for example:

27 = 2 tens and 7units = 20 + 7

156 = 1 hundred, 5 tens and 6 units = 100 + 50 + 6

7310 = 7 thousands, 3 hundreds, 1 ten and zero units = 7 + 3 + 1 + 0

Provide students with a series of numbers to partition independently.

As a class check results and discuss di fficulties.

Ask the students what happens to the place value of a number when a decimal point is

added?

For example: In the number 563.92, what is the place value of the 9 and the 2.

Discuss tenths, hundredths and thousandths.Provide students with a series of decimal numbers to partition.

As a class check results and discuss di fficulties.

Support:provide students

with number expanders

Whiteboard and

markers, paper and

pencils

7

Big Day Out

Select a well known Theme Park or local attraction. Obtain cost of admission figures and

any additional costs that may be incurred participating in activities at the location. Put

together a menu of possible snacks available to purchase for lunch.

In groups provide students with a budget for their day out. Each group will have to plan a

budget for the day which provides opportunities for a given family to experience as much as

possible, whilst still having money to purchase lunch.

Groups must record all purchases made and keep a track of this against the total budget.

Each group reports back to the class on what their imaginary family spent their money for

the day, the total money spent and change if any left over. They should also be encouragedto report on the fairness of the decisions they made for each family member, ie did some of

them miss out on activities whilst others participated etc.

Support:peer tutor

grouping strategies,

calculators to assist

budgeting

Theme park/local

attractions price lists,

paper and pencils

8

Problem Solving : Joins

Provide students with a series of 4 x 4 grids, for example:

Support:concrete material

to add totals

Extension:increase number

values and/or size of grid

used

4x4 grids, colour

pencils and lead

pencils, paper


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8/36

MATHEMATICS PROGRAM PROFORMA

STAGE: Year 5

ES1 S1 S2 S3

STRAND:

NUMBER AND ALGEBRA

TERM:

1 2 3 3

WEEK:

1 2 3 4 5 6 7 8 9 10

SUBSTRAND: Addition and Subtraction 1 KEY CONSIDERATIONS OVERVIEW

OUTCOMES

A student:

describes and represents mathematical situations in a

variety of ways using mathematical terminology and some

conventions MA3-1WM

selects and applies appropriate problem-solving strategies,

including the use of digital technologies, in undertaking

investigations MA3-2WM

gives a valid reason for supporting one possible solution

over another MA3-3WM

selects and applies appropriate strategies for addition and

subtraction with counting numbers of any size MA3-5NA

Background Information

In Stage 3, mental st rategies need to be continually reinforced.

Students may find recording (writing out) informal mental

strategies to be more efficient than using formal written algorithms,particularly in the case of subtraction. Eg, 8000 673 is easier to

calculate mentally than by using a formal algorithm. Written

strategies using informal mental strategies (empty number line):

The jump strategy can be used on an empty number line to count

up rather than back.

The answer will therefore be 7000 + 300 + 20 + 7 = 7327. Students

could share possible approaches and compare them to determine

the most efficient. The difference can be shifted one unit to the left

on an empty number line, so that 8000 673 becomes 7999 672,

which is an easier subtraction to calculate.

Written strategies using a formal algorithm (decomposition

method):

An inverse operation is an operation that reverses the effect of the

original operation. Addition and subtraction are inverse operations;

multiplication and division are inverse operations.

Language

Students should be able to communicate using the following

language: plus, sum, add, addition, increase, minus, the difference

between, subtract, subtraction, decrease, equals, is equal to, empty

number line, strategy, digit, estimate, round to, budget. Teachers

should model & use a variety of expressions for the operations ofaddition & subtraction, & should draw students' attention to the

fact that the words used for subtraction may require the operation

to be performed with the numbers in the reverse order to that in

which they are stated in the question. Eg, '9 take away 3' & 'reduce

9 by 3' require the operation to be performed with the numbers in

the same order as they are presented in the question (ie 9 3).

However, 'take 9 from 3', 'subtract 9 from 3' and '9 less than 3'

require the operation to be performed with the numbers in the

reverse order to that in which they are stated in the question (ie 3

9).

Use efficient mental and written strategies and apply

appropriate digital technologies to solve problems

use the term 'sum' to describe the result of adding two or

more numbers, eg 'The sum of 7 and 5 is 12'

add three or more numbers with different numbers of

digits, with and without the use of digital technologies, eg 42

000 + 5123 + 246

select and apply efficient mental, written and calculator

strategies to solve addition and subtraction word problems,

including problems involving money

- interpret the words 'increase' and 'decrease' in addition

and subtraction word problems, eg 'If a computer costs

$1599 and its price is then decreased by $250, how much do

I pay?'

record the strategy used to solve addition and subtraction

word problems- use empty number lines to record mental strategies

-use selected words to describe each step of the solution

process

check solutions to problems, including by using the inverse

operation

Use estimation and rounding to check the reasonableness

of answers to calculations

round numbers appropriately when obtaining estimates to

numerical calculations

use estimation to check the reasonableness of answers to

addition and subtraction calculations, eg 1438 + 129 is about

1440 + 130Create simple financial plans

use knowledge of addition and subtraction facts to create a

financial plan, such as a budget, eg organise a class

celebration on a budget of $60 for all expenses

-record numerical data in a simple spreadsheet

-give reasons for selecting, prioritising and deleting items

when creating a budget

Learning Across The Curriculum

Cross-curriculum priorities

Aboriginal &Torres Strait Islander histories & cultures Asia & Australias engagement with Asia

Sustainability

General capabilities

Critical & creative thinking

Ethical understanding

Information & communication technology capability

Intercultural understanding

Literacy

Numeracy

Personal & social capability

Other learning across the curriculum areas

Civics & citizenship

Difference & diversity

Work & enterprise


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Use efficient

mental and

written strategies

and apply

appropriate

digitaltechnologies to

solve problems

Use estimation

and rounding to

check the

reasonableness of

answers to

calculations

Create simple

financial plans

1

Mental Strategies

Remind the students of the methods of addition and subtraction that they used during

Term 1. Ask students for examples related to each of the methods.

Provide students with the following 12 additions, in pairs select those they can do in their

heads.

1. 314 + 53 2. 39 + 38 3. 146 + 194. 444 + 333 5. 533 + 388 6. 85 + 205

7. 374 + 456 8. 678 + 99 9. 56 + 13 + 7

10. 532 + 118 + 336 11. 60 + 20 + 30 12. 11 + 16 + 19 + 14

Collect answers and discuss the methods the children used.

Repeat for the following, 12 examples, reminding students that they are only identifying

the sums they can do mentally:

1. 277 23 2. 141 9 3. 340 130

4. 527 311 5. 450 149 6. 510 250

7. 87 38 8. 173 66 9. 277 178

10. 600 180 11. 900 749 12. 871 165

Ask students to look at the above two sets of questions again and this time complete the

additions sums on paper that they were unable to complete mentally. As a class collectmethods and solutions. Discuss the different ideas and clues the students used.

Provide students with the following questions:

1. 140 + 60 20 2. 210 8 + 40 3. 64 19 + 2 4. 100 39 39

5. 50 + 19 + 29 6. 43 + 17 30 7. 200 100 + 100 8. 750 + 50 50

9. 200 87 + 86 10. 500 74 + 75 11. 124 + 58 56

12. 315 + 47 44 13. 40 + 9 + 8 + 7 14. 136 14 12 10

15. 110 + 9 + 19 + 29 + 39 16. 130 9 19 29 39

Have students complete the first six questions and then discuss the methods used,

discussing what they were able to mentally and what strategies they employed for the

questions they had to do on paper.

Repeat with the next six questions. Encourage students to think about what they are

adding and subtracting to the first number. Use a number line to help them to see the

pattern.

Use the above for question 9 to show that 200 87 + 86 = 200 1 = 199. Emphasise the

importance of this strategy is to avoid mistakes.

Students complete the remaining questioning and discuss strategies used.

Support:peer tutor

grouping strategies

Whiteboard and

markers, paper and

pencils, number lines

2

Addition With Regrouping

Students need to be reminded that when they are adding numbers that have a sum of

Support:peer tutor

grouping strategies

Addition Hunt BLM,

clipboards, pencils,
http://www.google.com.au/url?q=http://www.smcdsb.on.ca/media/clipart_image_gallery/education_images/&sa=U&ei=MH8iU8jKOcLfkAW38YDYCA&ved=0CEEQ9QEwCg&sig2=MelqRcUauOI0PPb86mHL1A&usg=AFQjCNGmJH4L1KDK_dCZbabAAB1Re7MUgg


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more than 9 they must carry the tens amount over into the tens column when completing

addition sums. For example:

1

756+

162

918

In pairs provide students with a clipboard and a copy of the answer grid; Addition Hunt

(see attached).

Place a serious of addition problems around the playground. Students set off in pairs and

record their answer in the correct spot on the grid, demonstrating their working out. Whenthey complete each sum, they record whether they needed to apply regrouping to the

question or not and then hunt for another sum.

After a given time period is up, all students return to the classroom and revise questions

together.

whiteboard and

markers, large open

space

3

Subtraction With Regrouping (Decomposition Method)

Students revise subtraction using the decomposition method for regrouping. Students may

find the following rhyme useful for remembering what to do:

More on TOP

No need to STOP!

More on the FLOOR

Go next DOOR

And get 10 MORE!

Numbers the SAME

Zero is your GAME!

In pairs provide students with a clipboard and a copy of the answer grid; Subtraction

Hunt (see attached).

Have the students complete the Subtraction Hunt, as per the same format as the Addition

Hunt game from previous lesson.

After a given time period is up, all students return to the classroom and revise questions

together.

Support:peer tutor

grouping strategies

Subtraction Hunt

BLM, clipboards,

pencils, whiteboard

and markers, large

open space


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4

Rounding

Explain the students that; Roundingis a mental math strategy for adding and subtracting

numbers. When you round, you will likely need to adjust your answer to get the exact

answer.

For example:

- 23 + 58 can be rounded to 20 + 60 = 80.

23 is 3 more than 20 and 58 is 2 less than 60.

So adjust answer by adding 1.

Answer is 81.

- 76 - 40 can be rounded to 80 - 40 = 40.76 is 4 less than 80.

So adjust answer by subtracting 4.

Answer is 36

Provide students with a variety of subtraction and addition algorithms to revise rounding

to solve problems.

Support:concrete materials

to manipulate as required

Whiteboard and

markers, paper and

pencils

5

Money Problems

Provide students with a range of word problems, involving money for them to solve,

examples may include:

1. Lawrence gives $8.88 to Jessica. If Lawrence started with $94.28, how much money does he haveleft?

2. Bruce has $81.65 and Rachel has $60.21. How much more does Bruce have than Rachel?

3. After buying some tickets for $93.72, George has $8.33 left. Howmuch money didGeorge have to begin with?

4. Rachel has $38.13 and Lillian has $9.40. How much more does Rachel have than Lillian?

5. Deborah gives $3.60 to Charles. If Deborah started with $62.05, how much money does

she have left?

6. After buying some blocks for $76.35, Irene has $33.87 left. How much money did Irene

have to begin with?

7. Samuel gives $26.94 to Catherine. If Samuel started with $31.03, how much money does

he have left?

8. Andrea has $11.00 and Pamela has $6.19. How much more does Andrea have than

Pamela?

9. Jacob had $109.85. He bought a shirt for $25.50, a pair of thongs for $7.98 and a hat for

$11.36. How much money did Jacob spend altogether and how much money does he haveleft?

10. Maddi washed the and earned $10.70, she mowed the lawn for $15.55 and babysat a

neighbours child for $27.63. How much pocket money has Maddi earned? If she is saving

for concert tickets that cost $75.50, how much more money does she need to earn?

Students need to write a statement with each of their solutions, identifying the strategy

they used.

Support:provide concrete

money to manipulate when

solving problems

Whiteboard and

markers, paper and

pencils

10

Revision and Assessment


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ASSESSMENT OVERVIEW


13/36

A.

Regrouping: Y N

B.

Regrouping: Y N

C.

Regrouping: Y N

D.

Regrouping: Y N

E.

Regrouping: Y N

F.

Regrouping: Y N

G.

Regrouping: Y N

H.

Regrouping: Y N

I.

Regrouping: Y N

J.

Regrouping: Y N

K.

Regrouping: Y N

L.

Regrouping: Y N

M.

Regrouping: Y N

N.

Regrouping: Y N

O.

Regrouping: Y N

P.

Regrouping: Y N

Q.

Regrouping: Y N

R.

Regrouping: Y N

S.

Regrouping: Y N

T.

Regrouping: Y N

U.

Regrouping: Y N

V.

Regrouping: Y N

W.

Regrouping: Y N

X.

Regrouping: Y N

Y.

Regrouping: Y N


14/36

A.

Regrouping: Y N

B.

Regrouping: Y N

C.

Regrouping: Y N

D.

Regrouping: Y N

E.

Regrouping: Y N

F.

Regrouping: Y N

G.

Regrouping: Y N

H.

Regrouping: Y N

I.

Regrouping: Y N

J.

Regrouping: Y N

K.

Regrouping: Y N

L.

Regrouping: Y N

M.

Regrouping: Y N

N.

Regrouping: Y N

O.

Regrouping: Y N

P.

Regrouping: Y N

Q.

Regrouping: Y N

R.

Regrouping: Y N

S.

Regrouping: Y N

T.

Regrouping: Y N

U.

Regrouping: Y N

V.

Regrouping: Y N

W.

Regrouping: Y N

X.

Regrouping: Y N

Y.

Regrouping: Y N


15/36


STAGE: Year 5

ES1 S1 S2 S3

STRAND:

NUMBER AND ALGEBRA

TERM:

1 2 3 3

WEEK:

1 2 3 4 5 6 7 8 9 10

SUBSTRAND: Multiplication and Division 1 KEY CONSIDERATIONS OVERVIEW

OUTCOMES

A student:


variety of ways using mathematical terminology and someconventions MA3-1WM






selects and applies appropriate strategies for multiplication

and division, and applies the order of operations to

calculations involving more than one operation MA3-6NA


Students could extend their recall of number facts beyond

the multiplication facts to 10 10 by memorising multiples

of numbers such as 11, 12, 15, 20 and 25. They could alsoutilise mental strategies, eg '14 6 is 10 sixes plus 4 sixes'.

In Stage 3, mental strategies need to be continually

reinforced.

Students may find recording (writing out) informal mental

strategies to be more efficient than using formal written

algorithms, particularly in the case of multiplication.

An inverse operation is an operation that reverses the effect

of the original operation. Addition and subtraction are

inverse operations; multiplication and division are inverse

operations.

The area model for two-digit by two-digit multiplication in

Stage 3 is a precursor to the use of the area model for theexpansion of binomial products in Stage 5.

Language


language: multiply, multiplied by, product, multiplication,

multiplication facts, area, thousands, hundreds, tens, ones,

double, multiple, factor, divide, divided by, quotient,

division, halve, remainder, fraction, decimal, equals,

strategy, digit, estimate, round to

Solve problems involving multiplication of large numbers by 1 or 2

digit numbers using efficient mental & written strategies &

appropriate digital technologies

use mental & written strategies to multiply 3 & 4 digit numbers by1 digit numbers, including:

multiplying the 1000s, then the 100s, then t he 10s and then the

1s, eg

using an area model, eg 684 5

using the formal algorithm, eg 432 5

use mental & written strategies to multiply 2 & 3 digit numbers by2 digit numbers, including:

using an area model for 2 digit by 2 digit multiplication, eg 25 26

factorising the numbers, eg 12 25 = 3 4 25 = 3 100 = 300

using extended form (long multiplication) of the formal algorithm,

use digital technologies to multiply numbers of up to 4 digits

- check answers to mental calculations using digital technologies

apply appropriate mental 7 written strategies, 7 digitaltechnologies, to solve multiplication word problems

- use the appropriate operation when solving problems in real-life

situations

- use inverse operations to justify solutions

record the strategy used to solve multiplication word problems

- use selected words to describe each step of the solution process

Solve problems involving division by a 1 digit number, including

those that result in a remainder

use the term 'quotient' to describe the result of a division




Sustainability






Literacy

Numeracy





Work & enterprise


16/36

calculation, eg 'The quotient when 30 is divided by 6 is 5'

recognise 7 use different notations to indicate division, eg 25 4,

,

record remainders as fractions 7 decimals, eg or 6.25

use mental 7 written strategies to divide a number with 3 or

more digits by a 1 digit divisor where there is no remainder,

including:

dividing the 100s, then the 10s, and then the 1s, eg 3248 4


use mental & written strategies to divide a number with 3 or

more digits by a 1 digit divisor where there is a remainder,

including:

dividing the 10s and then the 1s, eg 243 4


- explain why the remainder in a division calculation is always lessthan the number divided by (the divisor)

show theconnection between division & multiplication, including

where there is a remainder, eg 25 4 = 6 remainder 1, so 25 = 4 6 + 1

use digital technologies to divide whole numbers by 1 & 2 digit

divisors

- check answers to mental calculations using digital technologies

apply appropriate mental & written strategies, & digital

technologies, to solve division word problems

- recognise when division is required to solve word problems

- use inverse operations to justify solutions to problems

use & interpret remainders in solutions to division problems, eg

recognise when it is appropriate to round up an answer, s uch as

'How many 5-seater cars are required to take 47 people to thebeach?'

record the strategy used to solve division word problems

- use selected words to describe each step of the solution process

Use estimation & rounding to check the reasonableness of

answers to calculations

round numbers appropriately when obtaining estimates to

numerical calculations

use estimation to check the r easonableness of answers to

multiplication & division calculations, eg '32 253 will be about, butmore than, 30 250'


17/36


Solve problems

involving

multiplication of

large numbers by

1 or 2 digit

numbers usingefficient mental &

written strategies

& appropriate

digital

technologies

Solve problems

involving division

by a 1 digit

number, including

those that result

in a remainder

Use estimation &

rounding to check

the

reasonableness of

answers to

calculations

5

Written Division

Students solve problems that involve dividing a three-digit number by a one-digit number

using written strategies, showing remainders as a fraction:

Students solve division problems interpreting when remainders need to be rounded up egfinding the number of cars with four seats to take 341 people to an event, the solution

would be 86 not 85 .

Variation: Students use calculators to check answers and discuss.

Support:concrete materials

to manipulate as required

Whiteboard and

markers, paper and

pencils, calculators

6

Mixed Operations

Students express each of the numbers from 1 to 100 using mixed operations.

eg

1 = 2 1 1

2 = 2 2 + 1

3 = 4 3 + 2

4 = 9 3 + 1

Extension: Students express

a number using all 4

operations.

Support:check with a

calculator

Whiteboard and

markers, paper and


7

Mixed Operations Game

In pairs, students are given a set of different-coloured counters each, three dice and agame board. Students create the game board by using any 25 numbers from 1 to 50. In

turns, students roll the three dice, use these numbers with any operations to create a

number from the board, and cover the number with a counter .The game continues until

one player has three counters in a row in any direction.

20 11 38 47 16

19 17 8 15 12

1 20 3 7 35

26 42 34 43 49

21 17 16 28 50

Extension: Students use four

dice and make game boardswith higher/lower numbers.

The game could also be

played with cards.

Whiteboard and

markers, paper andpencils, counters, 5x5

grids

8

Rounding up division

The teacher poses the scenario: A farmer has 49 eggs. He needs to put them into cartons,

that each hold a dozen eggs, to send to market. How many cartons does he need?

Possible questions include:

- how many eggs will fit into each carton?

- what strategy did you use to find the solution?

- can you think of another way that the farmer could pack the eggs?

Students record the strategies used. Students write their own problems involving division

with remainders. They publish their work using a computer software package eg

Powerpoint, Kidspix, Slideshow, etc

Extension: The teacher

poses the scenario involving

larger numbers of eggs and

different-sized cartons.

Whiteboard and

markers, paper and

pencils, computers
http://www.google.com.au/url?q=http://www.mycutegraphics.com/graphics/school/supplies/cartoon-calculator.html&sa=U&ei=iX8iU8urPM3RkQX1uYDQBA&ved=0CFkQ9QEwFg&sig2=aFjhVlbzQKJBJyDEKWiCEw&usg=AFQjCNG5qKFfP2UC6ju-z-Yu7zLwkvPzug


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9

Number Patterns

Students are given a table such as:

2 x8 = 16 16 2 = 82 x80 = 160 160 2 = 802 x800 =1600 1600 2 = 800

They are asked to continue the pattern and describe the number pattern created. Students

are encouraged to create further number patterns and are given access to a calculator.

Further number patterns could include:

10 x40 = 400 10 = 10 x500 = 5000 10 =20 x40 = 800 20 = 20 x500 = 10000 20 =70 x40 = 2800 70 = 70 x500 = 35 000 70 =


- what happens if you multiply a number by a multiple of ten?

- what happens if you divide a number by a multiple of ten?

- can you devise a strategy for multiplying by a multip le of ten?

- can you devise a strategy for dividing by a multiple of ten?

Support:individual support

as required

Tables of number

patterns, paper and


10


ASSESSMENT OVERVIEW
http://www.google.com.au/url?q=http://www.mycutegraphics.com/graphics/school/supplies/cartoon-calculator.html&sa=U&ei=iX8iU8urPM3RkQX1uYDQBA&ved=0CFkQ9QEwFg&sig2=aFjhVlbzQKJBJyDEKWiCEw&usg=AFQjCNG5qKFfP2UC6ju-z-Yu7zLwkvPzug


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STAGE: Year 5

ES1 S1 S2 S3

STRAND:

NUMBER AND ALGEBRA

TERM:

1 2 3 3

WEEK:

1 2 3 4 5 6 7 8 9 10

SUBSTRAND: Fractions and Decimals 1 KEY CONSIDERATIONS OVERVIEW

OUTCOMES

A student:








compares, orders and calculates with fractions, decimals

and percentages MA3-7NA

Background InformationIn Stage 3 Fractions and Decimals, students study fractions with

denominators of 2, 3, 4, 5, 6, 8, 10, 12 and 100. A unit fraction is

any proper fraction in which the numerator is 1,eg , , , ,...............

Fractions may be interpreted in different ways depending on the

context, eg two-quarters ( ) may be thought of as two equal parts

of one whole that has been divided into four e qual parts.

Alternatively, two-quarters ( ) may be thought of as two equal

parts of two wholes that have ea ch been divided into quarters.

Students need to interpret a variety of word problems and translate

them into mathematical diagrams and/or fraction notation.Fractions have different meanings depending on the context,

eg show on a diagram three-quarters ( ) of a pizza, draw a diagram

to show how much each child receives when four children share

three pizzas.

LanguageStudents should be able to communicate using the following

language: whole, equal parts, half, quarter, eighth, third, sixth,

twelfth, fifth, tenth, hundredth, thousandth, one-thousandth,

fraction, numerator, denominator, mixed numeral, whole number,

number line, proper fraction,

improper fraction, decimal, decimal point, digit, place value,

decimal places.The decimal 1.12 is read as 'one point one two' and not 'one point

twelve'.

When expressing fractions in English, the numerator is said first,

followed by the denominator.

However, in many Asian languages (eg Chinese, Japanese), the

opposite is the case: the denominator is said before the numerator.

Compare & order common unit fractions & locate & represent them on

a number line(ACMNA102)

place fractions with denominators of 2, 3, 4, 5, 6, 8, 10 & 12 on a

number line between 0 & 1

compare & order unit fractions with denominators of 2, 3, 4, 5, 6, 8,

10, 12 & 100

compare the relative value of unit fractions by placing them on anumber line between 0 & 1

investigate & explain the relationship between the value of a unitfraction & its denominator

Investigate strategies to solve problems involving addition &

subtraction of fractions with the same denominator(ACMNA103)

identify & describe proper fractions as fractions in which the

numerator is less than the denominator

identify & describe improper fractions as fractions in which the

numerator is greater than the denominator

express mixed numerals as improper fractions & vice versa, through

the use of diagrams & number lines, leading to a mental strategy

model & represent strategies, including using diagrams, to add properfractions with the same denominator, where the result may be a mixed

numeral

model & represent a whole number added to a proper fraction

subtract a proper fraction from another proper fraction with the same

denominator

model & represent strategies, including using diagrams, to add mixed

numerals with the same denominator

use diagrams, & mental and written strategies, to subtract a unit

fraction from any whole number including 1

solve word problems that involve addition & subtraction of fractions

with the same denominator use estimation to verify that an answer is

reasonable

Recognise that the place value system can be extended beyond

hundredths(ACMNA104) express thousandths as decimals

interpret decimal notation for thousandths

state the place value of digits in decimal numbers of up to three

decimal places

Compare, order & represent decimals(ACMNA105)

compare &order decimal numbers of up to three decimal places

interpret zero digit(s) at the end of a decimal

place decimal numbers of up to three decimal places on a number line

between 0 & 1




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water.

- By pouring, and using any of these other glasses, show me exactly a thi rd of a glass of

water? What fraction remains in the glass?

Draw a sketch of the three tumblers on the board. Ask one student to add a line to your

diagram on the board to show one-third of a glass.

- Who can show me two-thirds of a glass by drawing a line on the glass I have drawn on the

board?

4. I have 6 cups of milk. A recipe needs of a cup of milk. How many times can I make the

recipe before I run out of milk? Can you draw your answer?

5. I have 6 cups of milk. A recipe needs one-quarter ( ) of a cup of milk. How many times

can I make the recipe before I run out of milk? Can you draw your answer?

6. Draw what would happen if I have 6 cups of milk and a recipe needs three-quarters

( ) of a cup of milk. How many times can I make the recipe before I run out of milk?

7. Who can draw what would happen if I have 6 cups of milk and a recipe needs one-third

( ) of a cup of milk? How many times can I make the recipe before I run out of milk?

8. I have 6 cups of milk. A recipe needs two-thirds ( ) of a cup of milk. How many timescan I

make the recipe before I run out of milk? Can you draw your answer?

7

Related Fractions 2 (One-Third, One-Sixth, One-Ninth and One-Twelfth)

In this activity, students explore the relationships between the unit fractions and

through dividing a continuous unit. They then express the equivalence between variousunits, as well as the relationship between the unit fraction and the whole.

Write the fractions and on the board. Hold up a piece of wool approximately 90 cm

long.

- Using this piece of wool, how could you make one of these fractions?

- Which of these fractions will be the easiest to make? Why?

Select two students to demonstrate how to make one-third. Give the piece of wool to the

two students and send them to a quiet corner to work on their demonstration.

Distribute streamers or strips of paper or light card to each student. Explain that as well as

creating each of the fractions written on the board, the task is to write a procedure using

appropriate diagrams to allow other students to follow the methods developed.

Have the two students demonstrate how they made one-third of the length of wool and

justify why the answer is one-third.

- Now that you have made one-third, which of the fractions on the board would be the

easiest to make next? Why?

Provide sufficient opportunities in the class discussion to clarify the result of repeated

partitioning, say, halving one-third or finding one-third of one-third. Allocate the task of

writing the procedures for finding and of a strip of paper.

Have students share their procedures and ask students to explain what is the same and

what is different about the procedures.

Support:concrete examples

of fractions, individual

support as required

Wool, streamers or

strips of paper, paper

and pencils
http://www.google.com.au/url?q=http://www.brainpop.com/educators/community/bp-topic/adding-and-subtracting-fractions/&sa=U&ei=zn4iU92zIcLolAX2Xg&ved=0CHcQ9QEwJQ&sig2=-Zdb0q2HOpETHMs9NBUFPg&usg=AFQjCNEzpls4SK4MfBXXTQtcU26_uxR7wA


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10


ASSESSMENT OVERVIEW


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STAGE: Year 5

ES1 S1 S2 S3

STRAND:

MEASUREMENT AND GEOMETRY

TERM:

1 2 3 3

WEEK:

1 2 3 4 5 6 7 8 9 10

SUBSTRAND: Mass 1 KEY CONSIDERATIONS OVERVIEW

OUTCOMES

A student:






selects and uses the appropriate unit and device to

measure the masses of objects, and converts between units

of mass MA3-12MG


Gross mass is the mass of the contents of a container and the

container. Net mass is the mass of the contents only.

Local industries and businesses could provide sources for thestudy of measurement in tonnes, eg weighbridges, cranes,

hoists.

Language


language: mass, gross mass, net mass, measure, device,

scales, tonne, kilogram, gram.

As the terms 'weigh' and 'weight' are common in everyday

usage, they can be accepted in student language should they

arise. Weight is a force that changes with gravity, while mass

remains constant.

Choose appropriate units of measurement for mass

(ACMMG108)

recognise the need for a formal unit larger than the

kilogram use the tonne to record large masses, eg sand, soil, vehicles

record masses using the abbreviation for tonnes (t)

distinguish between the gross mass and the net mass of

containers holding substances, eg cans of soup

interpret information about mass on commercialpackaging (Communicating)

solve problems involving gross mass and net mass, egfind the mass of a container given the gross mass and

the net mass (Problem Solving)

select and use the appropriate unit and device to measure

mass, eg electronic scales, kitchen scales

determine the net mass of the contents of a containerafter measuring the gross mass and the mass of the

container (Problem Solving)

find the approximate mass of a small object by establishing

the mass of a number of that object, eg 'The stated weight of

a box of chocolates is 250 g. If there are 20 identical

chocolates in the box, what does each chocolate weigh?'




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Choose

appropriate units

of measurement

for mass

1

Lunchtime

Students weigh and record each item in their lunch box. Express each item in grams. Total

the number of grams of their lunch. Compare with other students.

Note: ensure the students have access to scales that can accurately measure small masses

in grams. Have alternate arrangements for students with lunch orders.

Extension: ask students to

use kitchen scales at home

to find the mass of their

breakfast and dinner, then

calculate the total mass of

food for the day.

Lunches, scales,

pencils and paper

2

Litterbugs

Students collect and sort litter found in the playground and place it into garbage bags that

have been labelled with categories of litter suggested during class discussion. Groups weigh

individual garbage bags and determine the total mass for each category of litter, and the

total mass of litter.

Note:it may take more than one day to collect a significant quantity of litter.

Variation:weigh empty garbage bins, and then the full garbage bins. Subtract the mass of

the bin from the total mass to find the mass of litter.

Support:peer tutor

grouping strategies

School litter, garbage

bags, devices for

weighing, pencil and

paper

3

The Average Lunch

Students find the average mass of lunch eaten by the students in their small group,

including fruit and drinks. Students use the measurement of each groups lunch mass, to

calculate the total mass of all lunches for the class for one day. Express the total in

kilograms and grams. Students then find how many 5kg crates would be needed for

carrying the lunches for the whole class.

Extension: discuss which

group member is the closest

to the average height and

weight for students in the

class. Using this students

mass, calculate how many

lunches would have to be

eaten to equal the mass.

Kitchen scales,

pencils and paper,

students lunches

4

Accurate?

Students work in pairs or small groups to check the accuracy of kitchen and bathroom

scales by using mass pieces. Students draw a table to record the measure of each mass,

and comment on the accuracy of each instrument.

Note:ensure the kitchen scales used are able to measure a mass of more than two

kilograms.

Extension:if the scales are

inaccurate, predict and

measure what happens

when the mass is increased.

500gm, 1kg, 2kg

mass, kitchen and

bathroom scales,

paper and pencils

5

Investigation

Students place each leg of a table on bathroom scales. Record the mass shown on each

scale. Explain why/why not the combined mass shown will be a true measure of the tables

mass. Find a way of checking the mass of the table. Predict what will happen if 10kg was

placed on the table top. Trial and record the results.

Note:ensure that all four bathroom scales are the same height.


as required, questioning

techniques

Small table, four

bathroom scales,

10kg mass for each

group, pencils and

paper

6

Which Unit Would You Use?

Students think of ten different animals, from very large, to small, and record this list.

Beside each animal name, students write the unit of mass which may be used to measure

each one.

Students research the mass of several of the listed animals and record the results.

Extension:students find the

difference between the

lightest animal and the

heaviest animal; students

find the number of small

Access to research

material on animals,

paper and pencils
http://www.google.com.au/url?q=http://www.picturesof.net/pages/090626-160363-222009.html&sa=U&ei=AIAiU5ybC8TllAXYwoEw&ved=0CDUQ9QEwBA&sig2=73IEjLLqIYB4c3JNeJyJ1w&usg=AFQjCNE0h5jM6vHcaTGk98Sss19DAWagiw


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Note:students may need to be reminded that resource material can refer to both imperial

and metric measurements such as ton or tonne.

animals required to balance

the mass of the largest

animal

7

School Bags Full

Students in groups of four or five find the average mass of their full school bags. This

measurement is used to calculate the mass of all bags in the class. Students predict the

mass of all bags in the school.

Extension:how many

teachers bags or baskets

make a tonne?

School bags, scales,

calculators, pencils

and paper

8

How Many Kids to the Elephant?

Students find the mass of the average student in the class. Students estimate and then

calculate, how many students would have the same mass as an elephant (average 4 tonne).Note:students should not be required to publically reveal their weight. Provision should be

made for them to weigh themselves and record on a piece of paper and hand this to the

teacher to use for final calculation.


as required, questioning

techniques

Bathroom scales,

calculators, pencils

and paper

9

Largest?

Students work in pairs or small groups to investigate:

Were dinosaurs the largest living creatures ever? Students research the question and order

the animals that they have studied, from heaviest to lightest. Calculate the difference in

mass between the heaviest and lightest animals in the list.

Support:peer tutor

grouping strategies

Access to research

material, pencils and

paper

10


ASSESSMENT OVERVIEW
http://www.google.com.au/url?q=http://www.picturesof.net/pages/090626-160363-222009.html&sa=U&ei=AIAiU5ybC8TllAXYwoEw&ved=0CDUQ9QEwBA&sig2=73IEjLLqIYB4c3JNeJyJ1w&usg=AFQjCNE0h5jM6vHcaTGk98Sss19DAWagiw


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STAGE: Year 5

ES1 S1 S2 S3

STRAND:


TERM:

1 2 3 3

WEEK:

1 2 3 4 5 6 7 8 9 10

SUBSTRAND: Angles 1 KEY CONSIDERATIONS OVERVIEW

OUTCOMES

A student:



measures and constructs angles, and applies angle

relationships to find unknown angles MA3-16MG


A circular protractor calibrated from 0 to 360 may be easier

for students to use to measure reflex angles than a

semicircular protractor calibrated from 0 to 180.

Language


language: angle, arm, vertex, protractor, degree.

Estimate, measure and compare angles using degrees

(ACMMG112)

identify the arms and vertex of an angle where both arms

are invisible, such as for rotations and rebounds recognise the need for a formal unit for the measurement

of angles

record angle measurements using the symbol for degrees

()

measure angles of up to 360 using a protractor

explain how a protractor is used to measure an angle(Communicating)

explore and explain how to use a semicircular protractorto measure a reflex angle (Communicating, Reasoning)

extend the arms of an angle where necessary tofacilitate measurement of the angle using a protractor

(Problem Solving)Construct angles using a protractor(ACMMG112)

construct angles of up to 360 using a protractor

identify that a right angle is 90, a straight angle is 180 and

an angle of revolution is 360

identify and describe angle size in degrees for each of the

classifications acute, obtuse and reflex

use the words 'between', 'greater than' and 'less than' todescribe angle size in degrees (Communicating)

compare the sizes of two or more angles in degrees, eg

compare angles in different two dimensional shapes

estimate angles in degrees and check by measuring




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Estimate,

measure and

compare angles

using degrees

Estimate,

measure and

compare angles

using degrees

1

Lets Talk About Angles

An ANGLE is an amount of TURN.

- What unit do we measure angles in?

We use the symbol to show degrees; like this 36 or 178 or 317.

What is the size of this angle? What is it called?

- What is the name of an angle smaller than 90?

An angle less than 90 is called an acuteangle. (Angles < 90 are called acuteangles)

- What is the name of angle larger than 90?

An angle greater than 90 is called an obtuseangle. (Angles > 90 are called obtuseangles)

- What about a line? Is it an angle?

A line is known as a straightangle. (A straightangle has a measurement of 180)

- What is the name of an angle larger than 180?

An angle greater than 180 is called a reflexangle. (A reflexangle is > 180, but < 360)

Estimate the size of these angles. What type of angle is it?

Support:provide angle

charts at desks for students

who require direct

comparison

Whiteboard and

markers, paper and

pencils, rulers

2

Protractors

Recap last lesson. Ask students to name the angles discussed and to find an example of each

if possible in the room. Discuss the measurement used to measure angles (degrees) andhow we find this measurement

Give children a protractor each. Discuss what the students know about how to use a

protractor.

Explain how to use a protractor to measure angles using -

http://www.amblesideprimary.com/ambleweb/mentalmaths/angleshapes.html

Explain the importance of accuracy. The centre of the protractor must be exactly on the

corner of the angle and the zero line of the protractor exactly on the arm of the angle.

- Do we use the inner or the outer scale? Choose a student to explain why.

Measure some angles together using the interactive whiteboard.

Get each student to look at the protractor. Get them to look at where the centre, the zero

line and the inner and outer scales are.

Allow students in their pairs to experiment using the protractors measuring angles around

the classroom. Ask them to find right-angles, straight lines, acute, obtuse etc.

Now give them an angle each to measure.


as required, particularly

with manipulating

protractor accurately

Whiteboard and

markers, paper and

pencils, rulers,

protractors,

computer, IWB
http://www.amblesideprimary.com/ambleweb/mentalmaths/angleshapes.htmlhttp://www.amblesideprimary.com/ambleweb/mentalmaths/angleshapes.htmlhttp://www.google.com.au/url?q=http://www.picturesof.net/search_term_pages/protractor.html&sa=U&ei=TIAiU6j7JY3jlAX8zYGgBw&ved=0CIEBEPUBMCo&sig2=ooyUoNimpUVnj7nIGzYV0g&usg=AFQjCNELK_z5zvrAAmdsf7iaB2w5aOq9mwhttp://www.amblesideprimary.com/ambleweb/mentalmaths/angleshapes.html


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- What is the angle? Write down all their answers on whiteboards.

- Who was closest?

- Who wasnt?

- What do they need to do to improve? Repeat.

3

Obtuse Or Acute

A game to be played in pairs.Decide who will be acute and who will be obtuse.

One student draws a straight line.

____________________

The other student draws another line from the centre of the first line to create one acuteangle and one obtuse.

____________________

The acute person estimates their angle and the obtuse estimates theirs.

They then work out the angle using a protractor to find out who was the closest. The one

who was closest gets a point.

Students swap who draws which line and repeat the above activity 10 times.

Support:peer tutor

grouping strategies

Whiteboard and

markers, paper and

pencils, rulers,

protractors

4

Investigating Angles

Pose the following problem for students to investigate:

1. Draw two lines that cross over each other:

____________________

2. Measure the 4 angles created using a protractor.

3. Repeat the process above 3-4 times.

4. What do you notice?

Discuss what the students discovered and create a list of generalisations that can be made

about angles.

Support:work in pairs Whiteboard and

markers, paper and

pencils, rulers,

protractors

10


ASSESSMENT OVERVIEW
http://www.google.com.au/url?q=http://www.picturesof.net/search_term_pages/protractor.html&sa=U&ei=TIAiU6j7JY3jlAX8zYGgBw&ved=0CIEBEPUBMCo&sig2=ooyUoNimpUVnj7nIGzYV0g&usg=AFQjCNELK_z5zvrAAmdsf7iaB2w5aOq9mw


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STAGE: Year 5

ES1 S1 S2 S3

STRAND:


TERM:

1 2 3 3

WEEK:

1 2 3 4 5 6 7 8 9 10

SUBSTRAND: 3D 1 KEY CONSIDERATIONS OVERVIEW

OUTCOMES

A student:





identifies three-dimensional objects, including prisms and

pyramids, on the basis of their properties, and visualises,

sketches and constructs them given drawings of different

views MA3-14MG


In Stage 3, the formal names for particular prisms and

pyramids are introduced while students are engaged in their

construction and representation. (Only 'family' names, suchas prism, were introduced in Stage 2.) This syllabus names

pyramids in the following format: square pyramid,

pentagonal pyramid, etc. However, it is also acceptable to

name pyramids using the word 'based', eg square-based

pyramid, pentagonal-based pyramid.

Prisms have two bases that are the same shape and size. The

bases of a prism may be squares, rectangles, triangles or

other polygons. The other faces are rectangular i f the faces

are perpendicular to the bases. The base of a prism is the

shape of the uniform cross-section, not necessarily the face

on which it is resting.

Pyramids differ from prisms as they have only one base andall the other faces are triangular. The triangular faces meet

at a common vertex (the apex). Pyramids do not have a

uniform cross-section.

Spheres, cones and cylinders do not fit into the classification

of prisms or pyramids as they have curved surfaces, not

faces, eg a cylinder has two flat surfaces and one curved

surface.

A section is a representation of an object as it would appear

if cut by a plane, eg if the corner were cut off a cube, the

resulting cut face would be a triangle. An important

understanding in Stage 3 is that the cross-sections parallel to

the base of a prism are uniform and the cross sectionsparallel to the base of a pyramid are not.

Students could explore these ideas by stacking uniform

objects to model prisms, and by stacking sets of seriated

shapes to model pyramids, eg

Note: such stacks are not strictly pyramids, but they do assist

understanding.

Compare, describe and name prisms and pyramids

identify and determine the number of pairs of parallel

faces of three-dimensional objects, eg 'A rectangular prism

has three pairs of parallel faces' identify the 'base' of prisms and pyramids

recognise that the base of a prism is not always the facewhere the prism touches the ground

name prisms and pyramids according to the shape of their

base, eg rectangular prism, square pyramid

visualise and draw the resulting cut face (plane section)

when a three-dimensional object receives a straight cut

recognise that prisms have a 'uniform cross-section' when

the section is parallel to the base

recognise that the base of a prism is identical to theuniform cross-section of the prism

recognise a cube as a special type of prism recognise that pyramids do not have a uniform cross-section when the section is parallel to the base

identify, describe and compare the properties of prisms

and pyramids, including:

number of faces

shape of faces

number and type of identical faces

number of vertices

number of edges

describe similarities and differences between prisms andpyramids, eg between a triangular prism and a

hexagonal prism, between a rectangular prism and arectangular(-based) pyramid

determine that the faces of prisms are always rectanglesexcept the base faces, which may not be rectangles

determine that the faces of pyramids are alwaystriangles except the base face, which may not be a

triangle

use the term 'apex' to describe the highest point above the

base of a pyramid or cone




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In geometry, a three-dimensional object is called a solid. The

three-dimensional object may in fact be hollow, but it is still

defined as a geometrical solid.

Language


language: object, shape, three dimensional object (3D

object), prism, cube, pyramid, base, uniform cross-section,

face, edge, vertex (vertices), apex, top view, front view, side

view, depth, net.In Stage 1, students were introduced to the terms 'flat

surface' and 'curved surface' for use in describing cones,

cylinders and spheres, and the terms 'faces', 'edges' and

'vertices' for use in describing prisms and pyramids.

Connect three-dimensional objects with their nets and other

two-dimensional representations (ACMMG111)

visualise and sketch three-dimensional objects from

different views, including top, front and side views

reflect on their own drawing of a three-dimensionalobject and consider how it can be improved

examine a diagram to determine whether it is or i s not the

net of a closed three-dimensional object

explain why a given net will not form a closed three-dimensional object

visualise and sketch nets for given three-dimensional

objects

recognise whether a diagram is a net of a particularthree-dimensional object

visualise and name prisms and pyramids, given diagrams of

their nets

select the correct diagram of a net for a given prism orpyramid from a group of similar diagrams where the

others are not valid nets of the object

show simple perspective in drawings by showing depth


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Variation: Students make prisms with a variety of volumes and discuss.

7

Three-Dimensional Viewpoints

The teacher prepares cards that show the front, top and side view of various prisms.

Students label each card, naming the view. They then use the cards to construct a three-

dimensional model, naming it according to the shape of its base.

Students display their labelled cards and models. The other students in the class match the

model to the cards.

Extension: Students make

their own cards and repeat

the activity.

Front, top and side

view cards of prims,

paper and pencils

10


ASSESSMENT OVERVIEW
http://www.google.com.au/url?q=http://www.picturesof.net/pages/090301-185073-234009.html&sa=U&ei=1YAiU_69G4fvkgXmiIC4AQ&ved=0CM8BEPUBMFE&sig2=iOush4tw1GjSfIFBa9N0lQ&usg=AFQjCNG4pF7_xRGfIT2CaT7stxnonos6kA


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STAGE: Year 5

ES1 S1 S2 S3

STRAND:

STATISTICS AND PROBABILITY

TERM:

1 2 3 3

WEEK:

1 2 3 4 5 6 7 8 9 10

SUBSTRAND: Chance 1 KEY CONSIDERATIONS OVERVIEW

OUTCOMES

A student:



conducts chance experiments and assigns probabilities as

values between 0 and 1 to describe their outcomes MA3-

19SP


Students will need some prior experience in ordering

fractions and decimals on a number line from 0 to 1.

The probability of chance events occurring can be orderedon a scale from 0 to 1. A probability of 0 describes the

probability of an event that is impossible. A probability of 1

describes the probability of an event that is certain. Events

with an equal likelihood of occurring or not occurring can be

described as having a probability of (or 0.5 or 50%). Other

expressions of probability fall between 0 and 1, eg events

described as unlikely will have a numerical value

somewhere between 0 and (or 0.5 or 50%).

The sum of the probabilities of the outcomes of any chance

experiment is equal to 1. This can be demonstrated by

adding the probabilities of all of the outcomes of a chance

experiment, such as rolling a die.

Language


language: chance, event, likelihood, certain, possible, likely,

unlikely, impossible, experiment, outcome, probability.

The probability of an outcome is the value (between 0 and 1)

used to describe the chance that the outcome will occur.

A list of all of the outcomes for a chance experiment is

known as the sample space; however, this term is not

introduced until Stage 4.

List outcomes of chance experiments involving equally likely

outcomes and represent probabilities of those outcomes

using fractions(ACMSP116)

use the term probability to describe the numerical valuethat represents the likelihood of an outcome of a chance

experiment

recognise that outcomes are described as equally likely

when any one outcome has the same chance of occurring as

any other outcome

list all outcomes in chance experiments where each

outcome is equally likely to occur

represent probabilities of outcomes of chance experiments

using fractions, eg for one throw of a standard six-sided die

or for one spin of an eight-sector spinner

determine the likelihood of winning simple games byconsidering the number of possible outcomes, eg in arock-paper-scissors game (Problem Solving, Reasoning)

Recognise that probabilities range from 0 to 1(ACMSP117)

establish that the sum of the probabilities of the outcomes

of any chance experiment is equal to 1

order commonly used chance words on an interval from

zero (impossible) to one (certain), eg equally likely would

be placed at (or 0.5)

describe events that are impossible and events that arecertain (Communicating)

describe the likelihood of a variety of events as beingmore or less than a half (or 0.5) and order the events on

an interval (Communicating)




Sustainability






Literacy

Numeracy





Work & enterprise


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List outcomes of

chance

experiments

involving equally

likely outcomes

and represent

probabilities of

those outcomes

using fractions

Recognise that

probabilities

range from 0 to 1

1

Fifty-Fifty

Students are asked to suggest events that have a fifty-fifty chance of occurring. Students

are asked where an equal chance event would occur on a number line marked from 0 to

1. Students list events that have no chance, an equal chance, or are certain, of occurring.

Students use knowledge of equivalent fractions and percentages to assign a numerical

value to the likelihood of a simple event occurring eg fifty-fifty is the same as 50%, a five

in- ten chance, , a one-in-two chance, 0.5 chance.

Support:equivalent fraction

charts for direct comparison

and number lines

Whiteboard and

markers, number

lines, paper and

pencils

2

Running Race

The teacher uses a game board representing a 1000 m track, with six counters (runners) at

the starting line.200m 400m 600m 800m 1000m

Runner 1

Runner 2

Runner 3

Runner 4

Runner 5

Runner 6

Students take turns to roll a dice and state the number shown on the die. They move the

runner with the corresponding number 200 m (one square) eg if 4 is rolled Runner 4 ismoved 200 m (one square).

The teacher allows the students to play for a few moves. Students are then asked to predict

which runner will win.


- what chance of winning has Runner 6? 4? 3? 1? 2? 5? Why?

- is any runner more likely to win than another? Why?

Students then prepare to play their own games by predicting which runner they think will

win. In pairs, they play the game. The teacher gathers all results. Students compare the

results with their prediction and discuss.

Support: individual game

board to physically engage

in activity. Questioning

techniques

Extension: Students design a

spinner to ensure that a

particular runner is more

likely to win than another.

Game boards,

counters, dice

3

Sampling

The teacher places one hundred counters into a paper bag, 70 red, 20 white and 10 green.

A student takes out 10 counters without looking. Students predict the proportion ofcounters of each colour in the bag using this sample.


- how many of each colour do you think are in the bag? Why?

- do you think your prediction is very accurate?

Students return the counters to the bag and select another sample of 10. They make

another prediction and compare this with that of other student.

Students discuss the predictions and compare with the actual sample. They are encouraged

to make up their own sample experiments using this as a model. Students discuss where

Support:questioning

techniques. Peer tutor

grouping strategies

Counters, paper bag,

paper and pencils
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sampling could be a useful tool.

4

Sampling the School Population

Students select a sample of a group of students and ask them to name their favourite food,

TV program, etc. From this sample students predict school population results.


- would we get different results if all students in the sample were from Year 2?

- were girls?

- were tall?

- had blue eyes?

- what strategies could be used to ensure the sample reflected the whole population?- what examples of sampling are used in real-life situations?

Support:questioning

techniques. Peer tutor

grouping strategies

Sample student

group, paper and

pencils

5

Heads and Tails Game

Students stand up and choose to be heads (place their hands on their head) or tails

(place their hands behind their back).

The teacher flips a coin and calls out heads or tails. If it is heads, the students who

chose heads remain standing and the students who chose tails sit down; and the reverse

for tails. Students standing then choose again either heads or tails. The game continues

until only one student remains standing and is declared the winner.


- did your choice of heads or tails affect your chances of getting out? Why?

- if the previous toss was heads, did this affect the chance that the next toss would be

heads? Why? Why not?Students ideas are recorded and then checked by playing several more games, where the

result of each flip of the coin is recorded, tallied and graphed. Students could try to record

the information in a table, list or diagram.

Support:questioning

techniques.

Coin, whiteboard and

markers, paper and

pencils

10


ASSESSMENT OVERVIEW
http://www.google.com.au/url?q=http://www.fotosearch.com/clip-art/toss.html&sa=U&ei=i4EiU9GGG8vhkgXr_oCIBw&ved=0CC8Q9QEwAQ&sig2=0Ws18L60a1htiRyzat06dQ&usg=AFQjCNE9QQJe1SBiPX8I0jjV0horV5BvNA


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maths program proforma yr 5 t2

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