year 4 mathematics qcat 2012 student booklet | fractions ... · 2 | qcats 2012 student booklet year...

MathematicsQueensland Comparable Assessment Tasks (QCATs) 2012 4

Given name: . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

Family name: . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

School: . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

Fractions everywhereStudent booklet

2

Setting the scene

Group discussionFractions are part of our daily life.

Look at the images displayed.

Where do you see fractions used in everyday life?

List some examples where fractions are used:

Share your examples with the class.

Fractions represent equal parts of a whole or parts on a number line.

The whole can be:

• a single unit, like a pie

• a collection in a set, like a carton of eggs

• a number line, like a measuring tape

• numbers, like on a digital weighing scale.

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

© The State of Queensland (QSA) 2012 Please read our copyright notice <www.qsa.qld.edu.au/copyright.html>.Queensland Studies Authority PO Box 307 Spring Hill Qld 4004Phone: (07) 3864 0299 Fax: (07) 3221 2533 Email: [email protected] Website: www.qsa.qld.edu.auImages p. 12 Apple: <www.123rf.com/photo_8912467_red-apple-over-white-background-isolated-fruit.html>; p. 14 Oranges: <www.123rf.com/photo_8806196_single-orange-on-white-background.html>; Apples: <www.123rf.com/photo_8770553_close-up-of-a-row-of-seven-shiny-red-apples-leading-away-from-the-viewer-at-an-oblique-apple.html>; Pineapple: <www.123rf.com/photo_5388998_pineapple-isolated-on-white-background.html>; Kiwi fruit: <www.123rf.com/photo_6187443_kiwi-fruit-isolated-on-white-background.html>.All other images © QSA.

| QCATs 2012 Student booklet Year 4 Mathematics

Look at the pictures below

In this assessment you will:• count fractions

• locate and represent fractions on a number line

• identify equivalent fractions

• connect fractions and decimal notations

• use fractions in daily life.

Fractions represent equal parts of a whole.

The whole can be:

equal parts of a whole (unit) • a single unit, like a pie

equal parts in a set • a collection in a set, like a

carton of eggs

equal parts on a line• a number line, like a

measuring tape.

Fractions can be represented in decimal notation.• Numbers, like on a digital

weighing scale.

12--- 1

2---

two equal parts of a pie

16--- one egg in a set

of six is missing

numbers show equal parts

apple weighs 0.25 kilograms

or of a kilogram14---

| 3Queensland Studies Authority

4

Representing a half, third and a quarter1. Make paper representations for halves and quarters by:

• folding paper strips to represent each fraction

• drawing a line along each fold mark

• gluing each paper strip into the box.

The first one is done for you.

2. Look at these two paper representations of fractions below.

These two representations are:

similar because

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

different because

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

thirds

halves

quarters

third third third


3. Complete the following.


to show 12

3

Number of

third parts

coloured

to show 11

2

half partsNumber of

half parts

coloured

3

show

Colour the half parts

Colour the third parts

Coloured quarter partsNumber of

quarter parts

coloured

9

to show

Colour the half partsNumber of

half parts

coloured2

1

2

to show

Colour the fifth partsNumber of

fifth parts

coloured

6

5

(i)

(ii)

(iii)

(iv)

Stop here: Wait for your teacher’s directions.


6

Counting fractions4. Count by the fraction in A on the number line in B.


Locating fractions on a number line

5. Locate the approximate position of each fraction or mixed number on the number line.

Draw straight lines to the number line.


0 1 2

0 1 2

to 11

2

2to

4

Count by quarters

Count by halves

Count by thirds

A B

0 1 2

0 1 2 3

0 1 2

to3

Count by quarters

to 21

2

to

Count by

. . . . . .

. . . . . . . . . . . . .

and . . . . . . .

1

4

1

4

(i)

(ii)

(iii)

(iv)

3 2

0 1 2 3 4

1

4

1

2

3

4

2

3

1

2

7

3


Identifying equivalent fractions

6. Colour each shape then write the equivalent fraction to show one third.


Here is a representation of three-quarters .

7. Colour of this set of marbles.

1

3

6

� �

9

set of marbles

3

4

3

4


8

8. Draw a line to “match” each mixed number representation in A with an

improper fraction in B.


A

Two and one quarter

(i)

(ii)

(iii)

(iv)

7

3

B

21

2

22

3

6

4

8

3

5

2

9

4


9. Draw a line from each fraction in A to “match” the equivalent fraction in B.


(v) Write two different fractions that are equivalent to .

11

2

1

2

6

4

A

1

4

B

2

10

1

5

4

8

2

8

12

10

6

5

(i)

(ii)

(iii)

(iv)

4

6

4

6 3�

and4

6�



10

Connecting fractions with decimal notation 10. Complete each row by:

• writing in words for each representation

• colouring in the representation and tenths

• locating the fraction on the number line

• writing the fraction in decimal notation.


six

parts

of ten

equal

Representation Tenths

0 60 1 2

Number line Decimal

partsequal

0 1 2

1 20 1 2

. . . . . . . . of ten

partsequal

of

. . . . . . . . . . . . . . . .

(i)

(ii)

. . . . . . . . . . . . . . . .


11. Complete each row.


kg pineapple1

2(i)

101

kg

(ii)

5kg kiwi fruit

10

kg0 2

(iii) kg watermelon1

4 100

kg

Mass Fraction Decimal notation

kg strawberries1

210

kg

5

0 5



12

Sharing an apple

12. Here is a whole apple.

It is then cut in half. Jack takes this half apple to school for morning tea.

(i) Draw Jack’s half in the box.

Jack eats morning tea with one friend.

He shares his half apple equally.

(ii) Write the fraction of the half apple each would get.

(iii) Draw a picture to show your answer.

(iv) Write the fraction of the whole apple each would get.


Thinking space



14

Using fractions


13. (i) Use the recipe to work out how much of each ingredient you will need to make fruit salad for 4 people.

Show your thinking below.

(ii) Explain how you worked out how much kiwi fruit was needed.

Use words and/or drawings.

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

oranges strawberries apples

pineapple kiwi fruit yoghurt


Gui

de to

mak

ing

judg

men

ts �

Yea

r 4 M

athe

mat

ics

Stu

dent

nam

e . .

. . .

. . .

. . .

. . .

. . .

. . .

. . .

. . .

. . .

. . .

. . .

. . .

. . .

. . .

Focu

s: A

pplie

s un

ders

tand

ings

of f

ract

ion

repr

esen

tatio

ns to

sol

ve a

rang

e of

pro

blem

s in

eve

ryda

y co

ntex

ts.

Feed

back

: . .

. . .

. . .

. . .

. . .

. . .

. . .

. . .

. . .

. . .

. . .

. . .

. . .

. . .

. . .

. . .

. . .

. . .

. . .

. . .

. . .

. . .

. . .

. . .

. . .

. . .

. . .

. . .

. . .

. . .

. . .

. . .

. . .

. . .

. . .

. . .

. . .

. . .

. . .

. . .

. . .

.

. . .

. . .

. . .

. . .

. . .

. . .

. . .

. . .

. . .

. . .

. . .

. . .

. . .

. . .

. . .

. . .

. . .

. . .

. . .

. . .

. . .

. . .

. . .

. . .

. . .

. . .

. . .

. . .

. . .

. . .

. . .

. . .

. . .

. . .

. . .

. . .

. . .

. . .

. . .

. . .

. . .

. . .

. . .

. . .

Und

erst

andi

ngSk

ills

Und

erst

andi

ngR

easo

ning

Pro

blem

sol

ving

Flue

ncy

Rep

rese

nts

and

mak

es c

onne

ctio

ns a

cros

s as

sorte

d fra

ctio

ns a

nd d

ecim

al n

otat

ion

in

fam

iliar

con

text

s.

Que

stio

ns 1

, 3 i–

ii, 6

, 7, 8

, 9, 1

0, 1

1, 1

2 ii

Exp

lain

s:

•si

mila

ritie

s an

d di

ffere

nces

bet

wee

n vi

sual

re

pres

enta

tions

of f

ract

ions

•st

rate

gies

to s

olve

kiw

i fru

it pr

oble

m.

Que

stio

ns 2

, 13

ii

App

lies

prob

lem

sol

ving

stra

tegi

es to

:

•lo

cate

and

repr

esen

t fra

ctio

ns o

n pa

rtitio

ned

and

non-

parti

tione

d nu

mbe

r lin

es

•de

term

ine

fruit

fract

ions

and

reci

pe

ingr

edie

nt a

mou

nts.

Que

stio

ns 3

iii–

iv, 5

, 12

i, iii

–iv,

13

i–ii

Use

s m

athe

mat

ical

pro

cedu

res

to:

•lo

cate

and

repr

esen

t fra

ctio

ns o

n pa

rtitio

ned

and

non-

parti

tione

d nu

mbe

r lin

es

•de

term

ine

amou

nts

of fr

uit.

Que

stio

ns 3

iii–

iv, 4

i–iv,

5, 1

0 i–

ii, 1

3 i

A B C D E

A

ccur

atel

y an

d ef

ficie

ntly

sho

ws

parti

tioni

ng (Q

3 iv

), co

unts

on

accu

rate

ly

(Q4

iv, 5

), an

d us

es n

umbe

r ope

ratio

ns

to s

olve

frui

t pro

blem

s (Q

10 ii

,13

i).

A

ppro

pria

tely

app

lies

equa

l par

titio

ning

, co

untin

g on

and

vis

ual r

epre

sent

atio

ns to

so

lve

prob

lem

s (Q

3 iii

, 4 ii

–iii,

5,1

0 i,

13 i)

.

U

ses

mod

elle

d pr

oced

ures

to s

olve

pr

oble

ms

(Q3

iii, 4

i–ii,

10

i, 13

i).

R

epre

sent

s m

ixed

frac

tions

(Q3

iii–i

v).

Det

erm

ines

num

ber o

f app

les

and

pine

appl

es fo

r rec

ipe

(Q13

i).

C

an re

pres

ent v

isua

lly a

s a

prob

lem

so

lvin

g st

rate

gy a

pple

par

ts (Q

12 i,

12

iii)

and

num

bers

of s

traw

berr

ies

and

oran

ges

need

ed fo

r rec

ipe

(Q13

i).

R

epre

sent

s pr

oper

and

mix

ed

fract

ions

on

a nu

mbe

r lin

e (Q

5) a

nd

iden

tifie

s yo

ghur

t am

ount

for r

ecip

e (Q

13 i)

.

R

epre

sent

s an

impr

oper

frac

tion

on a

nu

mbe

r lin

e (Q

5). D

eter

min

es a

pple

fra

ctio

n (Q

12 iv

) and

kiw

i fru

it am

ount

fo

r rec

ipe

(Q13

i).

M

akes

a s

impl

e st

atem

ent a

bout

si

mila

ritie

s, i.

e. li

ttle,

larg

er (Q

2).

P

rovi

des

appr

opria

te m

athe

mat

ical

de

scrip

tions

to e

xpla

in s

imila

ritie

s an

d di

ffere

nces

(Q2)

and

kiw

i fru

it st

rate

gies

(Q

13 ii

).

A

ccur

atel

y in

terp

rets

, con

verts

and

co

nnec

ts a

rang

e of

frac

tions

usi

ng

num

bers

, wor

ds (Q

9 v,

10)

and

de

cim

al re

pres

enta

tions

(Q10

,11

iii).

Id

entif

ies,

dra

ws

and

mat

ches

sim

ple

repr

esen

tatio

ns o

f pro

per (

Q3

i–ii,

11

i), i

mpr

oper

and

mix

ed fr

actio

ns

(Q8

ii–iii

, 9 i–

ii, 1

2 ii)

.

R

epre

sent

s si

mpl

e pr

oper

(Q1)

and

im

prop

er fr

actio

ns th

roug

h vi

sual

re

pres

enta

tions

i.e.

dra

win

g pi

ctur

es

(Q8

i, 8

iv).

C

onne

cts

com

plex

frac

tions

(Q

6, 7

, 9 ii

i, 9

iv) a

nd d

ecim

als

with

eq

uiva

lent

repr

esen

tatio

ns (Q

10 ii

, 11

i–ii)

.

P

rovi

des

accu

rate

and

cle

ar

expl

anat

ions

of d

iffer

ence

s, e

.g. r

efer

s to

larg

er/s

mal

ler e

qual

par

ts o

r hal

ves

(Q2)

and

kiw

i fru

it st

rate

gies

(Q13

ii).

year 4 mathematics qcat 2012 student booklet | fractions ... · 2 | qcats 2012 student booklet year...

Documents