Overcoming barriers in mathematics - The National …webarchive.nationalarchives.gov.uk/20110809101133/.../ws/nso/pdf/...teaching to help children working around the level 3 to level

The Coalition Government took office on 11 May 2010. This publication was published prior to that date and may not reflect current government policy. You may choose to use these materials, however you should also consult the Department for Education website www.education.gov.uk for updated policy and resources.

Overcoming barriers in mathematics

helping children move from level 3 to level 4

Learningand

teaching

Apply

Rev

ie

w and assess

TeachPractise

Overcoming barriers in mathematics – helping children move from level 3 to level 4

Curriculum and standards

Guidance

Year 5 and 6 teachers,

Mathematics subject

leaders, Head teachers

and LA consultants

Status: Recommended

Date of issue: 11-2007

Ref: 00695-2007PCK-EN

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00695-2007BKT-EN Overcoming barriers in mathematics – helping children move from level 3 to level 4© Crown copyright 2007 Primary National Strategy 3

Overcoming barriers in mathematics – helping children move from level 3 to level 4

Contents

Introduction ■ 4

What mathematics appears on the CD? ■ 4

How were the areas of mathematics identified? ■ 4

How do I access the materials? ■ 4

Who are these materials aimed at? ■ 4

How do the materials link to the Primary Framework? ■ 5

How are the CD materials structured? ■ 5

How should I use the materials on the CD? ■ 6

Contents of the CD ■ 7

What is available to help me build the materials into my planning? ■ 9

Attainment targets, common difficulties, objectives and ‘Can I...?’ questions ■ 10

Links between Objectives and Units ■ 20

Overcoming barriers in mathematics – helping children move from level 3 to level 4 00695-2007BKT-ENPrimary National Strategy © Crown copyright 20074

Introduction

Welcome to this CD-based resource. The materials are designed to help you ensure that, in mathematics, Year 5 and Year 6 children progress from level 3 to level 4 by the end of Key Stage 2. Increasing numbers of children are achieving level 4, but some children still meet barriers in their learning that slow or block their progress. The materials on the CD provide teaching resources and ideas upon which you can draw when planning additional support for those children. This CD is the first of similarly focused intervention materials that are to be developed for mathematics. We hope that you will find these materials useful when planning your teaching to help children working around the level 3 to level 4 border make good progress.

What mathematics appears on the CD?

The materials address key areas of mathematics that Year 5 and Year 6 children working at level 3 often find challenging: the areas of mathematics in which children need additional support to help them maintain progress over Key Stage 2. While the CD includes all the Year 5 and Year 6 learning objectives for mathematics, not all these objectives have materials to support them, only those that have been identified as common barriers to progress.

How were the areas of mathematics identified?

The decision as to which areas of mathematics to include on the CD was informed by a scrutiny of test scripts of children whose attainment fell below, but was close to, the level 4 boundary. This analysis was supported by evidence from other sources. It drew on QCA reports, research evidence and feedback from teachers and consultants. This evidence pointed to a number of common barriers in mathematics that often prevent children from making progress. These are the areas of mathematics that appear on the CD – the bits of mathematics children find difficult to learn, which are often the bits that are more difficult to teach.

How do I access the materials?

The materials on the CD are accessed through the learning objectives for mathematics as set out in the Primary Framework. The objectives are organised into the seven strands of the Framework to help you match them to the Unit of work you might be teaching. At the back of this booklet there is a sequence of charts that make links between level descriptions, common barriers to progress, the associated Year 5 and Year 6 objectives, and materials on the CD, with reference to the Blocks and Units within the Primary Framework. This provides a see-at-a-glance guide to support you in identifying key barriers in moving children from level 3 to level 4 and pinpointing where children are having difficulties and how to move them on.

The CD draws on existing materials, some of which can be found on the Primary Framework, and provides extra support and guidance on teaching approaches designed to support children in overcoming identified barriers to progress.

Who are these materials aimed at?

The materials are designed to be used flexibly and as appropriate for your planning and teaching context. There are aspects that require intervention by you, as the teacher, drawing on your knowledge of the children’s progress in mathematics, for example, when using the ‘Can I…?’ prompts and review questions to pinpoint


barriers to progress. After the barriers to learning have been identified, other elements might be used by a teaching assistant or additional adults to support learning, or might provide a focus for targeted booster support. These materials could be used with an individual child or with a group of children who share similar barriers to progress.

The materials are designed to be used with children who are at risk of not making the necessary progress to move from level 3 to secure level 4 and therefore not meeting age-related expectations by the end of Year 6.

How do the materials link to the Primary Framework?

The structure of the CD follows that of the Framework, with the strands and objectives providing the way into the ‘Can I…?’ questions and related teaching materials and resources. The grids at the end of this booklet show how these objectives fit into the Blocks and Units structure of the Framework, where further materials including ‘I can…’ targets and AfL prompts can be found.

How are the CD materials structured?

The entry point to access the materials has been aligned to six of the seven strands of mathematics used in the Primary Framework. The Using and applying mathematics strand is embedded in the materials rather than identified as a separate set of ‘Can I...?’ questions. This is to place the use and application of mathematics at the heart of the teaching and learning cycles to ensure that children have sufficient opportunity to apply their learning – and that the learning is sufficiently secure to enable them to use their mathematics in new contexts and make connections across their learning.


Learningand

teaching

Apply

Rev

ie

w and assess

TeachPractise

The materials on the CD support the review and assess – teach – practise – apply – review and assess cycle that underpins the Primary Framework. Each stage is supported by prompts and linked materials.

Below, the cycle is set out in more detail and shows how this informs the structure of the materials on the CD.

Example review

and assess questions

Use the example review questions to confirm that this is a barrier to learning

and identify any specific

misconceptions

Teaching guidance

The teaching guidance document provides

background information about

vocabulary, models and images and

teaching approaches

Consolidation and practice

Select from suggested

linked resources to provide

opportunities for consolidation and

practice

Opportunities to use and

apply

Use these prompts to ensure children

can apply their knowledge within mathematics and/or other areas of the curriculum

Confirming learning

Assess whether progress has been made by

asking some of the probing questions

Review and assess

Teach Practise Apply Review and assess

How should I use the materials on the CD?

The first step in using the CD is to carry out an assessment of the children’s learning to identify where support is needed. Select the objective linked to an identified barrier to learning for an individual or group of pupils. Then select the relevant ‘Can I…?’ question linked to this barrier. The tables on the next few pages explain the structure of screens on the CD and the linked resources.


Contents of the CD

From your tracking of pupil progress and ongoing assessment you will have identified potential barriers to learning. The Example review questions provide support for confirming that this area is a barrier to learning for your children and identifying any specific misconceptions. The questions might be used as starting points for discussion with small groups or individuals. Depending upon the area of mathematics, they include suggestions for timed questions, closed and open-ended questions, and questions requiring the use of practical equipment such as a counting stick or set of digit cards.

The Teaching guidance provides background information about appropriate vocabulary, models and images, and teaching approaches. The list of vocabulary is a useful reference point for key vocabulary that children need to be able to use and explain. The models and images are drawn from a variety of sources including the former unit plans, intervention materials and interactive teaching programs, and often include some suggestions for their use. The Teaching tips section provides a few starting points for tackling the area of mathematics with children, ways of linking concepts with other areas of the curriculum, or ways of overcoming misconceptions.


The Consolidation and practice pages provide links to a variety of existing resources that can be used by children within guided or independent work.

The ICT resources include interactive teaching programs (ITPs) and spreadsheets. Where the ITP guide symbol appears, this links to a guidance document to support the use of ITPs. Further ITPs can be found in the library of the Framework website at www.standards.dfes.gov.uk/primaryframeworks/library/Mathematics/ICTResources/itps/

Also linked to these pages are intervention materials drawn from Springboard 5, 6 and 7 packages and the Wave 3 ‘Supporting children with gaps in their mathematical understanding’ materials. In line with the Primary Framework, these materials have been linked where they could help children to overcome barriers to progress in a specific area of mathematics.

The Opportunities to use and apply pages give suggestions for how children might make use of a specific area of mathematics. This includes three key areas: applying understanding within a reasoning context (e.g. using knowledge of counting forwards/backwards to explain the rule for a sequence), applying within other areas of mathematics (e.g. using the ability to multiply and divide by 10 and 100 to work out conversions between units of measure) and finally, using and applying mathematics across the curriculum and within out-of-school contexts.

http://www.standards.dfes.gov.uk/primaryframeworks/library/Mathematics/ICTResources/itps/




The Confirming learning section for each ‘Can I…?’ question provides questions, prompts and activities to probe children’s understanding. These can be adapted to be used as assessment activities for individuals or small groups in order to assess whether progress has been made in this area of mathematics.

What is available to help me build the materials into my planning?

On the next few pages is a set of see-at-a-glance charts to help you to carry out your assessments and to plan appropriate learning and teaching. The level 3 and level 4 descriptions for the Number and algebra, Shape, space and measures and Handling data attainment targets are listed, together with the difficulties that the range of analyses has identified as most common in limiting children’s progress from level 3 to level 4. Following the level descriptions for each attainment target are charts with the learning objectives for Years 5 and 6 taken from the relevant strands that can be used to inform your planning. These have the appropriate ‘Can I …?’ questions that appear on the CD aligned to the objectives. The ‘Can I …?’ questions might be shared with the children as part of the assessment process, inviting them to identify the mathematics they can do in the context of the question and what they still find difficult. They might also be turned into ‘I can…’ statements to generate curricular targets, using the materials on the CD and the Framework to draw together success criteria to share and discuss with the children.


Att

ainm

ent t

arg

ets,

co

mm

on

diff

icul

ties,

ob

ject

ives

and

‘C

an I.

..?’ q

uest

ions

Num

ber

and

alg

ebra

Att

ainm

ent t

arg

et 2

: Num

ber

and

alg

ebra

Leve

l 3Le

vel 4

Com

mon

ly e

ncou

nter

ed d

iffic

ultie

s in

clud

e:

Pup

ils s

how

und

erst

andi

ng o

f pla

ce v

alue

in

num

bers

up

to 1

000

and

use

this

to m

ake

appr

oxim

atio

ns. T

hey

begi

n to

use

dec

imal

no

tatio

n an

d to

reco

gnis

e ne

gativ

e nu

mbe

rs,

in c

onte

xts

such

as

mon

ey a

nd te

mpe

ratu

re.

Pup

ils u

se m

enta

l rec

all o

f add

ition

and

su

btra

ctio

n fa

cts

to 2

0 in

sol

ving

pro

blem

s in

volv

ing

larg

er n

umbe

rs. T

hey

add

and

subt

ract

num

bers

with

two

digi

ts m

enta

lly

and

num

bers

with

thre

e di

gits

usi

ng w

ritte

n m

etho

ds. T

hey

use

men

tal r

ecal

l of t

he 2

, 3, 4

, 5

and

10 m

ultip

licat

ion

tabl

es a

nd d

eriv

e th

e as

soci

ated

div

isio

n fa

cts.

The

y so

lve

who

le-

num

ber p

robl

ems

invo

lvin

g m

ultip

licat

ion

or d

ivis

ion,

incl

udin

g th

ose

that

giv

e ris

e to

re

mai

nder

s. T

hey

use

sim

ple

fract

ions

that

ar

e se

vera

l par

ts o

f a w

hole

and

reco

gnis

e w

hen

two

sim

ple

fract

ions

are

equ

ival

ent.

Pup

ils u

se th

eir u

nder

stan

ding

of p

lace

val

ue

to m

ultip

ly a

nd d

ivid

e w

hole

num

bers

by

10 o

r 10

0. In

sol

ving

num

ber p

robl

ems,

pup

ils u

se

a ra

nge

of m

enta

l met

hods

of c

ompu

tatio

n w

ith th

e fo

ur o

pera

tions

, inc

ludi

ng m

enta

l re

call

of m

ultip

licat

ion

fact

s up

to 1

0 ×

10

and

quic

k de

rivat

ion

of c

orre

spon

ding

di

visi

on fa

cts.

The

y us

e ef

ficie

nt w

ritte

n m

etho

ds o

f add

ition

and

sub

trac

tion

and

of

shor

t mul

tiplic

atio

n an

d di

visi

on. T

hey

add

and

subt

ract

dec

imal

s to

two

plac

es a

nd

orde

r dec

imal

s to

thre

e pl

aces

. In

solv

ing

prob

lem

s w

ith o

r with

out a

cal

cula

tor,

pupi

ls

chec

k th

e re

ason

able

ness

of t

heir

resu

lts b

y re

fere

nce

to th

eir k

now

ledg

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the

cont

ext

or to

the

size

of t

he n

umbe

rs. T

hey

reco

gnis

e ap

prox

imat

e pr

opor

tions

of a

who

le a

nd u

se

sim

ple

fract

ions

and

per

cent

ages

to d

escr

ibe

thes

e. P

upils

reco

gnis

e an

d de

scrib

e nu

mbe

r pa

tter

ns, a

nd re

latio

nshi

ps in

clud

ing

mul

tiple

, fa

ctor

and

squ

are.

The

y be

gin

to u

se s

impl

e fo

rmul

ae e

xpre

ssed

in w

ords

. Pup

ils u

se a

nd

inte

rpre

t coo

rdin

ates

in th

e fir

st q

uadr

ant.

Usi

ng u

nder

stan

ding

of p

lace

val

ue to

mul

tiply

■

and

divi

de n

umbe

rs b

y 10

, 100

and

100

0

Rec

allin

g m

ultip

licat

ion

fact

s an

d de

rivin

g

■

asso

ciat

ed d

ivis

ion

fact

s. U

sing

kno

wn

fact

s an

d pl

ace

valu

e to

der

ive

asso

ciat

ed

mul

tiplic

atio

n an

d di

visi

on fa

cts

Usi

ng e

ffici

ent m

enta

l met

hods

to a

dd a

nd

■

subt

ract

two

num

bers

Und

erst

andi

ng a

nd u

sing

writ

ten

met

hods

■

for s

ubtr

actio

n an

d m

ultip

licat

ion

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ding

, writ

ing,

par

titio

ning

and

ord

erin

g

■

deci

mal

num

bers

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ng a

cal

cula

tor t

o so

lve

prob

lem

s an

d

■

inte

rpre

ting

the

num

bers

on

the

disp

lay

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ng fr

actio

ns a

nd p

erce

ntag

es to

■

desc

ribe

prop

ortio

ns o

f a w

hole

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ing

equi

vale

nt fr

actio

ns a

nd re

latin

g

■

fract

ions

to th

eir d

ecim

al e

quiv

alen

ts

Ord

erin

g an

d po

sitio

ning

pos

itive

and

■

nega

tive

num

bers

and

con

tinui

ng

sequ

ence

s th

at in

volv

e ne

gativ

e nu

mbe

rs

Usi

ng c

oord

inat

es in

the

first

qua

dran

t to

■

draw

, loc

ate

and

com

plet

e sh

apes


Co

untin

g a

nd u

nder

stan

din

g n

umb

er s

tran

d

Year

5 O

bjec

tives

Year

6 O

bjec

tives

Ove

rcom

ing

barr

iers

seq

uenc

es

Cou

nt fr

om a

ny g

iven

num

ber i

n w

hole

-nu

mbe

r and

dec

imal

ste

ps, e

xten

ding

bey

ond

zero

whe

n co

untin

g ba

ckw

ards

; rel

ate

the

num

bers

to th

eir p

ositi

on o

n a

num

ber l

ine

Find

the

diffe

renc

e be

twee

n a

posi

tive

and

a

nega

tive

inte

ger,

or tw

o ne

gativ

e in

tege

rs, i

n co

ntex

t

Can

I po

sitio

n po

sitiv

e an

d ne

gativ

e

■

num

bers

on

a nu

mbe

r lin

e an

d fin

d th

e di

ffere

nce

betw

een

them

?

Can

I co

unt o

n fro

m a

ny g

iven

num

ber i

n

■

who

le-n

umbe

r ste

ps, e

xten

ding

bey

ond

zero

whe

n co

untin

g ba

ckw

ards

?

Exp

lain

wha

t eac

h di

git r

epre

sent

s in

who

le

num

bers

and

dec

imal

s w

ith u

p to

two

plac

es,

and

part

ition

, rou

nd a

nd o

rder

thes

e nu

mbe

rs

Use

dec

imal

not

atio

n fo

r ten

ths,

hun

dred

ths

and

thou

sand

ths;

par

titio

n, ro

und

and

orde

r de

cim

als

with

up

to th

ree

plac

es, a

nd p

ositi

on

them

on

the

num

ber l

ine

Can

I re

ad, w

rite,

par

titio

n an

d or

der

■

deci

mal

num

bers

?

Exp

ress

a s

mal

ler w

hole

num

ber a

s a

fract

ion

of a

larg

er o

ne; f

ind

equi

vale

nt fr

actio

ns; r

elat

e fra

ctio

ns to

thei

r dec

imal

repr

esen

tatio

ns

Exp

ress

a la

rger

who

le n

umbe

r as

a fra

ctio

n of

a s

mal

ler o

ne; s

impl

ify fr

actio

ns b

y ca

ncel

ling

com

mon

fact

ors;

ord

er a

set

of

fract

ions

by

conv

ertin

g th

em to

frac

tions

with

a

com

mon

den

omin

ator

Und

erst

and

perc

enta

ge a

s th

e nu

mbe

r of

part

s in

eve

ry 1

00 a

nd e

xpre

ss te

nths

and

hu

ndre

dths

as

perc

enta

ges

Exp

ress

one

qua

ntity

as

a pe

rcen

tage

of

ano

ther

; fin

d eq

uiva

lent

per

cent

ages

, de

cim

als

and

fract

ions

Can

I ex

pres

s te

nths

and

hun

dred

ths

as

■

perc

enta

ges?

Can

I fin

d si

mpl

e eq

uiva

lent

frac

tions

?

■

Can

I re

late

sim

ple

fract

ions

to th

eir

■

deci

mal

equ

ival

ents

?

Use

seq

uenc

es to

sca

le n

umbe

rs u

p or

do

wn;

sol

ve p

robl

ems

invo

lvin

g pr

opor

tions

of

qua

ntiti

es

Sol

ve s

impl

e pr

oble

ms

invo

lvin

g di

rect

pr

opor

tion

by s

calin

g qu

antit

ies

up o

r dow

n


Kno

win

g a

nd u

sing

num

ber

fact

s st

rand

Year

5 O

bjec

tives

Year

6 O

bjec

tives

Ove

rcom

ing

barr

iers

seq

uenc

es

Use

kno

wle

dge

of p

lace

val

ue a

nd a

dditi

on

and

subt

ract

ion

of tw

o-di

git n

umbe

rs to

de

rive

sum

s an

d di

ffere

nces

and

dou

bles

and

ha

lves

of d

ecim

als

Use

kno

wle

dge

of p

lace

val

ue a

nd

mul

tiplic

atio

n fa

cts

to 1

0 ×

10

to d

eriv

e re

late

d m

ultip

licat

ion

and

divi

sion

fact

s in

volv

ing

deci

mal

s

Can

I us

e m

y ta

bles

to m

ultip

ly a

nd d

ivid

e?

■

Can

I us

e m

y ta

bles

to w

ork

out

■

mul

tiplic

atio

n an

d di

visi

on fa

cts

with

de

cim

als?

Rec

all q

uick

ly m

ultip

licat

ion

fact

s up

to

10 ×

10

and

use

them

to m

ultip

ly p

airs

of

mul

tiple

s of

10

and

100;

der

ive

quic

kly

corr

espo

ndin

g di

visi

on fa

cts

Use

kno

wle

dge

of m

ultip

licat

ion

fact

s to

de

rive

quic

kly

squa

res

of n

umbe

rs to

12

× 1

2 an

d th

e co

rres

pond

ing

squa

res

of m

ultip

les

of 1

0

Can

I us

e m

y ta

bles

to m

ultip

ly a

nd d

ivid

e?

■

Can

I us

e m

y ta

bles

to w

ork

out

■

mul

tiplic

atio

n an

d di

visi

on fa

cts

with

de

cim

als?

Iden

tify

pairs

of f

acto

rs o

f tw

o-di

git w

hole

nu

mbe

rs a

nd fi

nd c

omm

on m

ultip

les

Rec

ogni

se th

at p

rime

num

bers

hav

e on

ly

two

fact

ors

and

iden

tify

prim

e nu

mbe

rs le

ss

than

100

; fin

d th

e pr

ime

fact

ors

of tw

o-di

git

num

bers

Use

kno

wle

dge

of ro

undi

ng, p

lace

val

ue,

num

ber f

acts

and

inve

rse

oper

atio

ns to

es

timat

e an

d ch

eck

calc

ulat

ions

Use

app

roxi

mat

ions

, inv

erse

ope

ratio

ns a

nd

test

s of

div

isib

ility

to e

stim

ate

and

chec

k re

sults


Cal

cula

ting

str

and

Year

5 O

bjec

tives

Year

6 O

bjec

tives

Ove

rcom

ing

barr

iers

seq

uenc

es

Use

und

erst

andi

ng o

f pla

ce v

alue

to m

ultip

ly

and

divi

de w

hole

num

bers

and

dec

imal

s by

10

, 100

or 1

000

Cal

cula

te m

enta

lly w

ith in

tege

rs a

nd

deci

mal

s: U

.t ±

U.t,

TU

× U

, TU

÷ U

, U.t

× U

, U

.t ÷

U

Can

I m

ultip

ly a

nd d

ivid

e by

10

and

100

■

and

1000

?

Can

I ad

d an

d su

btra

ct tw

o nu

mbe

rs in

my

■

head

qui

ckly

?

Can

I us

e m

y ta

bles

to m

ultip

ly a

nd d

ivid

e?

■

Ext

end

men

tal m

etho

ds fo

r who

le-n

umbe

r ca

lcul

atio

ns

Ref

ine

and

use

effic

ient

writ

ten

met

hods

to

mul

tiply

and

div

ide

HTU

× U

, TU

× T

U, U

.t ×

U

and

HTU

÷ U

Use

effi

cien

t writ

ten

met

hods

to a

dd a

nd

subt

ract

inte

gers

and

dec

imal

s, to

mul

tiply

an

d di

vide

inte

gers

and

dec

imal

s by

a o

ne-

digi

t int

eger

, and

to m

ultip

ly tw

o-di

git a

nd

thre

e-di

git i

nteg

ers

by a

two-

digi

t int

eger

Can

I us

e a

writ

ten

met

hod

to s

ubtr

act?

■

Can

I us

e a

writ

ten

met

hod

to m

ultip

ly?

■

Use

effi

cien

t writ

ten

met

hods

to a

dd a

nd

subt

ract

who

le n

umbe

rs a

nd d

ecim

als

with

up

to tw

o pl

aces

Find

frac

tions

usi

ng d

ivis

ion,

and

per

cent

ages

of

num

bers

and

qua

ntiti

esR

elat

e fra

ctio

ns to

mul

tiplic

atio

n an

d di

visi

on;

expr

ess

a qu

otie

nt a

s a

fract

ion

or d

ecim

al;

find

fract

ions

and

per

cent

ages

of w

hole

-nu

mbe

r qua

ntiti

es

Can

I ca

lcul

ate

a fra

ctio

n of

a n

umbe

r or

■

quan

tity?

Can

I ca

lcul

ate

sim

ple

perc

enta

ges

of

■

who

le n

umbe

rs o

r qua

ntiti

es?

Use

a c

alcu

lato

r to

solv

e pr

oble

ms,

incl

udin

g th

ose

invo

lvin

g de

cim

als

or fr

actio

ns;

inte

rpre

t the

dis

play

cor

rect

ly in

the

cont

ext o

f m

easu

rem

ent

Use

a c

alcu

lato

r to

solv

e pr

oble

ms

invo

lvin

g m

ulti-

step

cal

cula

tions

Can

I in

terp

ret t

he n

umbe

rs o

n a

calc

ulat

or

■

disp

lay

(incl

udin

g m

oney

, mea

sure

men

t an

d ro

undi

ng u

p/do

wn)

?

Can

I us

e a

calc

ulat

or to

sol

ve p

robl

ems

■

with

mor

e th

an o

ne s

tep?


Sha

pe,

sp

ace

and

mea

sure

s

Att

ainm

ent t

arg

et 3

: Sha

pe,

sp

ace

and

mea

sure

s

Leve

l 3Le

vel 4

Com

mon

ly e

ncou

nter

ed d

iffic

ultie

s in

clud

e:

Pup

ils c

lass

ify 3

-D a

nd 2

-D s

hape

s in

var

ious

w

ays

usin

g m

athe

mat

ical

pro

pert

ies

such

as

refle

ctiv

e sy

mm

etry

for 2

-D s

hape

s. T

hey

use

non-

stan

dard

uni

ts, s

tand

ard

met

ric u

nits

of

leng

th, c

apac

ity a

nd m

ass,

and

sta

ndar

d un

its o

f tim

e, in

a ra

nge

of c

onte

xts.

Pup

ils m

ake

3-D

mat

hem

atic

al m

odel

s by

lin

king

giv

en fa

ces

or e

dges

, dra

w c

omm

on

2-D

sha

pes

in d

iffer

ent o

rient

atio

ns o

n gr

ids.

Th

ey re

flect

sim

ple

shap

es in

a m

irror

line

. Th

ey c

hoos

e an

d us

e ap

prop

riate

uni

ts a

nd

inst

rum

ents

, int

erpr

etin

g, w

ith a

ppro

pria

te

accu

racy

, num

bers

on

a ra

nge

of m

easu

ring

inst

rum

ents

. The

y fin

d pe

rimet

ers

of s

impl

e sh

apes

and

find

are

as b

y co

untin

g sq

uare

s.

Pup

ils u

se a

nd in

terp

ret c

oord

inat

es in

the

first

qua

dran

t. (A

ttai

nmen

t tar

get 2

: Num

ber

and

alge

bra)

Est

imat

ing,

mea

surin

g an

d ca

lcul

atin

g

■

angl

es w

ith a

ccur

acy

Est

imat

ing

a qu

antit

y an

d ch

oosi

ng

■

the

mos

t sen

sibl

e un

it of

mea

sure

and

eq

uipm

ent t

o us

e

Con

vert

ing

betw

een

units

of m

easu

re

■

Rea

ding

and

inte

rpre

ting

num

bers

on

■

a sc

ale

Find

ing

the

area

and

per

imet

er o

f rec

tang

les

■

Usi

ng c

oord

inat

es in

the

first

qua

dran

t to

■

draw

, loc

ate

and

com

plet

e sh

apes


Und

erst

and

ing

sha

pe

stra

nd

Year

5 O

bjec

tives

Year

6 O

bjec

tives

Ove

rcom

ing

barr

iers

seq

uenc

es

Iden

tify,

vis

ualis

e an

d de

scrib

e pr

oper

ties

of

rect

angl

es, t

riang

les,

regu

lar p

olyg

ons

and

3-

D s

olid

s; u

se k

now

ledg

e of

pro

pert

ies

to

draw

2-D

sha

pes,

and

to id

entif

y an

d dr

aw

nets

of 3

-D s

hape

s

Des

crib

e, id

entif

y an

d vi

sual

ise

para

llel a

nd

perp

endi

cula

r edg

es o

r fac

es; u

se th

ese

prop

ertie

s to

cla

ssify

2-D

sha

pes

and

3-D

so

lids

Mak

e an

d dr

aw s

hape

s w

ith in

crea

sing

ac

cura

cy a

nd a

pply

kno

wle

dge

of th

eir

prop

ertie

s

Com

plet

e pa

tter

ns w

ith u

p to

two

lines

of

sym

met

ry; d

raw

the

posi

tion

of a

sha

pe a

fter a

re

flect

ion

or tr

ansl

atio

n

Vis

ualis

e an

d dr

aw o

n gr

ids

of d

iffer

ent t

ypes

w

here

a s

hape

will

be a

fter r

efle

ctio

n, a

fter

tran

slat

ions

, or a

fter r

otat

ion

thro

ugh

90˚ o

r 18

0˚ a

bout

its

cent

re o

r one

of i

ts v

ertic

es

Rea

d an

d pl

ot c

oord

inat

es in

the

first

qu

adra

nt; r

ecog

nise

par

alle

l and

per

pend

icul

ar

lines

in g

rids

and

shap

es: u

se a

set

-squ

are

and

rule

r to

draw

sha

pes

with

per

pend

icul

ar o

r pa

ralle

l sid

es

Use

coo

rdin

ates

in th

e fir

st q

uadr

ant t

o dr

aw,

loca

te a

nd c

ompl

ete

shap

es th

at m

eet g

iven

pr

oper

ties

Can

I us

e co

ordi

nate

s to

dra

w, l

ocat

e an

d

■

com

plet

e sh

apes

?

Est

imat

e, d

raw

and

mea

sure

acu

te a

nd o

btus

e an

gles

usi

ng a

n an

gle

mea

sure

r or p

rotr

acto

r to

a s

uita

ble

degr

ee o

f acc

urac

y; c

alcu

late

an

gles

in a

str

aigh

t lin

e

Est

imat

e an

gles

, and

use

a p

rotr

acto

r to

mea

sure

and

dra

w th

em, o

n th

eir o

wn

and

in s

hape

s; c

alcu

late

ang

les

in a

tria

ngle

or

arou

nd a

poi

nt

Can

I es

timat

e an

d m

easu

re a

ngle

s le

ss

■

than

180

˚?

Can

I ca

lcul

ate

angl

es o

n a

stra

ight

line

■

and

in a

tria

ngle

?


Mea

suri

ng s

tran

d

Year

5 O

bjec

tives

Ye

ar 6

Obj

ectiv

esO

verc

omin

g ba

rrie

rs s

eque

nces

Rea

d, c

hoos

e, u

se a

nd re

cord

sta

ndar

d m

etric

un

its to

est

imat

e an

d m

easu

re le

ngth

, wei

ght

and

capa

city

to a

sui

tabl

e de

gree

of a

ccur

acy;

co

nver

t lar

ger t

o sm

alle

r uni

ts u

sing

dec

imal

s to

one

pla

ce

Sel

ect a

nd u

se s

tand

ard

met

ric u

nits

of

mea

sure

and

con

vert

bet

wee

n un

its u

sing

de

cim

als

to tw

o pl

aces

Can

I es

timat

e a

quan

tity

(mas

s, le

ngth

or

■

capa

city

) and

cho

ose

the

mos

t sen

sibl

e un

it of

mea

sure

and

equ

ipm

ent t

o us

e?

Can

I co

nver

t bet

wee

n un

its?

■

Inte

rpre

t a re

adin

g th

at li

es b

etw

een

two

unnu

mbe

red

divi

sion

s on

a s

cale

Rea

d an

d in

terp

ret s

cale

s on

a ra

nge

of

mea

surin

g in

stru

men

ts, r

ecog

nisi

ng th

at

the

mea

sure

men

t mad

e is

app

roxi

mat

e an

d re

cord

ing

resu

lts to

a re

quire

d de

gree

of

accu

racy

; com

pare

read

ings

on

diffe

rent

sc

ales

, for

exa

mpl

e w

hen

usin

g di

ffere

nt

inst

rum

ents

Can

I re

ad a

nd u

se a

sca

le o

n a

■

ther

mom

eter

, pro

trac

tor,

rule

r, w

eigh

ing

scal

e an

d m

easu

ring

cylin

der?

Dra

w a

nd m

easu

re li

nes

to th

e ne

ares

t m

illim

etre

; mea

sure

and

cal

cula

te th

e pe

rimet

er o

f reg

ular

and

irre

gula

r pol

ygon

s;

use

the

form

ula

for t

he a

rea

of a

rect

angl

e to

ca

lcul

ate

the

rect

angl

e’s

area

Cal

cula

te th

e pe

rimet

er a

nd a

rea

of re

ctilin

ear

shap

es; e

stim

ate

the

area

of a

n irr

egul

ar

shap

e by

cou

ntin

g sq

uare

s

Can

I w

ork

out t

he a

rea

and

perim

eter

of

■

a re

ctan

gle?

Rea

d tim

etab

les

and

time

usin

g 24

-hou

r cl

ock

nota

tion;

use

a c

alen

dar t

o ca

lcul

ate

time

inte

rval

s



Han

dlin

g d

ata

Att

ainm

ent t

arg

et 4

: Han

dlin

g d

ata

Leve

l 3Le

vel 4

Com

mon

ly e

ncou

nter

ed d

iffic

ultie

s in

clud

e:

Pup

ils e

xtra

ct a

nd in

terp

ret i

nfor

mat

ion

pres

ente

d in

sim

ple

tabl

es a

nd li

sts.

The

y co

nstr

uct b

ar c

hart

s an

d pi

ctog

ram

s, w

here

th

e sy

mbo

l rep

rese

nts

a gr

oup

of u

nits

, to

com

mun

icat

e in

form

atio

n th

ey h

ave

gath

ered

, an

d th

ey in

terp

ret i

nfor

mat

ion

pres

ente

d to

th

em in

thes

e fo

rms.

Pup

ils c

olle

ct d

iscr

ete

data

and

reco

rd th

em

usin

g a

frequ

ency

tabl

e. T

hey

unde

rsta

nd a

nd

use

the

mod

e an

d ra

nge

to d

escr

ibe

sets

of

data

. The

y gr

oup

data

, whe

re a

ppro

pria

te, i

n eq

ual c

lass

inte

rval

s, re

pres

ent c

olle

cted

dat

a in

freq

uenc

y di

agra

ms

and

inte

rpre

t suc

h di

agra

ms.

The

y co

nstr

uct a

nd in

terp

ret s

impl

e lin

e gr

aphs

.

Inte

rpre

ting

the

info

rmat

ion

on a

rang

e of

■

grap

hs a

nd c

hart

s

Dra

win

g a

conc

lusi

on fr

om a

gra

ph o

r

■

char

t in

orde

r to

answ

er a

que

stio

n

Und

erst

andi

ng th

e m

eani

ng o

f poi

nts

■

betw

een

labe

lled

divi

sion

s on

gra

phs

Usi

ng th

e la

ngua

ge o

f pro

babi

lity

to

■

desc

ribe

the

likel

ihoo

d of

eve

nts


Han

dlin

g d

ata

stra

nd

Year

5 O

bjec

tives

Year

6 O

bjec

tives

Ove

rcom

ing

barr

iers

seq

uenc

es

Des

crib

e th

e oc

curr

ence

of f

amilia

r eve

nts

usin

g th

e la

ngua

ge o

f cha

nce

or li

kelih

ood

Des

crib

e an

d pr

edic

t out

com

es fr

om d

ata

usin

g th

e la

ngua

ge o

f cha

nce

or li

kelih

ood

Can

I us

e th

e vo

cabu

lary

of p

roba

bilit

y

■

to p

redi

ct o

utco

mes

and

dis

cuss

and

ex

plai

n ev

ents

?

Ans

wer

a s

et o

f rel

ated

que

stio

ns b

y co

llect

ing,

sel

ectin

g an

d or

gani

sing

rele

vant

da

ta; d

raw

con

clus

ions

, usi

ng IC

T to

pre

sent

fe

atur

es, a

nd id

entif

y fu

rthe

r que

stio

ns to

ask

Sol

ve p

robl

ems

by c

olle

ctin

g, s

elec

ting,

pr

oces

sing

, pre

sent

ing

and

inte

rpre

ting

data

, us

ing

ICT

whe

re a

ppro

pria

te; d

raw

con

clus

ions

an

d id

entif

y fu

rthe

r que

stio

ns to

ask

Can

I so

rt a

nd in

terp

ret d

ata

in V

enn

and

■

Car

roll

diag

ram

s?

Can

I ex

plai

n to

som

eone

wha

t inf

orm

atio

n

■

a gr

aph

or c

hart

is s

how

ing?

Can

I dr

aw a

con

clus

ion

from

a g

raph

or

■

char

t?

Con

stru

ct fr

eque

ncy

tabl

es, p

icto

gram

s,

and

bar a

nd li

ne g

raph

s to

repr

esen

t the

fre

quen

cies

of e

vent

s an

d ch

ange

s ov

er ti

me

Con

stru

ct a

nd in

terp

ret f

requ

ency

tabl

es, b

ar

char

ts w

ith g

roup

ed d

iscr

ete

data

, and

line

gr

aphs

; int

erpr

et p

ie c

hart

s

Can

I un

ders

tand

the

mea

ning

of p

oint

s

■

betw

een

labe

lled

divi

sion

s on

gra

phs?

Can

I in

terp

ret w

hat t

he s

ecto

rs in

a p

ie

■

char

t rep

rese

nt?

Find

and

inte

rpre

t the

mod

e of

a s

et o

f dat

a D

escr

ibe

and

inte

rpre

t res

ults

and

sol

utio

ns

to p

robl

ems

usin

g th

e m

ode,

rang

e, m

edia

n an

d m

ean

Can

I w

ork

out t

he m

ode

and

rang

e

■

of a

set

of d

ata

and

use

this

to a

nsw

er

ques

tions

?


Link

s b

etw

een

Ob

ject

ives

and

Uni

ts

Usi

ng a

nd a

pp

lyin

g m

athe

mat

ics

stra

nd

Year

5 O

bjec

tives

Uni

tsYe

ar 6

Obj

ectiv

esU

nits

Sol

ve o

ne-s

tep

and

two-

step

pro

blem

s in

volv

ing

who

le n

umbe

rs a

nd d

ecim

als

and

all f

our

oper

atio

ns, c

hoos

ing

and

usin

g ap

prop

riate

ca

lcul

atio

n st

rate

gies

, inc

ludi

ng c

alcu

lato

r use

5D1,

5E1

, 5A

2,

5D2,

5A

3, 5

D3,

5E

3

Sol

ve m

ulti-

step

pro

blem

s, a

nd p

robl

ems

invo

lvin

g fra

ctio

ns, d

ecim

als

and

perc

enta

ges;

ch

oose

and

use

app

ropr

iate

cal

cula

tion

stra

tegi

es a

t eac

h st

age,

incl

udin

g ca

lcul

ator

use

6D1,

6E1

, 6A

2,

6D2,

6A

3, 6

D3,

6E

3

Rep

rese

nt a

puz

zle

or p

robl

em b

y id

entif

ying

an

d re

cord

ing

the

info

rmat

ion

or c

alcu

latio

ns

need

ed to

sol

ve it

; fin

d po

ssib

le s

olut

ions

and

co

nfirm

them

in th

e co

ntex

t of t

he p

robl

em

5E1,

5B

2, 5

E2,

5B

3, 5

E3Ta

bula

te s

yste

mat

ical

ly th

e in

form

atio

n in

a

prob

lem

or p

uzzl

e; id

entif

y an

d re

cord

the

step

s or

cal

cula

tions

nee

ded

to s

olve

it, u

sing

sym

bols

w

here

app

ropr

iate

; int

erpr

et s

olut

ions

in th

e or

igin

al c

onte

xt a

nd c

heck

thei

r acc

urac

y

6E1,

6B

2, 6

E2,

6B

3, 6

E3

Pla

n an

d pu

rsue

an

enqu

iry; p

rese

nt e

vide

nce

by c

olle

ctin

g, o

rgan

isin

g an

d in

terp

retin

g in

form

atio

n; s

ugge

st e

xten

sion

s to

the

enqu

iry

5C1,

5C

2, 5

C3

Sug

gest

, pla

n an

d de

velo

p lin

es o

f enq

uiry

; co

llect

, org

anis

e an

d re

pres

ent i

nfor

mat

ion,

in

terp

ret r

esul

ts a

nd re

view

met

hods

; ide

ntify

an

d an

swer

rela

ted

ques

tions

6C1

Exp

lore

pat

tern

s, p

rope

rtie

s an

d re

latio

nshi

ps

and

prop

ose

a ge

nera

l sta

tem

ent i

nvol

ving

nu

mbe

rs o

r sha

pes;

iden

tify

exam

ples

for w

hich

th

e st

atem

ent i

s tr

ue o

r fal

se

5B1,

5B

2, 5

B3

Rep

rese

nt a

nd in

terp

ret s

eque

nces

, pat

tern

s an

d re

latio

nshi

ps in

volv

ing

num

bers

and

sha

pes;

su

gges

t and

test

hyp

othe

ses;

con

stru

ct a

nd u

se

sim

ple

expr

essi

ons

and

form

ulae

in w

ords

then

sy

mbo

ls

6B1,

6B

2, 6

B3

Exp

lain

reas

onin

g us

ing

diag

ram

s, g

raph

s an

d te

xt; r

efin

e w

ays

of re

cord

ing

usin

g im

ages

an

d sy

mbo

ls

5A1,

5C

1, 5

E1,

5A2,

5C

2, 5

E2,

5A

3, 5

C3

Exp

lain

reas

onin

g an

d co

nclu

sion

s, u

sing

wor

ds,

sym

bols

or d

iagr

ams

as a

ppro

pria

te6A

1, 6

E1, 6

A2,

6E

2, 6

A3


Co

untin

g a

nd u

nder

stan

din

g n

umb

er s

tran

d

Year

5 O

bjec

tives

Uni

tsYe

ar 6

Obj

ectiv

esU

nits

Cou

nt fr

om a

ny g

iven

num

ber i

n w

hole

-num

ber

and

deci

mal

ste

ps, e

xten

ding

bey

ond

zero

whe

n co

untin

g ba

ckw

ards

; rel

ate

the

num

bers

to

thei

r pos

ition

on

a nu

mbe

r lin

e

5A1,

5A

2, 5

A3

Find

the

diffe

renc

e be

twee

n a

posi

tive

and

a ne

gativ

e in

tege

r, or

two

nega

tive

inte

gers

, in

cont

ext

6A1

Exp

lain

wha

t eac

h di

git r

epre

sent

s in

who

le

num

bers

and

dec

imal

s w

ith u

p to

two

plac

es,

and

part

ition

, rou

nd a

nd o

rder

thes

e nu

mbe

rs

5A1,

5A

2, 5

A3

Use

dec

imal

not

atio

n fo

r ten

ths,

hun

dred

ths

and

thou

sand

ths;

par

titio

n, ro

und

and

orde

r de

cim

als

with

up

to th

ree

plac

es, a

nd p

ositi

on

them

on

the

num

ber l

ine

6A1,

6A

2, 6

A3

Exp

ress

a s

mal

ler w

hole

num

ber a

s a

fract

ion

of a

larg

er o

ne; f

ind

equi

vale

nt fr

actio

ns; r

elat

e fra

ctio

ns to

thei

r dec

imal

repr

esen

tatio

ns

5E1,

5E

2, 5

E3E

xpre

ss a

larg

er w

hole

num

ber a

s a

fract

ion

of

a sm

alle

r one

; sim

plify

frac

tions

by

canc

ellin

g co

mm

on fa

ctor

s; o

rder

a s

et o

f fra

ctio

ns b

y co

nver

ting

them

to fr

actio

ns w

ith a

com

mon

de

nom

inat

or

6E1,

6E

2, 6

E3

Und

erst

and

perc

enta

ge a

s th

e nu

mbe

r of p

arts

in

eve

ry 1

00 a

nd e

xpre

ss te

nths

and

hun

dred

ths

as p

erce

ntag

es

5E2,

5E3

Exp

ress

one

qua

ntity

as

a pe

rcen

tage

of

anot

her;

find

equi

vale

nt p

erce

ntag

es, d

ecim

als

and

fract

ions

6E2,

6E3

Use

seq

uenc

es to

sca

le n

umbe

rs u

p or

dow

n;

solv

e pr

oble

ms

invo

lvin

g pr

opor

tions

of

quan

titie

s

5E2,

5E3

Sol

ve s

impl

e pr

oble

ms

invo

lvin

g di

rect

pr

opor

tion

by s

calin

g qu

antit

ies

up o

r dow

n6E

1, 6

E2,

6E3


Kno

win

g a

nd u

sing

num

ber

fact

s st

rand

Year

5 O

bjec

tives

Uni

tsYe

ar 6

Obj

ectiv

esU

nits

Use

kno

wle

dge

of p

lace

val

ue a

nd a

dditi

on a

nd

subt

ract

ion

of tw

o-di

git n

umbe

rs to

der

ive

sum

s an

d di

ffere

nces

and

dou

bles

and

hal

ves

of

dec

imal

s

5A1,

5A

2, 5

B2,

5E

2, 5

A3,

5B

3U

se k

now

ledg

e of

pla

ce v

alue

and

mul

tiplic

atio

n fa

cts

to 1

0 ×

10

to d

eriv

e re

late

d m

ultip

licat

ion

and

divi

sion

fact

s in

volv

ing

deci

mal

s

6A1,

6B

1, 6

E1,

6A2,

6B

2, 6

B3,

6E

3

Rec

all q

uick

ly m

ultip

licat

ion

fact

s to

10

× 1

0 an

d us

e th

em to

mul

tiply

pai

rs o

f mul

tiple

s of

10

and

100

; der

ive

quic

kly

corr

espo

ndin

g di

visi

on fa

cts

5A1,

5B

1, 5

E1,

5A2,

5B

2, 5

A3,

5B

3

Use

kno

wle

dge

of m

ultip

licat

ion

fact

s to

der

ive

quic

kly

squa

res

of n

umbe

rs to

12

× 1

2 an

d th

e co

rres

pond

ing

squa

res

of m

ultip

les

of 1

0

6B1,

6B

2, 6

B3

Iden

tify

pairs

of f

acto

rs o

f tw

o-di

git w

hole

nu

mbe

rs a

nd fi

nd c

omm

on m

ultip

les

5A1,

5B

1, 5

E1,

5A2

Rec

ogni

se th

at p

rime

num

bers

hav

e on

ly tw

o fa

ctor

s an

d id

entif

y pr

ime

num

bers

less

than

10

0; fi

nd th

e pr

ime

fact

ors

of tw

o-di

git n

umbe

rs

6B1,

6B

2, 6

B3

Use

kno

wle

dge

of ro

undi

ng, p

lace

val

ue,

num

ber f

acts

and

inve

rse

oper

atio

ns to

est

imat

e an

d ch

eck

calc

ulat

ions

5A1,

5B

1, 5

A2,

5B

2, 5

D2,

5A

3,

5B3,

5D

3

Use

app

roxi

mat

ions

, inv

erse

ope

ratio

ns a

nd

test

s of

div

isib

ility

to e

stim

ate

and

chec

k re

sults

6A1,

6B

1, 6

D1,

6A

2, 6

B2,

6D

2,

6A3,

6B

3, 6

D3


Cal

cula

ting

str

and

Year

5 O

bjec

tives

Uni

tsYe

ar 6

Obj

ectiv

esU

nits

Use

und

erst

andi

ng o

f pla

ce v

alue

to m

ultip

ly a

nd

divi

de w

hole

num

bers

and

dec

imal

s by

10,

100

or

100

0

5A1,

5D

1, 5

A2,

5D

2C

alcu

late

men

tally

with

inte

gers

and

dec

imal

s:

U.t

± U

.t, T

U ×

U, T

U ÷

U, U

.t ×

U, U

.t ÷

U6A

1, 6

D1,

6A

2,

6D2,

6A

3, 6

D3

Ext

end

men

tal m

etho

ds fo

r who

le-n

umbe

r ca

lcul

atio

ns5A

1, 5

E1, 5

A2

Use

effi

cien

t writ

ten

met

hods

to a

dd a

nd

subt

ract

who

le n

umbe

rs a

nd d

ecim

als

with

up

to

two

plac

es

5A1,

5B

1, 5

A2,

5D

2, 5

B3,

5D

3U

se e

ffici

ent w

ritte

n m

etho

ds to

add

and

su

btra

ct in

tege

rs a

nd d

ecim

als,

to m

ultip

ly a

nd

divi

de in

tege

rs a

nd d

ecim

als

by a

one

-dig

it in

tege

r, an

d to

mul

tiply

two-

digi

t and

thre

e-di

git

inte

gers

by

a tw

o-di

git i

nteg

er

6D1,

6E1

, 6A

2,

6D2,

6A

3, 6

D3,

6E

3

Ref

ine

and

use

effic

ient

writ

ten

met

hods

to

mul

tiply

and

div

ide

HTU

× U

, TU

× T

U, U

.t ×

U

and

HTU

÷ U

5E1,

5D

2, 5

A3,

5D

3, 5

E3

Find

frac

tions

usi

ng d

ivis

ion,

and

per

cent

ages

of

num

bers

and

qua

ntiti

es5E

1, 5

E2,

5E3

Rel

ate

fract

ions

to m

ultip

licat

ion

and

divi

sion

; ex

pres

s a

quot

ient

as

a fra

ctio

n or

dec

imal

; fin

d fra

ctio

ns a

nd p

erce

ntag

es o

f who

le-n

umbe

r qu

antit

ies

6E1,

6E

2, 6

E3

Use

a c

alcu

lato

r to

solv

e pr

oble

ms,

incl

udin

g th

ose

invo

lvin

g de

cim

als

or fr

actio

ns;

inte

rpre

t the

dis

play

cor

rect

ly in

the

cont

ext o

f m

easu

rem

ent

5D1,

5E1

, 5A

2,

5D2,

5E

2, 5

A3,

5B

3, 5

D3

Use

a c

alcu

lato

r to

solv

e pr

oble

ms

invo

lvin

g m

ulti-

step

cal

cula

tions

6A1,

6D

1, 6

E1,

6A2,

6B

2, 6

C2,

6D

2, 6

E2,

6A

3,

6B3,

6C

3, 6

D3,

6E

3


Und

erst

and

ing

sha

pe

stra

nd

Year

5 O

bjec

tives

Uni

tsYe

ar 6

Obj

ectiv

esU

nits

Iden

tify,

vis

ualis

e an

d de

scrib

e pr

oper

ties

of

rect

angl

es, t

riang

les,

regu

lar p

olyg

ons

and

3-D

so

lids;

use

kno

wle

dge

of p

rope

rtie

s to

dra

w

2-D

sha

pes,

and

to id

entif

y an

d dr

aw n

ets

of 3

-D

shap

es

5B1,

5B

2, 5

B3

Des

crib

e, id

entif

y an

d vi

sual

ise

para

llel a

nd

perp

endi

cula

r edg

es o

r fac

es; u

se th

ese

prop

ertie

s to

cla

ssify

2-D

sha

pes

and

3-D

sol

ids

6B1,

6B

2, 6

B3

Mak

e an

d dr

aw s

hape

s w

ith in

crea

sing

acc

urac

y an

d ap

ply

know

ledg

e of

thei

r pro

pert

ies

6B1,

6B

2, 6

B3

Com

plet

e pa

tter

ns w

ith u

p to

two

lines

of

sym

met

ry; d

raw

the

posi

tion

of a

sha

pe a

fter a

re

flect

ion

or tr

ansl

atio

n

5B2,

5D

3V

isua

lise

and

draw

on

grid

s of

diff

eren

t typ

es

whe

re a

sha

pe w

ill be

afte

r ref

lect

ion,

afte

r tr

ansl

atio

ns, o

r afte

r rot

atio

n th

roug

h 90

˚ or 1

80˚

abou

t its

cen

tre

or o

ne o

f its

ver

tices

6D2

Rea

d an

d pl

ot c

oord

inat

es in

the

first

qua

dran

t; re

cogn

ise

para

llel a

nd p

erpe

ndic

ular

line

s in

gr

ids

and

shap

es; u

se a

set

-squ

are

and

rule

r to

draw

sha

pes

with

per

pend

icul

ar o

r par

alle

l sid

es

5D1,

5D

2, 5

D3

Use

coo

rdin

ates

in th

e fir

st q

uadr

ant t

o dr

aw,

loca

te a

nd c

ompl

ete

shap

es th

at m

eet g

iven

pr

oper

ties

6D2

Est

imat

e, d

raw

and

mea

sure

acu

te a

nd o

btus

e an

gles

usi

ng a

n an

gle

mea

sure

r or p

rotr

acto

r to

a su

itabl

e de

gree

of a

ccur

acy;

cal

cula

te a

ngle

s in

a s

trai

ght l

ine

5D2,

5D

3E

stim

ate

angl

es, a

nd u

se a

pro

trac

tor t

o m

easu

re a

nd d

raw

them

, on

thei

r ow

n an

d in

sh

apes

; cal

cula

te a

ngle

s in

a tr

iang

le o

r aro

und

a po

int

6D2


Mea

suri

ng s

tran

d

Year

5 O

bjec

tives

Uni

tsYe

ar 6

Obj

ectiv

esU

nits

Rea

d, c

hoos

e, u

se a

nd re

cord

sta

ndar

d m

etric

un

its to

est

imat

e an

d m

easu

re le

ngth

, wei

ght

and

capa

city

to a

sui

tabl

e de

gree

of a

ccur

acy;

co

nver

t lar

ger t

o sm

alle

r uni

ts u

sing

dec

imal

s to

on

e pl

ace

5C1,

5D

1, 5

C2,

5D

2, 5

C3,

5D

3S

elec

t and

use

sta

ndar

d m

etric

uni

ts o

f mea

sure

an

d co

nver

t bet

wee

n un

its u

sing

dec

imal

s to

tw

o pl

aces

6C1,

6D

1, 6

C2,

6D

2, 6

C3,

6D

3

Inte

rpre

t a re

adin

g th

at li

es b

etw

een

two

unnu

mbe

red

divi

sion

s on

a s

cale

5C1,

5D

1, 5

C2,

5D

2, 5

C3,

5D

3R

ead

and

inte

rpre

t sca

les

on a

rang

e of

m

easu

ring

inst

rum

ents

, rec

ogni

sing

that

th

e m

easu

rem

ent m

ade

is a

ppro

xim

ate

and

reco

rdin

g re

sults

to a

requ

ired

degr

ee o

f ac

cura

cy; c

ompa

re re

adin

gs o

n di

ffere

nt s

cale

s,

for e

xam

ple

whe

n us

ing

diffe

rent

inst

rum

ents

6C1,

6D

1, 6

C2,

6C

3, 6

D3

Dra

w a

nd m

easu

re li

nes

to th

e ne

ares

t m

illim

etre

; mea

sure

and

cal

cula

te th

e pe

rimet

er

of re

gula

r and

irre

gula

r pol

ygon

s; u

se th

e fo

rmul

a fo

r the

are

a of

a re

ctan

gle

to c

alcu

late

th

e re

ctan

gle’

s ar

ea

5D1,

5D

2, 5

D3

Cal

cula

te th

e pe

rimet

er a

nd a

rea

of re

ctilin

ear

shap

es; e

stim

ate

the

area

of a

n irr

egul

ar s

hape

by

cou

ntin

g sq

uare

s

6D1,

6D

3

Rea

d tim

etab

les

and

time

usin

g 24

-hou

r clo

ck

nota

tion;

use

a c

alen

dar t

o ca

lcul

ate

time

inte

rval

s5D

1, 5

D3


Han

dlin

g d

ata

stra

nd

Year

5 O

bjec

tives

Uni

tsYe

ar 6

Obj

ectiv

esU

nits

Des

crib

e th

e oc

curr

ence

of f

amilia

r eve

nts

usin

g th

e la

ngua

ge o

f cha

nce

or li

kelih

ood

5C2,

5C

3D

escr

ibe

and

pred

ict o

utco

mes

from

dat

a us

ing

the

lang

uage

of c

hanc

e or

like

lihoo

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