year 3 - norfolk&suffolk hub · pdf filenorfolk and suffolk primary assessment working...

27
Norfolk and Suffolk Primary Assessment Working Party This project was led by the Educator Solutions Mathematics Team and funded by the Norfolk and Suffolk Maths Hub. Guidance on formative assessment materials to exemplify fluency, reasoning and problem solving Year 3 For more information and to make a booking www.educatorsolutions.org.uk or call 01603 307710

Upload: duongtu

Post on 06-Mar-2018

215 views

Category:

Documents


2 download

TRANSCRIPT

Page 1: YEAR 3 - Norfolk&Suffolk Hub · PDF fileNorfolk and Suffolk Primary Assessment Working Part y This project was led by the Educator Solutions Math ematics Team and funded by the Norfolk

No

rfolk

an

d S

uffo

lk P

rima

ry A

ss

es

sm

en

t Wo

rkin

g P

arty

Th

is p

roje

ct w

as

led

by th

e E

du

ca

tor S

olu

tion

s M

ath

em

atic

s T

ea

m

an

d fu

nd

ed

by th

e N

orfo

lk a

nd

Su

ffolk

Ma

ths

Hu

b.

Gu

ida

nc

e o

n fo

rma

tive

as

se

ss

me

nt m

ate

rials

to e

xe

mp

lify flu

en

cy, re

as

on

ing

an

d p

rob

lem

so

lvin

g

Ye

ar 3

For m

ore

info

rmatio

n a

nd to

mak

e a

bo

okin

g

ww

w.e

du

ca

tors

olu

tion

s.o

rg.u

k o

r ca

ll 01

60

3 3

077

10

Page 2: YEAR 3 - Norfolk&Suffolk Hub · PDF fileNorfolk and Suffolk Primary Assessment Working Part y This project was led by the Educator Solutions Math ematics Team and funded by the Norfolk

De

ar C

olle

agu

e

Ple

ase

find

atta

ch

ed

gu

ida

nce

writte

n b

y N

orfo

lk a

nd

Suffo

lk P

rima

ry te

ach

ers

to h

elp

un

pic

k

wh

at flu

en

cy, re

ason

ing a

nd

pro

ble

m s

olv

ing lo

oks lik

e in

ye

ar g

rou

ps 1

-6.

Ra

tion

ale

The

se

mate

rials

we

re p

rod

uce

d b

ecau

se

teach

ers

hig

hlig

hte

d a

ga

p o

n h

ow

to te

ach a

nd

asse

ss th

e P

urp

ose

of S

tud

y a

nd

the

thre

e a

ims o

f the

Prim

ary

ma

the

ma

tics c

urric

ulu

m (D

fE,

20

13

). Pre

vio

us in

ca

rna

tion

s o

f the

Prim

ary

Ma

them

atic

s N

atio

na

l Cu

rricu

lum

ha

ve

alw

ays

inclu

de

d g

uid

an

ce

(and

usua

lly o

bje

ctiv

es) o

n th

is a

rea

, alth

ou

gh

the

y h

ave

be

en k

no

wn

un

de

r

ma

ny d

iffere

nt n

am

es s

uch

as u

sin

g a

nd

ap

ply

ing, w

ork

ing m

ath

em

atic

ally

, pro

ble

m s

olv

ing o

r

inve

stig

atio

ns.

Alth

ou

gh

ea

ch

ye

ar g

rou

p c

on

tain

s o

bje

ctiv

es fo

r the

con

ten

t of th

e n

ew

cu

rricu

lum

(DfE

, 20

13

),

the

re a

re fe

w re

fere

nce

s in

the

bo

dy o

f the N

atio

na

l Cu

rricu

lum

tha

t exe

mp

lify flu

en

cy,

rea

so

nin

g o

r pro

ble

m s

olv

ing, a

nd

ye

t the

se

thre

e a

ims w

ill be

ob

se

rve

d, e

xa

min

ed

an

d te

ste

d.

In a

dd

ition to

the

se

mea

su

res th

ere

are

ma

ny (e

.g. N

RIC

H) w

ho

be

lieve

the

se a

ims a

re

pa

rticu

larly

imp

orta

nt w

ithin

the

lea

rnin

g o

f ma

them

atic

s fo

r all c

hild

ren

.

Org

an

isa

tion

of m

ate

rial

The

ma

teria

ls h

ave

bee

n p

rod

uce

d in

sin

gle

age

ye

ar g

rou

ps.

Tea

ch

ers

loo

ked

at a

nd

iden

tified

the b

ig id

ea

s in

ma

them

atic

s. T

en

big

ide

as w

ere

iden

tified

acro

ss e

ve

ry y

ea

r gro

up

. Th

ese

we

re in

form

ed

by th

e N

atio

na

l Cu

rricu

lum

ob

jectiv

es, th

e N

AH

T

KP

I’s (k

ey p

erfo

rma

nce

ind

icato

rs) a

nd

oth

er s

ou

rce

s s

uch

as N

CE

TM

an

d N

RIC

H. T

he

se

big

ide

as a

re o

nly

su

gge

stio

ns a

nd

co

uld

be

ch

ange

d, d

ele

ted o

r ad

ded

to d

ep

en

din

g o

n s

cho

ol

sp

ecific

crite

ria a

nd

foci.

Un

de

r ea

ch

big

ide

a a

re th

ree

bo

xe

s fo

r fluency, re

aso

nin

g a

nd

pro

ble

m s

olv

ing. T

he

first p

art o

f

ea

ch

bo

x in

clu

de

s s

om

e e

xe

mp

lificatio

n fo

r ea

ch

aim

. Th

ese s

tate

me

nts

are

inte

nde

d to

help

su

ppo

rt the

un

de

rsta

nd

ing o

f ea

ch

aim

with

in th

e b

ig id

ea

. Ho

we

ve

r, as a

bo

ve

, the

y a

re n

ot a

defin

itive

or c

om

ple

te lis

t and

tea

che

rs s

hou

ld c

ha

nge

an

d a

lter th

em

acco

rdin

gly

.

The

se

co

nd p

art o

f the b

ox in

clu

de

s s

om

e p

ossib

le a

ctiv

ities th

at c

ou

ld h

elp

sup

po

rt the

exe

mp

lifica

tion

of e

ach a

im. T

he

se

activ

ities h

ave

be

en s

ele

cte

d b

y th

e te

ache

rs a

nd

are

the

re

to s

up

po

rt the te

ach

ing a

nd le

arn

ing o

f ea

ch

aim

, bu

t are

no

t me

an

t to b

eco

me

a c

he

cklis

t.

Ma

ny o

f the a

ctiv

ities a

re th

e te

ach

er’s

ow

n, b

ut if th

ey b

elo

ng to

a s

ou

rce

this

ha

s b

ee

n

ackn

ow

led

ge

d u

nd

ern

ea

th th

e a

ctiv

ity. H

ow

eve

r, wh

ile th

is s

ectio

n is

usefu

l, the

bo

x w

hic

h

offe

rs p

ossib

le e

xe

mp

lificatio

n fo

r ea

ch

aim

is m

ore

impo

rtan

t in u

nde

rsta

nd

ing th

e p

urp

ose o

f

stu

dy o

f the

ma

them

atic

s c

urric

ulu

m.

For m

ore

info

rmatio

n a

nd to

mak

e a

bo

okin

g

ww

w.e

du

ca

tors

olu

tion

s.o

rg.u

k o

r ca

ll 01

60

3 3

077

10

Page 3: YEAR 3 - Norfolk&Suffolk Hub · PDF fileNorfolk and Suffolk Primary Assessment Working Part y This project was led by the Educator Solutions Math ematics Team and funded by the Norfolk

Ca

se

Stu

dy

Ca

se

Stu

dy

Wo

rkin

g P

arty

Th

is p

roje

ct w

as le

d b

y th

e E

du

ca

tor S

olu

tions M

ath

em

atic

s T

eam

(Alis

on

Bo

rthw

ick) a

nd

fun

de

d b

y th

e N

orfo

lk a

nd

Suffo

lk M

ath

s H

ub .

Pe

op

le w

ho c

ontrib

ute

d to

the m

ate

rials

Co

pyrig

ht a

nd

us

ag

e o

f the

ma

teria

ls

Re

pro

du

ce

d w

ith k

ind

pe

rmis

sio

n o

f NR

ICH

, Un

ive

rsity

of C

am

brid

ge

.

Exa

mp

les fro

m T

ea

ch

ing

for M

aste

ry m

ate

rials

, text ©

Cro

wn

Co

pyrig

ht 2

015

, illustra

tion

an

d

de

sig

n ©

Oxfo

rd U

niv

ers

ity P

ress 2

01

5, a

re re

pro

du

ce

d w

ith th

e k

ind

pe

rmis

sio

n o

f the

NC

ET

M

an

d O

xfo

rd U

niv

ers

ity P

ress. T

he T

ea

ch

ing

for M

aste

ry m

ate

rials

ca

n b

e fo

und

in fu

ll on th

e

NC

ET

M w

eb

site

ww

w.n

ce

tm.o

rg.u

k/re

so

urc

es/4

668

9 a

nd

the

Oxfo

rd O

wl w

eb

site

http

s://

ww

w.o

xfo

rdo

wl.c

o.u

k/fo

r-s

ch

oo

l/18

16

With

in th

e p

ossib

le a

ctiv

ities to

exe

mp

lify flu

en

cy, re

aso

nin

g a

nd

pro

ble

m s

olv

ing, te

ach

er’s

ch

ose

activ

ities fro

m a

va

riety

of s

ou

rce

s, in

clu

din

g th

eir o

wn

wh

ich

the

y fe

lt sup

po

rted

this

ma

them

atic

al a

rea. H

ow

eve

r this

do

es n

ot m

ea

n th

at th

ese

activ

ities a

re lim

ited

to th

is s

ectio

n,

an

d w

ou

ld b

e s

uita

ble

for u

se

in e

ach

are

a o

f flue

ncy, re

ason

ing a

nd p

rob

lem

so

lvin

g.

On

be

ha

lf of T

he

No

rfolk

an

d S

uffo

lk P

rima

ry A

sse

ssm

en

t Wo

rkin

g P

arty

Be

st w

ish

es,

Alis

on

Bo

rthw

ick

alis

on

.bo

rthw

ick@

ed

uca

tors

olu

tion

s.o

rg.u

k

David

Bo

ard

(St J

oh

n’s

Prim

ary

, No

rfolk

) L

orn

a D

en

ham

(Saxm

un

dh

am

Prim

ary

, Su

ffolk

)

Alis

on

Bo

rthw

ick (M

ath

em

atic

s A

dvis

er)

Vic

toria

Gate

sh

ill (Harle

sto

n P

rimary

, No

rfolk

)

Liz

Bo

nn

ely

kke (S

tan

ton

Prim

ary

, Su

ffolk

) R

os M

iller (H

eth

ers

ett J

un

ior, N

orfo

lk)

Hele

n C

hatfie

ld (C

aven

dis

h P

rimary

, Su

ffolk

) C

herri M

osele

y (F

reela

nce C

on

su

ltan

t)

Sh

eila

Day (W

ind

mill F

ed

era

tion

, No

rfolk

) H

ele

n N

orris

(Du

ssin

gd

ale

Prim

ary

, No

rfolk

)

Refe

ren

ces

Departm

ent fo

r Educatio

n (D

fE), (2

013), M

ath

em

atic

s

Pro

gra

mm

e o

f Stu

dy K

ey S

tages 1

an

d 2

. Lon

don

: DfE

.

McIn

tosh, J

. (201

5) F

inal R

eport o

f the C

om

mis

sio

n o

n

Assessm

ent W

ithou

t Leve

ls. L

ond

on: C

row

n C

opyrig

ht.

ww

w.N

RIC

H.m

ath

s.o

rg w

ww

.ncetm

.org

.uk

For m

ore

info

rmatio

n a

nd to

mak

e a

bo

okin

g

ww

w.e

du

ca

tors

olu

tion

s.o

rg.u

k o

r ca

ll 01

60

3 3

077

10

Page 4: YEAR 3 - Norfolk&Suffolk Hub · PDF fileNorfolk and Suffolk Primary Assessment Working Part y This project was led by the Educator Solutions Math ematics Team and funded by the Norfolk

Big

ide

as in

Ye

ar 3

1.

Co

un

t, com

pa

re a

nd

ord

er n

um

be

rs (u

p to

100

0).

2.

Re

co

gn

ise

and

use

the p

ositio

na

l, ad

ditiv

e a

nd

mu

ltiplic

ativ

e a

sp

ects

of p

lace

va

lue

(3 d

igit

nu

mb

ers

an

d to

on

e d

ecim

al p

lace

).

3.

De

ve

lop

num

be

r se

nse

to s

upp

ort m

en

tal c

alc

ula

tion.

4.

Ad

d a

nd s

ubtra

ct n

um

be

rs, re

co

gn

isin

g th

at th

ese

are

inve

rse

op

era

tion

s (u

p to

thre

e

dig

its).

5.

Mu

ltiply

an

d d

ivid

e n

um

be

rs, re

co

gn

isin

g th

at th

ese

are

inve

rse

opera

tion

s (fo

r at le

ast th

e

2, 3

, 4, 5

, 8 a

nd

10

time

s ta

ble

s a

nd

2 d

igit b

y 1

dig

it).

6.

Use

alg

eb

ra to

exp

ress p

atte

rns a

nd

gen

era

lisa

tion

s w

ithin

ma

them

atic

s.

7.

(a) R

eco

gn

ise

fractio

ns o

f sha

pe

s, o

bje

cts

and

qu

an

tities (u

nit a

nd

no

n-u

nit).

(b) C

alc

ula

te w

ith fra

ctio

ns (a

dd

an

d s

ub

tract w

ith th

e s

am

e d

eno

min

ato

r with

in a

wh

ole

).

8.

Ch

oo

se, u

se a

nd

com

pa

re a

va

riety

of u

nits

of m

ea

su

re to

an

app

rop

riate

leve

l of

accu

racy.

9.

Re

co

gn

ise

and

use

the p

rop

ertie

s o

f sh

ap

es, in

clu

din

g p

ositio

n a

nd d

irectio

n.

10

.

Co

llect, o

rga

nis

e a

nd in

terp

ret d

ata

.

Ex

am

ple

s from

Te

ach

ing

for M

aste

ry m

ate

rials, te

xt ©

Cro

wn

Co

py

righ

t 20

15

, illustra

�o

n a

nd

de

sign

© O

xfo

rd U

niv

ersity

Pre

ss

20

15

, are

rep

rod

uce

d w

ith th

e k

ind

pe

rmissio

n o

f the

NC

ET

M a

nd

Ox

ford

Un

ive

rsity P

ress. T

he

Te

ach

ing

for M

aste

ry m

ate

rials

can

be

fou

nd

in fu

ll on

the

NC

ET

M w

eb

site w

ww

.nce

tm.o

rg.u

k/re

sou

rces/4

66

89

an

d th

e O

xfo

rd O

wl w

eb

siteh

)p

s://

ww

w.o

xfo

rdo

wl.co

.uk

/for-sch

oo

l/18

16

Page 5: YEAR 3 - Norfolk&Suffolk Hub · PDF fileNorfolk and Suffolk Primary Assessment Working Part y This project was led by the Educator Solutions Math ematics Team and funded by the Norfolk

Year 3:

Big idea 1: Count, compare and order numbers (up to 1000)

Fluency Reasoning Problem solving

Exemplification of fluency

• Count forwards and backwards in

steps of different sizes to 1000

• Count in multiples of 4, 8, 50 and

100

• Compare and order numbers up to 1000 using different representations

Exemplification of reasoning

• Explain and reason about patterns in number

sequences

• Identify the missing number in a sequence

• Use mathematical language when comparing

numbers

Exemplification of problem solving

• Solve problems in context (using

language such as greater, less than etc)

• Recognise mathematical connections

between numbers and patterns of

numbers

• Decide how to check if your conjecture

is correct

For more information and to make a booking

www.educatorsolutions.org.uk or call 01603 307710

Page 6: YEAR 3 - Norfolk&Suffolk Hub · PDF fileNorfolk and Suffolk Primary Assessment Working Part y This project was led by the Educator Solutions Math ematics Team and funded by the Norfolk

Year 3:

Big idea 1: Count, compare and order numbers (up to 1000)

Possible activities to exemplify fluency

• Complete the sequences

45, __, __, __, __, __, __, __, 53

95, 96, 97, 98, ___, ___, ___, ___,

37, __, __, __, __, __, 97

79, 89, 99, ___, ___, ___,

345, ___, ___, ___, ___, ___, 945

426, ___, ___, ___, ___, ___, ___, 496

775, 785, 795, ___, ____, ____,

Possible activities to exemplify reasoning

• What could the tens digit of these number

sequences be and why?

__3, __3, __3, __3, __3, __3, __3,

__0, __5, __0, __5, __0

__2, __4, __6, __8, __0

Can you think of more ways to complete each?

Possible activities to exemplify problem solving

• Mystery number activities e.g

My numbers is a multiple of 50. It is between 200 and 400. It is not a multiple of 100. The hundreds digit is odd. What is my number?

For more information and to make a booking

www.educatorsolutions.org.uk or call 01603 307710

Page 7: YEAR 3 - Norfolk&Suffolk Hub · PDF fileNorfolk and Suffolk Primary Assessment Working Part y This project was led by the Educator Solutions Math ematics Team and funded by the Norfolk

Big idea 2:

Recognise the positional, additive and multiplicative aspects of place value (of 3 digit numbers and

to one decimal place)

Fluency Reasoning Problem solving

Exemplification of fluency • Understand that e.g 847 is 8

hundreds, 4 tens and 7 ones and

this gives the additive value of the

whole number

• Understand the position of 0 as a

place holder

• Understand the positional place

value of each digit

• Understand that in the number 847

we can find the multiplicative place

value of each digit by multiplying

each digit by the column it is in eg 8

x 100 = 800

Exemplification of reasoning

• Explain and justify statements about positions

of digits

• Convince a friend of the value of each digit in

a three-digit number

• Explain why 640 is ten times bigger than 64

Exemplification of problem solving

• Use understanding of the value and

position of digits to solve problems

• Work systematically to find patterns in

numbers

• Use apparatus to represent problems

and organise thinking

For more information and to make a booking

www.educatorsolutions.org.uk or call 01603 307710

Page 8: YEAR 3 - Norfolk&Suffolk Hub · PDF fileNorfolk and Suffolk Primary Assessment Working Part y This project was led by the Educator Solutions Math ematics Team and funded by the Norfolk

Big idea 2:

Recognise the positional, additive and multiplicative aspects of place value (of 3 digit numbers and

to one decimal place)

Possible activities to exemplify fluency

• Write these numbers correctly

(when read aloud)

735

834

518

750

803

607

701.4

530.8

Possible activities to exemplify problem solving

• ‘Always, sometimes, never – a 5 is worth

more than a 7’.

• A number with a 9 in the hundreds position is

greater than a number 3 in the hundreds

position.

• Is this statement always/sometimes/never

true?

Possible activities to exemplify problem

solving

• Use 1, 2 or 3 arrow cards from below to

make as many numbers 2 or 3 digit

numbers as possible….

3 0 0 7 0 8

For more information and to make a booking

www.educatorsolutions.org.uk or call 01603 307710

Page 9: YEAR 3 - Norfolk&Suffolk Hub · PDF fileNorfolk and Suffolk Primary Assessment Working Part y This project was led by the Educator Solutions Math ematics Team and funded by the Norfolk

Big idea 3:

Develop number sense to support mental calculation

Fluency Reasoning Problem solving

Exemplification of fluency

• Adapt methods of calculation to suit

the numbers allowing efficient and

flexible calculation

• Use doubles and near doubles

• Use near tens and near hundreds

• Use jottings when needed

• Use known facts to work out

unknown facts

Exemplification of reasoning

• Explain and justify statements about

strategies for calculating mentally

• Use the vocabulary of doubles, near doubles,

tens and near tens, partitioning to reason

about numbers

• Compare methods

Exemplification of problem solving

• Use the 4 operations to calculate

efficiently to eg reach a target number

• Recognise there might be more than

one possible solution and find them

• Solve problems in different ways and

discuss which is the most efficient for

you

For more information and to make a booking

www.educatorsolutions.org.uk or call 01603 307710

Page 10: YEAR 3 - Norfolk&Suffolk Hub · PDF fileNorfolk and Suffolk Primary Assessment Working Part y This project was led by the Educator Solutions Math ematics Team and funded by the Norfolk

Big idea 3:

Develop number sense to support mental calculation

Possible activities to exemplify fluency

• What is the most efficient way to

solve e.g

901 – 899?

378 + 201?

40 x 3?

Possible activities to exemplify reasoning

• Write 5, 3 digit numbers with a difference of 9

What do you notice?

655 – 8 =

495 – 8 =

725 – 8 =

645 – 8 =

Possible activities to exemplify problem

solving

• Make a model using 15 multilink cubes.

Cubes are worth

Blue – 12 points Pink – 15 points

Black – 18 points Green - 24 points

Can you make a model worth

150/200/250 points etc?

• Play ‘Countdown’

For more information and to make a booking

www.educatorsolutions.org.uk or call 01603 307710

Page 11: YEAR 3 - Norfolk&Suffolk Hub · PDF fileNorfolk and Suffolk Primary Assessment Working Part y This project was led by the Educator Solutions Math ematics Team and funded by the Norfolk

Big idea 4:

Add and subtract numbers, recognising that these are inverse operations (with up to three digits)

Fluency Reasoning Problem solving

Exemplification of fluency

• Mentally add and subtract single

digits and multiples of 10 to three

digit numbers

• Use number bonds to calculate

• Partition numbers to add and

subtract

• Choose and use appropriate

strategies for addition and

subtraction, depending on the

numbers involved, working flexibly

• Understand and use the fact that

addition is the inverse of

subtraction and vice versa

• Understand that addition is commutative and subtraction is not

Exemplification of reasoning

• Use rounding and approximation to estimate answers and make decisions

• Use trial and improvement to make decisions and justify

• Explain and correct mistakes within a calculation

• Use the mathematical language for addition and subtraction

Exemplification of problem solving

• Solve problems involving number, money and measures

• Choose and use appropriate operations and strategies

• Use different representations to solve problems e.g. Bar Model

For more information and to make a booking

www.educatorsolutions.org.uk or call 01603 307710

Page 12: YEAR 3 - Norfolk&Suffolk Hub · PDF fileNorfolk and Suffolk Primary Assessment Working Part y This project was led by the Educator Solutions Math ematics Team and funded by the Norfolk

Big idea 4:

Add and subtract numbers, recognising that these are inverse operations (with up to three digits)

Possible activities to exemplify fluency

• Which of these number sentences

have an answer that is between 50

and 60

100 – 50

200 - 150

174 - 119

333 – 276

932 – 871

Write 3 more subtraction sentences

with an answer between 50 and 60

Source: adapted from NCETM

Possible activities to exemplify reasoning

• Use these digits to complete the number sentences

2, 3, 4, 5, 6, 7, 8, 9

Possible activities to exemplify problem

solving

• Sam went to the toy shop with £150. He

left with between £40 and £20 change.

What could he have bought?

Scooter £119

Ball £8

Computer game £63

Large lego set £48

Doll £14

+ =

+ =

+ = 1 0

+ = 1 1

+ =

For more information and to make a booking

www.educatorsolutions.org.uk or call 01603 307710

Page 13: YEAR 3 - Norfolk&Suffolk Hub · PDF fileNorfolk and Suffolk Primary Assessment Working Part y This project was led by the Educator Solutions Math ematics Team and funded by the Norfolk

Big idea 5:

Multiply and divide numbers, recognising that these are inverse operations (using 2, 3, 4, 5, 8 and 10

x table and 2 digits by 1 digit

Fluency Reasoning Problem solving

Exemplification of fluency • Count in multiples of 2,3,4,5,8 and

10

• Know or quickly derive

multiplication and division facts for

these tables

• Represent multiplication and

division facts as arrays

• Use inverses to check calculations

and find a missing number

• Multiply a two-digit by one-digit

number

Exemplification of reasoning

• Explain how multiples and factors support multiplication and division

• Use the language of multiplication and division

• Use apparatus and pictures to explain thinking

Exemplification of problem solving

• Solve problems involving measures and

money in context using multiplication

and division

• Choose and use appropriate methods

and strategies

• Be able to derive all 8 facts in a fact

family

For more information and to make a booking

www.educatorsolutions.org.uk or call 01603 307710

Page 14: YEAR 3 - Norfolk&Suffolk Hub · PDF fileNorfolk and Suffolk Primary Assessment Working Part y This project was led by the Educator Solutions Math ematics Team and funded by the Norfolk

Big idea 5:

Multiply and divide numbers, recognising that these are inverse operations (using 2, 3, 4, 5, 8 and 10

x table and 2 digits by 1 digit

Possible activities to exemplify fluency

• Missing numbers

• 24 = x

• Which pairs of numbers could be written in the boxes?

• Making links - Cards come in packs of 4. How many packs do I need to buy to get 32 cards?

Source: adapted from NCETM

Possible activities to exemplify reasoning

• Explain why 27 x 5 = 227 must be incorrect

Possible activities to exemplify problem

solving

• 3 x 4 = 12

4 x 3 = 12

12 ÷ 3 = 4

12 ÷ 4 = 3

12 = 3 x 4

12 = 4 x 3

4 = 12 ÷ 3

• Roger has 40 patio slabs. Using all of

the slabs find three different ways that

he can arrange the slabs to form a

rectangular patio.

Source: adapted from NCETM

For more information and to make a booking

www.educatorsolutions.org.uk or call 01603 307710

Page 15: YEAR 3 - Norfolk&Suffolk Hub · PDF fileNorfolk and Suffolk Primary Assessment Working Part y This project was led by the Educator Solutions Math ematics Team and funded by the Norfolk

Big idea 6:

Use algebra to express patterns and generalisations within mathematics

Fluency Reasoning Problem solving

Exemplification of fluency • Understand and use the equal sign

as the balance of an equation

• Recognise symbols/letters can represent numbers

• Use mathematical representations to notice, continue and generate patterns

• Recognise cyclical and linear patterns

Exemplification of reasoning

• Describe and explain patterns, leading to

predictions

• Give another, and another and another

example

• Use vocabulary such as repeating pattern,

replace, missing, insert

• Generalise and specify

Exemplification of problem solving

• Solve problems involving equivalence

• Solve missing number and shape

problems

• Solve problems that result in finding a generalisation

For more information and to make a booking

www.educatorsolutions.org.uk or call 01603 307710

Page 16: YEAR 3 - Norfolk&Suffolk Hub · PDF fileNorfolk and Suffolk Primary Assessment Working Part y This project was led by the Educator Solutions Math ematics Team and funded by the Norfolk

Big idea 6:

Use algebra to express patterns and generalisations within mathematics

+ 3 = 4 x

Possible activities to exemplify fluency

• How many ways can you complete

Possible activities to exemplify reasoning

• NRICH Light the Lights

http://NRICH.maths.org/7044/solution

Possible activities to exemplify problem

solving

• 6 toy cars balance 2 dolls. 4 dolls

balance 1 toy robot

• If the robot weighs 3 kg, what does

each toy car weigh?

From NCETM ‘Teaching for Mastery’

Year 3

For more information and to make a booking

www.educatorsolutions.org.uk or call 01603 307710

Page 17: YEAR 3 - Norfolk&Suffolk Hub · PDF fileNorfolk and Suffolk Primary Assessment Working Part y This project was led by the Educator Solutions Math ematics Team and funded by the Norfolk

Big idea 7(a):

Recognise fractions of shapes, objects and quantities (unit and non unit)

Fluency Reasoning Problem solving

Exemplification of fluency • Recognise fractions as numbers

• Count in steps of , • Represent fractions in different

ways • Compare and order fractions • Estimate positions between whole

numbers on a number line

• Write fractions in words and numbers

Exemplification of reasoning

• Discuss why ‘the smaller the denominator, the larger the fraction’

• Use apparatus to explain why might be smaller than ¼

• Use fractions vocabulary of numerator, denominator, part-whole and whole

Exemplification of problem solving

• Solve equivalence problems using

concrete and pictorial representations

• Find a variety of ways to make a whole

For more information and to make a booking

www.educatorsolutions.org.uk or call 01603 307710

Page 18: YEAR 3 - Norfolk&Suffolk Hub · PDF fileNorfolk and Suffolk Primary Assessment Working Part y This project was led by the Educator Solutions Math ematics Team and funded by the Norfolk

Big idea 7(a):

Recognise fractions of shapes, objects and quantities (unit and non unit)

Possible activities to exemplify fluency • Estimate these positions on a

number line

Estimate the position of 7/8 on the number line

Possible activities to exemplify reasoning • The shape is divided into 4 equal parts. Do

you agree?

Explain why.

• ½ of a small pizza may be smaller than ¼ of a big pizza

Possible activities to exemplify problem solving • Share 3 cookies between 4 people.

How much does each person get?

Can you name the parts?

Can you share them a different way? 2 1

[

[[

For more information and to make a booking

www.educatorsolutions.org.uk or call 01603 307710

Page 19: YEAR 3 - Norfolk&Suffolk Hub · PDF fileNorfolk and Suffolk Primary Assessment Working Part y This project was led by the Educator Solutions Math ematics Team and funded by the Norfolk

Big idea 7(b):

Calculate with fractions (add and subtract with the same denominator, within a whole)

Fluency Reasoning Problem solving

Exemplification of fluency

• Add and subtract fractions with the same denominator

Exemplification of reasoning

• Use apparatus to explain addition and

subtraction of fractions

• Make and test conjectures about fractions

Exemplification of problem solving

• Solve word problems using fractions in

real life contexts

For more information and to make a booking

www.educatorsolutions.org.uk or call 01603 307710

Page 20: YEAR 3 - Norfolk&Suffolk Hub · PDF fileNorfolk and Suffolk Primary Assessment Working Part y This project was led by the Educator Solutions Math ematics Team and funded by the Norfolk

Big idea 7(b):

Calculate with fractions (add and subtract with the same denominator, within a whole)

Possible activities to exemplify fluency

• Fill in the numerator to make the answer less than 1

x/8 + x/8 = x/8

Can you complete the number sentence in 3 different ways?

Source: adapted from NCETM

Possible activities to exemplify reasoning

• True or false

+ =

Explain your reasoning

Possible activities to exemplify problem

solving

• There are some cookies on a plate.

Sam and Jo take some and leave 1/8 of

the original number. What fraction could

Sam and Jo have each taken?

Extension

• If Sam ate ½ of the cookies, what

fraction did Jo take?

• If Sam ate 8 cookies ( ½) , how many

were left on the plate

For more information and to make a booking

www.educatorsolutions.org.uk or call 01603 307710

Page 21: YEAR 3 - Norfolk&Suffolk Hub · PDF fileNorfolk and Suffolk Primary Assessment Working Part y This project was led by the Educator Solutions Math ematics Team and funded by the Norfolk

Big idea 8:

Choose, use and compare a variety of units of measure, to an appropriate level of accuracy

Fluency Reasoning Problem solving

Exemplification of fluency

• Convert quickly between e.g mm,

cm and m, ml and l and g and kg

• Accurately use a range of

measuring equipment

• Compare and order a variety of

measures

• Tell the time to the minute

Exemplification of reasoning

• Justify and explain thinking about measures

• Use the vocabulary associated with

measures

• Convince a friend why you need to use

measuring equipment accurately

• Use multiplication facts to read scales

Exemplification of problem solving

• Solve problems in real life context

• Use coins and notes to find different

amounts of money

• Solve practical problems with giving

change

• Decide on the correct equipment

needed to solve a problem

• Calculate time differences

For more information and to make a booking

www.educatorsolutions.org.uk or call 01603 307710

Page 22: YEAR 3 - Norfolk&Suffolk Hub · PDF fileNorfolk and Suffolk Primary Assessment Working Part y This project was led by the Educator Solutions Math ematics Team and funded by the Norfolk

Big idea 8:

Choose, use and compare a variety of units of measure, to an appropriate level of accuracy

Possible activities to exemplify fluency

• Who is tallest – Sarah who is 1.3 m

tall or David who is 143 cm tall?

• How much heavier is a cake

weighing 1.2 kg than a cake

weighing 900g?

Possible activities to exemplify reasoning

• Would you rather have ……

e.g

¼ kg of chocolate, 200 g of chocolate or ½ of

600g bar of chocolate. .Explain your

reasoning.

Possible activities to exemplify problem

solving

• Find the number of 2l bottles needed to

fill 10 cups with 300 ml each of juice.

For more information and to make a booking

www.educatorsolutions.org.uk or call 01603 307710

Page 23: YEAR 3 - Norfolk&Suffolk Hub · PDF fileNorfolk and Suffolk Primary Assessment Working Part y This project was led by the Educator Solutions Math ematics Team and funded by the Norfolk

Big idea 9:

Recognise and use the properties of shapes including position and direction

Fluency Reasoning Problem solving

Exemplification of fluency • Name and describe the properties

of a wide range of 2D and 3D shapes

• Link shapes and pictorial representations

• Recognise angles as a measure of a turn

• Identify right, acute and obtuse angles

Exemplification of reasoning

• Justify and explain thinking in the context of shapes

• Know and use accurately the vocabulary of shape, including symmetry, edges, vertices, faces, shape names, right angel, parallel, perpendicular

• Convince someone that a shape has been reflected accurately

• Conjecture which shapes tessellate and which do not

• What is the same and different between 2D and 3 D shapes

Exemplification of problem solving

• Solve problems in the context of shape

• Systemically sort shapes in a variety of ways

• Solve problems involving position and direction

For more information and to make a booking

www.educatorsolutions.org.uk or call 01603 307710

Page 24: YEAR 3 - Norfolk&Suffolk Hub · PDF fileNorfolk and Suffolk Primary Assessment Working Part y This project was led by the Educator Solutions Math ematics Team and funded by the Norfolk

Big idea 9:

Recognise and use the properties of shapes including position and direction

Possible activities to exemplify fluency

• Make some 2d shapes on a pinboard. Describe them using appropriate vocabulary

Possible activities to exemplify reasoning

• Can you draw a triangle with: right angle?

right angles?

• Can you draw a quadrilateral with:

1 right angle?

2 right angles?

5 right angles?

No right angle?

If some of these are impossible, can you explain why?

Possible activities to exemplify problem solving

• NRICH ‘Polydron’ https://NRICH.maths.org/4

• Can you make a net, then shape of a cuboid to hold a particular object e.g matchbox, small book etc

For more information and to make a booking

www.educatorsolutions.org.uk or call 01603 307710

Page 25: YEAR 3 - Norfolk&Suffolk Hub · PDF fileNorfolk and Suffolk Primary Assessment Working Part y This project was led by the Educator Solutions Math ematics Team and funded by the Norfolk

Fluency Reasoning Problem solving

Exemplification of fluency

• Interpret and present data using

bar charts, pictograms and tables

• Collect and sort information to

create a range of charts and tables

• Use simple scales

Exemplification of reasoning

• Use the vocabulary associated with statistics

• Interpret data and draw conclusions

• Justify reasons for presenting data in a

particular way

• Justify choice of scale

Exemplification of problem solving

• Collect and present data to solve a

problem

• Present data according to audience/

purpose

Big idea 10:

Collect, organise and interpret data

For more information and to make a booking

www.educatorsolutions.org.uk or call 01603 307710

Page 26: YEAR 3 - Norfolk&Suffolk Hub · PDF fileNorfolk and Suffolk Primary Assessment Working Part y This project was led by the Educator Solutions Math ematics Team and funded by the Norfolk

Big idea 10:

Collect, organise and interpret data

Possible activities to exemplify fluency

Source: adapted from NCETM

Possible activities to exemplify reasoning

• http://NRICH.maths.org/7522

Possible activities to exemplify problem

solving

• What kind of new playground

equipment should we buy? What would

the children in our school like? What do

we need to find out? How shall we

collect our data? How shall we present

our data to School Council/

Headteacher?

Source: adapted from NCETM

For more information and to make a booking

www.educatorsolutions.org.uk or call 01603 307710

Page 27: YEAR 3 - Norfolk&Suffolk Hub · PDF fileNorfolk and Suffolk Primary Assessment Working Part y This project was led by the Educator Solutions Math ematics Team and funded by the Norfolk

Da

te p

ub

lish

ed

Au

gu

st 2

01

6

For m

ore

info

rmatio

n a

nd to

mak

e a

bo

okin

g

ww

w.e

du

ca

tors

olu

tion

s.o

rg.u

k o

r ca

ll 01

60

3 3

077

10