YEAR 2 - Norfolk&Suffolk Hub · Norfolk and Suffolk Primary Assessment Working Part y This project...

No

rfolk

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d S

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sm

en

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Th

is p

roje

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as

led

by th

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du

ca

tor S

olu

tion

s M

ath

em

atic

s T

ea

m

an

d fu

nd

ed

by th

e N

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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 2

For m

ore

info

rmatio

n a

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mak

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find

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writte

n b

y N

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nd

Suffo

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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

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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

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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.

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ore

info

rmatio

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nd to

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ath

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Bo

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y th

e N

orfo

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Suffo

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ath

s H

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ho c

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the m

ate

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pyrig

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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

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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,

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on

Bo

rthw

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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

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un

dh

am

Prim

ary

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ffolk

)

Alis

on

Bo

rthw

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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

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rfolk

)

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ren

ces

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ent fo

r Educatio

n (D

fE), (2

013), M

ath

em

atic

s

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gra

mm

e o

f Stu

dy K

ey S

tages 1

an

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. 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

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nd to

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Big

ide

as in

Ye

ar 2

1.

Co

un

t, com

pa

re a

nd

ord

er n

um

be

rs (to

at le

ast 1

00

).

2.

Re

co

gn

ise

and

use

the p

ositio

na

l an

d a

dd

itive a

sp

ects

of p

lace

va

lue (2

dig

it num

be

rs).

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 (to

at le

ast 1

00

).

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, 5

and

10

time

s ta

ble

s).

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 (h

alv

es, q

ua

rters

an

d th

irds).

8.

Be

com

e fa

milia

r with

a v

arie

ty o

f un

its o

f me

asu

re to

an

app

rop

riate

leve

l of a

ccu

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

.

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llect, o

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nis

e a

nd in

terp

ret d

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ple

s from

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ach

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xt ©

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NC

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Te

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16

Year 2 Big idea 1: Count, compare and order numbers (to at least 100)

Fluency Reasoning Problem solving

Exemplification of fluency

• Count in steps from different

starting points, forwards and

backwards

• Represent numbers conceptually

• Represent numbers pictorially

• Partition numbers in different ways

• Order numbers smallest to largest,

largest to smallest

Exemplification of reasoning

• Use mathematical language: equal to, more

than, less than, most, least

• Use the symbols of greater than, less than

and equal to, to convince whether number 5

is greater than 7

• Using counting bears, Numicon, multi link etc

convince me that 7 is odd, 34 is even.

• Reason which number comes next in the

sequence 55, 60, 65, 70 …

Exemplification of problem solving

• Choose which number to start counting

from

• Recognise and talk about patterns in a

counting sequence

• Spot a missing number in a sequence

and explain why

• Decide how to check if the answer is

correct

• Recognise mathematical connections

between numbers and patterns of

numbers

• Identify, organise and interpret information correctly

For more information and to make a booking

www.educatorsolutions.org.uk or call 01603 307710


Possible activities to exemplify fluency

• Count forwards in 2’s from 7

• Count backwards in 10’s from 93

• Number 5 represented through 5

counters, Numicon, Cuisenaire,

dice, base 10

• Number 5 marked on a number

line, 5 marks, identified on a 100

square

• 25 = 20 + 5, 10 + 10 + 5, 19 + 6

Possible activities to exemplify reasoning

• 58 is odd because the digit 5 is an odd

number. Is this true?

• Write all the 2-digit numbers greater than 40

using these digits: 2 4 6 6. How do you know

you have them all? Prove it

Source: NCETM Mastery Booklet

• Amy thinks of a number. Her number: is an

even number, is between 20 and 25, has two

different digits. What is her number? Explain

your reasoning.


Possible activities to exemplify problem solving

• Here is a list of shoe sizes for the

children in Class 2. Can you put them in

order? How will you order them?

• The numbers have fallen off the

hundred square. Can you put them

back on in the right order? Where did

you start? Which number did you start

with? Which was the hardest number to

place?

Source: NRICH - Hundred Square

• Jo has £2·29.She only has £1 coins,

10p coins and 1p coins. How many of

each coin does she have? Can you

suggest a different answer?





• Steve says, ‘My number has two tens

and five ones.’ What is Steve’s

number? Amy has two more tens than

Steve. What is her number? Sam says,

‘My number has five tens.’ What

numbers can it be? What numbers can’t

it be?


• What might the next two dominoes be in

each of these sequences? Can you

explain why you chose those two

dominoes?

Source: NRICH - Domino Sequences



Big idea 2:

Recognise and use the positional and additive aspects of place value (2 digit numbers)



• Recognise the positional place

value of each digit in tens and ones

• Recognise the additive place value

of each digit so that when the

individual values of the digits are

added together they total the whole

number (e.g. 100 + 40 + 8 = 148)

•

Understand the position of zero as

a place holder


• Explain what each digit in the number 55

represents

• Convince a friend what each digit is worth in

64

• Look at these numbers 31, 32, 33, 34, 35, 36,

37, 38, 39. What do you notice?


• Use knowledge of place value to solve

problems

• Work systematically to notice patterns

in numbers

• Invent different ways of recording to

show the place value of numbers



Big idea 2:

Recognise and use the positional and additive aspects of place value (2 digit numbers)


• The number 45 is made up of …..?

• How many tens are there in the

number 67?

• 15 could be expressed as 5 + - ?


• Explain why there are not 4 tens in the

number 36

• Use a mathematical resource to show how

the number 25 can be represented (e.g.

Numicon, bead string, counters)

• I am thinking of a number. It has 3 tens. What

could the number be?


• When we use the digit 9 in a number it

will always be a big number in value.

Write down some numbers that would

show this, and also some numbers that

would not

• If the answer has a 6 in it, what could

the number be?

• Using an abacus with two spikes, how

many numbers can you make with 4

rings?



Big idea 3:

Develop number sense to support mental calculation



• Count forwards and backwards

• Reorder numbers

• Partition numbers in as many

different ways as possible

• Bridge through multiples of 10

• Use doubles and near doubles

• Use counting and subitising skills

• Use jottings when needed


• Discuss if counting forwards or counting

backwards is easier

• Explain how a calculation can be more easily

worked out by changing the order of the

numbers

• Predict if counting forwards or counting

backwards is more efficient in solving the

question 23 + 9. Test out your conjecture

• Use the vocabulary of doubles, place value,

digits, partitioning, etc


• Solve a problem by counting and then

solve it by calculating. Which is easier?

More efficient?

• Use knowledge of numbers to solve

problems

• Use different strategies to solve

problems (e.g. a number line,

partitioning numbers, counting forwards

and backwards)

• Use the inverse to support a calculation

(e.g. 54 – 47)



Big idea 3:

Develop number sense to support mental calculation


• Count in different multiples (e.g. 2, 3, 10)

• Use a bead string to locate numbers (e.g. 26, 58, 99)

• Count back in ones/twos/10s from 85

• Calculate 26 + 37 by starting at 26, and counting in jumps of 10s to 56, and then counting in 1s or 2s to 60 and then three more to 63

• Use arrow cards (place value cards) to partition numbers. Similarly, think of a number and then represent this number using arrow cards

• Calculate 23-19 by 19 + 1 + 2

• How many different ways can you partition 26?


• Explain which numbers are close to/next to 23, 67, 82

• Reorder these numbers to use knowledge of number facts: 7 + 5 + 3

• 39 + 40 is the same as 39 doubled, add 1. Explain why?

• Which number is closer to 67: 59 or 75

• Doubling is the same as multiplying by 2: true or false?

• Explain how many ones are in the number 54. How do you know?

• Captain Conjecture says ‘An odd number + an odd number = an even number’. Is this sometimes, always or never true? Explain your reasoning?

Source: NCETM Mastery Booklet.

Possible activities to exemplify problem

solving

• Solve 8 + 12 + 24 by counting and then

by calculating

• Roll a 1-6 dice twice. Use any

calculation strategy to make a number

on a 1-100 square. Can you get three

numbers in a row?

• Make a two digit number where the

ones digit is 4 less than the tens digit.

• A packet of crisps costs 54p. How much

change do you get from 50? 80P £1?

• I am thinking of a number. I doubled it

and added 5. My answer is 49. What

was my number?

• Choose two digit cards. What is the

biggest/smallest number you can

make?

• Using the digit cards 0-9. can you

make 5 even numbers and 5 odd

numbers?



Big Idea 4:

Add and subtract, recognising that there are inverse operations (to at least 100)



• Understand that addition is commutative and subtraction is not

• Understand the inverse of addition and subtraction

• Add and subtract using concrete objects

• Add and subtract using pictorial representations

• Use number bonds to at least 100


• Use a variety of mathematical language to describe addition and subtraction - sum and difference etc

• Explain what addition and subtraction are

• Use approximation to estimate answers and make decisions

• Explain how taking away and finding the difference are both subtraction calculation strategies


• Apply knowledge of adding and subtracting numbers to 100 to problems involving number, quantities and measures?

• Use the bar model to understand addition and subtraction questions

• Choose and use appropriate operations and strategies

• Use reasoning about addition and subtraction to solve number problems

• Work systematically and logically to solve a problem



Big Idea 4:



• ? + 13 = 19, 19 - ? = 7, ? = 11 + 4

• Using the numbers 23, 100, 77,

arrange them in different numbers

sentences using addition and

subtraction operations

• Use the inverse to check that 57 +

8 = 65


• Is 13+9 the same as 9+13? How can you

show me?

• True or false: you always start with the

biggest number when you are solving

subtraction questions?

• When I add two even numbers together I always get an even number. Convince me I am right


solving

• I think of a number and I add 2. The

answer is 17. What was my number? I

think of a number and I subtract 5. The

answer is 24. What was my number


• Hannah has 36p How much more does

she need to make 50p? £1?

• Dan needs 80 g of sugar for his recipe.

There are 45 g left in the bag. How

much more does he need to get? The

temperature was 26 degrees in the

morning and 11 degrees colder in the

evening. What was the temperature in

the evening? A tub contains 24 coins.

Saj takes 5 coins. Joss takes 10 coins.

How many coins are left in the tub?




Big Idea 4:


• There are three baskets, a brown one, a

red one and a pink one, holding a total

of ten eggs. The Brown basket has one

more egg in it than the Red basket.

The Red basket has three fewer eggs

than the Pink basket. How many eggs

are in each basket?

Source: NRICH – Eggs in Baskets



Big idea 5:

Multiply and divide numbers, recognising that there are inverse operations (for at least the 2, 5 and

10 times tables)



• Know and use multiplication facts to derive division facts, including counting insteps of 3

• Understand the link between multiplication and division

• Understand that multiplication is commutative and division is not

• Use commutativity and inverse relations to develop multiplicative reasoning

• Look for and recognise patterns within multiplication tables and connections between them

• Recognise division as both grouping and sharing

• Arrange objects into equal groups and arrays


• Use a variety of mathematical language to describe multiplication and division – multiplied by, divided by

• Use multiplication, division and equals signs to write mathematical statements for multiplication and division within the multiplication tables.

• Use apparatus and pictures to explain thinking


• Solve problems involving multiplication and division, using apparatus, arrays, repeated addition, mental methods, and multiplication and division facts, including problems in contexts

• Recognise multiplication and division as inverse operations and use this knowledge to solve problems

• Be able to derive all 8 facts in a fact family



Big idea 5:


10 times tables)


• Do pupils understand that 5 × is half of 10 ×?

• This array represents 5 × 3 = 15. Write three other multiplication or addition facts that this array shows. Write one division fact that this array shows


• How can I use 4 x 10 to help me solve 4 x 100?


• Which has the most biscuits: 4 packets of biscuits with 5 in each packet, or 3 packets of biscuits with 10 in each packet? Explain your reasoning


• Complete and compare the 5 and 10 times tables. What do you notice?

5 × 1 = 10 × 1 =

5 × 2 = 10 × 2 =

5 × 3 = 10 × 3 =

5 × 4 = 10 × 4 =



• Sally buys 3 cinema tickets costing £5 each. How much does she spend? Write the multiplication number sentence and calculate the cost. If Sally paid with a £20 note, how much change would she get? Source: NCETM Mastery Booklet

• Two friends share 12 sweets equally between them. How many do they each get? Write this as a division number sentence. Make up two more sharing stories like this one. Chocolate biscuits come in packs (groups) of 5. Sally wants to buy 20 biscuits in total. How many packs will she need to buy? Write this as a division number sentence. Make up two more grouping stories like this one




Big idea 5:


10 times tables)

For this activity, you'll need to work

with a partner, so the first thing to do is

find a friend! Together count from 1 up

to 20, clapping on each number, but

clapping more loudly and speaking

loudly on the numbers in the two times

table, and quietly on the other

numbers. Now clap the five times table

together up to about 30, so this time

you are clapping more loudly and

speaking loudly on the multiples of five

and quietly on the others. If one of you

claps the twos in this way and one of

you claps the fives, at the same time,

can you predict what you would hear?

Which numbers would be quiet?

Which numbers would be fairly loud

and which would be very loud? Now

try it - what did you hear?

Were you right?

Source: NRICH – Clapping Times



Big idea 5:


10 times tables)

• Look at these cards

Can you sort them so that they follow

round in a loop?

Source: NRICH – Ordering Cards



Big idea 6:

Use algebra to express patterns and generalisations within mathematics



• Understand and use the equals

sign correctly as a balance of an

equation

• Be able to spot, continue and

generate patterns in numbers,

shapes and data

• Be able to recognise, verbalise and

record patterns

• Use mathematical representations

to help pupils notice pattern (e.g.

arrays, Numicon)


• Describe and explain patterns

• Predict the next number in the sequence

• Offer generalisations using specific examples

• Use vocabulary such as repeating, pattern,

before, next

• Spot mistakes in patterns and explain why


• Solve problems involving equivalence

• Solve problems involving pattern

• Solve problems which involve finding all

the possibilities, so that generalisations

can be reached



Big idea 6:

Use algebra to express patterns and generalisations within mathematics


• Use balance scales to show how

12 on one side of an equation can

be represented in different

quantities such as counters,

Numicon etc (e.g. 6 + 6, 11 + 1)

• Continue the pattern: 3, 6, 9, 12….

• Suggest what numbers could go on

the other side of the equation: 12

= ?

• Investigate patterns on a hundred

square

• Solve missing box equations where

the missing value is in a different

place in the equation


• True or false: 26 is the next number in the sequence of 12

• Reason why 2, 4, 6 is a pattern

• Reason why 3, 4, 7, 6 is not a pattern

• I generalise that when I add an odd number to an odd number I always make an even number. Prove this using mathematical representations (e.g. Numicon)

• Pattern always go up in steps of true. Always, sometimes or never true?


solving

• If 35 cubes are equivalent to 7 counters,

what would 40 cubes be equal to?

• Which digits could go in the spaces?

? 3 + 5? = ??

• I have a bag of different coins. How can

I use pattern to help me count them all?

• Create the hardest pattern you can

think of using three 2D shapes

• I have a 1p, 2p, 5p and a 10p coin. How

many different amounts can I make?

How will I know when I have them all?

• Make a pattern, then take away one

piece. Can your friend spot the

mistake?



Big idea 7 (a):

Recognise fractions of shapes, objects and quantities (halves, quarters and thirds)



• Recognise, find, name and write

fractions and of a length, shape, set of objects or quantity

• Count in steps of ½ and ¼ up to 10

• Use concrete and pictorial representations of fractions

• Write simple fractions for example,

of 6 = 3 and recognise the

equivalence of and

• Recognise fractions as numbers

• Understand that fractions involve a relationship between a whole and parts of a whole


• Explain how fractions fit into the number

system

• Explain why ½ + ¼ does not equal a whole

• What is the same and what is different

between ½ and 1/4?

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


• Solve problems involving fractions of

shapes, objects and quantities

• Use fractions when programming floor

robots

• Use knowledge of fractions to support

telling the time



Big idea 7 (a):



• If you count in steps of one half starting from 0, how many steps will it take to reach: 2, 4 or 6. What do you notice?


• Which would you rather have, half of the

chocolate bar or one third? Why?

• Can you find half of this pack of 7 sweets?

Explain your reasoning

• Which is the biggest – one third, one quarter or one half? How can you prove that your

answer is correct?


solving

• Jo bought a bag of 12 cherries. Jo ate

half the number of cherries in the bag.

How many cherries did Jo eat?


• Sam bought a bag of 18 cherries. Sam

ate 6 cherries. What fraction of the bag

of cherries did Sam eat?


• Colour in 1/4 of each of these grids in a

different way. Try to think of an unusual

way. How many squares did you colour

each time? (Provide pupils with a 4x4

grid)




Big idea 7 (a):


• First, Ahmed used interlocking cubes to

make a rod four cubes long:

How many cubes did he need to make a

rod twice the length of that one?

How many cubes did he need to make

one three times the length?

How many cubes did he need to make

one four times the length?


rod half the length of his first one?


rod a quarter of the length of his first

one?

These rods are the ones Ahmed made:



Big idea 7 (a):


Which one is twice the length of Ahmed's

first rod?

Which one is three times the length?

Which one is four times the length?

Which one is half the length of his first

rod?

Which one is a quarter of the length of his

first rod?

Which one is the same length as his first

rod?

Source: NRICH – Making Longer, Making

Shorter



Big idea 8:

Become familiar with a variety of units of measure to an appropriate level of accuracy



• Choose and use appropriate standard units and correct apparatus to estimate and measure length/height in any direction (m/cm); mass (kg/g); temperature (°C); capacity (litres/ml) to the nearest appropriate unit, using rulers, scales, thermometers and measuring vessels

• Tell the time to five minutes

• Compare and order lengths, mass, volume/capacity and record the results using >, < and =

• Recognise and explain why we need standard units of measurement

• Use exchange to find the same amount of money

• Use multiplication facts to read scales

• Use vocabulary associated with measures


• Pupils can compare measures including

simple multiples such as ‘half as high’; ‘twice

as wide’

• Pupils reason which unit of measurement is

most applicable in different situations

• Explain how telling the time to five minutes

uses the five multiplication table


• Solve simple problems in a contexts

• Use a variety of information to reach

conclusions

• Decide on which apparatus to use to

solve a problem

• Find different combinations of coins

that equal the same amounts of

money



Big idea 8:



• How many coins make

20p?

Source: NRICH – Five Coins

Ben has five coins in his pocket.

How much money might he have?

• Pupils tell and write the time to five

minutes, including quarter past/to

the hour and draw the hands on a

clock face to show these times

• Draw the minute hand on the clock to show twenty-five past eight


• Which bottle holds more drink – 100ml or 1l?

How do you know?

Which measurement would show the capacity of this bottle?

2 cm 2 kg 2 °C 2l

• Rachel says ‘my apple weighs 25cm’. Is she correct? Explain how you know?

• Sam says I can make 97p using just four coins. Is he correct? Explain your reasoning


solving

• Here is a scale which shows the weight of a letter

How much does the letter weigh?



Big idea 8:


• Harry saves 20p coins. He has saved £3.20. How many coins has he saved? How do you know your answer is correct? Source: NCETM Mastery Booklet

• Rosie went into the sweet shop with 10p to

spend. There were chews for 2p, mini eggs

for 3p, Chocko bars for 5p and lollypops for

7p

What could she buy if she wanted to spend all her

money?

Alice, James, Katie and Henry went into the shop

too. They each had 20p to spend and they all

spent all of their money

Alice bought at least one of each kind of sweet.

Which one did she have two of?

• Measure these two lines.

• How much longer is line A than line B?

• Have a look at the sets of four

quantities below. Can you rank them in

order from smallest to largest? To help

you decide, you may need to find extra

information or carry out some

experiments. Can you convince us that

your order is right?

Time

Taken to travel to school For mustard and cress to

grow from seeds

Taken to eat a biscuit Between your 6th and 7th

birthdays



Big idea 8:


James spent his money on just one kind of sweet,

but he does not like chews. Which sweets did he

buy?

Katie bought the same number of sweets as

James but she had 3 different kinds. Which sweets

did she buy?

Henry chose 8 sweets. What could he have

bought?

Source: NRICH The Puzzling Sweet Shop

• Which clock face shows a time between 5

o’clock and 7 o’clock? How do you know?

(11.30, 2.30, 8.30, 2, 6)

• Jack says, ‘There isn’t any point in having a

minute hand on a clock because I can still tell

the time without it.’ Do you agree with him?

Explain your answer


• Holly uses a £1 coin to buy a pack of stickers. She was given 20p change. How much did the pack of stickers cost? Source: NCETM Mastery Booklet

• Mina and Seb share these coins so that they each have the same amount of money

Distance

You could jump up in the air You can kick a football You can run in half a minute

Length of a bug

Mass

Of a blown-up balloon

Of a bar of chocolate

Of a loaf of bread

Of your teacher

Source: NRICH – Order, Order!



Big idea 8:


Mina chooses her coins first

Seb takes the rest of the coins

Which coins could Mina choose?

Adapted from testbase

• The table shows how many 10p,

5p and 2p coins Tara has

How much money does she have

altogether?

Coin Number

10p 8

5p 4

2p 5



• Harry leaves school at

He gets home at

How long does he take to get home?

Source: NRICH

• What Is the Time? Can you put the

times on these clocks in order?

Big idea 8:




Big idea 9:

Recognise and use the properties of shapes, including position and direction



• Identify and describe the properties

of 2D and 3D shapes, including line

symmetry in a vertical line

• Identify 2D shapes on the surface

of 3D shapes

• Compare and sort 2D and 3D

shapes and everyday objects

• Order and arrange combinations of

mathematical shapes in patterns

and sequences

• Pupils identify what are shapes and

what are not shapes

• Recognise shapes, including those

in different orientations (e.g.

recognising that a tilted square is

still a square, not a diamond.)


• Use mathematical vocabulary to describe

position, direction and movement, including

movement in a straight line

• Use the concept and language of angles to

describe ‘turn’ by applying rotations

• What do you notice about 2D and 3D

shapes? What is the same and what is

different?

• Which shape is the odd one out? Why?


• Solve problems involving shape

• Visualise 3D shapes from 2D shapes

and vice versa

• Use a floor robot to solve problems

including position and direction

• Sort shapes in a logical way



Big idea 9:



• Here is a sequence of triangles,

circles and squares. Can you draw

the next three shapes in the

sequence?

• If you have some triangles like

these can you make the repeating

patterns below?

What other repeating patterns can

you make with these triangles?

Source – NRICH Repeating

Patterns


•

How do you know that this shape is a

triangle?

• Captain Conjecture says, ‘All shapes with

four sides are rectangles’.

Do you agree?

Explain your reasoning.


• One shape is in the wrong place on

the sorting grid

• Draw a cross ( ) on it. Can you

explain why this shape is in the wrong

place?


• Go on a shape walk. What 2D and 3D

shapes can you see?

• Cut a square across the diagonals

(creating 4 triangles). Rearrange the

pieces to make different shapes. What

different shapes can you make?

Describe the properties of the shapes

you make.

Can you make some shapes which

have at least one line of symmetry?


• Use the dots to draw a different hexagon

• You may use a ruler



Big idea 9:


• Put your finger on Start.

Move your finger up 1 square then

across 3 squares

Tick ( ) the animal your finger stops

on

How do you know if you are correct?

Shapes with

a square face

Shapes without a square

face

• Write the missing numbers in the 2 empty boxes

• Skeleton shapes are made with balls of

modelling clay and straws

This shows a cube and a skeleton cube:

How many balls of modelling clay and how

many straws does it take to make the cube?



Big idea 9:


• Rob and Jennie were making necklaces to sell at the school fair

They decided to make them very mathematical

Each necklace was to have eight beads, four of one colour and four of another

And each had to be symmetrical, like this

• Here are some piles of modelling clay

balls and straws:

• Look at the shapes below and decide

which piles are needed to make a

skeleton of each shape

Source – NRICH Skeleton Shapes

• This tile is rotated clockwise

through a three-quarter turn



Big idea 9:


How many different necklaces could they make?

Can you find them all?

How do you know there aren't any others?

What if they had 9 beads, five of one colour and four of another?

What if they had 10 beads, five of each?

Source - NRICH School Fair Necklaces

What will the tile look like after it

has been turned?

• Here are two shape patterns

Draw a shape in each empty box to

make the patterns correct.



Big idea 10:

Collect, organise and interpret data



• Interpret and construct simple

pictograms, tally charts, block

diagrams and simple tables

• Use concrete and pictorial representations to display data


• Use mathematical vocabulary when

explaining about graphs and charts

• Recognise and reason why we need to

collect data


• Solve problems involving data



Big idea 10:



• Generate data with the children on

a daily basis. For example, use an

IWB to identify who is having

school dinner or a packed lunch

• Present data in different ways:

pictograms, tally charts, block

diagrams and simple tables.

• Check whether children can answer

questions about the data. For

example: which is most popular?

Which is least popular?

• Children may be able to answer

simple retrieval questions, but can

they extend to finding the total

number or finding a difference?


• Start with three pairs of socks. Now

mix them up so that no mismatched

pair is the same as another

mismatched pair


• Which bar/shape/picture shows the most …?

How do you know?

• How many cars were counted altogether? How do you know?


solving

• This diagram shows the number of

animals at a farm

How many sheep and cows are

there altogether?

(b) There are more ducks than

horses. How many more?



Big idea 10:


• Now try it with four pairs of socks.

Is there more than one way to do

it?

• Source – NRICH Mixed-up Socks

• Fill in the empty boxes Source – NRICH What Shape and Colour?

• Ben made a graph.

Tick ( ) the bag that shows Ben’s

sweets



Big idea 10:


•

• Where is a diagram for sorting

numbers

Write each number in the correct box

One is done for you



Big idea 10:


•

Write Jane and Kiz in the correct boxes

on the sorting diagram



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