“lesson starters“ - · pdf fileeffective starters 4 fractions starter 5 starter...

Full Mathematics Team ListTeam Leader / Senior Adviser

Alison Hartley

Primary Mathematics Consultants

Lynsey Edwards (Senior Consultant)Sue BaileyTracy DimmockSue FarrarAnne PorterEmma RadcliffeAngeli SlackAndrew TaylorPeter Toogood

Secondary Mathematics Consultants

Carole AshLouise HastewellMary LedwickMaureen MageeHelen Monaghan

Team Contact Details

Phone: 01257 516102Fax: 01257 516103E-Mail: [email protected]

Write to LPDS Centreus at… Southport Road CHORLEY PR7 1NG

Website: www.lancsngfl.ac.uk/curriculum/math

Lancashire Mathematics Newsletter Autumn Term 2009

ContentsTeam News 2

What Can I Do in Mathematics? 2

Renewed Framework for Mathematics 3

Mental Mathematics Staff Meeting 3

Effective Starters 4

Fractions Starter 5

Starter Activities - Level 5 6

Maths of the Month 8

Subject Leader Autumn Planner 9

Children Who Attain Level 4 in English But Not Mathematics at Key Stage 2

10

Maths is Special 12

Numbers Count 14

One-to-One Tuition 16

Behaviour for Learning in the Mathematics Classroom

17

Lancashire Maths Challenge 2009 18

Puzzle Page 20

The Lancashire Mathematics Team

The Lancashire Mathematics Newsletters each follow a subject theme. The newsletter contains resources to support you in that area of mathematics, including teaching ideas, staff meetings, staff INSET, starter activities, ideas for incorporating ICT and useful resources.

Current news and issues from the world of mathematics teaching will still be incorporated. This term’s theme is:

“Lesson Starters“

This newsletter will be available to download in the autumn term from our website.

2 The Lancashire Mathematics Team

These resources accompany the booklet 'Securing Level 3 and Securing Level 4 in Mathematics'.

They allow teachers and pupils to establish whether they are secure in key areas of learning related to level 3 or 4 in mathematics.

They can be ordered for free or downloaded from Teachernet at www.teachernet.gov.uk.Level 3 DCSF-00434-2009Level 4 DCSF-00133-2009

Team News...

Congratulations to Shirley Bush – our Senior Mathematics Consultant who has taken up a well-deserved post as a Regional Adviser for Mathematics with the Primary National Strategy. Her work for Lancashire has been invaluable in promoting and raising attainment in mathematics across the county. She will be sorely missed and we wish her every success in the future. Lancashire’s loss is the country’s gain!

Also congratulations to Lynsey Edwards on her appointment to Senior Mathematics Consultant. Lynsey has been an extremely valued and influential member of the Lancashire Mathematics Team for seven years. She continually strives for mathematics to be taught well and to be enjoyed by all children. Her appointment will ensure the high standards of the mathematics team will be continued.

However, it is with regret that we are saying goodbye to Tim Kirk who has been with the Mathematics Team for two years. He is returning to school at the end of his successful secondment. His work in schools and for the team has been of huge value and Tim would be welcomed back to the team at any time!

What Can I Do in Mathematics?

Renewed Framework for Mathematics

In late June this year, the government published the white paper entitled “Your child, your schools, our future – building a 21st century schools system”.

Just prior to this being published, it was incorrectly reported that schools would no longer have to plan and teach from the National Strategy Renewed Frameworks for Mathematics and Literacy.

The white paper actually states that successful schools have “taken on teaching frameworks developed by The National Strategies, including for the daily literacy and numeracy hours, and used them with enthusiasm… and we expect every school to continue with this practice.”

Download the full report from www.dcsf.gov.uk/21stcenturyschoolssystem.

The Lancashire Mathematics Team 3

Mental Mathematics Staff Meeting

A staff meeting focusing on mental mathematics, which looks in particular at the starter session, is now available to download from the Lancashire Mathematics Team website.

The CPD pack includes a PowerPoint presentation, presenter’s notes and appropriate handouts.

This is the staff meeting delivered recently to mathematics subject leaders at their network meetings.

The staff meeting (as well as previous staff meetings on shape and space; data handling and algebra) can be downloaded from www.lancsngfl.ac.uk/curriculum/math and then clicking on the School Based CPD tab on the left-hand side.


Effective Starters

The 6 Rs define what the role of the starter should be...

RehearseTo practise and consolidate existing skills, set in a context to involve children in

problem solving through the use and application of these skills.

Recall To secure knowledge of facts, build up speed and accuracy.

RefreshTo draw on and revisit previous learning in order to assess, review and

strengthen previously acquired knowledge and skills, or to return to work that children found difficult.

RefineTo sharpen methods and procedures, extend and explain ideas to develop and

deepen children’s knowledge.

ReadTo use mathematical vocabulary and interpret images, diagrams, text and

symbols correctly.

ReasonTo use and apply acquired knowledge, skills and understanding through making

informed choices/decisions, predicting, hypothesising and proving.

Starter sessions:

Occur in every lesson;•Should cover all aspects of mathematics;•Are objective led not activity led;•Are differentiated appropriately using targeted questions or separate starter sessions for •different groups;Should include counting and/or rapid recall •every day as one part of the starter;Do not have to link to the main part of the •lesson;

Guidance on the content – over the week address the following;

Curricular target area (twice per week)•Past target area•Assessing the prior learning of the upcoming •unitAny specific class issues•Revisiting curricular areas to obtain •assessment information.


Fractions Starter

Objective: Identify and estimate fractions of shapes; use diagrams to compare fractions and establish equivalents.

Activity: Hold up a large sheet of paper. Establish that the children can see the whole of one side of the sheet of paper and you can see the whole of the other side of the sheet. Fold the sheet in half.

Q: What fraction of the whole sheet of paper can you see now?Q: What fraction of the whole sheet of paper can I see now?

Agree that the class and you can each see half of the sheet and ½ + ½ = 1. Unfold the sheet to confirm this, draw a line down the fold and refold.

Fold the folded sheet and display a quarter. Ask the same two questions and by unfolding and refolding the sheet, confirm that ¼ + ¼ + ¼ + ¼ = 1 whole and establish that ¼ + ¼ = ½. Draw on fold lines, building up to the representation below.

Continue to fold, generating eighths and sixteenths. Each time, pose the questions and agree the fraction and confirm the fraction statements. Unfold the sheet and invite the children to recall the fractional parts they have identified and used. Write these onto the sheet (see below).

With the annotated sheet displayed, ask a series of questions involving these fractions, such as:

Q: How many quarters are there in the whole sheet?Q: I am looking at one half of the sheet: how many eighths can I see?Q: How many eighths are there in a quarter of the sheet?Q: How many sixteenths are there in one half of the sheet?Q: I am looking at four sixteenths, how many eighths can I see?Q: If I shaded in three eighths and you shaded one half, which part would be bigger?Q: If we removed one sixteenth, what fraction would be left?Q: I see one quarter and one eighth, how many eighths is that altogether?Q: If I halve one quarter, what fraction would this give me?Q: If I halve one sixteenth, what fraction would I get?Q: Can you explain to me what happens to the denominator of the fraction as I keep halving?Q: What can you tell me about the relationship between halves, quarters, eighths and sixteenths?Q: Suppose I start with a sheet and divide it into three parts. I then divide these three parts into three parts, what fractions would I get this time?



Starter Activities - Level 5

We

have

put

toge

ther

som

e id

eas

for s

tart

er a

ctiv

ities

/ qu

estio

ns fo

r eac

h of

the

seve

n st

rand

s w

ithin

the

mat

hem

atic

s cu

rric

ulum

, for

eac

h of

the

six

Rs

disc

usse

d ea

rlier

in th

e ne

wsl

ette

r. Th

is is

just

a s

ampl

e of

the

reso

urce

. Lev

els

1 an

d 3

are

also

on

our w

ebsi

te u

nder

the

Act

iviti

es a

nd

Res

ourc

es ta

b an

d th

e M

enta

l and

Ora

l Sta

rter

s ta

b.

C

ount

ing

and

unde

rsta

ndin

g nu

mbe

r K

now

ing

and

usin

g nu

mbe

r fac

ts

Cal

cula

ting

Und

erst

andi

ng s

hape

M

easu

ring

Han

dlin

g da

ta

Inte

rpre

ting

pie

char

ts

Reh

ears

e To

pra

ctis

e an

d co

nsol

idat

e ex

istin

g sk

ills, u

sual

ly m

enta

l ca

lcul

atio

n sk

ills, s

et in

a

cont

ext t

o in

volv

e ch

ildre

n in

pr

oble

m s

olvi

ng th

roug

h th

e us

e an

d ap

plic

atio

n of

thes

e sk

ills; u

se o

f voc

abul

ary

and

lang

uage

of n

umbe

r, pr

oper

ties

of s

hape

s or

des

crib

ing

and

reas

onin

g.

Writ

e th

e la

rges

t who

le n

umbe

r to

mak

e th

is s

tate

men

t tru

e.

50 +

<

73

Num

ber s

cale

s IT

P w

ill pr

ovid

e an

imag

e to

sup

port

this

type

of q

uest

ion.

D

ecim

al n

umbe

r lin

e IT

P –

give

me

a de

cim

al fr

actio

n th

at

lies

betw

een

3.4

and

3.5

Ord

erin

g fra

ctio

ns o

n a

num

ber l

ine/

cou

ntin

g st

ick.

Use

targ

et b

oard

s to

stim

ulat

e qu

estio

ns s

uch

as:

Whi

ch 2

num

bers

mul

tiplie

d to

geth

er g

ive

an a

nsw

er

near

est t

o 1?

Q

uick

fire

que

stio

ns s

uch

as:

Writ

e in

the

two

mis

sing

dig

its.

0 ×

0 =

3000

W

hat i

s th

irty

times

forty

tim

es

ten?

Si

x tim

es a

num

ber i

s th

ree

thou

sand

. Wha

t is

the

num

ber?

W

rite

two

fact

ors

of tw

enty

-four

w

hich

add

to m

ake

elev

en.

Gor

don’

s IT

P –

Perc

enta

ge

Frac

tion

chai

ns.

True

or f

alse

? 10

% =

1/1

0 so

20%

mus

t equ

al

1/20

.

Feel

y ba

g –

desc

ribe

prop

ertie

s of

2D

and

3D

sh

apes

usi

ng L

evel

5

voca

bula

ry –

cla

ss d

raw

and

na

me

shap

e ba

sed

on

desc

riptio

n.

Sort

shap

es a

ccor

ding

to

prop

ertie

s –

use

Car

roll

diag

ram

s, V

enn

diag

ram

s.

Gor

don’

s IT

P –

Car

roll

shap

e U

se IT

P C

alcu

latin

g an

gles

-

Exam

ple

ques

tion:

if w

e kn

ow

the

size

of 2

of 3

ang

les

on a

st

raig

ht li

ne/ i

n a

trian

gle,

wha

t is

the

mis

sing

ang

le?

Play

bin

go o

n w

hite

boar

ds

whe

re fo

cus

is to

mat

ch v

arie

ty

of o

bjec

ts/ m

easu

rem

ents

to a

n im

peria

l uni

t of m

easu

rem

ent.

Eg: B

lock

of c

hees

e - l

b;

Bottl

e of

milk

- pi

nt.

Pack

et o

f but

ter -

oz;

D

ista

nce

from

Lan

cast

er to

Pr

esto

n - m

iles.

H

eigh

t of t

he te

ache

r – ft

and

in

ches

. M

easu

ring

Cyl

inde

r ITP

co

nver

t qua

ntiti

es fr

om l

to m

l

Whe

n gi

ven

who

le s

ampl

e si

ze

and

fract

ion

or %

of s

peci

fic

grou

p, id

entif

y nu

mer

ical

siz

e of

gr

oup.

e.

g.: S

ampl

e si

ze is

325

, whi

te

sect

ion

is 3

0%. H

ow m

any

chos

e w

hite

?

Th

is c

hart

show

s th

e am

ount

of

mon

ey s

pent

in a

toy

shop

in

thre

e m

onth

s.

0£1

0 000

£20 0

00£3

0 000

Octob

er

Nove

mber

Dece

mber

Step

han

says

, ‘In

Nov

embe

r th

ere

was

a 1

00%

incr

ease

on

the

mon

ey s

pent

in O

ctob

er’.

Is h

e co

rrect

? Ex

plai

n ho

w y

ou

can

tell

from

the

char

t. R

ecal

l To

sec

ure

know

ledg

e of

fact

s,

usua

lly n

umbe

r fac

ts; b

uild

up

spee

d an

d ac

cura

cy; r

ecal

l qu

ickl

y na

mes

and

pro

perti

es

of s

hape

s, u

nits

of m

easu

re o

r ty

pes

of c

harts

and

gra

phs

to

repr

esen

t dat

a.

Cou

nt o

n or

bac

k in

ste

ps o

f co

nsta

nt s

ize.

Whe

n us

ing

inte

gers

, the

sta

rt nu

mbe

r sh

ould

not

be

a m

ultip

le o

f the

st

ep s

ize.

U

se c

ount

ing

stic

k to

re

pres

ent t

erm

s in

a s

eque

nce.

C

ount

ing

in s

teps

of d

ecim

als

Num

ber d

ials

ITP

–Usi

ng

know

ledg

e of

tabl

e/di

visi

on

fact

s an

d re

latin

g to

mul

tiple

s of

0.

1 an

d 0.

01.

Rel

ate

to c

onve

rting

cm

to m

; cl

to l

Fizz

Buz

z –

reca

ll of

squ

are

num

bers

, prim

e nu

mbe

rs,

mul

tiple

s of

…, f

acto

rs o

f…

Wha

t’s m

y nu

mbe

r?

e.g.

: I th

ink

of a

num

ber,

squa

re it

and

sub

tract

12.

My

answ

er is

52.

Wha

t num

ber d

id

I thi

nk o

f?

I thi

nk o

f a n

umbe

r, di

vide

it b

y 10

, div

ide

it by

10

agai

n. M

y an

swer

is 0

.3. W

hat n

umbe

r di

d I t

hink

of?

Rev

eal a

sha

pe –

dis

cuss

ion

arou

nd w

hat i

t mig

ht b

e/ c

anno

t po

ssib

ly b

e ba

sed

on

know

ledg

e of

pro

perti

es a

t Le

vel 5

. 20

que

stio

ns –

Yes

/No

answ

ers.

Targ

et b

oard

/ bin

go –

Rec

all

rela

tions

hips

bet

wee

n un

its o

f m

easu

re –

impe

rial t

o m

etric

.

Mat

ch s

ampl

es o

f dat

a to

su

itabl

e gr

aphs

or c

harts

.


Ref

resh

To

dra

w o

n an

d re

visi

t pre

viou

s le

arni

ng; t

o as

sess

, rev

iew

and

st

reng

then

chi

ldre

n’s

prev

ious

ly

acqu

ired

know

ledg

e an

d sk

ills

rele

vant

to la

ter l

earn

ing;

retu

rn

to a

spec

ts o

f mat

hem

atic

s w

ith

whi

ch th

e ch

ildre

n ha

ve h

ad

diffi

culty

; dra

w o

ut th

e ke

y po

ints

for l

earn

ing.

Use

a c

ount

ing

stic

k an

d id

entif

y th

e 4th

and

7th te

rms.

C

alcu

late

mis

sing

term

s.

Exte

nd b

y in

clud

ing

deci

mal

va

lues

in th

e se

quen

ce o

r ste

p si

ze.

Bin

go –

squ

are

root

s of

per

fect

sq

uare

s to

12x

12.

Wou

ld y

ou ra

ther

hav

e 17

.5%

of

£20

0 or

30%

of £

120?

R

atio

and

Pro

porti

on IT

P

Her

e is

an

equi

late

ral t

riang

le

insi

de a

rect

angl

e.

x

12°

Cal

cula

te th

e va

lue

of a

ngle

x.

Pl

ay y

our c

ards

righ

t – u

sing

1

suit

from

a p

ack

of c

ards

. En

cour

age

use

of p

roba

bilit

y w

hen

mak

ing

high

er/lo

wer

de

cisi

on. E

xten

d to

mor

e su

its.

Spot

the

delib

erat

e m

ista

kes

– sc

ale,

key

, acc

urac

y of

gra

ph

or c

hart

agai

nst g

athe

red

data

.

Ref

ine

To s

harp

en m

etho

ds a

nd

proc

edur

es; e

xpla

in s

trate

gies

an

d so

lutio

ns; e

xten

d id

eas

and

deve

lop

and

deep

en th

e ch

ildre

n’s

know

ledg

e; re

info

rce

thei

r und

erst

andi

ng o

f key

co

ncep

ts; b

uild

on

earli

er

lear

ning

so

that

stra

tegi

es a

nd

tech

niqu

es b

ecom

e m

ore

effic

ient

and

pre

cise

.

This

seq

uenc

e of

num

bers

go

es u

p by

40

each

tim

e.

40, 8

0, 1

20, 1

60, 2

00,…

Th

is s

eque

nce

cont

inue

s.

Will

the

num

ber 2

140

be in

the

sequ

ence

? E

xpla

in h

ow y

ou

know

. A

and

B ar

e tw

o nu

mbe

rs o

n th

e nu

mbe

r lin

e be

low

.

The

diffe

renc

e be

twee

n A

and

B is

140

. Wha

t are

the

valu

es

of A

and

B?

This

thre

e-di

git n

umbe

r has

2

and

7 as

fact

ors.

29

4 W

rite

anot

her t

hree

-dig

it nu

mbe

r whi

ch h

as 2

and

7 a

s fa

ctor

s.

Tariq

won

one

hun

dred

pou

nds

in a

mat

hs c

ompe

titio

n. H

e ga

ve tw

o-fif

ths

of h

is p

rize

mon

ey to

cha

rity.

How

muc

h of

hi

s pr

ize

mon

ey, i

n po

unds

, did

he

hav

e le

ft?

Cal

cula

ting

angl

es IT

P -

Angl

es a

roun

d a

poin

t – fi

nd

mis

sing

ang

le.

Gor

don’

s IT

P Ar

ea -F

ind

area

of

righ

t ang

led

trian

gle

whe

n le

ngth

s of

the

2 pe

rpen

dicu

lar

side

s ar

e kn

own.

A til

e is

0.2

m lo

ng.

One

hun

dred

tile

s ar

e pl

aced

en

d to

end

in a

row

. How

long

is

the

row

? H

ow m

any

seco

nds

in 1

5 m

inut

es?

Wha

t do

you

mea

n?

Giv

e th

e sa

mpl

e si

ze, m

edia

n an

d m

ode

of a

set

of d

ata.

With

ta

lk p

artn

ers,

find

the

mea

n of

th

e da

ta.

Line

gra

ph IT

P –

tell

your

talk

pa

rtner

the

stor

y be

hind

the

grap

h. T

he m

ore

outra

geou

s th

e be

tter,

as lo

ng a

s th

e in

terp

reta

tion

of th

e gr

aph

is

corre

ct.

Rea

d To

use

mat

hem

atic

al

voca

bula

ry a

nd in

terp

ret

imag

es, d

iagr

ams

and

sym

bols

co

rrect

ly; r

ead

num

ber

sent

ence

s an

d pr

ovid

e eq

uiva

lent

s; d

escr

ibe

and

expl

ain

diag

ram

s an

d fe

atur

es

invo

lvin

g sc

ales

, tab

les

or

grap

hs; i

dent

ify s

hape

s fro

m a

lis

t of t

heir

prop

ertie

s; re

ad a

nd

inte

rpre

t wor

d pr

oble

ms

or

puzz

les;

cre

ate

thei

r ow

n pr

oble

ms

and

lines

of e

nqui

ry.

p an

d q

each

sta

nd fo

r who

le

num

bers

. p

+ q

= 10

00

p is

150

gre

ater

than

q.

Cal

cula

te th

e nu

mbe

rs p

and

q.

If I k

now

237

x 1

7 =

4029

, how

ca

n I c

alcu

late

238

x 1

8?

Set o

f bal

ance

d sc

ales

with

2.

1kg

mar

ked

as th

e to

tal o

n on

e si

de. O

ppos

ite s

ide

has

2 ob

ject

s on

it. T

he la

rger

obj

ect

is tw

ice

as h

eavy

as

the

smal

ler

one.

How

muc

h do

es e

ach

obje

ct w

eigh

?

Dat

a ha

ndlin

g IT

P . P

upils

po

se a

nd a

nsw

er q

uest

ions

re

latin

g to

var

iety

of g

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nts

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ages

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pare

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pres

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ith d

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ple

size

s.

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: 2 p

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harts

; 1 p

ie c

hart

and

1 pi

ctog

ram

; 2 li

ne g

raph

s w

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ques

tions

and

allo

w

expl

anat

ions

of r

easo

ning

.


Have you seen the free resources available from the BEAM website at www.beam.co.uk/mathsofthemonth.php?

The resources cover games and activities which are separated into strands and age ranges.

BEAM - Maths of the Month

Maths of the Month

9–11 February 2009 © BEAM Education www.beam.co.uk

you need:• squared paper

1. These are all odd numbers.

And these are all even.

How many odd numbers are there below 100? And how many even?

2. On Planet Zog, these are Zodd numbers.

And these are Zeven.

Use squared paper to work out some more Zodd numbers, and some more Zeven ones.

3. How many Zodd numbers are there below 100? And how many Zeven ones?

1 7 59

2 6 108

1

3

4 8 7 2

12 9 6 15

5

Going dotty

Maths of the Month

5–7 December 2004 © BEAM Education www.beam.co.uk

1. Join the dots however you like.

Can you make each one different?

2. Can you finish these squares?

These can easily be adapted for use in starter sessions, particularly those focusing on reasoning and refining skills.


Subject Leader Autumn Planner

These are suggestions for maths subject leader to use as a check list for their action planning

Autumn Term 2009 Maths Subject Leader Autumn Planner

Shaded areas are choice for

that term (not all in one term!) Sept – mid Oct Oct – end Dec

Auditing & action planning; setting priorities PDMs Analysis of data and work scrutiny; Curricular and numerical target setting PDMs Pupil Progress meetings Book sampling Pupil interviews Walkthrough Focused support/monitoring SATs analysis Curricular targets set

Share revised action plan, to include CPD and SL support programme, at staff meeting. With headteacher, use school data such as RAISE Online, FFT and/or Lancashire grids to inform discussion of standards and setting of numerical targets. Agree procedures for monitoring children’s progress across the term/year e.g. agreed school tracker for monitoring termly progress Ensure all teachers have an effective learning environment which includes a working wall and process success criteria to support children’s learning in mathematics.

Conduct Pupil interviews on identified area Ensure that children’s progress is tracked on a termly basis using formative and summative assessment e.g. APP, teacher assessments, QCA Identify pupil underperformance Scrutiny of work on identified school focus Where targets have been set discuss with teachers at PDM a review of year group curricular targets Set whole school/year group curricular targets for second half term as a result of analysis and audit.

Whole school planning

Subject leader to complete a scrutiny of short term plans. Support teachers with the use of the Renewed Framework.

Children identified for additional support

SL supports headteacher in ensuring resources and capacity to deliver intervention programmes are in place. Organise training as needed. Children selected for intervention programmes. Training for TAs responsible for delivering intervention programmes.

Implementation of intervention groups. Review impact of additional support programmes. Identification of underperforming pupils

Subject Leader support and continued professional development programme; Monitoring of teaching and learning

Agree with headteacher specific CPD programme and focus of support for the year linked to mini audit. Agree monitoring programme with headteacher (pupil discussions, book scrutinies, pupil progress meetings, etc) in accordance with the action plan. SL to deliver relevant maths subject specific CPD

Subject leaders to attend Maths subject leader support meeting

Research Paper: Children Who Attain Level 4 in English but not Mathematics at Key Stage 2


Key factors affecting attainment in mathematics

The factors identified in this report that appear

to affect the proportion of pupils who attain

level 4 in English but not mathematics by the

end of Key Stage 2 are identified below.

Uneven progress in mathematics through

Key Stage 2

Over half of the target-group pupils in the focus

schools attained the ‘benchmark’ level of 2b or

above in mathematics at the end of Key Stage 1,

but did not go on to attain level 4 by the end of

Key Stage 2. Progress for the target-group pupils

(measured using average annual increases in

point score) was markedly lower in Years 3 and

4 than in upper Key Stage 2. In fact the progress

the pupils made over Key stage 2 fell well below

the two levels expected, and while there was

greatest progress made in Year 6, this was not

enough to compensate for the poor progress

made over Years 3 and 4.

Differences in the attainment of girls and

boys

A high proportion of the target-group pupils

in the focus schools were girls. In Lancashire

we are currently running programmes on

improving girls progress and attainment in

mathematics.

The proportion of special educational

needs (SEN) pupils in the cohort

Overall there was a positive correlation between

the number of pupils in a cohort who were

identified as having special educational needs

and the proportion of pupils in the cohort who

attained level 4 or above in English but not

mathematics. The focus of the support for these

children tended to be on improving English skills

and behaviour management rather than on

mathematics.

Level 5 attainment in mathematics

It was generally the case that where the

proportion of pupils who attained level 4 in

English but not in mathematics was significant,

the proportion of pupils attaining level 5 in

mathematics was low. Put another way, schools

that had a low percentage of pupils attaining

level 5 in mathematics also tended to have a

relatively high proportion of pupils who attained

level 4 in English but not mathematics.

Key areas of mathematics that pupils

who attained level 4 in English but

not mathematics found particularly

challenging when compared to pupils

who attained level 4

Problem solving, communication and

reasoning

Solving multi-step problems, particularly •

those involving money and time.

Reasoning about numbers, including •

the identification and use of the inverse

operation to undo a process.

Thinking through the steps in a question •

in a logical sequence and representing this

to show their workings or to explain their


Research Paper: Children Who Attain Level 4 in English but not Mathematics at Key Stage 2

method.

Number and the number system

Completing a sequence involving three-digit •

numbers.

Recognising equivalence of fractions and •

decimals.

Recognising and finding simple fractions of •

shapes and numbers.

Solving problems involving multiples and •

factors of numbers.

Questions involving comparisons of two-digit •

and three-digit numbers and understanding

relative values.

Calculation

Multi-step problems involving multiplication •

and division of two-digit and three-digit

numbers.

Responding at speed to mental calculation •

involving subtraction of two-digit numbers

and calculations involving multiples of 10 in

all four operations.

Choosing and working out the calculations •

needed to solve money problems including

those involving change.

Calculating time differences. •

Calculations involving decimals. •

Handling data and measures

Accurate reading of scales that had non-•

unit intervals when identifying values as a

measure of quantity and when identifying

values on a graph or chart.

Choosing and working out the appropriate •

calculations needed to answer a question

using data read from a table, graph or chart

Labelling appropriately a scale on a graph or •

chart, or the groups in a Carroll diagram.

Useful resources for schools

Overcoming barriers in mathematics –

helping children move from level 3 to

level 4

(DCSF 00695-2007)



level 3

(DCSF 00149-2008)



level 2

(DCSF 00021-2009)

These materials are designed to help teachers

ensure that children make expected progress.

Lancashire Girls and Mathematics Programme

– access to this programme can be gained

through the school’s SIP.

Lancashire Mathematics Team website:

www.lancsngfl.ac.uk/curriculum/math.

The full report can be found at:

http://nationalstrategies.standards.dcsf.gov.uk/

node/166696.


Maths is Special


The ‘Maths Is Special’ event seems to go from strength to strength each year. This year the Special School Network cluster chose the theme of food for all the events and this turned out to be a great success. The children thoroughly enjoyed learning about mathematics through a range of practical activities which involved problem

solving related to food.

The KS2 ‘Maths is Special’ event took place at Pear

Tree School and a special thank you goes to the

school for holding

the event and to

the different schools

who provided the

fun and meaningful

games. The practical

activities included

data handling, length

which involved

making a monster, a

number gingerbread man bingo game, investigating

different shapes by making your own boat using

a variety of different foods, symmetry, and making

your own pizza. Students from Pear Tree School led

the children through a Dave Godfrey song to end

the event. All participating schools The Acorns,

Bleasdale, Great Arley, Holly Grove, Kingsbury,

Pear Tree, Pendle View, Red Marsh and The Loyne

received a framed certificate and all the children

received individual certificates.

The event was further extended this year with the

inclusion coordinator for Pear Tree School inviting

four of the school’s link primary schools to take

part in a ‘Maths is Fun’ day. Ten children from

each school who would benefit from this practical

experience, came to

take part in similar

mathematical activities.

The teachers gained

ideas of how they could

support children in the

mainstream setting.

Building on the success

of other years, seven

schools took part in the KS3 ‘Maths is Special’ event

where the children had to work as a team to meet

'Maths is Special' at Pear Tree School


certain challenges. The ‘Brunch Crunch’ had

five rounds based on problem solving linked to

the theme of food with elements of number,

measures, ratio and proportion, memory and

spatial awareness. The participants all enjoyed

making and eating a trifle that they had made as

one of the challenges. Many thanks to Michelle

Westhead, Lee Toulson, Ian Richardson and Rachel

Kay for organising such varied and interesting

activities. All participants were awarded certificates

with Great Arley coming second and Broadfield

winning the event. Both teams received medals

and money to buy mathematics equipment for their

schools. Congratulations also to Chorley Astley

Park School, Broadfield Specialist School, Great

Arley, Pendle Community High School , Sir Tom

Finney Community, Tor View and West Lancashire

Community High.

Thank you to all the members of the team who

organised such super activities as without this hard

work the events wouldn’t be able to take place. A

special thanks to Lee Toulson of Astley Park School

and Carol Davies and Heather Hambilton of Pear

Tree School for their hard work in organising and

hosting the events.KS3 'Maths is Special' at Astley Park

Primary School Link Day at Pear Tree School

'Maths is Special' at Pear Tree School

Numbers Count


What is Numbers Count?

Numbers Count is a new numeracy intervention that is at the heart of the Every Child Counts (ECC) initiative. It draws upon the recommendations of the Williams Review of Mathematical Teaching in the Early Years Setting and Primary Schools, upon lessons learned from existing intervention programmes and upon the findings from the ECC research phase (2007-08).

Numbers Count aims to enable Year 2 children who have the greatest difficulties with mathematics to make greater progress towards expected levels of attainment so that they will catch up with their peers and achieve Level 2 or where possible Level 2B or better by the end of KS1.

The 12 lowest attaining Year 2 children in a school normally receive Numbers Count support during the course of a year. Each child is on the programme for approximately12 weeks, starting in September, January or April. Numbers Count aims to ensure the development of a numerate child who is confident and who enjoys actively learning mathematics.

A Numbers Count Teacher normally works on a 0.6 timetable, teaching four children every morning or afternoon on a one to one basis and planning a personalised programme for each child. S/he undertakes a specialised professional development programme and liaises closely with each child’s class teacher and parents or carers. S/he is trained and supported by a Local Authority Teacher Leader, who in turn is trained and supported by a National Trainer.

A Numbers Count Lesson takes place in a dedicated teaching area and lasts for 30 minutes. It is lively and active and uses a wide variety of resources. It focuses on number because research has shown that number development underpins children’s learning across all aspects of mathematics.

Numbers Count was launched in September 2008 and will be built up and refined during the ECC development phase (2008-10), by drawing on impact data, feedback from a wide range of participants and stakeholders and the findings of an independent evaluation study commissioned by the DCSF. Numbers Count Teacher Leaders and teachers will contribute actively to its development so that Numbers Count can provide increasingly effective support for young children who have difficulties with mathematics.

Professional Development for Numbers Count Teachers

Numbers Count Teachers are trained through a one-year professional development programme. The professional development includes:

10 days of face to face events which •are focused on delivering the Numbers Count programme, early mathematical development and teaching and learning;At least 5 individual support visits from Emma •Radcliffe as Teacher Leader;Analysing and sharing video recordings of •Numbers Count children with colleagues;Participating in at least six Learning Partner •visits with other Numbers Count Teachers;Attending additional network meetings as •necessary;An opportunity to apply to study for all •or part of the MA Early Mathematical Interventions through distance learning with Edge Hill University.

Further Professional Development is available


for teachers in their second year as a Numbers Count Teacher. This includes:

5 days of face-to-face events•At least one individual support visit from a •Teacher LeaderLearning Partner Visits•

Lancashire Schools Involved in Every Child Counts 2008-2009

School Name

The Blessed Sacrament Catholic Primary School, Preston

St Joseph’s Catholic Primary School, Preston

Preston St Matthew’s CE Primary School

Seven Stars Primary School

Accrington Hyndburn Park Primary School

Cherry Fold Community Primary School

Nelson Walverden Primary School

Walter Street Primary School

Lord Street Primary School, Colne

St. John’s Skelmersdale

The Numbers Count Teacher at each of the schools has been working towards gaining their accreditation. They have had to provide evidence that they have met the Standards and Requirements of a Numbers Count teacher. In order to achieve their accreditation they also have to have worked as a Numbers Count Teacher for a year.

Schools Involved in Every Child Counts 2009-2010

During the academic year of 2009/10, 24 new Numbers Count Teachers will be trained by the Teacher Leader. The teachers will work across the Lancashire consortium with seventeen teachers working in Lancashire, four teachers working in Blackburn with Darwen and three

teachers working in Blackpool.

The Impact of Numbers Count Within Lancashire - Spring Term 2009

The table below shows the average score for Lancashire compared to the average scores nationally for Term 2.

Lessons Taught

Lessons lostAt-

titude survey gains (pts)

Age equiva-

lent score

(months)

Stand-ardised scores gains (pts)

Child abs

Other reasons

NationalTerm 2

40.7 5.6% 16.2% 10.3 14.8 16.9

Lancs Term 2

45.8 4% 15.9% 14.5 18.7 21.4

Attitude Survey

Children’s confidence and attitudes towards •mathematics are assessed through the use of the Numbers Count Attitude Survey when children enter and exit the programme. This includes children’s questions, teacher’s questions based on the participation in whole class and group work and parent’s questions. Additional gains around the children’s •attitudes have also been reported by many schools. This related to an overall positive attitude across the curriculum, not just in mathematics.

Maths Age Equivalent Gains During the Numbers Count Programme

Children take a Sandwell Early Numeracy Test when they enter and exit the programme. The test includes practical, pictorial, oral and written tasks and questions. It is administrated by the Numbers Count Teacher on entry and a trained Link Teacher on exit. The results have improved significantly comparing Term 1 and Term 2. The LA has achieved age equivalent gains that are above the national average.

One to One Tuition - Real Personalisation!


This is a huge new strategy nationally,

spearheaded by Sue Hackman on

behalf of pupils in Key Stages 2 and 3

and, in National Challenge schools, in

KS4 in English and mathematics. The

introduction to the guidance for Local

Authorities states:-

“Ensuring that the right support is in

place for all children, regardless of

class or social background is important

in closing the attainment gap. For

those who can afford it, individual

tuition has always been the preferred

method of additional support for

pupils not achieving their potential.

While our current catch-up arrangements are

effective for many, we know that they are not

working for all pupils. Some need a level of support

which is beyond our control to deliver in the

context of whole class or small groups. Without an

individualised approach it will be very hard for this

group to make the progress needed to achieve their

full potential.

Even in the personalised classroom, we know that

some pupils would benefit, at key moments, from an

intensive burst of individual tuition, which the class

teacher can guide and reinforce, but simply does not

have the time to deliver.”

Lancashire has funding for over 6000 places in

these key stages from September 2009, rising

incrementally next year. The roll out has already

started in KS2. Tutors have to be qualified teachers

and tuition can take place in or out the school day in

various venues. By the time you read this the LA will

already have decided on a funding formula to meet

the needs of the target cohort and the roll out will

have started in earnest.

The target cohort will comprise students who are

disadvantaged and vulnerable e.g. looked after

children and who are unable to afford extra one to

one tuition. All schools will have a percentage of

their students in this category and so all schools will

be involved in this project in one way or another.

The funding is ring-fenced.

As teachers of mathematics, you will potentially

be involved in two ways. Firstly in liaising with the

tutor on the child’s identified needs [using APP

assessment tools] before and after the ten hour long

sessions and secondly, as a potential tutor. The pilots

identified the difficulties in recruiting tutors and Sue

Hackman has therefore insisted on a high rate of

pay for tutors. It is recommended at £25 per hour.

The LA is mandated to provide support and training

for tutors and to assist schools in every possible way

with discharging their responsibilities in this initiative.

There will be extra consultants in primary and

secondary maths and English to support the project

in schools.

A project co-ordinator has been appointed to deal

with front line support. If you have any queries at

all please email Hilary King at one-to-one-tuition@

lancashire.gov.uk or telephone 01257 516120.

Alternatively you may access the materials available

at present on http://www.teachernet.gov.uk/

teachingandlearning/schoolstandards/mgppilot/.


These prompts were developed as part of the course for NQTs in mathematics

1. Non-verbal signals reduce intrusion into the lessonOften a look is as effective as verbally reprimanding a pupil. But remember this strategy may not work as well with children on the autistic spectrum.

2. Focus on pupils making choicesThey are more likely to cooperate if they feel some control over outcomes. If we present two choices that are both acceptable to us then they are less likely to make a different and unacceptable choice. ‘I need you to move seats you can move to either here or there’

3. Direction and delaySometimes called ‘take up time’. Pupils may be influenced by peer pressure not to comply with instructions. There are times when giving a pupil thinking time and moving away from them helps pupils to comply and not lose face.

4. Rules to provide distanceCorrecting pupils with direct reference to rules shifts possible resentment away from teachers. ‘What’s the school rule about mobile phones?’

5. Partial agreementPupils who try to justify their non-compliance are trying to express their own needs and acknowledgement of these needs allows a connection that can simulate compliance.

6. Tactical ignoring of secondary behaviourIf the pupil follows teacher instructions but does so with an ‘attitude’ for example tutting or sighing, this secondary behaviour can be ignored. The initial objective has been achieved and responding to the secondary behaviours is likely to be confrontational and distract from the flow of the lesson.

7. Choice/consequenceBefore a consequence is imposed, pupils should be given an explicit choice to comply or to accept the consequence; for example, ‘Peter I need you to move seats now or you will be given a detention. Your choice’

8. Assertive directionPupils need clear instructions and are more likely to comply if delivered assertively. I need you to be quiet whilst I’m speaking…thank you.’ The use of ‘Thank you’ following the instructions allows the teacher to model politeness while conveying the expectation that pupils will comply. The tone of voice should make it clear that this is an instruction not a request.

9. Broken recordA first response to overt non-compliance could be to repeat the assertive statement in a calm neutral way possible two or three times.

10. Label the behaviour not the pupilWhen directly challenging inappropriate behaviour, pupil’s self esteem is vulnerable. Express your disapproval of the behaviour not the pupil. Use ‘ I find it very difficult to carry on when you are interrupting me, listen quietly, thanks’ rather than ‘ you need to learn some manners and stop being so rude. Just shut up!’ (‘you’ messages can be confrontational).

Behaviour for Learning - Support for NQTs

Lancashire Mathematics Challenge 2009


The Year 7 Lancashire Mathematics Challenge this year was based around the Jules Verne book, ‘Around The World in Eighty Days’. The questions for the district finals and the County finals were once again set by Maureen Magee and proved a good test of pupils’ team work and skill.

The district finals saw Phil Fogg off on a gap year prior to going to university. He worked in various countries and teams had to assist him with key tasks and work out how much money he had earned on his travels.

Once again the host schools for the district finals did an excellent job and aside from the fire alarm going off at one venue all went without a hitch. Some schools decided to involve their PTA in providing refreshments which proved extremely successful.

Soon June 18th was upon us and it was time for the County Final. Our nine district winners arrived at Woodlands with their parents, teachers and some headteachers.

The theme stayed with Phil Fogg only this time he was on holiday with his companion Nancy. The atmosphere in the Oak Room was buzzing as our young mathematicians worked as teams to solve the context based challenges. The final result was very close but this year the Mathematics Challenge champions were the four young ladies from Lancaster Girls Grammar School. Well done!

Once again the Maths Challenge was only made possible through the sponsorship of Lancashire County Developments and the hard work of the Lancashire Mathematics Team of consultants. Not forgetting our very able administrative officer Alison Kenyon who developed the resources and made sure everything ran smoothly at each venue.

We look forward to visiting the winning schools for next years district rounds and meeting your young Year 7 mathematicians.

First Prize: Lancaster Girls' Grammar School

Third Prize: Clitheroe Royal Grammar School

Second Prize: Leyland St. Mary's Catholic Technology College

Business Award: Broughton Business and Enterprise College


Date Venue First Second Third

Monday 23rd March

St Christopher's CE High School

Clitheroe Royal Grammar School

Bowland High - With Specialist

Status In Performing Arts

The Hollins Technology

College

Thursday 26th March

All Hallows Catholic High

School

Leyland St Mary's Catholic

Technology College

Balshaw's Church Of England High

School

All Hallows Catholic High

School

Tuesday 28th April

Bacup And Rawtenstall

Grammar School

Bacup & Rawtenstall

Grammar School

All Saints Catholic Language College

Fearns Community

Sports College

Wednesday 29th April

Carr Hill High School and Sixth

Form Centre

Lytham St Anne's Technology And Performing Arts

College

Cardinal Allen Catholic High

School

Carr Hill High School & 6th Form Centre

Tuesday 5th May

Tarleton High School: A

Community Technology

College

Up Holland High School-Specialist

Music, Maths & Computing

College

Tarleton High School : A

Community Technology

College

Ormskirk School

Thursday 7th May

Albany Science College

Longridge High School - A Maths And Computing

College

Parklands High School - A Specialist

Language College

Bishop Rawstorne CE Language

College

Wednesday 13th May

Archbishop Temple CE High & Technology

College

Broughton Business &

Enterprise College

Our Lady's Catholic High

School

Ashton Community

Science College

Thursday 14th May

Lancaster Royal Grammar School

Lancaster Girls' Grammar

Ripley St Thomas Church Of

England High School

Lancaster Royal Grammar School

Wednesday 20th May

West Craven High Technology

College

Colne Primet High School

Pendle Vale College

Ss John Fisher And Thomas More Roman Catholic High

School

Thursday 18th June

The Final - Woodlands Conference

Centre, Chorley

Lancaster Girls' Grammar

Leyland St Mary's Catholic

Technology College

Clitheroe Royal Grammar School

Business Question - Broughton Business & Enterprise College

Winners 2009

The Lancashire Mathematics Team

Puzzle Page

Holy NumbersA church hymn book contains 700 hymns, numbered 1 to 700.

Each Sunday the people in the church sing four different hymns.

The numbers of the hymns are displayed to them in a frame by dropping in single-digit boards like this:

The board for 6 may be turned upside down to serve as a 9.

What is the minimum number of small boards that is needed to show any possible combination of four hymn numbers?

How many of each number must there be? Taken from www.nrich.maths.org.uk.

Solution to previous puzzleHe picks one piece of fruit from the box labelled Oranges and Lemons.

If it is a lemon, then that box should actually say Lemons. The box labelled Oranges can’t contain just oranges, and must really be the mixed one.

This leaves the box labelled Lemons to contain oranges.

2

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