APP in mathematics at Key Stage 3: Assessment...

11
The Coalition Government took office on 11 May 2010. This publication was published prior to that date and may not reflect current government policy. You may choose to use these materials, however you should also consult the Department for Education website www.education.gov.uk for updated policy and resources. Assessing pupils' progress in mathematics at Key Stage 3: Assessment guidelines

Transcript of APP in mathematics at Key Stage 3: Assessment...

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

Assessing pupils' progress in mathematics at Key Stage 3: Assessment guidelines

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Assessing pupils’ progress in mathematics at Key Stage 3: Assessment guidelines

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Assessing pupils’ progress in mathematics at Key Stage 3: Assessment guidelines

First published in 2008 Ref: 00730-2008BKT-EN

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1The National Strategies | Secondary Assessing Pupil Progress at Key Stage 3: Assessment guidelines

© Crown copyright 2008 00730-2008BKT-EN

Disclaimer

The Department for Children, Schools and Families wishes to make it clear that the Department and its agents accept no responsibility for the actual content of any materials suggested as information sources in this publication, whether these are in the form of printed publications or on a website.

In these materials icons, logos, software products and websites are used for contextual and practical reasons. Their use should not be interpreted as an endorsement of particular companies or their products.

The websites referred to in these materials existed at the time of going to print.

Please check all website references carefully to see if they have changed and substitute other references where appropriate.

HER

TFO

RD O

FFSE

T LT

D 1

2-20

08

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1The National Strategies | Secondary Assessing Pupil Progress at Key Stage 3: Assessment guidelines

© Crown copyright 2008 00730-2008BKT-EN

Mat

hem

atic

s ass

essm

ent g

uide

lines

: lev

els 2

and

3

Pupi

l nam

e……

……

……

….C

lass

/gro

up…

……

……

……

..Dat

e……

……

Usi

ng a

nd a

pply

ing

mat

hem

atic

sN

umbe

rs a

nd th

e nu

mbe

r sy

stem

Calc

ulat

ing

Alg

ebra

Shap

e, s

pace

and

mea

sure

Han

dlin

g da

ta

Leve

l 3•s

elec

t the

m

athe

mat

ics t

hey

use

in a

wid

er ra

nge

of

clas

sroo

m a

ctiv

ities

•try

diff

eren

t ap

proa

ches

and

find

w

ays o

f ove

rcom

ing

diff

icul

ties t

hat a

rise

whe

n th

ey a

re so

lvin

g pr

oble

ms

•beg

in to

org

anis

e th

eir

wor

k an

d ch

eck

resu

lts

•use

and

inte

rpre

t m

athe

mat

ical

sym

bols

an

d di

agra

ms

•und

erst

and

a ge

nera

l st

atem

ent b

y fin

ding

pa

rtic

ular

exa

mpl

es

that

mat

ch it

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iew

thei

r wor

k an

d re

ason

ing

•und

erst

and

plac

e va

lue

in

num

bers

to 1

000

•use

pla

ce v

alue

to m

ake

appr

oxim

atio

ns

•rec

ogni

se n

egat

ive

num

bers

in

cont

exts

such

as t

empe

ratu

re

•use

sim

ple

frac

tions

that

are

se

vera

l par

ts o

f a w

hole

and

re

cogn

ise

whe

n tw

o si

mpl

e fr

actio

ns a

re e

quiv

alen

t

•beg

in to

use

dec

imal

not

atio

n in

co

ntex

ts su

ch a

s mon

ey

•der

ive

asso

ciat

ed d

ivis

ion

fact

s fr

om k

now

n m

ultip

licat

ion

fact

s

•add

and

subt

ract

two-

digi

t nu

mbe

rs m

enta

lly

•add

and

subt

ract

thre

e di

git

num

bers

usi

ng w

ritte

n m

etho

d

•mul

tiply

and

div

ide

two

digi

t nu

mbe

rs b

y 2,

3, 4

or 5

as w

ell a

s 10

with

who

le n

umbe

r ans

wer

s an

d re

mai

nder

s

•use

men

tal r

ecal

l of a

dditi

on

and

subt

ract

ion

fact

s to

20 in

so

lvin

g pr

oble

ms i

nvol

ving

larg

er

num

bers

•sol

ve w

hole

num

ber p

robl

ems

incl

udin

g th

ose

invo

lvin

g m

ultip

licat

ion

or d

ivis

ion

that

may

gi

ve ri

se to

rem

aind

ers

•rec

ogni

se a

wid

er

rang

e of

sequ

ence

s

•beg

in to

und

erst

and

the

role

of ‘

=’ (t

he

‘equ

als’

sign

)

•cla

ssify

3-D

and

2-D

shap

es in

var

ious

w

ays u

sing

mat

hem

atic

al p

rope

rtie

s suc

h as

refle

ctiv

e sy

mm

etry

for 2

-D sh

apes

•beg

in to

reco

gnis

e ne

ts o

f fam

iliar

3-D

sh

apes

, e.g

. cub

e, c

uboi

d, tr

iang

ular

pris

m,

squa

re-b

ased

pyr

amid

•rec

ogni

se sh

apes

in d

iffer

ent o

rient

atio

ns

and

refle

ct sh

apes

, pre

sent

ed o

n a

grid

, in

a ve

rtic

al o

r hor

izon

tal m

irror

line

•des

crib

e po

sitio

n an

d m

ovem

ent

•use

a w

ider

rang

e of

mea

sure

s inc

ludi

ng

non-

stan

dard

uni

ts a

nd st

anda

rd m

etric

un

its o

f len

gth,

cap

acity

and

mas

s in

a ra

nge

of c

onte

xts

•use

stan

dard

uni

ts o

f tim

e

•gat

her i

nfor

mat

ion

•con

stru

ct b

ar c

hart

s and

pi

ctog

ram

s, w

here

the

sym

bol

repr

esen

ts a

gro

up o

f uni

ts

•use

Ven

n an

d Ca

rrol

l dia

gram

s to

reco

rd th

eir s

ortin

g an

d cl

assi

fyin

g of

info

rmat

ion

•ext

ract

and

inte

rpre

t in

form

atio

n pr

esen

ted

in si

mpl

e ta

bles

, lis

ts, b

ar c

hart

s and

pi

ctog

ram

s

Leve

l 2•s

elec

t the

m

athe

mat

ics t

hey

use

in so

me

clas

sroo

m

activ

ities

•dis

cuss

thei

r wor

k us

ing

mat

hem

atic

al

lang

uage

•beg

in to

repr

esen

t th

eir w

ork

usin

g sy

mbo

ls a

nd si

mpl

e di

agra

ms

•pre

dict

wha

t com

es

next

in a

sim

ple

num

ber,

shap

e or

sp

atia

l pat

tern

or

sequ

ence

and

giv

e re

ason

s for

thei

r op

inio

ns

•exp

lain

why

an

answ

er is

cor

rect

•cou

nt se

ts o

f obj

ects

relia

bly

•beg

in to

und

erst

and

the

plac

e va

lue

of e

ach

digi

t; us

e th

is to

or

der n

umbe

rs u

p to

100

•beg

in to

use

hal

ves a

nd

quar

ters

and

rela

te th

e co

ncep

t of

hal

f of a

smal

l qua

ntity

to th

e co

ncep

t of h

alf o

f a sh

ape

•use

the

know

ledg

e th

at

subt

ract

ion

is th

e in

vers

e of

ad

ditio

n an

d un

ders

tand

hal

ving

as

a w

ay o

f ‘un

doin

g’ d

oubl

ing

and

vice

ver

sa

•use

men

tal r

ecal

l of a

dditi

on a

nd

subt

ract

ion

fact

s to

10

•use

men

tal c

alcu

latio

n st

rate

gies

to

solv

e nu

mbe

r pro

blem

s in

clud

ing

thos

e in

volv

ing

mon

ey

and

mea

sure

s

•rec

ord

thei

r wor

k in

writ

ing

•cho

ose

the

appr

opria

te

oper

atio

n w

hen

solv

ing

addi

tion

and

subt

ract

ion

prob

lem

s

•rec

ogni

se

sequ

ence

s of

num

bers

, inc

ludi

ng

odd

and

even

nu

mbe

rs

•use

mat

hem

atic

al n

ames

for c

omm

on

3-D

and

2-D

shap

es

•des

crib

e th

eir p

rope

rtie

s, in

clud

ing

num

bers

of s

ides

and

cor

ners

•des

crib

e th

e po

sitio

n of

obj

ects

•dis

tingu

ish

betw

een

stra

ight

and

turn

ing

mov

emen

ts, r

ecog

nise

righ

t ang

les

in tu

rns a

nd u

nder

stan

d an

gle

as a

m

easu

rem

ent o

f tur

n

•beg

in to

use

a w

ider

rang

e of

mea

sure

s in

clud

ing

to u

se e

very

day

non-

stan

dard

an

d st

anda

rd u

nits

to m

easu

re le

ngth

an

d m

ass

•beg

in to

und

erst

and

that

num

bers

ca

n be

use

d no

t onl

y to

cou

nt d

iscr

ete

obje

cts b

ut a

lso

to d

escr

ibe

cont

inuo

us

mea

sure

s

•sor

t obj

ects

and

cla

ssify

them

us

ing

mor

e th

an o

ne c

riter

ion

•und

erst

and

voca

bula

ry re

latin

g to

han

dlin

g da

ta

•col

lect

and

sort

dat

a to

test

a

sim

ple

hypo

thes

is

•rec

ord

resu

lts in

sim

ple

lists

, ta

bles

, pic

togr

ams a

nd b

lock

gr

aphs

•com

mun

icat

e th

eir f

indi

ngs,

usin

g th

e si

mpl

e lis

ts, t

able

s, pi

ctog

ram

s and

blo

ck g

raph

s th

ey h

ave

reco

rded

BL

IE

Key:

BL-B

elow

Lev

el

IE-In

suff

icie

nt E

vide

nce

Ove

rall

asse

ssm

ent (

tick

one

box

only

)Lo

w 2

S

ecur

e 2

Hig

h 2

Low

3

Sec

ure

3

Hig

h 3

Page 6: APP in mathematics at Key Stage 3: Assessment guidelineswsassets.s3.amazonaws.com/ws/nso/pdf/96ce8155ab25c4849a7... · 2011-06-06 · show understanding of situations by describing

2 The National Strategies | Secondary Assessing Pupil Progress at Key Stage 3: Assessment guidelines

00730-2008BKT-EN © Crown copyright 2008

3The National Strategies | Secondary Assessing Pupil Progress at Key Stage 3: Assessment guidelines

© Crown copyright 2008 00730-2008BKT-EN

Mat

hem

atic

s ass

essm

ent g

uide

lines

: lev

els 3

and

4

Pupi

l nam

e……

……

……

….C

lass

/gro

up…

……

……

……

..Dat

e……

……

Usi

ng a

nd a

pply

ing

mat

hem

atic

sN

umbe

rs a

nd th

e nu

mbe

r sy

stem

Calc

ulat

ing

Alg

ebra

Shap

e, s

pace

and

mea

sure

sH

andl

ing

data

Leve

l 4•d

evel

op o

wn

stra

tegi

es

for s

olvi

ng p

robl

ems

•use

thei

r ow

n st

rate

gies

w

ithin

mat

hem

atic

s and

in

app

lyin

g m

athe

mat

ics

to p

ract

ical

con

text

s

•pre

sent

info

rmat

ion

and

resu

lts in

a c

lear

and

or

gani

sed

way

•sea

rch

for a

solu

tion

by

tryi

ng o

ut id

eas o

f the

ir ow

n

•rec

ogni

se a

nd d

escr

ibe

num

ber p

atte

rns

•rec

ogni

se a

nd d

escr

ibe

num

ber r

elat

ions

hips

in

clud

ing

mul

tiple

, fac

tor

and

squa

re

•use

pla

ce v

alue

to

mul

tiply

and

div

ide

who

le

num

bers

by

10 o

r 100

•rec

ogni

se a

ppro

xim

ate

prop

ortio

ns o

f a w

hole

an

d us

e si

mpl

e fr

actio

ns

and

perc

enta

ges t

o de

scrib

e th

ese

•ord

er d

ecim

als t

o th

ree

deci

mal

pla

ces

•beg

in to

und

erst

and

sim

ple

ratio

•use

a ra

nge

of m

enta

l met

hods

of

com

puta

tion

with

all

oper

atio

ns

•rec

all m

ultip

licat

ion

fact

s up

to 1

0 ×

10 a

nd q

uick

ly d

eriv

e co

rres

pond

ing

divi

sion

fact

s

•use

eff

icie

nt w

ritte

n m

etho

ds o

f ad

ditio

n an

d su

btra

ctio

n an

d of

sh

ort m

ultip

licat

ion

and

divi

sion

•mul

tiply

a si

mpl

e de

cim

al b

y a

sing

le d

igit

•sol

ve p

robl

ems w

ith o

r with

out

a ca

lcul

ator

•che

ck th

e re

ason

able

ness

of

resu

lts w

ith re

fere

nce

to th

e co

ntex

t or s

ize

of n

umbe

rs

•beg

in to

use

sim

ple

form

ulae

exp

ress

ed in

w

ords

•use

and

inte

rpre

t co

ordi

nate

s in

the

first

qu

adra

nt

•use

the

prop

ertie

s of 2

-D a

nd 3

-D

shap

es

•mak

e 3-

D m

odel

s by

linki

ng g

iven

fa

ces o

r edg

es a

nd d

raw

com

mon

2-

D sh

apes

in d

iffer

ent o

rient

atio

ns

on g

rids

•ref

lect

sim

ple

shap

es in

a m

irror

lin

e, tr

ansl

ate

shap

es h

oriz

onta

lly o

r ve

rtic

ally

and

beg

in to

rota

te a

sim

ple

shap

e or

obj

ect a

bout

its c

entr

e or

a

vert

ex

•cho

ose

and

use

appr

opria

te u

nits

and

in

stru

men

ts

•int

erpr

et, w

ith a

ppro

pria

te a

ccur

acy,

nu

mbe

rs o

n a

rang

e of

mea

surin

g in

stru

men

ts

•fin

d pe

rimet

ers o

f sim

ple

shap

es a

nd

find

area

s by

coun

ting

squa

res

•col

lect

and

reco

rd d

iscr

ete

data

•gro

up d

ata,

whe

re a

ppro

pria

te,

in e

qual

cla

ss in

terv

als

•con

tinue

to u

se V

enn

and

Carr

oll d

iagr

ams t

o re

cord

th

eir s

ortin

g an

d cl

assi

fyin

g of

in

form

atio

n

•con

stru

ct a

nd in

terp

ret

freq

uenc

y di

agra

ms a

nd si

mpl

e lin

e gr

aphs

•und

erst

and

and

use

the

mod

e an

d ra

nge

to d

escr

ibe

sets

of

data

Leve

l 3•s

elec

t the

mat

hem

atic

s th

ey u

se in

a w

ider

rang

e of

cla

ssro

om a

ctiv

ities

•try

diff

eren

t app

roac

hes

and

find

way

s of

over

com

ing

diff

icul

ties

that

aris

e w

hen

they

are

so

lvin

g pr

oble

ms

•beg

in to

org

anis

e th

eir

wor

k an

d ch

eck

resu

lts

•use

and

inte

rpre

t m

athe

mat

ical

sym

bols

an

d di

agra

ms

•und

erst

and

a ge

nera

l st

atem

ent b

y fin

ding

pa

rtic

ular

exa

mpl

es th

at

mat

ch it

•rev

iew

thei

r wor

k an

d re

ason

ing

•und

erst

and

plac

e va

lue

in

num

bers

to 1

000

•use

pla

ce v

alue

to m

ake

appr

oxim

atio

ns

•rec

ogni

se n

egat

ive

num

bers

in c

onte

xts s

uch

as te

mpe

ratu

re

•use

sim

ple

frac

tions

th

at a

re se

vera

l par

ts o

f a

who

le a

nd re

cogn

ise

whe

n tw

o si

mpl

e fr

actio

ns a

re e

quiv

alen

t

•beg

in to

use

dec

imal

no

tatio

n in

con

text

s suc

h as

mon

ey

•der

ive

asso

ciat

ed d

ivis

ion

fact

s fr

om k

now

n m

ultip

licat

ion

fact

s

•add

and

subt

ract

two-

digi

t nu

mbe

rs m

enta

lly

•add

and

subt

ract

thre

e-di

git

num

bers

usi

ng w

ritte

n m

etho

d

•mul

tiply

and

div

ide

two-

digi

t nu

mbe

rs b

y 2,

3, 4

or 5

as w

ell a

s 10

with

who

le n

umbe

r ans

wer

s an

d re

mai

nder

s

•use

men

tal r

ecal

l of a

dditi

on a

nd

subt

ract

ion

fact

s to

20 in

solv

ing

prob

lem

s inv

olvi

ng la

rger

nu

mbe

rs

•sol

ve w

hole

num

ber p

robl

ems

incl

udin

g th

ose

invo

lvin

g m

ultip

licat

ion

or d

ivis

ion

that

m

ay g

ive

rise

to re

mai

nder

s

•rec

ogni

se a

wid

er ra

nge

of

sequ

ence

s

•beg

in to

und

erst

and

the

role

of ‘

=’ (t

he ‘e

qual

s’ si

gn)

•cla

ssify

3-D

and

2-D

shap

es in

var

ious

w

ays u

sing

mat

hem

atic

al p

rope

rtie

s su

ch a

s ref

lect

ive

sym

met

ry fo

r 2-D

sh

apes

•beg

in to

reco

gnis

e ne

ts o

f fam

iliar

3-D

sh

apes

, e.g

. cub

e, c

uboi

d, tr

iang

ular

pr

ism

, squ

are-

base

d py

ram

id

•rec

ogni

se sh

apes

in d

iffer

ent

orie

ntat

ions

and

refle

ct sh

apes

, pr

esen

ted

on a

grid

, in

a ve

rtic

al o

r ho

rizon

tal m

irror

line

•des

crib

e po

sitio

n an

d m

ovem

ent

•use

a w

ider

rang

e of

mea

sure

s in

clud

ing

non-

stan

dard

uni

ts a

nd

stan

dard

met

ric u

nits

of l

engt

h,

capa

city

and

mas

s in

a ra

nge

of

cont

exts

•use

stan

dard

uni

ts o

f tim

e

•gat

her i

nfor

mat

ion

•con

stru

ct b

ar c

hart

s and

pi

ctog

ram

s, w

here

the

sym

bol

repr

esen

ts a

gro

up o

f uni

ts

•use

Ven

n an

d Ca

rrol

l dia

gram

s to

reco

rd th

eir s

ortin

g an

d cl

assi

fyin

g of

info

rmat

ion

•ext

ract

and

inte

rpre

t in

form

atio

n pr

esen

ted

in

sim

ple

tabl

es, l

ists

, bar

cha

rts

and

pict

ogra

ms

BL

IE

Key:

BL-B

elow

Lev

el

IE-In

suff

icie

nt E

vide

nce

Ove

rall

asse

ssm

ent (

tick

one

box

only

)Lo

w 3

S

ecur

e 3

Hig

h 3

Low

4

Sec

ure

4

Hig

h 4

Page 7: APP in mathematics at Key Stage 3: Assessment guidelineswsassets.s3.amazonaws.com/ws/nso/pdf/96ce8155ab25c4849a7... · 2011-06-06 · show understanding of situations by describing

2 The National Strategies | Secondary Assessing Pupil Progress at Key Stage 3: Assessment guidelines

00730-2008BKT-EN © Crown copyright 2008

3The National Strategies | Secondary Assessing Pupil Progress at Key Stage 3: Assessment guidelines

© Crown copyright 2008 00730-2008BKT-EN

Mat

hem

atic

s ass

essm

ent g

uide

lines

: lev

els 4

and

5

Pupi

l nam

e……

……

……

….C

lass

/gro

up…

……

……

……

..Dat

e……

……

Usi

ng a

nd a

pply

ing

mat

hem

atic

sN

umbe

rs a

nd th

e nu

mbe

r sys

tem

Calc

ulat

ing

Alg

ebra

Shap

e, s

pace

and

mea

sure

Han

dlin

g da

ta

Leve

l 5•i

dent

ify a

nd

obta

in n

eces

sary

in

form

atio

n to

car

ry

thro

ugh

a ta

sk a

nd

solv

e m

athe

mat

ical

pr

oble

ms

•che

ck re

sults

, co

nsid

erin

g w

heth

er

thes

e ar

e re

ason

able

•sol

ve w

ord

prob

lem

s an

d in

vest

igat

ions

fr

om a

rang

e of

co

ntex

ts

•sho

w u

nder

stan

ding

of

situ

atio

ns b

y de

scrib

ing

them

m

athe

mat

ical

ly u

sing

sy

mbo

ls, w

ords

and

di

agra

ms

•dra

w si

mpl

e co

nclu

sion

s of t

heir

own

and

give

an

expl

anat

ion

of th

eir

reas

onin

g

•use

und

erst

andi

ng o

f pla

ce v

alue

to

mul

tiply

and

div

ide

who

le

num

bers

and

dec

imal

s by

10, 1

00

and

1000

and

exp

lain

the

effe

ct

•rou

nd d

ecim

als t

o th

e ne

ares

t de

cim

al p

lace

and

ord

er n

egat

ive

num

bers

in c

onte

xt

•rec

ogni

se a

nd u

se n

umbe

r pa

tter

ns a

nd re

latio

nshi

ps

•use

equ

ival

ence

bet

wee

n fr

actio

ns a

nd o

rder

frac

tions

and

de

cim

als

•red

uce

a fr

actio

n to

its s

impl

est

form

by

canc

ellin

g co

mm

on

fact

ors

•und

erst

and

sim

ple

ratio

•use

kno

wn

fact

s, pl

ace

valu

e,

know

ledg

e of

ope

ratio

ns a

nd

brac

kets

to c

alcu

late

incl

udin

g us

ing

all f

our o

pera

tions

with

dec

imal

s to

two

plac

es

•use

a c

alcu

lato

r whe

re a

ppro

pria

te

to c

alcu

late

frac

tions

/per

cent

ages

of

quan

titie

s/m

easu

rem

ents

•und

erst

and

and

use

an a

ppro

pria

te

non-

calc

ulat

or m

etho

d fo

r sol

ving

pr

oble

ms t

hat i

nvol

ve m

ultip

lyin

g an

d di

vidi

ng a

ny th

ree-

digi

t num

ber

by a

ny tw

o-di

git n

umbe

r

•sol

ve si

mpl

e pr

oble

ms i

nvol

ving

or

derin

g, a

ddin

g, su

btra

ctin

g ne

gativ

e nu

mbe

rs in

con

text

•sol

ve si

mpl

e pr

oble

ms i

nvol

ving

ra

tio a

nd d

irect

pro

port

ion

•app

ly in

vers

e op

erat

ions

and

ap

prox

imat

e to

che

ck a

nsw

ers

to p

robl

ems a

re o

f the

cor

rect

m

agni

tude

•con

stru

ct, e

xpre

ss

in sy

mbo

lic

form

, and

use

si

mpl

e fo

rmul

ae

invo

lvin

g on

e or

tw

o op

erat

ions

•use

and

inte

rpre

t co

ordi

nate

s in

all

four

qua

dran

ts

•use

a w

ider

rang

e of

pro

pert

ies o

f 2-D

and

3-

D sh

apes

and

iden

tify

all t

he sy

mm

etrie

s of

2-D

shap

es

•use

lang

uage

ass

ocia

ted

with

ang

le a

nd

know

and

use

the

angl

e su

m o

f a tr

iang

le

and

that

of a

ngle

s at a

poi

nt

•rea

son

abou

t pos

ition

and

mov

emen

t and

tr

ansf

orm

shap

es

•mea

sure

and

dra

w a

ngle

s to

the

near

est

degr

ee, w

hen

cons

truc

ting

mod

els a

nd

draw

ing

or u

sing

shap

es

•rea

d an

d in

terp

ret s

cale

s on

a ra

nge

of

mea

surin

g in

stru

men

ts, e

xpla

inin

g w

hat

each

labe

lled

divi

sion

repr

esen

ts

•sol

ve p

robl

ems i

nvol

ving

the

conv

ersi

on

of u

nits

and

mak

e se

nsib

le e

stim

ates

of a

ra

nge

of m

easu

res i

n re

latio

n to

eve

ryda

y si

tuat

ions

•und

erst

and

and

use

the

form

ula

for t

he

area

of a

rect

angl

e an

d di

stin

guis

h ar

ea

from

per

imet

er

•ask

que

stio

ns, p

lan

how

to

answ

er th

em a

nd c

olle

ct th

e da

ta re

quire

d

•in

prob

abili

ty, s

elec

t met

hods

ba

sed

on e

qual

ly li

kely

ou

tcom

es a

nd e

xper

imen

tal

evid

ence

, as a

ppro

pria

te

•und

erst

and

and

use

the

prob

abili

ty sc

ale

from

0 to

1

•und

erst

and

and

use

the

mea

n of

dis

cret

e da

ta a

nd c

ompa

re

two

sim

ple

dist

ribut

ions

, usi

ng

the

rang

e an

d on

e of

mod

e,

med

ian

or m

ean

•und

erst

and

that

diff

eren

t ou

tcom

es m

ay re

sult

from

re

peat

ing

an e

xper

imen

t

•int

erpr

et g

raph

s and

dia

gram

s, in

clud

ing

pie

char

ts, a

nd d

raw

co

nclu

sion

s

•cre

ate

and

inte

rpre

t lin

e gr

aphs

w

here

the

inte

rmed

iate

val

ues

have

mea

ning

Leve

l 4•d

evel

op o

wn

stra

tegi

es fo

r sol

ving

pr

oble

ms

•use

thei

r ow

n st

rate

gies

with

in

mat

hem

atic

s and

in

appl

ying

mat

hem

atic

s to

pra

ctic

al c

onte

xts

•pre

sent

info

rmat

ion

and

resu

lts in

a c

lear

an

d or

gani

sed

way

•sea

rch

for a

solu

tion

by tr

ying

out

idea

s of

thei

r ow

n

•rec

ogni

se a

nd d

escr

ibe

num

ber

patt

erns

•rec

ogni

se a

nd d

escr

ibe

num

ber

rela

tions

hips

incl

udin

g m

ultip

le,

fact

or a

nd sq

uare

•use

pla

ce v

alue

to m

ultip

ly a

nd

divi

de w

hole

num

bers

by

10 o

r 10

0

•rec

ogni

se a

ppro

xim

ate

prop

ortio

ns o

f a w

hole

and

use

si

mpl

e fr

actio

ns a

nd p

erce

ntag

es

to d

escr

ibe

thes

e

•ord

er d

ecim

als t

o th

ree

deci

mal

pl

aces

•beg

in to

und

erst

and

sim

ple

ratio

•use

a ra

nge

of m

enta

l met

hods

of

com

puta

tion

with

all

oper

atio

ns

•rec

all m

ultip

licat

ion

fact

s up

to 1

0 ×

10 a

nd q

uick

ly d

eriv

e co

rres

pond

ing

divi

sion

fact

s

•use

eff

icie

nt w

ritte

n m

etho

ds o

f ad

ditio

n an

d su

btra

ctio

n an

d of

sh

ort m

ultip

licat

ion

and

divi

sion

•mul

tiply

a si

mpl

e de

cim

al b

y a

sing

le

digi

t

•sol

ve p

robl

ems w

ith o

r with

out a

ca

lcul

ator

•che

ck th

e re

ason

able

ness

of r

esul

ts

with

refe

renc

e to

the

cont

ext o

r siz

e of

num

bers

•beg

in to

use

si

mpl

e fo

rmul

ae

expr

esse

d in

w

ords

•use

and

inte

rpre

t co

ordi

nate

s in

the

first

qua

dran

t

•use

the

prop

ertie

s of 2

-D a

nd 3

-D sh

apes

•mak

e 3-

D m

odel

s by

linki

ng g

iven

face

s or

edg

es a

nd d

raw

com

mon

2-D

shap

es in

di

ffer

ent o

rient

atio

ns o

n gr

ids

•ref

lect

sim

ple

shap

es in

a m

irror

line

, tr

ansl

ate

shap

es h

oriz

onta

lly o

r ver

tical

ly

and

begi

n to

rota

te a

sim

ple

shap

e or

ob

ject

abo

ut it

s cen

tre

or a

ver

tex

•cho

ose

and

use

appr

opria

te u

nits

and

in

stru

men

ts

•int

erpr

et, w

ith a

ppro

pria

te a

ccur

acy,

nu

mbe

rs o

n a

rang

e of

mea

surin

g in

stru

men

ts

•fin

d pe

rimet

ers o

f sim

ple

shap

es a

nd fi

nd

area

s by

coun

ting

squa

res

•col

lect

and

reco

rd d

iscr

ete

data

•gro

up d

ata,

whe

re a

ppro

pria

te,

in e

qual

cla

ss in

terv

als

•con

tinue

to u

se V

enn

and

Carr

oll d

iagr

ams t

o re

cord

th

eir s

ortin

g an

d cl

assi

fyin

g of

in

form

atio

n

•con

stru

ct a

nd in

terp

ret

freq

uenc

y di

agra

ms a

nd si

mpl

e lin

e gr

aphs

•und

erst

and

and

use

the

mod

e an

d ra

nge

to d

escr

ibe

sets

of

data

BL

IE

Key:

BL-B

elow

Lev

el

IE-In

suff

icie

nt E

vide

nce

Ove

rall

asse

ssm

ent (

tick

one

box

only

)Lo

w 4

S

ecur

e 4

Hig

h 4

Low

5

Sec

ure

5

Hig

h 5

Page 8: APP in mathematics at Key Stage 3: Assessment guidelineswsassets.s3.amazonaws.com/ws/nso/pdf/96ce8155ab25c4849a7... · 2011-06-06 · show understanding of situations by describing

4 The National Strategies | Secondary Assessing Pupil Progress at Key Stage 3: Assessment guidelines

00730-2008BKT-EN © Crown copyright 2008

5The National Strategies | Secondary Assessing Pupil Progress at Key Stage 3: Assessment guidelines

© Crown copyright 2008 00730-2008BKT-EN

Mat

hem

atic

s ass

essm

ent g

uide

lines

: lev

els 5

and

6

leve

ls 5

and

6

P

upil

nam

e……

……

……

….C

lass

/gro

up…

……

……

……

..Dat

e……

……

Usi

ng a

nd a

pply

ing

mat

hem

atic

sN

umbe

rs a

nd th

e nu

mbe

r sy

stem

Calc

ulat

ing

Alg

ebra

Shap

e, s

pace

and

mea

sure

Han

dlin

g da

ta

Leve

l 6•s

olve

pro

blem

s an

d ca

rry

thro

ugh

subs

tant

ial t

asks

by

bre

akin

g th

em

into

smal

ler,

mor

e m

anag

eabl

e ta

sks,

usin

g a

rang

e of

ef

ficie

nt te

chni

ques

, m

etho

ds a

nd

reso

urce

s, in

clud

ing

ICT;

giv

e so

lutio

ns to

an

appr

opria

te d

egre

e of

ac

cura

cy

•int

erpr

et, d

iscu

ss a

nd

synt

hesi

se in

form

atio

n pr

esen

ted

in a

var

iety

of

mat

hem

atic

al fo

rms

•pre

sent

a c

onci

se,

reas

oned

arg

umen

t, us

ing

sym

bols

, di

agra

ms,

grap

hs a

nd

rela

ted

expl

anat

ory

text

s

•use

logi

cal a

rgum

ent t

o es

tabl

ish

the

trut

h of

a

stat

emen

t

•use

the

equi

vale

nce

of

frac

tions

, dec

imal

s and

pe

rcen

tage

s to

com

pare

pr

opor

tions

•cal

cula

te p

erce

ntag

es a

nd fi

nd th

e ou

tcom

e of

a g

iven

per

cent

age

incr

ease

or d

ecre

ase

•div

ide

a qu

antit

y in

to tw

o or

mor

e pa

rts i

n a

give

n ra

tio a

nd so

lve

prob

lem

s inv

olvi

ng ra

tio a

nd d

irect

pr

opor

tion

•use

pro

port

iona

l rea

soni

ng to

solv

e a

prob

lem

, cho

osin

g th

e co

rrec

t nu

mbe

rs to

take

as 1

00%

, or a

s a

who

le

•add

and

subt

ract

frac

tions

by

writ

ing

them

with

a c

omm

on d

enom

inat

or,

calc

ulat

e fr

actio

ns o

f qua

ntiti

es

(frac

tion

answ

ers)

, mul

tiply

and

div

ide

an in

tege

r by

a fr

actio

n

•use

syst

emat

ic tr

ial a

nd

impr

ovem

ent m

etho

ds a

nd

ICT

tool

s to

find

appr

oxim

ate

solu

tions

to e

quat

ions

such

as

x³ +

x =

20

•con

stru

ct a

nd so

lve

linea

r eq

uatio

ns w

ith in

tege

r co

effic

ient

s, us

ing

an

appr

opria

te m

etho

d

•gen

erat

e te

rms o

f a se

quen

ce

usin

g te

rm-t

o-te

rm a

nd

posi

tion-

to-t

erm

def

initi

ons

of th

e se

quen

ce, o

n pa

per a

nd

usin

g IC

T; w

rite

an e

xpre

ssio

n to

des

crib

e th

e nt

h te

rm o

f an

arith

met

ic se

quen

ce.

•plo

t the

gra

phs o

f lin

ear

func

tions

, whe

re y

is g

iven

ex

plic

itly

in te

rms o

f x;

reco

gnis

e th

at e

quat

ions

of

the

form

y =

mx

+ c

corr

espo

nd to

stra

ight

-line

gr

aphs

•con

stru

ct fu

nctio

ns a

risin

g fr

om re

al-li

fe p

robl

ems a

nd

plot

thei

r cor

resp

ondi

ng

grap

hs;

•int

erpr

et g

raph

s aris

ing

from

re

al si

tuat

ions

•cla

ssify

qua

drila

tera

ls b

y th

eir g

eom

etric

pr

oper

ties

•sol

ve g

eom

etric

al p

robl

ems u

sing

pr

oper

ties o

f ang

les,

of p

aral

lel a

nd

inte

rsec

ting

lines

, and

of t

riang

les a

nd

othe

r pol

ygon

s

•ide

ntify

alte

rnat

e an

d co

rres

pond

ing

angl

es; u

nder

stan

d a

proo

f tha

t the

sum

of

the

angl

es o

f a tr

iang

le is

180

° and

of a

qu

adril

ater

al is

360

°

•dev

ise

inst

ruct

ions

for a

com

pute

r to

gene

rate

and

tran

sfor

m sh

apes

and

pat

hs

•vis

ualis

e an

d us

e 2-

D re

pres

enta

tions

of

3-D

obj

ects

•enl

arge

2-D

shap

es, g

iven

a c

entr

e of

en

larg

emen

t and

a p

ositi

ve w

hole

-nu

mbe

r sca

le fa

ctor

•kno

w th

at tr

ansl

atio

ns, r

otat

ions

and

re

flect

ions

pre

serv

e le

ngth

and

ang

le a

nd

map

obj

ects

ont

o co

ngru

ent i

mag

es

•use

stra

ight

edg

e an

d co

mpa

sses

to d

o st

anda

rd c

onst

ruct

ions

•ded

uce

and

use

form

ulae

for t

he a

rea

of a

tria

ngle

and

par

alle

logr

am, a

nd th

e vo

lum

e of

a c

uboi

d; c

alcu

late

vol

umes

an

d su

rfac

e ar

eas o

f cub

oids

•kno

w a

nd u

se th

e fo

rmul

ae fo

r the

ci

rcum

fere

nce

and

area

of a

circ

le

•des

ign

a su

rvey

or e

xper

imen

t to

capt

ure

the

nece

ssar

y da

ta fr

om o

ne

or m

ore

sour

ces;

desi

gn, t

rial a

nd, i

f ne

cess

ary,

refin

e da

ta c

olle

ctio

n sh

eets

; co

nstr

uct t

able

s for

larg

e di

scre

te a

nd

cont

inuo

us se

ts o

f raw

dat

a, c

hoos

ing

suita

ble

clas

s int

erva

ls; d

esig

n an

d us

e tw

o-w

ay ta

bles

•sel

ect,

cons

truc

t and

mod

ify, o

n pa

per

and

usin

g IC

T:

-pie

char

ts fo

r cat

egor

ical

dat

a

-bar c

hart

s and

freq

uenc

y di

agra

ms

for d

iscr

ete

and

cont

inuo

us d

ata

-sim

ple

time

grap

hs fo

r tim

e se

ries

-scat

ter g

raph

s•

and

iden

tify

whi

ch a

re m

ost u

sefu

l in

the

cont

ext o

f the

pro

blem

•fin

d an

d re

cord

all

poss

ible

mut

ually

ex

clus

ive

outc

omes

for s

ingl

e ev

ents

an

d tw

o su

cces

sive

eve

nts i

n a

syst

emat

ic w

ay

•kno

w th

at th

e su

m o

f pro

babi

litie

s of a

ll m

utua

lly e

xclu

sive

out

com

es is

1 a

nd

use

this

whe

n so

lvin

g pr

oble

ms

•com

mun

icat

e in

terp

reta

tions

and

re

sults

of a

stat

istic

al su

rvey

usi

ng

sele

cted

tabl

es, g

raph

s and

dia

gram

s in

supp

ort

Leve

l 5•i

dent

ify a

nd o

btai

n ne

cess

ary

info

rmat

ion

to c

arry

thro

ugh

a ta

sk

and

solv

e m

athe

mat

ical

pr

oble

ms

•che

ck re

sults

, co

nsid

erin

g w

heth

er

thes

e ar

e re

ason

able

•sol

ve w

ord

prob

lem

s an

d in

vest

igat

ions

from

a

rang

e of

con

text

s

•sho

w u

nder

stan

ding

of

situ

atio

ns b

y de

scrib

ing

them

mat

hem

atic

ally

us

ing

sym

bols

, wor

ds

and

diag

ram

s

•dra

w si

mpl

e co

nclu

sion

s of t

heir

own

and

give

an

expl

anat

ion

of th

eir

reas

onin

g

•use

und

erst

andi

ng o

f pl

ace

valu

e to

mul

tiply

an

d di

vide

who

le

num

bers

and

dec

imal

s by

10,

100

and

100

0 an

d ex

plai

n th

e ef

fect

•rou

nd d

ecim

als t

o th

e ne

ares

t dec

imal

pla

ce a

nd

orde

r neg

ativ

e nu

mbe

rs

in c

onte

xt

•rec

ogni

se a

nd u

se

num

ber p

atte

rns a

nd

rela

tions

hips

•use

equ

ival

ence

bet

wee

n fr

actio

ns a

nd o

rder

fr

actio

ns a

nd d

ecim

als

•red

uce

a fr

actio

n to

its

sim

ples

t for

m b

y ca

ncel

ling

com

mon

fa

ctor

s

•und

erst

and

sim

ple

ratio

•use

kno

wn

fact

s, pl

ace

valu

e,

know

ledg

e of

ope

ratio

ns a

nd b

rack

ets

to c

alcu

late

incl

udin

g us

ing

all f

our

oper

atio

ns w

ith d

ecim

als t

o tw

o pl

aces

•use

a c

alcu

lato

r whe

re a

ppro

pria

te

to c

alcu

late

frac

tions

/per

cent

ages

of

quan

titie

s/m

easu

rem

ents

•und

erst

and

and

use

an a

ppro

pria

te

non-

calc

ulat

or m

etho

d fo

r sol

ving

pr

oble

ms t

hat i

nvol

ve m

ultip

lyin

g an

d di

vidi

ng a

ny th

ree-

digi

t num

ber b

y an

y tw

o-di

git n

umbe

r

•sol

ve si

mpl

e pr

oble

ms i

nvol

ving

or

derin

g, a

ddin

g, su

btra

ctin

g ne

gativ

e nu

mbe

rs in

con

text

•sol

ve si

mpl

e pr

oble

ms i

nvol

ving

ratio

an

d di

rect

pro

port

ion

•app

ly in

vers

e op

erat

ions

and

ap

prox

imat

e to

che

ck a

nsw

ers t

o pr

oble

ms a

re o

f the

cor

rect

mag

nitu

de

•con

stru

ct, e

xpre

ss in

sym

bolic

fo

rm, a

nd u

se si

mpl

e fo

rmul

ae in

volv

ing

one

or tw

o op

erat

ions

•use

and

inte

rpre

t coo

rdin

ates

in

all

four

qua

dran

ts

•use

a w

ider

rang

e of

pro

pert

ies o

f 2-D

an

d 3-

D sh

apes

and

iden

tify

all t

he

sym

met

ries o

f 2-D

shap

es

•use

lang

uage

ass

ocia

ted

with

ang

le a

nd

know

and

use

the

angl

e su

m o

f a tr

iang

le

and

that

of a

ngle

s at a

poi

nt

•rea

son

abou

t pos

ition

and

mov

emen

t and

tr

ansf

orm

shap

es

•mea

sure

and

dra

w a

ngle

s to

the

near

est

degr

ee, w

hen

cons

truc

ting

mod

els a

nd

draw

ing

or u

sing

shap

es

•rea

d an

d in

terp

ret s

cale

s on

a ra

nge

of

mea

surin

g in

stru

men

ts, e

xpla

inin

g w

hat

each

labe

lled

divi

sion

repr

esen

ts

•sol

ve p

robl

ems i

nvol

ving

the

conv

ersi

on

of u

nits

and

mak

e se

nsib

le e

stim

ates

of a

ra

nge

of m

easu

res i

n re

latio

n to

eve

ryda

y si

tuat

ions

•und

erst

and

and

use

the

form

ula

for t

he

area

of a

rect

angl

e an

d di

stin

guis

h ar

ea

from

per

imet

er

•ask

que

stio

ns, p

lan

how

to a

nsw

er th

em

and

colle

ct th

e da

ta re

quire

d

•in

prob

abili

ty, s

elec

t met

hods

bas

ed

on e

qual

ly li

kely

out

com

es a

nd

expe

rimen

tal e

vide

nce,

as a

ppro

pria

te

•und

erst

and

and

use

the

prob

abili

ty

scal

e fr

om 0

to 1

•und

erst

and

and

use

the

mea

n of

di

scre

te d

ata

and

com

pare

two

sim

ple

dist

ribut

ions

, usi

ng th

e ra

nge

and

one

of m

ode,

med

ian

or m

ean

•und

erst

and

that

diff

eren

t out

com

es

may

resu

lt fr

om re

peat

ing

an

expe

rimen

t

•int

erpr

et g

raph

s and

dia

gram

s, in

clud

ing

pie

char

ts, a

nd d

raw

co

nclu

sion

s

•cre

ate

and

inte

rpre

t lin

e gr

aphs

whe

re

the

inte

rmed

iate

val

ues h

ave

mea

ning

BL

IE

Key:

BL-B

elow

Lev

el

IE-In

suff

icie

nt E

vide

nce

Ove

rall

asse

ssm

ent (

tick

one

box

only

)Lo

w 5

S

ecur

e 5

Hig

h 5

Low

6

Sec

ure

6

Hig

h 6

Page 9: APP in mathematics at Key Stage 3: Assessment guidelineswsassets.s3.amazonaws.com/ws/nso/pdf/96ce8155ab25c4849a7... · 2011-06-06 · show understanding of situations by describing

4 The National Strategies | Secondary Assessing Pupil Progress at Key Stage 3: Assessment guidelines

00730-2008BKT-EN © Crown copyright 2008

5The National Strategies | Secondary Assessing Pupil Progress at Key Stage 3: Assessment guidelines

© Crown copyright 2008 00730-2008BKT-EN

Mat

hem

atic

s ass

essm

ent g

uide

lines

: lev

els 5

and

6

leve

ls 5

and

6

P

upil

nam

e……

……

……

….C

lass

/gro

up…

……

……

……

..Dat

e……

……

Usi

ng a

nd a

pply

ing

mat

hem

atic

sN

umbe

rs a

nd th

e nu

mbe

r sy

stem

Calc

ulat

ing

Alg

ebra

Shap

e, s

pace

and

mea

sure

Han

dlin

g da

ta

Leve

l 6•s

olve

pro

blem

s an

d ca

rry

thro

ugh

subs

tant

ial t

asks

by

bre

akin

g th

em

into

smal

ler,

mor

e m

anag

eabl

e ta

sks,

usin

g a

rang

e of

ef

ficie

nt te

chni

ques

, m

etho

ds a

nd

reso

urce

s, in

clud

ing

ICT;

giv

e so

lutio

ns to

an

appr

opria

te d

egre

e of

ac

cura

cy

•int

erpr

et, d

iscu

ss a

nd

synt

hesi

se in

form

atio

n pr

esen

ted

in a

var

iety

of

mat

hem

atic

al fo

rms

•pre

sent

a c

onci

se,

reas

oned

arg

umen

t, us

ing

sym

bols

, di

agra

ms,

grap

hs a

nd

rela

ted

expl

anat

ory

text

s

•use

logi

cal a

rgum

ent t

o es

tabl

ish

the

trut

h of

a

stat

emen

t

•use

the

equi

vale

nce

of

frac

tions

, dec

imal

s and

pe

rcen

tage

s to

com

pare

pr

opor

tions

•cal

cula

te p

erce

ntag

es a

nd fi

nd th

e ou

tcom

e of

a g

iven

per

cent

age

incr

ease

or d

ecre

ase

•div

ide

a qu

antit

y in

to tw

o or

mor

e pa

rts i

n a

give

n ra

tio a

nd so

lve

prob

lem

s inv

olvi

ng ra

tio a

nd d

irect

pr

opor

tion

•use

pro

port

iona

l rea

soni

ng to

solv

e a

prob

lem

, cho

osin

g th

e co

rrec

t nu

mbe

rs to

take

as 1

00%

, or a

s a

who

le

•add

and

subt

ract

frac

tions

by

writ

ing

them

with

a c

omm

on d

enom

inat

or,

calc

ulat

e fr

actio

ns o

f qua

ntiti

es

(frac

tion

answ

ers)

, mul

tiply

and

div

ide

an in

tege

r by

a fr

actio

n

•use

syst

emat

ic tr

ial a

nd

impr

ovem

ent m

etho

ds a

nd

ICT

tool

s to

find

appr

oxim

ate

solu

tions

to e

quat

ions

such

as

x³ +

x =

20

•con

stru

ct a

nd so

lve

linea

r eq

uatio

ns w

ith in

tege

r co

effic

ient

s, us

ing

an

appr

opria

te m

etho

d

•gen

erat

e te

rms o

f a se

quen

ce

usin

g te

rm-t

o-te

rm a

nd

posi

tion-

to-t

erm

def

initi

ons

of th

e se

quen

ce, o

n pa

per a

nd

usin

g IC

T; w

rite

an e

xpre

ssio

n to

des

crib

e th

e nt

h te

rm o

f an

arith

met

ic se

quen

ce.

•plo

t the

gra

phs o

f lin

ear

func

tions

, whe

re y

is g

iven

ex

plic

itly

in te

rms o

f x;

reco

gnis

e th

at e

quat

ions

of

the

form

y =

mx

+ c

corr

espo

nd to

stra

ight

-line

gr

aphs

•con

stru

ct fu

nctio

ns a

risin

g fr

om re

al-li

fe p

robl

ems a

nd

plot

thei

r cor

resp

ondi

ng

grap

hs;

•int

erpr

et g

raph

s aris

ing

from

re

al si

tuat

ions

•cla

ssify

qua

drila

tera

ls b

y th

eir g

eom

etric

pr

oper

ties

•sol

ve g

eom

etric

al p

robl

ems u

sing

pr

oper

ties o

f ang

les,

of p

aral

lel a

nd

inte

rsec

ting

lines

, and

of t

riang

les a

nd

othe

r pol

ygon

s

•ide

ntify

alte

rnat

e an

d co

rres

pond

ing

angl

es; u

nder

stan

d a

proo

f tha

t the

sum

of

the

angl

es o

f a tr

iang

le is

180

° and

of a

qu

adril

ater

al is

360

°

•dev

ise

inst

ruct

ions

for a

com

pute

r to

gene

rate

and

tran

sfor

m sh

apes

and

pat

hs

•vis

ualis

e an

d us

e 2-

D re

pres

enta

tions

of

3-D

obj

ects

•enl

arge

2-D

shap

es, g

iven

a c

entr

e of

en

larg

emen

t and

a p

ositi

ve w

hole

-nu

mbe

r sca

le fa

ctor

•kno

w th

at tr

ansl

atio

ns, r

otat

ions

and

re

flect

ions

pre

serv

e le

ngth

and

ang

le a

nd

map

obj

ects

ont

o co

ngru

ent i

mag

es

•use

stra

ight

edg

e an

d co

mpa

sses

to d

o st

anda

rd c

onst

ruct

ions

•ded

uce

and

use

form

ulae

for t

he a

rea

of a

tria

ngle

and

par

alle

logr

am, a

nd th

e vo

lum

e of

a c

uboi

d; c

alcu

late

vol

umes

an

d su

rfac

e ar

eas o

f cub

oids

•kno

w a

nd u

se th

e fo

rmul

ae fo

r the

ci

rcum

fere

nce

and

area

of a

circ

le

•des

ign

a su

rvey

or e

xper

imen

t to

capt

ure

the

nece

ssar

y da

ta fr

om o

ne

or m

ore

sour

ces;

desi

gn, t

rial a

nd, i

f ne

cess

ary,

refin

e da

ta c

olle

ctio

n sh

eets

; co

nstr

uct t

able

s for

larg

e di

scre

te a

nd

cont

inuo

us se

ts o

f raw

dat

a, c

hoos

ing

suita

ble

clas

s int

erva

ls; d

esig

n an

d us

e tw

o-w

ay ta

bles

•sel

ect,

cons

truc

t and

mod

ify, o

n pa

per

and

usin

g IC

T:

-pie

char

ts fo

r cat

egor

ical

dat

a

-bar c

hart

s and

freq

uenc

y di

agra

ms

for d

iscr

ete

and

cont

inuo

us d

ata

-sim

ple

time

grap

hs fo

r tim

e se

ries

-scat

ter g

raph

s•

and

iden

tify

whi

ch a

re m

ost u

sefu

l in

the

cont

ext o

f the

pro

blem

•fin

d an

d re

cord

all

poss

ible

mut

ually

ex

clus

ive

outc

omes

for s

ingl

e ev

ents

an

d tw

o su

cces

sive

eve

nts i

n a

syst

emat

ic w

ay

•kno

w th

at th

e su

m o

f pro

babi

litie

s of a

ll m

utua

lly e

xclu

sive

out

com

es is

1 a

nd

use

this

whe

n so

lvin

g pr

oble

ms

•com

mun

icat

e in

terp

reta

tions

and

re

sults

of a

stat

istic

al su

rvey

usi

ng

sele

cted

tabl

es, g

raph

s and

dia

gram

s in

supp

ort

Leve

l 5•i

dent

ify a

nd o

btai

n ne

cess

ary

info

rmat

ion

to c

arry

thro

ugh

a ta

sk

and

solv

e m

athe

mat

ical

pr

oble

ms

•che

ck re

sults

, co

nsid

erin

g w

heth

er

thes

e ar

e re

ason

able

•sol

ve w

ord

prob

lem

s an

d in

vest

igat

ions

from

a

rang

e of

con

text

s

•sho

w u

nder

stan

ding

of

situ

atio

ns b

y de

scrib

ing

them

mat

hem

atic

ally

us

ing

sym

bols

, wor

ds

and

diag

ram

s

•dra

w si

mpl

e co

nclu

sion

s of t

heir

own

and

give

an

expl

anat

ion

of th

eir

reas

onin

g

•use

und

erst

andi

ng o

f pl

ace

valu

e to

mul

tiply

an

d di

vide

who

le

num

bers

and

dec

imal

s by

10,

100

and

100

0 an

d ex

plai

n th

e ef

fect

•rou

nd d

ecim

als t

o th

e ne

ares

t dec

imal

pla

ce a

nd

orde

r neg

ativ

e nu

mbe

rs

in c

onte

xt

•rec

ogni

se a

nd u

se

num

ber p

atte

rns a

nd

rela

tions

hips

•use

equ

ival

ence

bet

wee

n fr

actio

ns a

nd o

rder

fr

actio

ns a

nd d

ecim

als

•red

uce

a fr

actio

n to

its

sim

ples

t for

m b

y ca

ncel

ling

com

mon

fa

ctor

s

•und

erst

and

sim

ple

ratio

•use

kno

wn

fact

s, pl

ace

valu

e,

know

ledg

e of

ope

ratio

ns a

nd b

rack

ets

to c

alcu

late

incl

udin

g us

ing

all f

our

oper

atio

ns w

ith d

ecim

als t

o tw

o pl

aces

•use

a c

alcu

lato

r whe

re a

ppro

pria

te

to c

alcu

late

frac

tions

/per

cent

ages

of

quan

titie

s/m

easu

rem

ents

•und

erst

and

and

use

an a

ppro

pria

te

non-

calc

ulat

or m

etho

d fo

r sol

ving

pr

oble

ms t

hat i

nvol

ve m

ultip

lyin

g an

d di

vidi

ng a

ny th

ree-

digi

t num

ber b

y an

y tw

o-di

git n

umbe

r

•sol

ve si

mpl

e pr

oble

ms i

nvol

ving

or

derin

g, a

ddin

g, su

btra

ctin

g ne

gativ

e nu

mbe

rs in

con

text

•sol

ve si

mpl

e pr

oble

ms i

nvol

ving

ratio

an

d di

rect

pro

port

ion

•app

ly in

vers

e op

erat

ions

and

ap

prox

imat

e to

che

ck a

nsw

ers t

o pr

oble

ms a

re o

f the

cor

rect

mag

nitu

de

•con

stru

ct, e

xpre

ss in

sym

bolic

fo

rm, a

nd u

se si

mpl

e fo

rmul

ae in

volv

ing

one

or tw

o op

erat

ions

•use

and

inte

rpre

t coo

rdin

ates

in

all

four

qua

dran

ts

•use

a w

ider

rang

e of

pro

pert

ies o

f 2-D

an

d 3-

D sh

apes

and

iden

tify

all t

he

sym

met

ries o

f 2-D

shap

es

•use

lang

uage

ass

ocia

ted

with

ang

le a

nd

know

and

use

the

angl

e su

m o

f a tr

iang

le

and

that

of a

ngle

s at a

poi

nt

•rea

son

abou

t pos

ition

and

mov

emen

t and

tr

ansf

orm

shap

es

•mea

sure

and

dra

w a

ngle

s to

the

near

est

degr

ee, w

hen

cons

truc

ting

mod

els a

nd

draw

ing

or u

sing

shap

es

•rea

d an

d in

terp

ret s

cale

s on

a ra

nge

of

mea

surin

g in

stru

men

ts, e

xpla

inin

g w

hat

each

labe

lled

divi

sion

repr

esen

ts

•sol

ve p

robl

ems i

nvol

ving

the

conv

ersi

on

of u

nits

and

mak

e se

nsib

le e

stim

ates

of a

ra

nge

of m

easu

res i

n re

latio

n to

eve

ryda

y si

tuat

ions

•und

erst

and

and

use

the

form

ula

for t

he

area

of a

rect

angl

e an

d di

stin

guis

h ar

ea

from

per

imet

er

•ask

que

stio

ns, p

lan

how

to a

nsw

er th

em

and

colle

ct th

e da

ta re

quire

d

•in

prob

abili

ty, s

elec

t met

hods

bas

ed

on e

qual

ly li

kely

out

com

es a

nd

expe

rimen

tal e

vide

nce,

as a

ppro

pria

te

•und

erst

and

and

use

the

prob

abili

ty

scal

e fr

om 0

to 1

•und

erst

and

and

use

the

mea

n of

di

scre

te d

ata

and

com

pare

two

sim

ple

dist

ribut

ions

, usi

ng th

e ra

nge

and

one

of m

ode,

med

ian

or m

ean

•und

erst

and

that

diff

eren

t out

com

es

may

resu

lt fr

om re

peat

ing

an

expe

rimen

t

•int

erpr

et g

raph

s and

dia

gram

s, in

clud

ing

pie

char

ts, a

nd d

raw

co

nclu

sion

s

•cre

ate

and

inte

rpre

t lin

e gr

aphs

whe

re

the

inte

rmed

iate

val

ues h

ave

mea

ning

BL

IE

Key:

BL-B

elow

Lev

el

IE-In

suff

icie

nt E

vide

nce

Ove

rall

asse

ssm

ent (

tick

one

box

only

)Lo

w 5

S

ecur

e 5

Hig

h 5

Low

6

Sec

ure

6

Hig

h 6

Mat

hem

atic

s ass

essm

ent g

uide

lines

: lev

els 6

and

7

leve

ls 6

and

7

Pup

il na

me…

……

……

……

.Cla

ss/g

roup

……

……

……

…..D

ate…

……

Usi

ng a

nd a

pply

ing

mat

hem

atic

sN

umbe

rs a

nd

the

num

ber

syst

em

Calc

ulat

ing

Alg

ebra

Shap

e, s

pace

and

mea

sure

Han

dlin

g da

ta

Leve

l 7•s

olve

incr

easi

ngly

de

man

ding

pro

blem

s an

d ev

alua

te so

lutio

ns;

expl

ore

conn

ectio

ns

in m

athe

mat

ics a

cros

s a

rang

e of

con

text

s: nu

mbe

r, al

gebr

a, sh

ape,

sp

ace

and

mea

sure

s, an

d ha

ndlin

g da

ta; r

efin

e or

ex

tend

the

mat

hem

atic

s us

ed to

gen

erat

e fu

ller

solu

tions

•giv

e re

ason

s for

cho

ice

of

pres

enta

tion,

exp

lain

ing

sele

cted

feat

ures

and

sh

owin

g in

sigh

t int

o th

e pr

oble

ms s

truc

ture

•jus

tify

gene

ralis

atio

ns,

argu

men

ts o

r sol

utio

ns

•app

reci

ate

the

diff

eren

ce

betw

een

mat

hem

atic

al

expl

anat

ion

and

expe

rimen

tal e

vide

nce

•und

erst

and

and

use

prop

ortio

nalit

y

•cal

cula

te th

e re

sult

of a

ny

prop

ortio

nal c

hang

e us

ing

mul

tiplic

ativ

e m

etho

ds

•und

erst

and

the

effe

cts o

f m

ultip

lyin

g an

d di

vidi

ng

by n

umbe

rs b

etw

een

0 an

d 1,

add

, sub

trac

t, m

ultip

ly a

nd d

ivid

e fr

actio

ns

•mak

e an

d ju

stify

est

imat

es

and

appr

oxim

atio

ns o

f ca

lcul

atio

ns; e

stim

ate

calc

ulat

ions

by

roun

ding

nu

mbe

rs to

one

sign

ifica

nt

figur

e an

d m

ultip

lyin

g an

d di

vidi

ng m

enta

lly

•use

a c

alcu

lato

r eff

icie

ntly

an

d ap

prop

riate

ly

to p

erfo

rm c

ompl

ex

calc

ulat

ions

with

num

bers

of

any

size

, kno

win

g no

t to

roun

d du

ring

inte

rmed

iate

st

eps o

f a c

alcu

latio

n

•squ

are

a lin

ear e

xpre

ssio

n, a

nd

expa

nd a

nd si

mpl

ify th

e pr

oduc

t of

two

linea

r exp

ress

ions

of t

he fo

rm (x

±

n) a

nd si

mpl

ify th

e co

rres

pond

ing

quad

ratic

exp

ress

ion

•use

alg

ebra

ic a

nd g

raph

ical

m

etho

ds to

solv

e si

mul

tane

ous

linea

r equ

atio

ns in

two

varia

bles

•sol

ve in

equa

litie

s in

one

varia

ble

and

repr

esen

t the

solu

tion

set o

n a

num

ber l

ine

•use

form

ulae

from

mat

hem

atic

s and

ot

her s

ubje

cts;

subs

titut

e nu

mbe

rs

into

exp

ress

ions

and

form

ulae

; de

rive

a fo

rmul

a an

d, in

sim

ple

case

s, ch

ange

its s

ubje

ct

•fin

d th

e ne

xt te

rm a

nd n

th te

rm o

f qu

adra

tic se

quen

ces a

nd fu

nctio

ns

and

expl

ore

thei

r pro

pert

ies

•plo

t gra

phs o

f sim

ple

quad

ratic

and

cu

bic

func

tions

, e.g

. y =

x²,

y =

3x²

+ 4,

y =

•und

erst

and

and

appl

y Py

thag

oras

’ the

orem

whe

n so

lvin

g pr

oble

ms i

n 2-

D

•cal

cula

te le

ngth

s, ar

eas a

nd v

olum

es in

pla

ne

shap

es a

nd ri

ght p

rism

s

•enl

arge

2-D

shap

es, g

iven

a c

entr

e of

enl

arge

men

t an

d a

frac

tiona

l sca

le fa

ctor

, on

pape

r and

usi

ng

ICT;

reco

gnis

e th

e si

mila

rity

of th

e re

sulti

ng

shap

es

•fin

d th

e lo

cus o

f a p

oint

that

mov

es a

ccor

ding

to a

gi

ven

rule

, bot

h by

reas

onin

g an

d us

ing

ICT

•rec

ogni

se th

at m

easu

rem

ents

giv

en to

the

near

est

who

le u

nit m

ay b

e in

accu

rate

by

up to

one

-hal

f of

the

unit

in e

ither

dire

ctio

n

•und

erst

and

and

use

mea

sure

s of s

peed

(and

oth

er

com

poun

d m

easu

res s

uch

as d

ensi

ty o

r pre

ssur

e)

to so

lve

prob

lem

s

•sug

gest

a p

robl

em to

exp

lore

usi

ng st

atis

tical

m

etho

ds, f

ram

e qu

estio

ns a

nd ra

ise

conj

ectu

res;

iden

tify

poss

ible

sour

ces o

f bia

s and

pla

n ho

w to

m

inim

ise

it

•sel

ect,

cons

truc

t and

mod

ify, o

n pa

per a

nd u

sing

IC

T su

itabl

e gr

aphi

cal r

epre

sent

atio

n to

pro

gres

s an

enq

uiry

incl

udin

g fr

eque

ncy

poly

gons

and

lin

es o

f bes

t fit

on sc

atte

r gra

phs

•est

imat

e th

e m

ean,

med

ian

and

rang

e of

a se

t of

gro

uped

dat

a an

d de

term

ine

the

mod

al c

lass

, se

lect

ing

the

stat

istic

mos

t app

ropr

iate

to th

e lin

e of

enq

uiry

•com

pare

two

or m

ore

dist

ribut

ions

and

mak

e in

fere

nces

, usi

ng th

e sh

ape

of th

e di

strib

utio

ns

and

mea

sure

s of a

vera

ge a

nd ra

nge

•und

erst

and

rela

tive

freq

uenc

y as

an

estim

ate

of

prob

abili

ty a

nd u

se th

is to

com

pare

out

com

es o

f an

exp

erim

ent

•exa

min

e cr

itica

lly th

e re

sults

of a

stat

istic

al

enqu

iry, a

nd ju

stify

the

choi

ce o

f sta

tistic

al

repr

esen

tatio

n in

writ

ten

pres

enta

tion

Leve

l 6•s

olve

pro

blem

s and

car

ry

thro

ugh

subs

tant

ial

task

s by

brea

king

them

in

to sm

alle

r, m

ore

man

agea

ble

task

s, us

ing

a ra

nge

of e

ffic

ient

te

chni

ques

, met

hods

an

d re

sour

ces,

incl

udin

g IC

T; g

ive

solu

tions

to a

n ap

prop

riate

deg

ree

of

accu

racy

•int

erpr

et, d

iscu

ss a

nd

synt

hesi

se in

form

atio

n pr

esen

ted

in a

var

iety

of

mat

hem

atic

al fo

rms

•pre

sent

a c

onci

se,

reas

oned

arg

umen

t, us

ing

sym

bols

, dia

gram

s, gr

aphs

and

rela

ted

expl

anat

ory

text

s

•use

logi

cal a

rgum

ent t

o es

tabl

ish

the

trut

h of

a

stat

emen

t

•use

the

equi

vale

nce

of fr

actio

ns,

deci

mal

s and

pe

rcen

tage

s to

com

pare

pr

opor

tions

•cal

cula

te p

erce

ntag

es

and

find

the

outc

ome

of a

gi

ven

perc

enta

ge in

crea

se

or d

ecre

ase

•div

ide

a qu

antit

y in

to tw

o or

mor

e pa

rts i

n a

give

n ra

tio a

nd so

lve

prob

lem

s in

volv

ing

ratio

and

dire

ct

prop

ortio

n

•use

pro

port

iona

l re

ason

ing

to so

lve

a pr

oble

m, c

hoos

ing

the

corr

ect n

umbe

rs to

take

as

100%

, or a

s a w

hole

•add

and

subt

ract

frac

tions

by

writ

ing

them

with

a

com

mon

den

omin

ator

, ca

lcul

ate

frac

tions

of

quan

titie

s (fr

actio

n an

swer

s), m

ultip

ly a

nd

divi

de a

n in

tege

r by

a fr

actio

n

•use

syst

emat

ic tr

ial a

nd

impr

ovem

ent m

etho

ds a

nd IC

T to

ols t

o fin

d ap

prox

imat

e so

lutio

ns

to e

quat

ions

such

as x

³ + x

= 2

0

•con

stru

ct a

nd so

lve

linea

r equ

atio

ns

with

inte

ger c

oeff

icie

nts,

usin

g an

ap

prop

riate

met

hod

•gen

erat

e te

rms o

f a se

quen

ce u

sing

te

rm-t

o-te

rm a

nd p

ositi

on-t

o-te

rm d

efin

ition

s of t

he se

quen

ce,

on p

aper

and

usi

ng IC

T; w

rite

an

expr

essi

on to

des

crib

e th

e nt

h te

rm

of a

n ar

ithm

etic

sequ

ence

.

•plo

t the

gra

phs o

f lin

ear f

unct

ions

, w

here

y is

giv

en e

xplic

itly

in te

rms

of x

; rec

ogni

se th

at e

quat

ions

of

the

form

y =

mx

+ c

corr

espo

nd to

st

raig

ht-li

ne g

raph

s

•con

stru

ct fu

nctio

ns a

risin

g fr

om

real

-life

pro

blem

s and

plo

t the

ir co

rres

pond

ing

grap

hs;

•int

erpr

et g

raph

s aris

ing

from

real

si

tuat

ions

•cla

ssify

qua

drila

tera

ls b

y th

eir g

eom

etric

pr

oper

ties

•sol

ve g

eom

etric

al p

robl

ems u

sing

pro

pert

ies o

f an

gles

, of p

aral

lel a

nd in

ters

ectin

g lin

es, a

nd o

f tr

iang

les a

nd o

ther

pol

ygon

s

•ide

ntify

alte

rnat

e an

d co

rres

pond

ing

angl

es;

unde

rsta

nd a

pro

of th

at th

e su

m o

f the

ang

les o

f a

tria

ngle

is 1

80° a

nd o

f a q

uadr

ilate

ral i

s 360

°

•dev

ise

inst

ruct

ions

for a

com

pute

r to

gene

rate

an

d tr

ansf

orm

shap

es a

nd p

aths

•vis

ualis

e an

d us

e 2-

D re

pres

enta

tions

of 3

-D

obje

cts

•enl

arge

2-D

shap

es, g

iven

a c

entr

e of

enl

arge

men

t an

d a

posi

tive

who

le-n

umbe

r sca

le fa

ctor

•kno

w th

at tr

ansl

atio

ns, r

otat

ions

and

refle

ctio

ns

pres

erve

leng

th a

nd a

ngle

and

map

obj

ects

ont

o co

ngru

ent i

mag

es

•use

stra

ight

edg

e an

d co

mpa

sses

to d

o st

anda

rd

cons

truc

tions

•ded

uce

and

use

form

ulae

for t

he a

rea

of a

tria

ngle

an

d pa

ralle

logr

am, a

nd th

e vo

lum

e of

a c

uboi

d;

calc

ulat

e vo

lum

es a

nd su

rfac

e ar

eas o

f cub

oids

•kno

w a

nd u

se th

e fo

rmul

ae fo

r the

circ

umfe

renc

e an

d ar

ea o

f a c

ircle

•des

ign

a su

rvey

or e

xper

imen

t to

capt

ure

the

nece

ssar

y da

ta fr

om o

ne o

r mor

e so

urce

s; de

sign

, tr

ial a

nd, i

f nec

essa

ry, r

efin

e da

ta c

olle

ctio

n sh

eets

; co

nstr

uct t

able

s for

larg

e di

scre

te a

nd c

ontin

uous

se

ts o

f raw

dat

a, c

hoos

ing

suita

ble

clas

s int

erva

ls;

desi

gn a

nd u

se tw

o-w

ay ta

bles

•sel

ect,

cons

truc

t and

mod

ify, o

n pa

per a

nd u

sing

IC

T: -pie

char

ts fo

r cat

egor

ical

dat

a

-bar c

hart

s and

freq

uenc

y di

agra

ms f

or

disc

rete

and

con

tinuo

us d

ata

-sim

ple

time

grap

hs fo

r tim

e se

ries

-scat

ter g

raph

s•

and

iden

tify

whi

ch a

re m

ost u

sefu

l in

the

cont

ext

of th

e pr

oble

m

•fin

d an

d re

cord

all

poss

ible

mut

ually

exc

lusi

ve

outc

omes

for s

ingl

e ev

ents

and

two

succ

essi

ve

even

ts in

a sy

stem

atic

way

•kno

w th

at th

e su

m o

f pro

babi

litie

s of a

ll m

utua

lly

excl

usiv

e ou

tcom

es is

1 a

nd u

se th

is w

hen

solv

ing

prob

lem

s

•com

mun

icat

e in

terp

reta

tions

and

resu

lts o

f a

stat

istic

al su

rvey

usi

ng se

lect

ed ta

bles

, gra

phs a

nd

diag

ram

s in

supp

ort

BL

IE

Key:

BL-B

elow

leve

l IE

-Insu

ffic

ient

evi

denc

e

Ove

rall

asse

ssm

ent (

tick

one

box

only

) L

ow 6

S

ecur

e 6

Hig

h 6

Low

7

Sec

ure

7

Hig

h 7

Page 10: APP in mathematics at Key Stage 3: Assessment guidelineswsassets.s3.amazonaws.com/ws/nso/pdf/96ce8155ab25c4849a7... · 2011-06-06 · show understanding of situations by describing

6 The National Strategies | Secondary Assessing Pupil Progress at Key Stage 3: Assessment guidelines

00730-2008BKT-EN © Crown copyright 2008

Mat

hem

atic

s ass

essm

ent g

uide

lines

: lev

els 7

and

8

Pupi

l nam

e……

……

……

….C

lass

/gro

up…

……

……

……

..Dat

e……

……

Usi

ng a

nd a

pply

ing

mat

hem

atic

sN

umbe

rs a

nd th

e nu

mbe

r sys

tem

Calc

ulat

ing

Alg

ebra

Shap

e, s

pace

and

mea

sure

Han

dlin

g da

ta

Leve

l 8•d

evel

op a

nd fo

llow

alte

rnat

ive

met

hods

and

app

roac

hes

•ref

lect

on

lines

of e

nqui

ry w

hen

expl

orin

g m

athe

mat

ical

task

s

•sel

ect a

nd c

ombi

ne k

now

n fa

cts

and

prob

lem

-sol

ving

stra

tegi

es

to so

lve

prob

lem

s of i

ncre

asin

g co

mpl

exity

•con

vey

mat

hem

atic

al m

eani

ng

thro

ugh

prec

ise

and

cons

iste

nt

use

of sy

mbo

ls

•exa

min

e ge

nera

lisat

ions

or

solu

tions

reac

hed

in a

n ac

tivity

, co

mm

entin

g co

nstr

uctiv

ely

on th

e re

ason

ing

and

logi

c or

the

proc

ess

empl

oyed

, or t

he re

sults

obt

aine

d

•dis

tingu

ish

betw

een

prac

tical

de

mon

stra

tion

and

proo

f; kn

ow u

nder

lyin

g as

sum

ptio

ns,

reco

gnis

ing

thei

r im

port

ance

an

d lim

itatio

ns, a

nd th

e ef

fect

of

vary

ing

them

•und

erst

and

the

equi

vale

nce

betw

een

recu

rrin

g de

cim

als a

nd

frac

tions

•use

frac

tions

or

perc

enta

ges t

o so

lve

prob

lem

s inv

olvi

ng

repe

ated

pro

port

iona

l ch

ange

s or t

he c

alcu

latio

n of

the

orig

inal

qua

ntity

gi

ven

the

resu

lt of

a

prop

ortio

nal c

hang

e

•sol

ve p

robl

ems i

nvol

ving

ca

lcul

atin

g w

ith p

ower

s, ro

ots a

nd n

umbe

rs

expr

esse

d in

stan

dard

form

, ch

ecki

ng fo

r cor

rect

ord

er

of m

agni

tude

and

usi

ng a

ca

lcul

ator

as a

ppro

pria

te

•fac

toris

e qu

adra

tic e

xpre

ssio

ns

incl

udin

g th

e di

ffer

ence

of t

wo

squa

res,

e.g.

: x² –

9 =

(x +

3) (

x –

3)

•man

ipul

ate

alge

brai

c fo

rmul

ae,

equa

tions

and

exp

ress

ions

, fin

ding

co

mm

on fa

ctor

s and

mul

tiply

ing

two

linea

r exp

ress

ions

•der

ive

and

use

mor

e co

mpl

ex fo

rmul

ae

and

chan

ge th

e su

bjec

t of a

form

ula

•eva

luat

e al

gebr

aic

form

ulae

, su

bstit

utin

g fr

actio

ns, d

ecim

als a

nd

nega

tive

num

bers

•sol

ve in

equa

litie

s in

two

varia

bles

and

fin

d th

e so

lutio

n se

t

•ske

tch,

inte

rpre

t and

iden

tify

grap

hs o

f lin

ear,

quad

ratic

, cub

ic a

nd re

cipr

ocal

fu

nctio

ns, a

nd g

raph

s tha

t mod

el re

al

situ

atio

ns

•und

erst

and

the

effe

ct o

n a

grap

h of

ad

ditio

n of

(or m

ultip

licat

ion

by)

a co

nsta

nt

•und

erst

and

and

use

cong

ruen

ce

and

mat

hem

atic

al si

mila

rity

•und

erst

and

and

use

trig

onom

etric

al re

latio

nshi

ps

in ri

ght-

angl

ed tr

iang

les,

and

use

thes

e to

solv

e pr

oble

ms,

incl

udin

g th

ose

invo

lvin

g be

arin

gs

•und

erst

and

the

diff

eren

ce

betw

een

form

ulae

for p

erim

eter

, ar

ea a

nd v

olum

e in

sim

ple

cont

exts

by

cons

ider

ing

dim

ensi

ons

•est

imat

e an

d fin

d th

e m

edia

n, q

uart

iles

and

inte

rqua

rtile

rang

e fo

r lar

ge d

ata

sets

, in

clud

ing

usin

g a

cum

ulat

ive

freq

uenc

y di

agra

m

•com

pare

two

or m

ore

dist

ribut

ions

and

m

ake

infe

renc

es, u

sing

the

shap

e of

the

dist

ribut

ions

and

mea

sure

s of a

vera

ge a

nd

spre

ad in

clud

ing

med

ian

and

quar

tiles

•kno

w w

hen

to a

dd o

r mul

tiply

two

prob

abili

ties

•use

tree

dia

gram

s to

calc

ulat

e pr

obab

ilitie

s of

com

bina

tions

of i

ndep

ende

nt e

vent

s

Leve

l 7•s

olve

incr

easi

ngly

dem

andi

ng

prob

lem

s and

eva

luat

e so

lutio

ns; e

xplo

re c

onne

ctio

ns

in m

athe

mat

ics a

cros

s a ra

nge

of c

onte

xts:

num

ber,

alge

bra,

sh

ape,

spac

e an

d m

easu

res,

and

hand

ling

data

; ref

ine

or e

xten

d th

e m

athe

mat

ics u

sed

to g

ener

ate

fulle

r sol

utio

ns

•giv

e re

ason

s for

cho

ice

of

pres

enta

tion,

exp

lain

ing

sele

cted

fe

atur

es a

nd sh

owin

g in

sigh

t int

o th

e pr

oble

ms s

truc

ture

•jus

tify

gene

ralis

atio

ns, a

rgum

ents

or

solu

tions

•app

reci

ate

the

diff

eren

ce b

etw

een

mat

hem

atic

al e

xpla

natio

n an

d ex

perim

enta

l evi

denc

e

•und

erst

and

and

use

prop

ortio

nalit

y

•cal

cula

te th

e re

sult

of a

ny

prop

ortio

nal c

hang

e us

ing

mul

tiplic

ativ

e m

etho

ds

•und

erst

and

the

effe

cts o

f m

ultip

lyin

g an

d di

vidi

ng b

y nu

mbe

rs b

etw

een

0 an

d 1,

ad

d, su

btra

ct, m

ultip

ly a

nd

divi

de fr

actio

ns

•mak

e an

d ju

stify

est

imat

es

and

appr

oxim

atio

ns o

f ca

lcul

atio

ns; e

stim

ate

calc

ulat

ions

by

roun

ding

nu

mbe

rs to

one

sign

ifica

nt

figur

e an

d m

ultip

lyin

g an

d di

vidi

ng m

enta

lly

•use

a c

alcu

lato

r eff

icie

ntly

an

d ap

prop

riate

ly

to p

erfo

rm c

ompl

ex

calc

ulat

ions

with

num

bers

of

any

size

, kno

win

g no

t to

roun

d du

ring

inte

rmed

iate

st

eps o

f a c

alcu

latio

n

•squ

are

a lin

ear e

xpre

ssio

n, a

nd e

xpan

d an

d si

mpl

ify th

e pr

oduc

t of t

wo

linea

r ex

pres

sion

s of t

he fo

rm (x

± n

) and

si

mpl

ify th

e co

rres

pond

ing

quad

ratic

ex

pres

sion

•use

alg

ebra

ic a

nd g

raph

ical

met

hods

to

solv

e si

mul

tane

ous l

inea

r equ

atio

ns

in tw

o va

riabl

es

•sol

ve in

equa

litie

s in

one

varia

ble

and

repr

esen

t the

solu

tion

set o

n a

num

ber

line

•use

form

ulae

from

mat

hem

atic

s and

ot

her s

ubje

cts;

subs

titut

e nu

mbe

rs

into

exp

ress

ions

and

form

ulae

; der

ive

a fo

rmul

a an

d, in

sim

ple

case

s, ch

ange

its

subj

ect

•fin

d th

e ne

xt te

rm a

nd n

th te

rm o

f qu

adra

tic se

quen

ces a

nd fu

nctio

ns

and

expl

ore

thei

r pro

pert

ies

•plo

t gra

phs o

f sim

ple

quad

ratic

and

cu

bic

func

tions

, e.g

. y =

x²,

y =

3x² +

4,

y =

•und

erst

and

and

appl

y Py

thag

oras

’ the

orem

whe

n so

lvin

g pr

oble

ms i

n 2-

D

•cal

cula

te le

ngth

s, ar

eas a

nd

volu

mes

in p

lane

shap

es a

nd

right

pris

ms

•enl

arge

2-D

shap

es, g

iven

a

cent

re o

f enl

arge

men

t and

a

frac

tiona

l sca

le fa

ctor

, on

pape

r an

d us

ing

ICT;

reco

gnis

e th

e si

mila

rity

of th

e re

sulti

ng sh

apes

•fin

d th

e lo

cus o

f a p

oint

that

m

oves

acc

ordi

ng to

a g

iven

rule

, bo

th b

y re

ason

ing

and

usin

g IC

T

•rec

ogni

se th

at m

easu

rem

ents

gi

ven

to th

e ne

ares

t who

le u

nit

may

be

inac

cura

te b

y up

to o

ne-

half

of th

e un

it in

eith

er d

irect

ion

•und

erst

and

and

use

mea

sure

s of

spee

d (a

nd o

ther

com

poun

d m

easu

res s

uch

as d

ensi

ty o

r pr

essu

re) t

o so

lve

prob

lem

s

•sug

gest

a p

robl

em to

exp

lore

usi

ng

stat

istic

al m

etho

ds, f

ram

e qu

estio

ns a

nd

rais

e co

njec

ture

s; id

entif

y po

ssib

le so

urce

s of

bia

s and

pla

n ho

w to

min

imis

e it

•sel

ect,

cons

truc

t and

mod

ify, o

n pa

per a

nd

usin

g IC

T su

itabl

e gr

aphi

cal r

epre

sent

atio

n to

pro

gres

s an

enqu

iry in

clud

ing

freq

uenc

y po

lygo

ns a

nd li

nes o

f bes

t fit

on sc

atte

r gr

aphs

•est

imat

e th

e m

ean,

med

ian

and

rang

e of

a

set o

f gro

uped

dat

a an

d de

term

ine

the

mod

al c

lass

, sel

ectin

g th

e st

atis

tic m

ost

appr

opria

te to

the

line

of e

nqui

ry

•com

pare

two

or m

ore

dist

ribut

ions

and

m

ake

infe

renc

es, u

sing

the

shap

e of

the

dist

ribut

ions

and

mea

sure

s of a

vera

ge a

nd

rang

e

•und

erst

and

rela

tive

freq

uenc

y as

an

estim

ate

of p

roba

bilit

y an

d us

e th

is to

co

mpa

re o

utco

mes

of a

n ex

perim

ent

•exa

min

e cr

itica

lly th

e re

sults

of a

stat

istic

al

enqu

iry, a

nd ju

stify

the

choi

ce o

f sta

tistic

al

repr

esen

tatio

n in

writ

ten

pres

enta

tion

BL

IE

Key:

BL-B

elow

Lev

el

IE-In

suff

icie

nt E

vide

nce

Ove

rall

asse

ssm

ent (

tick

one

box

only

)Lo

w 7

S

ecur

e 7

Hig

h 7

Low

8

Sec

ure

8

Hig

h 8

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