primary maths - prim-ed publishing - ff sample unit.… · primary maths is a photocopiable,...

2014 CurriculumPRIMARY

MATHS

Year 6Book 2 of 2

Resources and

teacher ideas for every objective

of the 2014 Curriculum

PM Year 6 Book 2 of 2.indd 1 26/11/2014 15:42:29

Primary Maths Prim-Ed Publishing www.prim-ed.com iii

Foreword

Primary Maths is a photocopiable, six-level, year–specific series designed to address the Primary National Curriculum for Mathematics objectives of: • number • ratioandproportion • algebra • measurement • geometry • statistics.

Each book in the Primary Maths series includes: • atleastoneactivitypageforeachobjective • comprehensiveteachersnotestoaccompanyeachactivity • additionalteachersnotesonactivitiesandgames • assessmentchecklists • additionalphotocopiableresources • interactive whiteboard resources available to download.

The Year 6 books in the Primary Maths series are: Primary Maths - Number, Ratio, Proportion and Algebra Primary Maths - Measurement, Geometry and Statistics

Measurement ..................................2–35 Conversions ........................................ 2–19

Area and perimeter ........................20–29

Volume ..............................................30–35

Geometry ......................................36–77 2-D shapes .......................................36–39

3-D shapes .......................................40–45

Nets ....................................................46–51

Classifying shapes ..........................52–57

Angles in shapes .............................58–65

Circles ................................................66–67

Angles ................................................ 68–71

Coordinates ......................................72–77

Teachers notes: How to use this book ............................. iv–v

Setting up a maths classroom ...................vi

Activities and games ............................vi–vii

Assessment checklists ..........................viii–x

Additional resources ..........................xi–xvii

Pupil activities with accompanying teachers notes:

Statistics .......................................78–99 Pie charts ..........................................78–87

Line graphs .......................................88–91

Averages ...........................................92–99

Contents

iv www.prim-ed.com Prim-Ed Publishing Primary Maths

How to use this book

The Primary Maths series provides teachers with a number of varied and challenging activities. At least one activity, often more, is provided for each objective of the Primary National Curriculum for Mathematics.

Suggestions for using the activities in this book:

Objective:• Decide which curriculum objective you wish to address and choose the appropriate activity page(s).

Oral work and mental calculation starter:• Choose which oral and mental activities you will use, from the list provided, to introduce the lesson or sharpen

pupils’ skills.• Someoftheactivitieshaveaccompanyinginteractivewhiteboardactivitiestohelpintroducethelessonandcapture

pupils’ attention.• These activities should occupy the first 5–10 minutes of the lesson.

Main teaching activity:• Decide how much teacher input you will provide for the main activity and whether pupils will be working

individually, in pairs or as a group.• Depending upon the abilities of the pupils in your class, decide whether any additional activities will be needed, from

the list provided, or whether these can be used during subsequent lessons.• This activity should occupy approximately 40 minutes.

Plenary:• Decide what opportunities will be provided during the plenary session. Will pupils be given the opportunity to share

and explain work, compare strategies used or summarise the key facts they have learnt?• Think about how you can use the plenary session to assess pupils’ progress and therefore inform your future

planning.• The plenary should occupy the final 15 minutes of the lesson.

Pupil activity pages:The pupil activities follow a common format:

Title explanation

After initial discussion, some activities can be completed individually, and others in small groups or as a whole class.

The ‘Challenge’ activity can be completed by early finishers or those pupils requiring extension of the task. Pupils may need to complete the activity on the back of the worksheet or investigate an activity further by using concrete materials or creating their own ideas linked to the objective.

The objective provides the teacher with the focus of the activity. It is written in the form of a general objective.

Teachers notes

An icon denotes the curriculum strand for each activity.

Number

Measurement

Geometry

Statistics

GGeometry

NNumber

MMeasurement

SStatistics

Primary Maths Prim-Ed Publishing www.prim-ed.com v

AAssessment

How to use this book

AssessmentAssessmentchecklistshavebeenincludedfortheYear6‘Measurement’,‘Geometry’and‘Statistics’objectives.Seepages viii–x. These can be used to assess each pupil’s understanding of the key objectives covered.

• Teachingnotesforthe‘Measurement’,‘Geometry’and‘Statistics’strandshavebeenincludedonpagesvi–vii.These comprise background information and suggested activities and games.

• Extra teacher resources have been included on pages xi–xvii. These can be enlarged if necessary and used in appropriate activities or as display posters.

• Interactivewhiteboardactivitieshavebeenprovidedtohelpteachsomeoftheobjectives.Thesecanbedownloaded from www.prim-ed.com.

The objective tells the teacher which strand and objective from the Primary National Curriculum for Mathematics is being covered.

Oral work and mental calculation activities are suggested, for introducing the lesson or sharpening/developing oral and mental skills. The activities should occupy the first 10 minutes of the lesson.

Some activities have interactive whiteboard activities available to download. If an interactive activity is provided it is listed here.

The title of the main teaching activity is given. The photocopiable activity is on the page facing the teachers notes. The main activity should occupy approximately 40 minutes.

Answers to all activities are provided.

Suggest ions for addit iona l activities are provided. They can be completed during the lesson, or in subsequent lessons. They can be used to aid differentiation.

Teachers pagesAteacherspageaccompanieseachpupilworksheet.Itprovidesthefollowinginformation:

Use the key to write the appropriate code next to each task the pupil completes.

A summary of the tasks pupils will complete.

Teachers notes

vi www.prim-ed.com Prim-Ed Publishing Primary Maths

Setting up a mathematics classroom

By having the following materials and visual representations around them, pupils can better engage in mathematical learning.

• Allowroomtomovesopupilscaninvestigatethingsaround the room. Organise desks and floor space appropriately.

• Displaya‘Numbers’chartthatincludesthousands,ten thousands, hundred thousands and millions.

• Displayanumberlineatalevelwherepupilscanuseit.Includenegativenumbersonthenumberline.

• Display numbers, number words and a visualrepresentation of numbers.

• Displayaplacevaluechartwhichincludesfractions(tenths, hundredths and thousandths).

• Displaya100square.

• Ensureyouhaveagoodrangeofmathsgamesanduse them regularly.

• Providecalculators.

• Display‘timestables’charts.

• Haveananalogueanddigitalclockintheclassroom(12-hour and 24-hour).

• Displaypicturesoflabelled2-Dand3-Dshapes.

• Provideathermometer.

• Provideconstructionmaterials suchas cardboardboxes, cylinders, paper, scissors and so on.

• Ensure youhaveadequate concretematerials toteach each strand (refer to pages vi–vii).

• Allowpupilsopportunitiestoinvestigateoutsidetheclassroom in the school environment.

• Display a chart showing equivalent fractions,decimals and percentages.

• Displayormakevariousgraphssuchaspictograms,bar charts, block graphs, Venn diagrams, Carroll diagrams, line graphs and pie charts.

• Displaya classbirthdaychartwhich includes themonths of the year.

• Displayanduseacalendar.

• Display a poster showing equivalentmetric andimperial measures.

• Have computer software related tomathematicsavailable for use on the classroom computer(s) or in the computer room.

• Displayapostershowingdifferentangles.

• Providearangeofmeasuringequipmentforlength,mass and capacity.

• Displaytheeightcompassdirections:N,S,E,W,NE,NW,SE,SW.

• Ensure youhave a good selection of interactivemaths resources for use on a whiteboard (refer to www.prim-ed.com).

Teachers notes

Statistics — Activities and games

Brainstorm a list of topics pupils would like to collect data about. Collect the data and record it on a pie chart. Complete a table recording daily temperature for one month. Display as a line graph. Calculate the mean, range, mode and the median.

Materials required

• gridpaper• graphpaper• tapemeasure

Materials required

• gridpaper• graphpaper(pagexvii)• variousgraphsforreference

Primary Maths Prim-Ed Publishing www.prim-ed.com vii

Measurement – Activities and games

• Useapieceofwool,cottonorstring24cmlong.Jointhe ends to make a loop. Use a sheet of grid paper to find the smallest and largest area you can cover using the loop. Draw outlines on the grid paper. Record the perimeter and area of each.

• Provideopportunitiestoreadscaleswhereeachcalibration is not labelled; for example, a measuring tape marked in hundredths but labelled in tenths, a scale marked in grams but labelled in kilograms.

• Providepupilswithvariousreal-lifesituationsinwhichthey are required to distinguish the difference between perimeter and area; for example, new fencing around the school would require knowing the perimeter of the school. New lawn for a particular area within the school grounds would require knowing the area.

• Withinthelimitsoftheschoolpremises,markoutanarea 100 m x 100 m – one hectare. If space does not allow, mark out either an area 100 m x 50 m or 50 m x 50 m to give pupils an idea of 0.5 or 0.25 of a hectare and, therefore, some indication of the actual size of a hectare.

• Collectavarietyofcontainerstocomparecapacities.– Compare 2 L soft drink bottles, 2 L cordial bottles and

2 L ice-cream containers.– Compare 1 L milk cartons, 1 L standard measuring

containers and 1 L soft drink bottles.– Compare 500 mL containers with each other.– Discuss the actual capacity of each of the containers,

asking for suggestions as to why they change.

• Collectanumberofcardboardpackages—cerealboxes,cake mix boxes etc.—and record the capacity of each box by filling the box with sand, rice or beans.

Measure the capacity by cupfuls. Cut the boxes open and compare their surface areas. Check to see whether the box with the largest surface area also has the largest capacity.

• Useavarietyofcontainerswiththesamebaseareabutdifferent heights – measure both surface area and base area to see what the ratio between surface area and volume is in each case.

• Useasmallnumberofcubestobuildanarrangement.Ask pupils to increase the size of the arrangement by double or triple the amount, so the new arrangement looks the same as the original, just larger.

Materials required

• rulers/metreruler • balancescales• trundlewheel • bathroomscales• 1-cmcubes • tapemeasure• gridpaper• containersofvaryingcapacity

Geometry – Activities and games

• Pupilsdraw3-Dmodels,includingsolidlinesforwhattheycan see and dotted lines for the parts of the models that cannot be seen.

• Pupilsmakeasimpleshapewithdimensionslessthan2cm,putting their initials on one side. Use 2-cm grid paper to draw and describe how they would move their shape from one square to another by flipping, sliding and rotating.

• Pupilsmake their own logowith at least one line ofsymmetry.

Make a logo for their favourite sport with a line of reflectional symmetry.

Design a logo for the school with a line of rotational symmetry.

• UseVenndiagramstoclassifythree-dimensionalshapes.Classifications may include:

– odd and even vertices;

– plane and non-plane faces;

– prisms, pyramids and others;

– regular and irregular;

– square faces, triangular faces and other faces; or

– parallel or perpendicular faces or edges.

• Investigateshapesinbuildings,structures,playequipmentand other parts of the environment. Give reasons why certain shapes are used in particular situations; for example, the triangle for rigidity.

• Useaprotractortomeasureanglesinregular2-Dshapes.Classify the shapes according to whether they have acute, right or obtuse angles.

• Plot coordinates in all four quadrants. Draw a shapeinto one quadrant and its reflection into the other three quadrants.

• Drawnetstoconstruct3-Dshapes.

Materials required

• 2-Dand3-Dshapepictures (see pages xii and xiii)

• 2-Dshapesfortessellation /symmetry

• constructionmaterialfor 3-Dmodels

• mirrors

• patternblocks• modellingclay• protractors• gridpaper• toothpick

Teachers notes

viii www.prim-ed.com Prim-Ed Publishing Primary Maths

AAssessment

Pupils’ namesSo

lve

prob

lem

s in

volv

ing

the

calc

ulat

ion

and

conv

ersi

on o

f un

its o

f m

easu

re.

Use

deci

mal

not

atio

n up

to

thre

e de

cim

al p

lace

s.

Use,

rea

d, w

rite

and

conv

ert

betw

een

stan

dard

uni

ts o

f le

ngth

.

Use,

rea

d, w

rite

and

conv

ert

betw

een

stan

dard

uni

ts o

f m

ass.

Use,

rea

d, w

rite

and

conv

ert

betw

een

stan

dard

uni

ts o

f vo

lum

e.

Use,

rea

d, w

rite

and

conv

ert

betw

een

stan

dard

uni

ts o

f tim

e.

Conv

ert

betw

een

mile

s an

d ki

lom

etre

s.

Reco

gnis

e th

at s

hape

s w

ith t

he s

ame

area

can

hav

e di

ffer

ent

perim

eter

s.

Reco

gnis

e th

at s

hape

s w

ith t

he s

ame

perim

eter

can

hav

e di

ffer

ent

area

s.

Reco

gnise

whe

n it

is po

ssib

le t

o us

e fo

rmul

ae f

or a

rea.

Reco

gnise

whe

n it

is po

ssib

le t

o us

e fo

rmul

ae f

or v

olum

es o

f sh

apes

.

Calc

ulat

e th

e ar

ea o

f pa

ralle

logr

ams.

Calc

ulat

e th

e ar

ea o

f tr

iang

les.

Calc

ulat

e, e

stim

ate

and

com

pare

vol

ume

of c

ubes

and

cub

oids

.

KeyD = DemonstratedNFO = Needs further

opportunity

Year 6 Measurement – assessment checklist

Primary Maths Prim-Ed Publishing www.prim-ed.com ix

AAssessmentYear 6 Geometry – assessment checklist

Pupils’ names Draw

2-D

sha

pes,

give

n di

men

sion

s.

Draw

2-D

sha

pes,

give

n an

gles

.

Reco

gnis

e, d

escr

ibe

and

build

sim

ple

3-D

shap

es.

Reco

gnis

e, d

escr

ibe

and

build

net

s.

Com

pare

and

cla

ssify

geo

met

ric s

hape

s ba

sed

on t

heir

prop

ertie

s an

d si

zes.

Find

unk

now

n an

gles

in t

riang

les.

Find

unk

now

n an

gles

in r

egul

ar

poly

gons

.

Illus

trat

e an

d na

me

part

s of

circ

les.

Know

tha

t th

e di

amet

er o

f a

circ

le is

tw

ice

the

radi

us.

Reco

gnise

ang

les

whe

re t

hey

mee

t at

a

poin

t.

Reco

gnise

ang

les

whe

re t

hey

are

on a

st

raig

ht li

ne.

Reco

gnise

ang

les

that

are

ver

tical

ly

oppo

site.

Find

miss

ing

angl

es.

Desc

ribe

posit

ions

on

the

full

coor

dina

te g

rid.

Draw

, tra

nsla

te a

nd re

flect

sim

ple

shap

es.


opportunity

x www.prim-ed.com Prim-Ed Publishing Primary Maths

AAssessment

Pupils’ names

Inte

rpre

t pi

e ch

arts

.

Cons

truc

t pi

e ch

arts

.

Use

pie

char

ts t

o so

lve

prob

lem

s.

Inte

rpre

t lin

e gr

aphs

.

Cons

truc

t lin

e gr

aphs

.

Use

line

grap

hs t

o so

lve

prob

lem

s.

Calc

ulat

e an

d in

terp

ret

the

mea

n as

an

ave

rage

.


opportunity

Year 6 Statistics – assessment checklist

Primary Maths Prim-Ed Publishing www.prim-ed.com xi

AAssessmentTeachers notes

12 12

3

4

5678

9

1011

0013

14

15

16

1718

19

20

21

22

2312 1

2

3

4

5678

9

1011

0013

14

15

16

1718

19

20

21

22

23

12 12

3

4

5678

9

1011

0013

14

15

16

1718

19

20

21

22

2312 1

2

3

4

5678

9

1011

0013

14

15

16

1718

19

20

21

22

23

24-hr clocks

Teacher resources

xii www.prim-ed.com Prim-Ed Publishing Primary mathematics

2-D shapes

Teacher resources

Primary mathematics Prim-Ed Publishing www.prim-ed.com xiii

3-D shapes

Teacher resources

xiv www.prim-ed.com Prim-Ed Publishing Primary mathematics

Parts of a circle

radius

diameter

circumference

Radius is the distance from the centre of a circle to any point on the edge of the circle.

Diameter is the distance across the circle, through the centre.

Circumference is the distance (perimeter) around the circle.

Teacher resources

Primary mathematics Prim-Ed Publishing www.prim-ed.com xv

Angles

Teacher resources

xvi www.prim-ed.com Prim-Ed Publishing Primary mathematics

Coordinates in four quadrants

-10 -9 -8 -7 -6 -5 -4 -3 -2 -1 1

1

2

2

3

3

4

4

5

5

6

6

7

7

8

8

9

9

10

10Y

X

-10

-9

-8

-7

-6

-5

-4

-3

-2

-1

Teacher resources

Primary mathematics Prim-Ed Publishing www.prim-ed.com xvii

Bar/Line graphs

TEACHER INFORMATION

92 www.prim-ed.com Prim-Ed Publishing Primary Maths

STATISTICS

SStatistics

Objectives• Interpretandconstructlinegraphsandusethesetosolveproblems. • Calculateandinterpretthemeanasanaverage. Oral work and mental calculation• Usethevocabulary:average, mode, range, most

common, most frequent, spread.

• Investigatetheanswertoaquestion;forexample,What is the most common shoe size in our class? Discuss how to collect the information and how to record it. Display the shoe sizes in order from smallest to largest. Which shoe size is the most common? (This is the mode). What are the smallest and largest shoe sizes? (This is the range).

• Writeaselectionofnumbersontheboard;forexample, 4, 8, 9, 6, 8. Ask pupils to name the mode and the range.

Interactive whiteboard activityInteractive whiteboard activity available to support this copymaster. Visit www.prim-ed.com.

Main teaching activityMode and range of data (page 93)

Additional activities suitable for developing the objectives• Provideaselectionofnumbers;forexample,16,17,

12, 14, 18, 17, 13. Ask pupils to write them from smallest to largest, then identify the mode and range.

• Measureandrecordthetemperatureat12nooneachday for one week. State the mode and the range.

• Lookatagraphshowingtestscoresorracetimes.Work out the mode and range.

Answers1. (a) 8, 22, 22, 23, 26, 29 (b) 22 (c) 8 to 29

2. (a) 18 ºC (b) 14 ºC to 23 ºC

3. (a) 16 ºC, 17 ºC, 18 ºC, 19 ºC, 21 ºC, 21 ºC, 21 ºC, 23 ºC, 24 ºC, 24 ºC, 26 ºC, 27 ºC (b) 21 ºC (c) 16 ºC to 27 ºC

Challenge: Teacher check

Objective

Primary Maths Prim-Ed Publishing www.prim-ed.com 93

SStatistics

CHALLENGEMeasure the height of five classmates. What is the:

(a) mode height? (b) range of heights? to

MODE AND RANGE OF DATA

Finds the mode and range of a set of data.

1. The following runs were scored during a class game of cricket. Calculate the mode (average) by finding the most common score.

Pupils RunsMark 22

Holly 26

Michelle 29

John 22

Sandra 23

Will 8

(a) Order the scores from lowest to highest.

, , , , ,

(b) The mode is .

(c) The range of scores is from to .

2. The temperature was recorded for one week. Calculate the mode (average) temperature for that week.

Sunday 21 ºC

Monday 19 ºC

Tuesday 14 ºC

Wednesday 18 ºC

Thursday 18 ºC

Friday 20 ºC

Saturday 23 ºC

(a) The mode is ºC.

(b) The range of temperatures is from

ºC to ºC.

Mode: The most frequently occurring score and there may be more than one mode; e.g. The data are bimodal, having 8 and 9 occurring the most frequently.

Range: The spread of scores from the lowest to the highest, or a spread in which a category may be placed.

3. Look at the line graph.

(a) Order the temperatures from lowest to highest.

, , , ,

, , , ,

, , ,

(b) The mode is ºC.

(c) The range of temperatures is from

ºC to ºC.

TEACHER INFORMATION


STATISTICS

SStatistics

Objective• Calculateandinterpretthemeanasanaverage.

Oral work and mental calculation• Usethevocabulary:average, mode, range, median,

most common, most frequent, spread.

• Investigatetheanswertoaquestion;forexample,What is the most common shoe size in our class? Discuss how to collect the information and how to record it. Display the shoe sizes in order from smallest to largest. Which shoe size is the most common? (This is the mode). What are the smallest and largest shoe sizes? (This is the range). If the shoe sizes are arranged from smallest to largest, what is the middle size? (This is the median).

• Writeaselectionofnumbersontheboard;forexample, 4, 8, 9, 6, 8. Ask pupils to name the mode, range and median.

Main teaching activityMode/Range/Median (page 95)

Additional activities suitable for developing the objective• Provideaselectionofnumbers;forexample,16,17,

12, 14, 18, 17, 13. Ask pupils to write them from smallest to largest, then identify the mode, range and median.

• Measureandrecordthetemperatureat12nooneachday for one week. State the mode, range and median.

• Lookatagraphshowingtestscoresorracetimes.Work out the mode, range and median.

• Inputtestscoresintoacomputer.Usethecomputerto work out the mode, range and median of the test scores.

• Comparethemode,medianandrangeofthetimestaken to travel to school by those pupils who walk and those pupils who travel by car.

• Investigatewhichfootballteamfromagivenselection scored the most goals in one season. Calculate the mode, range and median.

Answers1. (a) 14°C, 15°C, 15°C, 16°C, 17°C, 18°C, 19°C

(b) 14°C to 19°C (c) 16°C (d) 15°C (e) No

2. (a) 5, 7, 8, 10, 12, 12, 14, 15 (b) 5 to 15 (c) 11 (d) 12 (e) No

3. (a) 43%, 52%, 52%, 54%, 61%, 61%, 61%, 69%, 76%, 83%, 89%, 89%, 92%, 95% (b) 43% to 95% (c) 65% (d) 61% (e) No


Objective


SStatistics

CHALLENGEFind out the class size of every class in your school. Work out the:

(a) range (b) median (c) mode

MODE/RANGE/MEDIAN

Calculatestherange,medianandmodeofasetofdata.

Sunday 17°CMonday 15°CTuesday 14°CWednesday 16°CThursday 15°CFriday 19°CSaturday 18°C

1. The temperature was recorded for one week.(a) Order the temperatures from lowest to highest.

, , , , , , .

(b) The range of temperatures is from to .

(c) The median temperature is .

(d) The mode temperature is .

(e) Are the median and mode temperatures the same? yes no

2. The number of goals scored were recorded for five weeks.(a) Order the number of goals from lowest to highest.

, , , , , , , .

(b) The range of goals scored is from to .

(c) The median score is .

(d) The mode score is .

(e) Are the median and mode scores the same? yes no

3. Look at the maths test results.

(a) Order the test results from lowest to highest.

, , , , , , , , , , , , ,

(b) The range of scores is from to . (c) The median score is .

(d) The mode score is . (e) Are the median and mode scores the same? yes no


Median: The middle score, when scores are arranged in ascending or descending order; e.g. 1, 3, 6, 8 (median), 8, 9, 9 Note: If there were only six scores, then the median would be found 1, 3, 6, 8, 8, 9 6 + 8 14 ÷ 2 = 7 2

Mode: The most frequently occurring score. There may be more than one mode; e.g. The data are bimodal, having 8 and 9 occurring most frequently.

Sunday 17°CMonday 15°CTuesday 14°CWednesday 16°CThursday 15°CFriday 19°CSaturday 18°C

Arsenal 5Aston Villa 12Chelsea 7Manchester United 15Newcastle United 12Liverpool 10Tottenham 14West Ham 8

Arsenal 5Aston Villa 12Chelsea 7Manchester United 15Newcastle United 12Liverpool 10Tottenham 14West Ham 8

52% 76% 61% 54% 52% 95% 61% 69% 83% 89% 43% 89% 61% 92%52% 76% 61% 54% 52% 95% 61% 69% 83% 89% 43% 89% 61% 92%

TEACHER INFORMATION


STATISTICS

SStatistics

Objective• Calculateandinterpretthemeanasanaverage.


mean, most common, most frequent, spread.

• Demonstratehowtocalculatethemeanbyaddinga group of data and dividing by the number in the group.

• Investigatetheanswertoaquestion;forexample,What is the most common shoe size in our class? Discuss how to collect the information and how to record it. Display the shoe sizes in order from smallest to largest. Which shoe size is the most common? (This is the mode). What are the smallest and largest shoe sizes? (This is the range). If the shoe sizes are arranged from smallest to largest, what is the middle size? (This is the median). Which is the average shoe size? (This is the mean).

• Writeaselectionofnumbersontheboard;forexample, 4, 8, 9, 6, 8. Ask pupils to name the mode, range, median and mean.

Main teaching activityCalculating the mean (page 97)

Additional activities suitable for developing the objective• Provideaselectionofnumbers;forexample,16,17,

12, 14, 18, 17, 13. Ask pupils to write them from smallest to largest, then identify the mode, range, median and mean.

• Measureandrecordthetemperatureat12nooneachday for one week. State the mode, range, median and mean.

• Lookatagraphshowingtestscoresorracetimes.Work out the mode, range, median and mean.

• Inputtestscoresintoacomputer.Usethecomputerto work out the mode, range, median and mean of the test scores.

• Comparethemode,mean,medianandrangeofthetimes taken to travel to school by those pupils who walk and those pupils who travel by car.

• Investigatewhichfootballteamfromagivenselection scored the most goals in one season. Calculate the mode, mean, range and median.

Answers1. 156 ÷ 6 = 26

2. (a) 168 mm ÷ 12 (b) 14 mm

3. Teacher check

4. 95%

5. 328.6 km

Challenge: £565 299.80

Objective


SStatistics

CHALLENGEUse your calculator to find the mean house price.

£285 499, £585 000, £420 500, £555 000, £980 500

CALCULATING THE MEAN

Calculatesthemeanofasetofdata.

You can calculate the mean or average of something by adding a group of data and dividing the total by the number in the group; for example, Harry weighs 44 kg, Alex weighs 40 kg, Jessica weighs

38 kg and Belinda weighs 42 kg; therefore, 44 + 40 + 38 + 42 = 164 kg ÷ 4 pupils = 41 kg. 41 kg is the average weight of the four children.

1. The following goals were scored and recorded during a football season. Calculate the mean (average) by adding the scores together then dividing that number by the number of goal kickers there are. You may wish to use a calculator.

Total score =

÷

Mean (average) goals =

2. The rainfall was recorded monthly for one year. Calculate the mean (average) monthly rainfall.

(a) Total = mm ÷

(b) The average monthly rainfall was mm.

3. Measure the height of five classmates in centimetres and record the results. Find the mean by adding the amounts together then dividing by five.

Mean = cm

4. Find the mean of the following results.

100%, 95%, 80%, 100%, 100%, 90%, 95%, 100%.

Players Goals

William 27

Xin 36

Thomas 15

Hajid 21

Jade 39

Tarah 18

5. Calculate the mean distance travelled over five days.

139 km, 522 km, 381 km, 413 km, 188 km.

Jan. Feb. March April May June July Aug. Sep. Oct. Nov. Dec.

28 mm 26 mm 22 mm 23 mm 8 mm 5 mm 3 mm 4 mm 9 mm 11 mm 13 mm 16 mm

Jan. Feb. March April May June July Aug. Sep. Oct. Nov. Dec.

28 mm 26 mm 22 mm 23 mm 8 mm 5 mm 3 mm 4 mm 9 mm 11 mm 13 mm 16 mm

Name

Height

Name

Height

TEACHER INFORMATION


STATISTICS

SStatistics

Objectives• Interpretandconstructlinegraphsandusethesetosolveproblems.

• Calculateandinterpretthemeanasanaverage.


mean, most common, most frequent, spread.

• Investigatetheanswertoaquestion;forexample,What is the most common shoe size in our class? Discuss how to collect the information and how to record it. Display the shoe sizes in order from smallest to largest. Which shoe size is the most common? (This is the mode). What are the smallest and largest shoe sizes? (This is the range). If the shoe sizes are arranged from smallest to largest, what is the middle size? (This is the median). Which is the average shoe size? (This is the mean).

• Writeaselectionofnumbersontheboard;forexample, 4, 8, 9, 6, 8. Ask pupils to name the mode, range, median and mean.

Interactive whiteboard activityInteractive whiteboard activity available to support this copymaster. Visit www.prim-ed.com.

Main teaching activityMode/Range/Median/Mean (page 99)

Additional activities suitable for developing the objectives• Provideaselectionofnumbers;forexample,16,17,

12, 14, 18, 17, 13. Ask pupils to write them from smallest to largest, then identify the mode, range, median and mean.

• Measureandrecordthetemperatureat12nooneachday for one week. State the mode, range, median and mean.

• Lookatagraphshowingtestscoresorracetimes.Work out the mode, range, median and mean.

• Inputtestscoresintoacomputer.Usethecomputerto work out the mode, range, median and mean of the test scores.

• Comparethemode,mean,medianandrangeofthetimes taken to travel to school by those pupils who walk and those pupils who travel by car.

• Investigatewhichfootballteamfromagivenselection scored the most goals in one season. Calculate the mode, mean, range and median.

Answers1. (a) 16 °C to 27 °C (b) 21.42 °C

(c) 21 °C (d) 21 °C


Objective


SStatistics

CHALLENGE

Calculate the range, mean, median and mode for a set of class test results.

MODE/RANGE/MEDIAN/MEAN

Calculatestherange,median,meanandmodeofasetofdata.

1. Look at the line graph below.

(a) The range of measures are from

to .

(b) The mean temperature for Newtown

Community is .

(c) The median temperature is .

(d) The mode temperature for Newtown

Community is .


Median: The middle score, when scores are arranged in ascending or descending order; e.g. 1, 3, 6, 8 (median), 8, 9, 9 Note: If there were only six scores, then the median would be found 1, 3, 6, 8, 8, 9 6 + 8 14 ÷ 2 = 7 2

Mean: The total of a set of scores divided by the number of scores; e.g. 1 + 3 + 6 + 8 + 8 + 9 + 9 7

Mode: The most frequently occurring score. There may be more than one mode; e.g. The data are bimodal, having 8 and 9 occurring most frequently.

primary maths - prim-ed publishing - ff sample unit.… · primary maths is a photocopiable,...

Documents