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Y E X P L O R I N G M A T H S

M e a s u r e m e n t L O W E R P R I M A R Y 1

Activities,blackline masters &assessment pagesthat are fun and

easy to use

BevDunbar

EXPLORINGEXPLORING

LengthAreaand

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IntroductionExploring Length and Area

Measurement is an important aspect of any mathematics program.It is a practical way to apply number skills to solve problems specificto each student’s stage of development. Both the classroom and theplaygound can be utilised, and a wide variety of everyday objects usedas measuring objects.

Exploring Length and Area is a companion to the other Measurementbooks in the Exploring Maths series. Here are over 35 action-packedideas for developing skills in exploring, comparing and using informalunits in fun, practical ways. And the activities can range from simple tosuper-challenging, to help you cater for different ability groups.

Making your teaching life easier is a major aim of this series. The bookis divided into sequenced units. Each unit is packed with enoughphotocopiable playing cards, activity cards and worksheets for smallgroups or a whole class to explore for at least a week at a time. You’llalso find easy-to-follow instructions, with assessment help in the form ofclearly stated outcomes linked to outcome indicators (see p.91).

Each activity is designed to maximise the way in which your studentsconstruct their own understandings about length and area. The activitiesare generally open-ended and encourage each student to think andwork mathematically. The emphasis is always on practical manipulationof materials and the development of individual recording skills, ratherthan just writing answers into a textbook.

Look forward to exploring length and area with your students.

Copyright © Bev Dunbar Maths Matters 2001Exploring Length and Area ISBN 186509 223 1

Published by Blake EducationLocked Bag 2022Glebe NSW 2037

Series editor: Garda TurnerIllustration and design by Janart Design Studio

Printed by Printing CreationsThe blackline masters in this book may be reproducedby the original purchaser for use with their class(es) only.

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Contents

How to use this Book 2

Exploring Length Language 3

Comparing Lengths 15

Using Informal Length Units 31

Measuring with Metres 49

Exploring Area Language 63

Comparing Areas 71

Using Informal Area Units 79

Outcome Indicators Record 91

Sample Yearly Topics 92

Sample Weekly Program 93


Exploring Length and Area2

Over 35 Teaching IdeasMore than 35 exciting teaching ideas have been placed into 7 sections to assistyour lesson planning for the whole class or small groups. Each activity hasclearly coded learning outcomes and easy-to-follow instructions. Activities areopen-ended and encourage your students to think for themselves.

Over 40 Blackline MastersThere are 4 types of blackline masters.

How to use this Book

Reusable Resourcese.g. p.11 What is nearer?These support your free exploration as well asstructured activities. Laminate them for reusewith small groups.

Playing Cardse.g. p.40 Match my lengthCut these out, shuffle and use over and overagain for small group games. Photocopy eachset in different colours.

Activity Cardse.g. p.73 Which covers more?Use these as an additional stimulus in groupwork. The language is simple andeasy-to-follow. Encourage your students toinvent their own activity cards too.

Sample Recording Sheetse.g. p. 61 Metre TabloidThese provide reusable examples to supportthe development of students’ ownrecording skills.

Outcomes Indicator RecordThe complete list of learning outcomes is available on page 91.Use this to record individual student progress.

Sample Yearly ProgramsYou’ll never be stuck for programming ideas again. See page 92for examples of how to organise a 40 week term forMathematics in your classroom.Sample Weekly ProgramOn pages 93 and 94 you’ll find examples of how to organise aselection of activities for Comparing Lengths and Using InformalUnits as 5-day units for your class.

Exploring Length and Area

40

How many beans

long is your

little finger?

How many

paperclips long

is your

pencil case?

How many

toothpicks long

is your desk?

How many finger

widths long is

your ruler?

How many jelly

beans long is

your pencil?

Find something a

little bit shorter

than 15 beans.

Find something a

little bit longer

than 12

paperclips.

Find something

exactly the same

length as

8 toothpicks.

Find something

almost as long

as 14 finger

widths.

Find something

as long as 10

jelly beans.

Ex l i g L g h nd A ea 73

Your hand or your foot print?Estimate first, then find a wayto check.Who has the largest handand foot area in your group?

Your body outline or yourfriend s outline?Estimate first, then find a wayto check.Who has the smallest body

outline in your group?

Which covers more ...


Exploring Length and Area 61

Activity

Metre competition recordMy metre estimate

My metre measure

1

2

3

4

5

6



What is nearer?What are you trying to do?� Describe, recognise near/far distances (L1-6)

How many can play?� Whole class, small groups

What do you need?� Pencils, paper� Near/far picture cards (BLM p.11)� (Optional) A whistle

How do you play?� What does near mean? Who is near you now?

Describe some other things that are near you.What are some other words for near?e.g. close, next to, beside.

� What is the opposite of near? (far)Describe some things that are far from you now.What are some other words for far?e.g. at a distance from, far away, a long way away.

� Where do you live? Is your home near to your friends? ... to your grandma? ... to ourschool? Who lives the closest to school? ... the furthest away? Who do you know wholives the furthest away from you in the whole world?

� Draw a picture showing 3 things that are very near to where you are now and 3 thingsthat are very far away.

Variations� Play What is nearer? in small groups. Shuffle the picture cards. Select a card and

answer questions from your friends. e.g. What is the nearest object? What is closer thanthe sheep?

� Play Who is nearest? Find a large open space, e.g. the playground. Run around all overthis space. Stop when you hear the signal, e.g. a whistle. Who is nearest to you now?Who is the furthest away?

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Length challengesWhat are you trying to do?� Order 3 or more lengths (L2-5)

How many can play?� Up to the whole class, in small groups

What do you need?� Straws, ping-pong balls, timers, a long, flat surface� Paper fish (BLM p. 28), fans (books or small flat boards), a long, flat surface� Snails, coloured dot stickers (to identify each team’s snail), a long, flat surface� Small toy cars, a long ramp (wooden board), a long, flat surface� String/wool, scissors for measuring distances� Length challenges cards (BLMs pp.29,30)� (Optional) Medals (gold/silver/bronze)

How do you play?� Discuss different types of length investigations you could carry out as a class.

e.g. Is the person with the longest hair the tallest person in the class? Does theperson with the longest legs have the longest stride? How can you find out?

� Discuss the Olympic Games and how many events involve length. e.g. Who canthrow a javelin the longest distance? Who can jump over the highest bar on thehigh jump?

� Explain the different Length challenge activities. Break the class into 4 teams.Decide on a name for each team. In turn, each team explores ways to create thelongest length possible for each activity. This is the practice stage. Each team canelect their fastest member as their team’s challenger.

� When each team has rotated through all 4 practice activities, the competitors fromeach team compete in the first Length challenge e.g. How far can you blow? Therest of the class can be the audience. (Alternately, all 4 activities can run at eachtime with a member from each team as the competitors and other team membersas supporters.)

� (Optional) Award medals to the winning teams.

Variation� Create your own length challenges. Compete with another class. You could even

have a whole school challenge!



How far can you blow?

You need a straw, a ping-pong balland a timer.

What is the furthest distance youcan blow the ball in 10 seconds?

How far can it swim?

You need a paper fish, a fanand a timer.

What is the furthest distance youcan make a paper fish swimin 10 seconds?



How far can it crawl?You need a snail and a timer.What is the furthest distanceit can crawl in 1 minute?

How far can it roll?Use a toy car and a ramp.What is the furthest distanceyou can make the car travelusing the ramp?


BodymeasuresWhat are you trying to do?� Use informal units to estimate, measure straight lengths (L3-1)

� Order 3 or more lengths using informal units (L3-4)

How many can play?� Small groups, up to the whole class

What do you need?� Body measures worksheet (BLM p.35)� Body measures cards (BLM pp.36,37)

How do you play?� Discuss all the different body units we could use to measure length, e.g. footsteps,

strides, handspans, body lengths.

� Discuss what to do when measuring length if there are parts of units left over.e.g. I am more than 6 footsteps long but less than 7. I’m about 6 and a halffootsteps long!

� Divide class into teams. Decide on a suitable distance to measure. Identify thestart and finish line, e.g. from the fence to the big tree. Discuss how many childrenlying down end to end in a line will measure this distance. Each group recordstheir estimate then checks and records their actual body length measure.

� Were all group measures identical? Why? Why not?

� Repeat for other distances using different body lengths. Identify distances tomeasure standing side by side, at arms length, or with arms and legs outstretched.Estimate first how many units you will need, then check by measuring with yourbodies. Record your discoveries on the worksheet.

� Discuss the advantages and disadvantages of measuring using body units tomeasure length.

Variation� Use the Body measures cards. Invent more like this for another group to use.

Find your own way to record your discoveries. Discuss any problems you notice.e.g. Are all footsteps the same length? Does this matter?



The actualmeasure


Body measuresOur

estimate

The actualmeasure

Body measuresOur

estimate

Body unit

Body unit



The longest strideWhat is a stride?In your group, who has the longest stride?Estimate first, then check.How many footsteps long is your stride?Record your discoveries.

The longest reachWhat is a reach?How far can you reach without falling over?Measure your reach with footsteps.Who has the furthest reach in your team?Record your discoveries.



The longest jumpYou need start and finish markers.How far can you jump from a standing start?Can you jump further with a running start?Measure your distances in handspans.Record your discoveries.

The longest stretchYou need start and finish markers.How far can you stretch out your arms and legs?Are you longer standing up or lying down?Measure your distances in handspans.Record your discoveries.



Flying highWhat are you trying to do?� Estimate, measure to the nearest half, quarter metre (L4-2)

� Order 3 or more lengths using metres (L4-3)

Howmany can play?� The whole class, small groups, pairs

What do you need?� Reference book about flying objects� Sample paper planes� Paper, scissors, pencils, glue/stapler/sticky tape� Metre measures (string, rulers, monsters)� Flying high record sheet (BLM p.59)

How do you play?� Discuss types of flying objects, eg. a bird, helicopter, jumbo jet, balloon, kite,

rocket. What does ‘a better flyer’ mean? Discuss why some objects might bebetter at flying than others.

� Challenge the class to design and make a paper flying object which goes thefurthest distance in metres. Discuss the sample paper planes. Discuss possibleconstruction techniques. Discuss possible test techniques.

� Construct your flying object. Test how far it can fly. Experiment by attachingsmall objects or by rearranging the shape in some way. Do heavier objects flyfurther? Do wider objects fly further? Record flight distances in metres on yourrecord sheet.

� Discuss advantages/disadvantages of sample class models with everyone.Does one model stand out as the Class Champion Flyer?

Variations� Construct, test and record flight details for other flying objects.

� Challenge another class to design and make a flying object that travelsfurther than your Class Champion Flyer.



Flying highFlight 1 Flight 2 Flight 3 Furthest

distance

Plane 1

Plane 2

Plane 3

Flying highFlight 1 Flight 2 Flight 3 Furthest

distance

Plane 1

Plane 2

Plane 3



Which coversmore?What are you trying to do?� Compare the size of 2 areas (A2-1)

� Order 3 or more areas (A2-2)

Howmany can play?� Pairs, small groups, whole class

What do you need?� Different shaped cloths (towels, washers etc.)� Chalk� Which covers more? activity cards (BLM pp.73, 74)� Fruit, vegetables

Howdo you play?� How many different large areas do you know about at school?

e.g. outdoor playing areas, wet areas, out-of-bounds areas. Think of just 2 areas.Which area is the larger? What makes you think this? e.g. I imagined overlappingone on top of the other.

� How can you compare 2 similar size areas? e.g. 2 towels - If they look about thesame size I can place one on top of the other and see if one is larger.

� What’s another way to compare areas? e.g. A piece of paper and a book cover-I can cut the paper up and rearrange it on top of the book to see if it covers thesame area.

� How can you compare 2 areas if they aren’t flat? e.g. 2 apples - I can peel themand compare the area covered by peel. Or I can wrap a piece of paper aroundone and then see if I need a larger piece to wrap the other one.

� With a partner, find pairs of objects that you think:a) both cover the same area.b) have one area smaller or larger than the other.

� Estimate first, check by imagining/overlapping/cutting/wrapping. Record yourfavourite discoveries.

� Discuss problems together. e.g. What do you do/say if there is just a smalldifference in area? What strategy did you use to check areas that couldn’t bepicked up and compared directly?

Variation� Use the Which covers more? cards then invent even more challenges for another

team to try.



Your hand or your foot print?Estimate first, then find a wayto check.Who has the largest handand foot area in your group?

Your body outline or yourfriend’s outline?Estimate first, then find a wayto check.Who has the smallest bodyoutline in your group?




The surface of an orangeor a banana?Estimate first, then finda way to check.In a pile of fruit,which piece hasthe largest surface area?

The surface of a carrotor a potato?Estimate first, then finda way to check.In a pile of vegetables,which piece has the largestsurface area?






Rearrange itWhat are you trying to do?� Use informal units to estimate,

measure areas (A3-1)

� Order 3 or more areasusing informal units (A3-2)

Howmany can play?� Small groups, whole class

What do you need?� Various geometric tiles� Pencils, paper� Geometric biscuits (e.g. Shapes)� Rearrange it shapes (BLM pp.88,89 - preferably on cardboard)� Rearrange it puzzle cards (BLM p.90)

How do you play?

� Demonstrate how to trace around same shaped tiles on paper to create the

outline of a large shape.

� Discuss how you can now use this as a puzzle by asking a friend to look at youroutline then estimate how many tiles you need to cover the whole picture.

� Explore further by tracing tiles, swapping tracings, estimating and rearrangingtiles to check your estimates. Are you a Champion Area Estimator?

Variations

� Repeat the above activities, but use tessellating biscuit shapes in place of tiles,or make biscuit shapes with a cookie cutter and playdough.

� Cut out one set of Rearrange it shapes. How many different new shapes canyou discover by rearranging these pieces? Trace these onto paper as one largeoutline puzzle for a friend to try.

� Try the activity on the matching puzzle card. You may need to make extracopies of the shapes to complete each puzzle.

Answers:



L Shapes

Pentagons



T Shapes

Trapeziums


This shape is atrapezium. It lookslike a squarestretched on onecorner. Find a wayto fit 4 trapeziumstogether to makeone large rectangle.

TrapeziumThis shape lookslike a squashedletter T.Find a way to fit 4T-shapes togetherto make onelarge square.

Letter T

This shape is anunusual pentagon.Find a way to fit 4pentagons togetherto make one largerpentagon.

PentagonThis shape lookslike a squashed L.Find a way to fit 4L-shapes togetherto make one largerL-shape.

Letter L



E X P L O R I N G M A T H S

NUMBERExploring 1-5Exploring 6-10Games and Activitiesfor 0-10Exploring 0-50 NumerationExploring 0-50 Operations

Numbers to 50 Picture PackExploring 0-100 NumerationExploring 0-100 OperationsExploring CalculatorsExploring FractionsExploring Money

MEASUREMENTExploring Length/AreaExploring Volume/MassExploring Temperature/Time

EXPLORING LENGTH AND AREA MEASUREMENT LOWER PRIMARY

About the authorOriginally a primary school teacher, Bev Dunbar is now actively involved inteacher education as a Mathematics Consultant and University Lecturerin Mathematics Education.

Bev is a passionate believer in fun, practical resources which help teachers makemaths lessons a highlight of the day.

• 7 carefully sequenced units to developyoung students’ skills with measuringlength and area

• Over 35 activity-based, easy-to-useteaching ideas

• Sets of useful activity cards forindependent small group work

• More than 40 blackline masters• An outcome indicators record to record

individual progress

In fact, almost everything you needto explore length and areain your classroom.

Titles in the Exploring Maths series

The Exploring Maths series is designed to provide busy teacherswith practical resources that are mathematically up-to-date, fun andeasy to use. Each book contains a wealth of activities, blackline mastersand assessment tasks for a whole life-time of teaching. These activitiesencourage your children to think mathematically by exploring,experimenting, being creative and taking risks. By asking questions andactive discovery, children learn to enjoy using mathematics as part oftheir everyday lives.

Exploring Length and Area includes:

M

ISBN 1-86509-223-1

9 781865 092232

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