Assignment #1

Planning for Two Weeks of Teaching Mathematics

Measurement - length

INTRODUCTION

Topic:

This two week unit of mathematics has been constructed for use in a year

one/two class depending on their current understanding of measurement.

This class in the early years band will focus on length which is encompassed

in the measurement strand. Throughout this unit students will to learn how

to measure the different items that are in and around the classroom. The

aim is that students will learn and understand that it is important to know

how to measure things, and that this in turn relates to the real world. For

example measuring shoes to fit their feet in the shoe store, or measuring up

their house when they are doing renovations etc. It is the connections that

these students are able to make between their learning in the classroom to

the ‘real world’ that makes this unit of work relevant for a year (one) two

class.

Year Level:

Year 2 (1) – Early Years – Towards Standard One

Context:

This unit of work has been constructed with intention that it will be taught in

a well established urban school. This school is an independently run single

sex school that offers classes from Kindergarten through to year 12. This is a

small school with approx 1000 students, with the majority of these students

coming from a privileged background. Within this specific class there are 23

students whom are of different learning levels. As such the use of small

group activities will enable the teacher to circulate the class to monitor the

progress and level of understanding of each of the children. By creating

small groups which include students of different abilities, those students with

a lower level of comprehension will benefit as those with a higher level will

be able to share and explain their understanding and methods with the

group. Furthermore the students who have a higher level of understanding

will also benefit, as they will be able to cement their understandings through

explaining the tasks.

Recent Relevant Learning:

This class will have been exposed to measurement ideas and concepts in

their previous years at school. As such it will be assumed that they have a

relatively good understanding of, and ability to compare and order different

lengths. Because of the students differing ability levels, the first activity of

the unit has been designed to assess their level of understanding. It would

also be a good idea to discuss with the students last year teacher to discover

what the students have covered in regards to measurement and length.

Time Frame:

This unit of work is designed to be taught over two weeks, with each week

having allocated 200 minutes for mathematics. This equates to one lesson

per day of approximately 40 minutes, over the two week period.

Aim:

The educational aim for this unit of work is for the students to gain

knowledge and understanding about length and its use in measurement. As

such students will be learning how to compare and measure lengths using

informal units. This will then progress into using and interpreting lengths in

metres.

Mathematical Language:

According to Bobis et al (2009) students in the early years order and

compare objects using dichotomous language. This means that the students

will be using language such as smaller, larger, bigger, little, smaller, longer,

largest, etc. The use of this type of mathematical language allows students

to “make multiple comparisons with measurable attributes” (Bobis.

2009:157). Throughout this unit students will also be exposed to other

mathematical language such as measurement, length, size, order, estimate,

equal, more than, less than, units, and metre.

PRESENTATION OF THE UNIT

SACSA Framework:

SELECT STRAND(S) Exploring, Analysing, and Modelling DataX Measurement Number Pattern and Algebraic Reasoning Spatial Sense and Geometric Reasoning

IDENTIFY ESSENTIAL LEARNINGS TO BE EMPHASISED

Futures Identity InterdependenceX ThinkingX Communication

KEY COMPETENCIES TO BE EMPHASISED

X KC1: collecting, analysing and organising information KC2: communicating ideas and information KC3: planning and organising activities KC4: working with others in teams KC5: using mathematical ideas and techniquesX KC6: solving problems KC7: using technology

OUTCOME 1.41.4 Compares and orders the measurable attributes of distance, surface, space, mass, turn/angle and time to describe the size of a wide range of familiar figures, objects and events. [T] [C] [KC1] 

KEY IDEAChildren construct concepts of size and measurable attributes by comparing a wide variety of familiar figures, objects and events drawn from the world around them. [Id] [T] [C] [KC1]

OUTCOME 1.51.5 Chooses and uses a variety of strategies to measure the size of a wide variety of figures, objects and events drawn from the world around them. [T] [C] [KC6] 

KEY IDEA

Children develop strategies that directly compare and quantify measurable attributes of a wide variety of figures, objects and events drawn from the world around them. [T] [C] [KC6]

Sequence of Lessons:

Stage 1 - Finding Out / Prior Knowledge

Stage 1 - Lesson 1 What is length? / Comparing length

1). Begin this topic with a classroom discussion about length

Ask:

What are long things?

What are short things?

What is the opposite of long?

What is the opposite of short?

2). Put the two Giraffes up on the board or smart board (see Appendix A).

Ask:

Which has a longer neck?

Which has a shorter neck?

3). Each child is to now create a monkey puppet (Appendix B). This is done

by colouring in the monkey face, body, hands, and feet, then cutting out.

Students then choose a length of freeze tape to attach the hands and feet

to the body.

4). Ask the students to arrange the monkeys on the floor in order of the

length of their arms

5). Now ask them to compare the length of the legs, and place the monkeys

in order.

© Robyn Farnhill

Stage 2 – Exploring the Idea

Stage 2 - Lesson 2 Measuring Our Height

This lesson involves students measuring themselves and each other using

informal units.

1). Start by discussing how we could measure our height (informal units)

2). The aim of this exercise is for the students to work in pairs to trace each

other into a piece of butchers’ paper. Once the shape is traced the

students can cut out their outline and compare their cut-out heights with

each other.

3). Students can now use their body cut-out to find an object in the

classroom or school that is the same height as them.

4). Re-group students on the floor

Discuss:

What we found that was the same height as us.

Did we have any problems measuring our heights (see if the students

discuss the inaccuracy of tracing eg: Anna traced around her feet

whilst they were pointed etc)

What else could be measured by tracing and comparing?

5). If time permits students could measure another part of their body that

was suggested in the discussion above. Eg: hands, feet, legs.

© Robyn Farnhill

Stage 2 - Lesson 3 Class Challenge

This lesson involves students measuring distances using a different form of

informal units.

1). Students are told that today they will be taking part in a length challenge

(eg: maths is exciting)

2). Talk about how we measured things yesterday (tracing). Discuss that for

today’s’ challenge you will be using string/ ribbon to measure distances.

3). Discuss / read through the challenge activities (Appendix C). The class

will be divided up into four teams. Allow each team to have a practice at

each of the four stations, Encourage the students to find ways to make the

objects travel the greatest lengths.

4). Whilst practicing, encourage students to find out who in their group can

make the object at each station travel the furthest distance. Students can

be shown how to compare who makes the objects go further by measuring

the length with a piece of string, then comparing the string.

5). After each team is adequately practiced, ask one player from each team

to step forward to compete at each station. Again use string or ribbon to

measure which teams object moves the greatest length.

6). As a class re-cap on the two units that you have used so far to measure

length. Eg: tracing and string/ribbon

(Dunbar. 2001:27)

Stage 3 – Getting the idea

This lesson involves students measuring length using their bodies as the

informal units.

Stage 3 - Lesson 4 Body Rulers

1). Ask the class if I was to use Stacey’s (shortest student in the class) body

to measure the length on this classroom how many of her bodies long

would it be?? Ask the students to guess by putting a tally up on the

board with each child’s name and guess.

Eg:

NAME

Stacey’s body

length:

GUESS

Sarah 3

Angie 6

Ashleigh 5

Tiffany 4

Maddi 7

2). Now use Stacey to measure the length of the room. whilst doing this

discuss how you would make it accurate, with no overlapping, or gaps

between body lengths. Show the students how you can mark the end of

one body length with a piece of chalk or tape on the carpet, then put your

toes on this mark to begin the new length. Also take the opportunity to

discuss what to do if there are still parts to measure, eg: remainders.

Record this on the board

Eg:

NAME

Stacey’s body

length:

GUESS

ANSWE

R

Sarah 3 8

Angie 6 8

Ashleig

h5 8

Tiffany 4 8

Maddi 7 8

3). Now ask the class if you put up another column with Kate’s (tallest child

in the class) name in it, would you expect Kate’s body to use as many,

more or less body lengths to measure the classroom?? Ask the students

to guess how many Kate’s it will take.

Eg:

NAME

Stacey’s body

length:

GUESS

ANSWER

Kate’s body

length:

GUESS

ANSWER

Sarah 3 8 7

Angie 6 8 7

Ashleigh 5 8 9

Tiffany 4 8 8

Maddi 7 8 6

4). Now use Kate to measure the room. Record the finding on the board.

Discuss that because she is taller less Kate’s are needed to measure the

length. Also talk about how tricky it is to use you whole body, because of

overlapping, and gaps between your body lengths, and difficulty marking

the floor if you are lying down. Discuss that it may be easier to create

body rulers.

5). Students take it in turns to lie on a piece of butchers’ paper. Another

student marks the top of their head and the bottom of their toes on the

paper. These marks become the ends of the body ruler. Have students

cut out and decorate their body ruler with their names.

6). Once completed have the students pick at least 4 items that they would

like to measure. Have the students rule up a chart in their maths book like

the one done on

the board as

a class.

Eg:

Adapted from Dunbar (2001)

Stage 3 - Lesson 5 Body Part Measuring

This lesson builds on the previous lesson. Rather than just using the

students height as their unit of measurement the students are able to

explore using other body parts as units of measure. This lesson will also help

students to see the difference and compare using different units of measure.

1). Recap that in the last lesson we used our body rulers to measure object.

Ask the students what other parts of our bodies we could use to measure

objects.

OBJECT

MEASURE

D

My body length:

GUESS

My ACUAL body

length:

ANSWER

Eg: table 1 1

2). Show the students the Body Measures card (Appendix D). Discuss the

different measurement units that are being used in this activity.

3). Divide the class into pairs. Get all the pairs to measure a certain

distance in the school. Eg: from the fence to the sandpit. Have the

students estimate the distances for each body measure frost then test

their guesses. Record the estimates and results on the Body Measures

Card (Appendix D).

4). After measuring is done, gather the class together and discuss

o What they discovered

o Were all the different pairs measurement the same? Why/why not

o What are the disadvantages of measuring with body units?

o What are the advantages of using body units?

(Dunbar. 2001:34-35)

Stage 3 - Lesson 6 Length Challenge

This lesson allows students to use informal units other than their body parts.

1). Students are shown a variety of objects that could be used as informal

units

Eg: books, pop sticks, toothpicks, pencils, erasers, etc.

2). Students are challenged to use these different measurement units to

measure and record different objects on their worksheet. (Appendix E)

3). Re-group on the floor and discuss

o What did we measure?

o Was one of the units of measurement easier to use than the rest? If

yes, why?

o Was on e of the units hared to use? If yes, why?

Adapted from Dunbar (2001)

Stage 3 - Lesson 7 Curved Measurement

So far the students have used informal measurement to determine the

length of straight objects. This lesson is designed to get students to think

about measuring curved objects.

1). Begin by asking the class how you could measure objects that aren’t

straight.

Eg: using string or small informal units such as paper clips.

2). On a large piece of butchers paper ask each student to draw a wiggly

snake then cut it out.

3). Have the children estimate which snake looks longest, and which looks

shortest, by ordering the snakes on the floor. Record these estimates on

the board.

4). Have each students measure their snake using a piece of string. Now

compare if their estimates were correct.

5). Now have the students find several curved objects around the room to

measure. This time have the students use paperclips, before they

measure the object have them estimate its length first by recording in

their maths books.

Stage 4 – Organising the Idea

Stage 4 - Lesson 8 Metre Monsters

So far we have learnt about informal units of measurement. In this stage we

will be re-capping these units and trying find a way to resolve the problems

with informal units, by looking at metre.

1). As a class discuss

o What have we learnt so far about measuring object?

o How can we measure curves?

o What are the problems with informal measuring units?

o Discuss the value in using a set form of measurement, such as a

metre.

2). Show students a metre ruler and let students know that today each of

them will be making their own metre measurement, which we will call a

metre monster.

3). Have each student trace the metre ruler onto a large piece of butcher

paper. They may then turn this ruler into a monster by decorating it with

a face, colour, streamers etc. Then cut out the monster.

4). Discuss what would be the advantage of all of us measuring with the

same length. Eg: all get the same answer.

5). Let’s test this theory: Decide as a class which 5 objects we will all

measure. Eg: bookshelf, desk, door, length of classroom, length of veranda

etc. Each student will now estimate how many of their Metre Monsters it

will take to measure each object, record this in their maths book, and then

test their estimation

Revise what to do when a whole Metre Monster is not needed (eg: half),

overlapping and leaving gaps between measurements.

Eg:

Object Estimation/Guess Actual Metre

Monsters

Desk 2 1 and 1/2

Classroom 8 5

6). Re-group on the floor and discuss our answers.

Emphasis the benefits of all using the same unit of measurement.

(Adapted from Barron. H “Inchworm

Measurement, and Teachers Resources

Galore “Metre Monster”)

Stage 4 - Lesson 9 Metre Toss

The aim of this lesson if to give students an opportunity to practice

measuring distances in metres. (this activity is best done on grass as the

balls would not bounce as far away)

1). Each student will be given a beanbag to toss as far as they can. Once

they have tossed it they must Record how far they think they have tossed

it. Then measure this distance using their Metre Monsters.

2). Repeat this task several times challenging the students to beat their

previous scores

3). Now carry out the same activity, but instead of a beanbag, have the

students toss another item of their choice (hoop, cone, basketball, tennis

ball etc). Each item the students choose should be thrown, estimated, and

measured at least twice to show variations.

4). Re-group as a class and discuss what you have learnt today about

measuring. Emphasise leaving no gaps between metre monsters, and not

overlapping metre monsters.

© Robyn Farnhill

Stage 5 - Application

Stage 5 - Lesson 10 Garden Beds

This final lesson gives the students an opportunity to apply what they have

learnt about measuring lengths. This final task extend the students as it

gives them the opportunity to measure around / out objects (perimeter).

1). Tell the class: Today you are each going to become gardeners, your job is

to measure out a garden bed using you metre monsters. Students can

work in pairs or small groups of up to 4. Use PE cones to mark out a

garden bed that looks like this

5 metre monsters

2 metre monsters 2 metre monsters

5 metre monsters

2). Once each group has marked out their garden bed, the teacher will check

all the garden beds

3). Now challenge each group to use their metre monsters to count/add up

how many metres there are around the outside of the garden bed. Before

they do this ask each student to write down their estimate of how many

metres there will be around the perimeter, and why they think this is so.

4). Re-group as a class and share your findings, emphasise the importance of

being able to use length to measure objects in their lives (such as garden

beds). Ask the class if they can think of any other times they may use

length to measure an object?

5). Finally re-cap what you have learnt during this unit on length. Ask

students what their favourite tasks were, and what the most interesting

thing they learnt was.

© Robyn Farnhill

Teaching Resources:

o Appendices A – G

o Freeze Tape

o Staplers

o Butchers Paper

o Scissors

o Coloured Pencils

o String

o Pop-sticks

o Erasers

o Straws

o Snail

o Toy car

o Toy car ramp

o Toothpicks

o Ping pong ball

o Timer

o Marker cones

o Straw

o Beanbags

o Hoops

o Basketballs

o Tennis balls

CONCLUSION

Assessment:

Assessment will be a continual process throughout this unit on length. Firstly

the activity sheets and recording charts that the students produce in their

lessons will be checked during the lesson and after the lesson. The purpose

of checking the work during the lesson is to help target students immediately

if they are struggling to understand a concept, in order to quickly help them

to progress on the right track. After the lesson concludes the teacher can

collect the students work samples to help them fill out the class rubric, to

identify any areas of length that need additional work.

These rubrics (Appendix F and G) will be used throughout the unit to assess

what the students understand about length, and to help direct the next

lesson. The rubrics are used ‘as assessment for learning’ as they enable the

teacher to see which students need additional help in certain areas of

understanding. For example if the teacher can see that the majority of the

class has not yet grasped ordering of different lengths, then this principle

can be emphasised in the next lesson.

Curriculum Outcomes:

In regards to the key idea,

“Children construct concepts of size and measurable attributes by

comparing a wide variety of familiar figures, objects and events

drawn from the world around them. [Id] [T] [C] [KC1]”

It will be expected that by the end of this unit students will be able to;

o comparing, sorting, classifying, ordering, constructing and arranging a

variety of objects and events with a particular measurable attribute in

mind

o comparing, recording (including appropriate software) and describing

the size of figures and objects drawn from their personal activities,

communities and environments with respect to distance and length

In regards to the key idea,

“Children develop strategies that directly compare and quantify

measurable attributes of a wide variety of figures, objects and

events drawn from the world around them. [T] [C] [KC6]”

It will be expected that by the end of this unit students will be able to;

o use comparative language to describe the size of objects [T] [C]

o individually and collectively designing, constructing and refining

measuring devices to compare, order and quantify particular

measurable attributes [T] [KC3]

o exploring and using a wide variety of units of comparison to match and

quantify measurable attributes of familiar figures, objects and events,

and discussing the implication of the use of that information [T] [C]

[KC2] [KC6]

In regards to the outcome 1.4,

“Compares and orders the measurable attributes of distance,

surface, space, mass, turn/angle and time to describe the size of a

wide range of familiar figures, objects and events. [T] [C] [KC1]”

It will be expected that by the end of this unit students will be able to;

o chooses appropriate measurable attribute(s) to measure, and

discusses reasons for their choice, when classifying, building,

constructing, designing and planning [C] [T] [KC2] 

o uses everyday and comparative language, and arbitrary units of

comparison, to describe the size of 2-D figures and 3-D solids drawn

from their personal activities, communities and environments [C] [T]

[KC2] 

In regards to the outcome 1.5,

“Chooses and uses a variety of strategies to measure the size of a

wide variety of figures, objects and events drawn from the world

around them. [T] [C] [KC6]”

It will be expected that by the end of this unit students will be able to;

o directly compares and matches objects and events, and uses

comparative language to describe and communicate size [T] [C] [KC1] 

o considers and discusses the attribute to be measured, and the relative

size of the unit of comparison, with what is being measured [T] [C]

[KC2] 

o uses consistent arbitrary units as standards to compare, order and

communicate [T] [C] [KC1] [KC2] 

o constructs and uses own measuring tools and scales (e.g. balances,

tape measures, timers), or those constructed by others, to measure

attributes of figures, objects and events [T] [C] 

o measures for a variety of purposes (e.g. in order to build, construct,

design, generate data, sort, classify and search for patterns from their

everyday life). [T]

Unit Benefits:

A benefit of this unit of work is that it allows students to experience

measurement in a very hands-on, un-intimidating style of learning. It allows

students to learn by doing, and experimenting rather than passively listening

and trying to ‘memorise’ what they are being told. Furthermore students are

able to connect what they will be learning in their maths lesson to their real

world, as they are measuring objects that they see and use every day.

Length is also is also a vital mathematical principle that is used in our daily

lives and also has principles that are used cross curricular in physical

education, science, art, drama, and design and technology. Most importantly

though is that this unit of work is designed to make maths enjoyable and

interactive, thus allowing students to embrace and feel positive about

mathematics.

REFERENCES

Bobis, J., Mulligan, J., Lowrie, T. (2009). Mathematics for Children:

Challenging Children to Think Mathematically 3rd Ed. Pearson Education

Australia, NSW

Department of Education, Training and Employment, DETE, South Australian

Curriculum Standards and Accountability Framework, Adelaide

Accessed via the internet 10/3/09

http://www.sacsa.sa.edu.au

Dunbar, B. (2001) Exploring Maths: Exploring Length and Area. Blake

Education, NSW

Accessed online 20/3/2009 via,

http://www.blake.com.au/v/vspfiles/downloadables/Members/

9781865092232_Exploring-Maths_Exploring-Length-and-Area_Final.pdf

Barron, Inchworm Measurement, An Educator's Reference Desk Lesson Plan

Accessed via the internet 22/3/09

http://eduref.org/Virtual/Lessons/Mathematics/Measurement/MEA0203.html

Maths300 website. Carlton South , Victoria

Accessed inline 20/3/2009

http://www1.curriculum.edu.au/maths300/

Teachers Resources Galore website. Metre Monster.

Accessed via the internet 22/3/09

http://www.teacherresourcesgalore.com/maths_procedural_texts.htm

APPENDICES

Appendix AGiraffe picture

Appendix BMonkey Puppet

Appendix CLength ChallengesDunbar, B. (2001) Exploring Maths: Exploring Length and Area. Blake

Education, NSW

Appendix DBody MeasuresDunbar, B. (2001) Exploring Maths: Exploring Length and Area. Blake

Education, NSW

Appendix ELength Challenge Worksheet

Appendix FAssessment Rubric #1

Appendix GAssessment Rubric #2

Appendix A – Giraffe Picture

Appendix B – Monkey Puppet

Appendix C – Length Challenges

Appendix D – Body Measures

Appendix E – Length Challenge Worksheet

Length Challenge

How many pop-sticks does it take to measure the long side of your desk?

Can you find an object in the class that is as long as 10 pop-sticks?

I measured……………………………..………………………………………………

How many toothpicks does it take to measure the long side of your English book?

Can you find an object in the classroom that is as long as 6 toothpicks?

I measured……………………………..………………………………………………

How many pencils does it take to measure your chair leg?

Can you find an object in the classroom that is as long as 5 pencils?

I measured……………………………..………………………………………………

How many erasers does it take to measure the self of the bookcase?

Can you find an object in the classroom that is as long as 12 erasers?

I measured……………………………..………………………………………………

Appendix F – Assessment Rubric #1

SCALE: 3 Highly Competent, 2 Shows understanding, 1 Needs WorkAppendix G – Assessment Rubric #2

SCALE: 3 Highly Competent, 2 Shows understanding, 1 Needs Work