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Purpose

In this unit we explore the size of a centimetre, construct centimetre rulers, and then use these rulers to measure the length of objects.

Achievement Objectives
GM2-1: Create and use appropriate units and devices to measure length, area, volume and capacity, weight (mass), turn (angle), temperature, and time.
Specific Learning Outcomes
• Recognise the need for a standard unit of length.
• Recognise a centimetre length.
• Estimate and measure to the nearest centimetre.
Description of Mathematics

When students can measure lengths effectively using non-standard units, they are ready to move to the use of standard units. The motivation for moving to this stage often follows from experiences in which students have used different non-standard units for measuring the same length. They can then appreciate that consistency in the units used allows for easier and more accurate communication of length measures.

Students' measurement experiences must enable them to:

1. develop an understanding of the size of the standard unit
2. estimate and measure using the unit

The usual sequence used in primary school is to introduce the centimetre first, then the metre, followed later by the kilometre and the millimetre.

The centimetre is often introduced first because it is small enough to measure common objects. The size of the centimetre unit can be established by constructing it, for example by cutting 1-centimetre pieces of paper or straws. Most primary classrooms also have a supply of 1 cm cubes that can be used to measure objects. An appreciation of the size of the unit can be built up through lots of experience in measuring everyday objects. The students should be encouraged to develop their own reference for a centimetre, for example, a fingertip.

As the students become familiar with the size of the centimetre they should be given many opportunities to estimate before measuring. After using centimetre units to measure objects the students should develop their own centimetre rulers, and be introduced to the standard centimetre ruler. Some classrooms have linked cubes which can be joined to form 10 cm rulers. Alternatively pieces of drinking straw could be threaded together.

The correct use of a ruler to measure objects requires specific instruction. The correct alignment of the zero on the ruler with one end of the object needs to be clarified.

Metres and millimetres are established using a similar sequence of experiences: first construct the unit and then use it to measure appropriate objects.

The learning opportunities in this unit can be differentiated by providing or removing support to students and by varying the task requirements. Ways to differentiate include:

• discussing as a class how to measure each part of the body
• setting up stations with instructions for each body part to be measured
• providing templates for the sweatshirt measurements
• encouraging students to work in pairs or small groups. Strategically organising these groups might allow for greater peer learning, extension, and scaffolding.

The activities in this unit can be adapted to make them more interesting by adding contexts that are familiar to students. The clothing you are collect measurements for could be for a hypothetical sports top for your class, or for a new school uniform.

Te reo Māori kupu such as ine (measure), estimate (whakatau tata), mitarau (centimetre), and roa (length, long) could be introduced in this unit and used throughout other mathematical learning. You could also encourage students, who speak a language other than English at home, to share the words related to measurement that they use at home.

Required Resource Materials
• Paper of two different colours
• 1 cm grid paper
• Cardboard
• Sweatshirt
• Labels from students' clothing
• 1 cm cubes
• Metre rulers
• Tape measures
• ​Streamer or crepe paper
Activity

#### Getting Started

1. Ask the students to make an outline of their hand on paper and to cut it out and paste it on to a sheet of paper of another colour. You might need to model this process. Ask students what parts of their hand drawing they think they could measure. Demonstrate each idea (e.g. yes I could measure the length of my pinky finger). Identify and demonstrate what handspan is. Ask students to estimate how many 1 cm blocks wide they think their handspan is and then to measure it, using the collection of 1 cm blocks. Look for students to measure in a straight line, from the baseline, without any gaps or overlaps.
2. Have students share their measurements with a partner, and then with the whole class.
3. Provide further questions for students to investigate:
Which finger is the longest?
How long is you thumb?
4. Share students' findings as a class:
Who has the largest handspan?
What is the difference between the largest and smallest handspan?
5. Ask the students if they know of any other way of measuring in centimetres besides using the blocks. Check their suggestions by placing 1cm blocks on the different measures e.g. 30cm ruler, metre ruler, tape measure.
6. Explain to the students that they are going to make their own centimetre rulers. Model the following process and provide frequent opportunities for students to stop and share their work. Provide students with 1cm grid paper to cut a strip from and some cardboard to paste it on to. Have them number the lines. Ensure students label the 0 point at one end of the ruler and then put the numbers on the lines, not the spaces. As an extension students could measure the length of the different hand-measurements that they measured with blocks.

#### Exploring

1. Focus on the length of a single cm by asking the students to draw a line that is 1 cm long. Ask them to find objects in the classroom that are one cm long (or wide). For example, the width of a finger tip can used to estimate a cm.
2. Have the students remove their shoe and trace an outline of their foot and then estimate its length in centimetres. They can then measure it accurately with the rulers they have made and record the measurement of it. The footprints can be ordered from largest to smallest.
3. Tell the students they are going to measure different parts of their body and record it under the heading of All About Me. Prior to starting, build a chart of ideas for measuring e.g. smiles, hair, arms (wrists to elbows), legs (knees to ankles), necks, wrists, waists etc.
4. Pose the problem of how to measure around something. Accept suggestions and provide string and tape measures. Encourage the students to estimate first and to see if there are any patterns and relationships. Is there another part of your body the same as the measurement from wrist to elbow, or around your ankle etc?
5. Collect the measurements for the parts of the body selected and collate on a class chart.
6. Explain to the students that the PTA has decided to purchase new sports tops for the school and they need information about sizes. You could adapt this context to better reflect the interests, cultural backgrounds, and current learning that are relevant to your students.
Could we measure one person in the class and have all the tops made using their measurements?
7. Discuss with the class the range in measurements found from their measuring over the last couple of days.
8. Suggest to the students that we could help the PTA by sending them patterns that would fit people in our class.
9. Show them a sweatshirt and discuss all the measurements that need to be made and provide them with a large sheet of paper to draw their patterns on.
10. Provide a range of measuring equipment and go over how to use them properly, focusing particularly on measuring from the zero mark and not the edge.
11. The students could place the school logo on their pattern and then provide measurements for where it is located. Share their finished patterns and discuss the differences.
What was the longest/shortest arm length?
What is the difference between them?

#### Reflecting

1. Look at labels from students’ clothing. Highlight the information that is on them.
E.g. Size 8, Height 130cm, Chest 68cm, Waist 60cm.
2. Ask the students if they would expect all 8 year olds to be 130cm. Link back to findings in the previous activity.
Would we expect them to be close to 130cm?
3. Give the students the opportunity to investigate the heights of eight-year-olds and nine-year-olds. Relate the investigation to the age of the students in the class. You might do some further teaching around using the PPDAC statistical investigation cycle to ensure the validity of this investigation.
4. Discuss methods of measuring longer lengths.
5. Look at a metre ruler and identify the number of centimetres and show how a 1cm cube fits into the spaces.
6. Discuss how to measure lengths longer than a metre and have a student demonstrate marking off and repositioning the ruler.
7. After the students have measured their height ask them to record it on a piece of card and then cut a piece of paper that length. (streamer, crepe papers). Attach this to the edge of the card with tape.
8. Display the students’ paper heights in order along the wall and discuss:
Are most eight year olds in our class close to 130cm?
Does the tallest person in our class have the longest feet?