Perplexing Perimeters
In the process of constructing their own “rulers” the students develop a sense of the size of a centimetre and metre. As the students select the appropriate “ruler” for the tasks they learn to choose that the section of the measuring instrument we are using/making is determined by the exactness of the measurement needed. In addition this unit reinforces the number skills of students as they calculate the perimeter of objects using centimetres or metres.
- make appropriate measurements accurately using standard units
- perform addition calculations to find perimeters of objects
Measurement is an important part of maths as a whole, and the primary maths programme in particular. It is an important area of study because measuring, approximating and estimating are everyday experiences. In the process of making their own standard metric “ruler” the students begin to develop their own mental image of a centimetre and a metre. This unit also provides opportunities for the students to appreciate that all measurements are approximate and that the selection of the measuring tool for a task depends on the precision required.
Measurement also provides a context for the further development and reinforcement of number skills. Students can “measure” without the use of number up to the stage of indirect comparison. However as soon as they repeatedly use a unit to measure an object they need numbers to keep track of the repetitions.
This unit is also designed to allow students to practice their additive strategies as they calculate the perimeters of objects. Students at the Advanced Additive Stage (Stage 6) of the number framework realise that numbers are abstract units that can be “operated” on as wholes or can be partitioned and recombined. This is called part-whole thinking. Students at this stage are learning to choose appropriately from a repertoire of partitioning strategies.
measure, approximate, estimate, accurate, perimeter, centimetre, rectangle, combine, sum, strategies
Getting Started (Session 1)
In this session we make our own centimetre rulers and metre tapes so that we can measure the perimeter of objects in the classroom and playground.
- Gather the class on the mat and tell them that you would like to know if the perimeter of this book is longer or shorter than the perimeter of the box.
Can anyone tell me what a perimeter is?
How could we find out which is longer?
- Tell the students that they are going to make their own centimetre rulers.
What is a centimetre?
Can you show me with your fingers how big a centimetre is?
Can you find me something that is one centimetre long? (Centimetre cube, point to markings on a ruler) - Give the students a 10 centimetre long strip of card.
How long do you think this strip is?
How could we check? (Use a ruler, line centimetre cubes along the strip.) - Discuss how they can use the centimetre cube to make centimetre markings on the strip to create their own ruler.
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- Talk about where the number markings are positioned and why they are at the “end” of each centimetre. Talk about where the “0” would go and how this relates to the “0” on commercially produced rulers.
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- Remind the students of the question that was posed at the start of the session and ask for volunteers to compare the perimeters of the two objects. How can you keep track of the measurement? (Record and then add the length of the sides later.) Do you need to measure all of the sides?
- When the measurements have been made ask the students to sum the side lengths. This provides a good opportunity to practice and share strategies for adding numbers.
How did you combine the numbers?
- Repeat with the second object and then make the comparison. This provides further opportunities to share strategies for adding and subtracting numbers.
Exploring (Session 2)
We begin this session by posing a perimeter problem that is “too large” for our 10 cm rulers. We discuss the need for a larger measuring instrument and then construct and use a 5 metre tape.
- Gather the class on the mat and tell them that you would like to know if the perimeter of our classroom is larger or smaller than a perimeter area marked on the playground.
How could we find out which is larger? Are our centimetre rulers appropriate for this? Why not? What could we use? (metres) How many of our centimetre rulers make a metre? How do you know?
- Line 10 of the rulers end to end to show a metre.
- Place a strip of adding machine tape alongside the rulers and discuss how it can be used to make markings on the tape.
- Give each pair of students a 3 metre strip of paper and tell them that they are going to use their 10 cm ruler to create a metre measuring tape.
- Circulate as the students construct their tape. How many centimetres in a metre? How do you write centimetre? What does this line mean on your tape? How many centimetres are there in 2 metres? What objects would you chose to measure with the tape rather than the ruler? How accurate is your tape? Why?
- Remind the students of the question that was posed at the start of the session and ask for volunteers to compare the perimeters of the two objects.
How can you keep track of the measurement? (Record and then add the length of the sides later)
Do you need to measure all of the sides?
How accurate do you need to be? (As the question posed was one of comparison the level of accuracy will depend on how close the perimeters of the two objects are.) - If the measurement requires parts of metres to be used than discuss ways of recording these.
1 m, 20 cm 120 cm - When the measurements have been made ask the students to sum the side lengths. This provides a good opportunity to practice and share strategies for adding numbers.
How did you combine the numbers?
- Repeat with the second object and then make the comparison. This provides further opportunities to share strategies for adding and subtracting numbers.
- When the measurements have been made ask the students to sum the side lengths. This provides a good opportunity to practice and share strategies for adding numbers.
Exploring (Session 3)
In this session the students are involved in a Perimeter Hunt. This involves them finding objects whose perimeter is of a certain length (in either metres or centimetres).
- Give each pair of students a 14-page booklet into which to record the results of their perimeter hunt.
- Tell them to head up each page in turn with the following lengths.
0 - 10 cm
10 - 20 cm
20 - 30 cm
30 - 40 cm
40 - 50 cm
50 – 60 cm
60 – 70 cm
70 – 80 cm
90 – 100 cm
1 – 2 metres
2 – 3 metres
5 – 10 metres
10 – 20 metres
Over 20 metres - Pose the perimeter hunt challenge: Find objects that have perimeters which match the measure on each page. The pairs should use their handmade measuring tools and record their findings on each page.
- Draw the object, labelling the measurement for each side, and stating its perimeter.
Exploring (Session 4)
In this session the students investigate open ended problems involving perimeter. Students may work in pairs to answer the problems.
- What shapes can you draw that have perimeter of 20 centimetre?
- Explain using words or a diagram why the perimeter of a rectangle can be found by using a combination of addition and multiplication.
- How could you find the perimeter of a shoebox?
- If you find the perimeter of a rectangle does it matter which length you increase by one unit to increase the perimeter? Is the same true of the area of the same rectangle? Draw some examples to support your answer.
Reflecting
In today’s session we compare the objects we found to match the measure in the Perimeter Hunt and discuss the findings in our investigations.
- Show the students an object and ask them to estimate which “page” of the book it belongs on.
- Check the predictions.
What length do you think this side would be?
What do you use to make your estimate?
What about the length of this side? [pointing to another side]
- Using the agreed estimates ask the students to calculate the perimeter. Share the strategies used for summing the side lengths.
- Next ask the students to consider which perimeter was the easiest to find objects for.
Why do you think that [perimeter] was the easiest? - Share the objects found for that perimeter length.
- Ask one pair to read out the side measures for their object while the rest of the students check the calculation mentally.Share the strategies used to sum the numbers mentally.
- Repeat with other perimeter measures.
Dear Parents and Whanau,
In maths this week we have constructed our own measuring instruments so that we develop a good understanding of the size of metres and centimetres. We have used our measuring tools to find objects for our Perimeter Hunt. Our home task this week is to find at least 5 objects to add to our book. We need to draw the object, state the length of each side (in metres or centimetres) and then calculate the perimeter.
Please ask your child to explain perimeter and to tell you how they worked it out for each of the 5 chosen objects. Encourage them to combine the numbers in different ways.
Thank you for your encouragement and support.
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