Outlining area

Purpose

This unit of work explores the measurement of area. Students estimate and measure area using square centimetres. 

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 area.
  • Measure surfaces using square centimetres.
  • Estimate the measure of surfaces using square centimetres.
Description of Mathematics

When students can measure areas 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 where the students have used different non-standard units for the same area and have realised that consistency in the units used would allow for the easier and more accurate communication of area measures.

Students’ measurement experiences must enable them to:

  1. develop an understanding of the size of a square metre and a square centimetre;
  2. estimate and measure using square metres and square centimetres.

The usual sequence used in primary school is to introduce the square centimetre and then the square metre.

The square centimetre is introduced first, because it is small enough to measure common objects. The size of the square centimetre can be established by constructing it, for example by cutting 1-centimetre pieces of paper. Most primary classrooms also have a supply of 1-cm cubes that can be used to measure the area of 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 fingernail or a small button.

As the students become familiar with the size of the square centimetre they should be given many opportunities to estimate before using precise measurement. They can also be given the task of using centimetre-squared paper to create different shapes of the same area.

Opportunities for Adaptation and Differentiation

This unit can be differentiated by varying the scaffolding provided or altering the difficulty of the tasks to make the learning opportunities accessible to a range of learners. For example:

  • provide smaller shapes for students to work with that have an area of a whole number of square centimetres
  • model how to visualise the first row and column of a grid and use this to estimate area.

The context in this unit can be adapted to recognise diversity and student interests to encourage engagement. For example, the activities could focus on measuring familiar objects such as leaves in autumn, or shells flowing a trip to the beach. For the activities to work there needs to be a collection of objects, all with a range of areas around 120cm.

Required Resource Materials
Activity

Session 1

We start this unit with a guessing game which introduces the idea of estimation.

  1. Show the students the outline of an object, for example; a small book, a pebbles packet or a calculator.
    What do you think that this could be the outline of?
    How many cubes do you think I would need to cover this shape?
  2. Give each student a cube and ask them to write their guess on a piece of paper. Introduce the idea that an estimate is a thoughtful guess. 

    I think the area of the mystery object is ......cubes

    James T

    Show the class a shape made with 5 cm cubes. 
    cubes

    Ask the students to record the shape on cm squared paper.
    What is the area of this shape?

  3. If the students say 5 squares tell them that the unit square is called a square centimetre.
    Why do you think it is called a square centimetre?
  4. Ask a volunteer to make a different shape with the 5 cubes. Tell them that the shape must be flat and the whole sides of the squares must touch.
    What is the area of this shape? ( 5 square centimetres or 5 square cm )
  5. Give each student 5 cm cubes and challenge them to find other shapes that can be made with the cubes. Ask them to record the shapes on the cm grid paper.
    Shapes to make box's 

    (These shapes are called pentominoes and there are 12 distinct shapes that can be made)

  6. Share shapes. Check again that the students understand that each has an area of 5 square cm.

Session 2

  1. Look at the outline of the mystery object from yesterday.
 How can we work out whose guess was closest to the area of the object? 
  2. Give each pair of students an outline of the mystery object and ask them to work out its area in square centimetres. Have cm cubes and squared paper available and support students to make decisions about how they will measure the area. Share areas and approaches used.
  3. Talk about how to handle part squares.
  4. Ask the students to write what they think the object is, and their measurement for its area, on the object’s outline. Display the outlines on a Mystery Object chart.

Session 3

  1. Pose the question: What objects do you think have about the same area as our Mystery Object? Note that students will need to use their estimation skills to accurately identify objects of a similar area and discuss possible estimation strategies. 
  2. Brainstorm ideas for objects that have about the same area as the Mystery Object. Write the names of these objects on strips of paper and put them into a hat.
  3. Working with a partner the students take a strip, and find the object it names. They then make an outline of the object, calculate its area, and write the name of the object and its area on the outline. 
  4. At the end of the session work together to order the objects measured from smallest area to largest area, and identify objects with a similar area to the Mystery Object.

Session 4

  1. Establish a challenge: Today we’re going to challenge ourselves to identify objects with a specific area. We’ll need to use our estimation skills.  
  2. Before the session fill the hat with strips of paper. Each strip needs to have the measurement of an area written on it. Include several strips of the same measurement.
  3. Students work in pairs to take a strip with the measurement of an area, and draw or find five objects with that area.
  4. As a class, review the task together and find out how successful students were at estimating area. Discuss useful estimation strategies.
  5. Students who have been working with the same measurement compare results and discuss any differences, checking each other’s measurements.

Session 5

Today we use the measurement skills we've been working on to find out who has the largest foot.

  1. How could we find out?
    About how many square cm do you think it would be? Why do you think that?
  2. Ask small groups of students to think about a way of measuring feet to find out whose is the largest.
  3. When the outline is made the students need to work out the area of their foot.
  4. Share outlines and measurements. Display from smallest to largest.
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Level Two