This unit begins by having students use their bodies to measure the area of different shapes drawn on the floor. A further understanding of area is developed through the use of beans, counters and blocks to measure the area of objects in the classroom.
- Cover a shape with non-standard area units and count the number used.
- Compare and order areas of shapes using non-standard area units.
Non-standard units are objects which are used because they are known to students and are readily available, for example, paces for length, books for area, and cups for volume. Non-standard units introduce the students to the idea that units are repeated and counted in order to provide a measure of an attribute of an object. For example, the width of the desk is 4 handspans.
Non-standard units introduce most of the principles associated with measurement:
- Measures are expressed by counting the total number of units used.
- During a measurement activity, the unit must not change.
- Units are repeated across the attribute being measured with no gaps or overlapping of the units.
- Sometimes fractions of a unit (such as half and quarter) need to be used in order to get a more accurate measure.
- Units of measure are not absolute but are chosen for appropriateness. For example, the length of the room could be measured by handspans but a pace is more appropriate.
Prior to introducing standard units, students need to realise that non-standard units tend to be personal and are not the most suitable for communication. For example, my hands are smaller than yours, so telling me to measure a piece of cloth three hands wide may not be useful.
Covering surfaces with a single unit will also lead to discussion about shapes that tessellate, and are therefore useful for covering surfaces, and those that don’t. For example, rectangles and squares tessellate the plane, whereas circles don’t. Tessellating with non-standard units establishes the need to cover surfaces without leaving gaps and without overlapping. It also demonstrates the advantages of using arrays that can be readily counted by using multiplication, for example, 3 rows of 6 tiles gives an area of 18 tiles.
From the earliest of these experiences, students should be encouraged to estimate. Initially these estimates may be no more than guesses, but estimating involves the students in developing a sense of the size of the unit. As everyday life involves estimating at least as frequently as finding exact measures, the skill of estimating is important.
At this stage students can also be introduced to the appropriateness of units of measure. For example, a hand is more appropriate than a finger tip for measuring the area of a desktop.
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:
- using a digital camera to record students' responses to reduce the required writing time
- providing additional 'challenges' where students need to choose their own unit of measure, rather than having it provided to them
- having students work in pairs or small groups to create their own measuring challenges for other groups to complete.
The context for this unit can be adapted to suit the interests and experiences of your students. For example, for session 1 you could draw outlines of characters from a book you are reading the class. Similarly, for other activities, both the shapes being measured and the units being used to measure them could be chosen to appeal to your students.
Today we introduce non-standard measures and use our bodies as measuring tools. Before the lesson starts mark out on the floor several large areas of different shapes with tape or chalk.
- Explain to the students that they are going to cover the shapes on the floor by lying in them. Looking at one shape at a time estimate how many students will be able to lie in each, then check. Discuss the need for all available space to be used up. As you measure each area record the number of students that can fit into that space in a chart.
How many students do you think will be able to lie in this space?
Will this space fit more or less students than the last one?
Which space will fit the most / least students?
- Explain to the students that they are now going to draw their own shapes in the playground with chalk. As they draw a shape they are to estimate how many students will be able to lie in it and record that number inside the shape.
- As a class, measure the area of some of the shapes.
How many students do you think will fit into this space?
Can you find a space that will fit the same number of students as this one?
Can you find an area that is smaller / larger than this one?
- Discuss the idea that you need to be able to fully cover the object in order to measure its area (no gaps or overlaps).
These sessions explore the use of non-standard measures and compare areas using non-standard measuring units.
Over the following days set up non-standard measuring tasks. For each task have students estimate, measure and then compare their results with others to order areas.
Measuring tasks you could use include:
- Covering sheets of newspaper with shoes. How many muddy shoes can fit onto a sheet of newspaper while they dry?
- Covering a sheet of newspaper with memo cube paper.
- Covering book covers with mosaic shapes (triangles, hexagons or squares)
- Cutting shapes out of paper and covering them with beans.
- How many books laid flat does it take to cover the mat?
- Measuring the area of 3 different size chair seats (a staff chair, a senior student’s chair and a junior student's chair) using blocks.
Today students use their measuring skills to compare the areas of their feet and hands and find out which is larger.
- Have students look at their hands and feet. Get them to estimate which of them has the greatest area.
Look at your hands and feet. Do you think your feet or hands take up the most space?
- Students then draw around one hand and cut out the outline, and draw around one foot and cut out the outline. Ask the students for their ideas about how they could compare the area of their hands and feet, for example, counters, tiles, blocks, direct comparison.
- Students record whether their hand or foot is larger and explain how they found that out. Discuss what they have found out.
Whose foot is larger than their hand?
How did you work that out?
- Tell the students that you want them to put themselves in order according to the area of their feet. Discuss ideas for doing this. Select one of the ideas (blocks) and ask the students to use it to measure their feet.
- Put the feet in order on a chart and display.