E2.2 Explain the relationships between millimetres, centimetres, metres, and kilometres as metric units of length, and use benchmarks for these units to estimate lengths.
Activity 1: Inverse Relationship Between Millimetre, Centimetre and Metre
Teachers draw a two-metre line on the floor or on the board using masking tape. This line can be straight, vertical, horizontal, slanted or zigzagged. The teacher gives each student either a tape measure in millimetres (Tape A), centimetres (Tape B), or a tape measure of one metre (Tape C). They are then asked to measure the tape length and record their measurement in their math journal.
Image A student kneels in front of a line drawn on the floor. He/she measures the line with a tape
measure in
centimeters, "Tape "A"". A student kneels in front of a line drawn on the floor. They measure the line with a tape
measure that is not marked
in centimeters. "The student measures the line with a tape measure in centimeters, "Tape measure "B"".
Students repeat this exercise over five consecutive days. The length of the line differs each day to measure either 3 metres, 4 metres, 5 metres, or 6 metres. At the end of the week, students record the results in a table similar to the one below.
|
Featured Length |
Tape Measure A |
Tape Measure B |
Tape Measure C |
|
Day 1 line |
2 000 mm |
200 cm |
2 m |
|
Day 2 line |
3 000 mm |
300 cm |
3 m |
|
Day 3 line |
4 000 mm |
400 cm |
4 m |
|
Day 4 line |
5 000 mm |
500 cm |
5 m |
|
Day 5 line |
6 000 mm |
600 cm |
6 m |
Teachers share and record student observations.
- The 2 000 millimetre measurement obtained with Tape A equals the 200 centimetre measurement obtained with Tape B and equals the 2 metre measurement obtained with Tape C.
- The 3 m measurement obtained with tape C equals the 300 cm measurement obtained with tape B and the 3 000 mm measurement obtained with tape A.
- There are always 100 times more centimetres than metres.
- There are always 1 000 times more millimetres than metres.
Teachers should support students to make connections between the measurements noted and make the following conjectures.
- One hundred centimetres equals 1 metre.
- There are 10 millimetres in 1 centimetre.
- There are 1 000 millimetres in 1 metre.
- When the same length is measured in metres, centimetres and millimetres, the number of centimetres needed to measure the length is greater than the number of metres since the centimetre is smaller than the metre (inverse relationship). The same is true for millimetres: the number of millimetres needed to measure the length is greater than the number of centimetres and the number of metres, since the millimetre is smaller than the centimetre and the metre (inverse relationship)
These conjectures can be verified by other similar situations and one can then formulate the generalization that there are always 100 centimetres in a metre, 1 000 millimetres in a metre or 10 millimetres in a centimetre.
Source: adapted and translated from Guide d’enseignement efficace des mathématiques, de la maternelle à la 3e année, Mesure, p. 64-65.
Activity 2: Creating Benchmarks
Invite students to find benchmarks that represent 1 mm, 1 cm, 1 m, and 1 km. For example, students could choose the lead of their pencil (1 mm), the width of their index finger (1 cm), the length of their arms (1 m), and the distance from the school to the post office (1 km). Ask students to explain their benchmarks. Then ask them if they can use their benchmarks to estimate lengths that have more than one unit (for example, 20 mm, 10 cm, 10 km).