Problem
Take one A4 sheet of paper. Tear or cut it into strips length-wise. How many strips will you need to make up a length of 1m by laying the strips end to end?

What is this problem about?
This is first a practical measuring task coupled with some arithmetic. The most efficient way to do this problem is by measuring the length of an A4 sheet and dividing 1m by this length. However, sticking strips together and measuring until the strips have reached 1m in length is another way to solve the problem. The number of strips can then be counted.

It might be a good idea to try the first method and then check it by the practical method. It is possible that there might be a difference between the two methods if the strips have not been laid end to end carefully enough.

There is a little twist in this problem in that the length of a strip doesn’t divide 1m exactly. So the children will have to realise that to make up the full 1m they have to tear off an ‘extra’ strip.

Achievement Objectives
Measurement (Level 2)
- carry out practical measuring tasks, using appropriate metric units for length

Mathematical Processes
- devise and use problem solving strategies to explore situations mathematically (use equipment)

Resources
A4 sheets of paper
1 metre and 30 cm rulers
Blackline master of the problem (English)
Blackline master of the problem (Maaori)

Specific learning outcomes
The children will be able to:
- measure using cm and metres

Teaching sequence

1. Interest the children in the problem by asking them to stand 1 metre from a given line. Check estimates.
2. Reinforce their estimates of 1 metre by asking questions that encourage the children to develop a "sense" of a metre.
   What lengths are 1 metre long?
3. Pose the problem.
4. As the children work on the problem check their use of rulers to measure the length of the A4 paper and the metre strip.
   How many centimetres are there in a metre? How do you know? (100 on the ruler)
5. Share solutions

Extension to the problem
What is the longest strip that you could make using a single sheet of A4 paper with no joins?

Solution
An A4 sheet is approximately 29.7cm long. 100 divided by 29.7 is 3 and some left over. To make at least 1m requires four A4 lengths.