How many strips?
This problem solving activity has a measurement focus.
Ariana needs a metre ruler, but she can't find one.
She knows that the wooden table is exactly 1 metre long.
She makes herself a ruler from an A4 sheet of paper torn into strips lengthways which she then tapes together end to end.
How many strips does Ariana need?
- Measure using centimetres and metres.
- Use additive strategies.
- Devise and use problem solving strategies to explore situations mathematically (use equipment).
This measuring task involves students demonstrating their estimate of 1 metre, creating their own metre ruler from carefully joining A4 length strips of paper end to end, and using this 'ruler' to measure objects about them.
Note: The length of an A4 strip doesn’t divide into 1m exactly. Students will need 3 'and a bit' strips.
- Copymaster of the problem (Māori)
- Copymaster of the problem (English)
- A4 sheets of paper
- 1 metre and 30 centimetre rulers
The Problem
Ariana needs a metre ruler, but she can't find one.
She knows that the wooden table is exactly 1 metre long.
She makes herself a ruler from an A4 sheet of paper torn into strips lengthways which she then tapes together end to end.
How many strips does Ariana need?
Teaching Sequence
- Engage the students in the problem by asking them to stand 1 metre from a given line. Check estimates.
- Consolidate their personal benchmarks of 1 metre by asking questions that encourage the students to develop a "sense" of a metre.
What lengths are 1 metre long? - Pose the problem.
- As the students 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) - Share solutions
Extension
Using your 'paper ruler', find and write down at least 5 shapes in the room that measure (close to) 1 metre around their outside edge.
What is the longest single strip, without joins, that you can tear from an A4 sheet of paper?
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.
Solution to the Extension
Possible solutions may include the perimeter of: a large picture book, the seat on a small stool, a laptop screen.
There is a theoretical limit to the length that can be made. Obviously this depends on the width of the strip and how carefully it is torn!