Rich Learning Tasks

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Questions to facilitate the learning

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Could you just look at your blue line and know it is just a LITTLE longer than the red one if you folded it in

half? How? What would you have to do to check?

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How does your red line compare to your blue line in length?

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Would a line that is exactly twice as long as the red line be longer or shorter than your blue line? Why?

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Would everyone who does this task end up with the same length line? Why or why not?

Scaffolding the learning

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Will the blue line be longer or shorter than the red line? How do you know?

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Do you think it will be a lot longer?

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How could you use the lines in the background to help you?

Extending the learning

Students might consider making the blue line a little longer if it’s folded twice. They would then see it is

actually more than four times as long as the red line. Alternatively, they could start with the long line and

draw the short line to meet the original conditions.

What’s the point of this task?

This task provides an opportunity for students to compare lengths directly. But, more importantly, it builds

visualisation skills by having students imagine what half or twice as long as something would be. The task

starts students on the road to proportional thinking by relating the concepts of half and twice and by

helping students to see that the problem is not about absolute lengths, but relative lengths. Two students

could be correct with very different lines because it is the relationship between the two lines that matters.

Rather than asking that the folded line be exactly the same as the original, the phrase ‘a little longer’ is

used so that students will not be hung up on being perfect, which is not really what the task is about.

Folding Lines

Measurement