Rich Learning Tasks

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Questions to facilitate the learning
• Why were B and C an even number of units apart? How about C and D?
• Could B and C have been an odd number of units apart? Why or why not?
• Could A and D have been an odd number of units apart? How?
• What did you notice about the values of D – A?
• How could that have helped you figure out the placement of A, B and C if D were at 100?
Scaffolding the learning
• What are possible positions for point A? Choose one.
• How far apart do you want A and B to be?
• Do you have a choice now about where to put C? How do you figure out where C goes?
What’s the point of this task?
This task provides an opportunity to think of multiplication as comparison—in this case, comparison of
length. Students are free to choose how far apart points A and B are, allowing for either simple or more
complicated multiplications. Hopefully, some students will come to the generalisation that points A and D
have to be 11 times as far apart as A and B.
For example, if a student chose A and B to be 3 apart with A at 60, he/she will have to do lots of
calculation to figure out why D would have to be at 93. But if he/she had chosen A as 100 and A and B as
5 apart, D would be at 155. Asking students to work backward from D at 100 adds to the computational
value of the problem.
Extending the learning
Encourage students who are ready to choose A and B to be a decimal or fractional distance apart to see
whether or how their results change.
Number Number Line Spacing