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Copyright © 3P Learning – These resources have been created in partnership with Dr. Marian Small.
For more information visit
www.mathletics.comNumber
Walking Back and Forth
Questions to facilitate the learning
•
If you went forward 2, back 2, forward 3 and back 3, would you land where you started? Why or why not?
•
If you went forward 2, back 3, forward 3 and back 2, would you land where you started? Why or why not?
•
If you started at 4, could you go forward 2, back 3, forward 4 and back 4 and land where you started?
Why or why not?
•
If you had started at a different number, could you have still taken the same number of steps?
•
Could you pick any three numbers to start with and then choose the fourth one so that you land where
you need to?
Scaffolding the learning
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You are standing on [5]. Where would you be if you went forward 1 step? Why is that easy to predict?
•
Suppose you go forward 2 and want to get back to where you were. What could you do?
•
Suppose you go forward 2 and then back 1. Will you be where you started? Will you be ahead? Will you
be behind?
What’s the point of this task?
Engaging in this task provides students with an opportunity to practice the counting sequence, observe the
effect of moving forward and backward on a number line and explore, informally, the inverse relationship
between addition and subtraction.
Although some students may assume you must go backward as many steps as you go forward each time
to get back to the start number, they will come to realise that it is simply the total forward and the total
backward that must match.
Extending the learning
Students might take an extra group of steps forward only or an extra group of steps forward and an
extra group of steps back or they might be restricted from ever using the same number of steps in the
four movements.