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Copyright © 3P Learning – These resources have been created in partnership with Dr. Marian Small.
For more information visit
www.mathletics.comAway from Home
Questions to facilitate the learning
•
Is A more than halfway to B or not? If not, could it have been if you had chosen a different value for []?
•
Is C closer to A or to B? Explain your thinking.
•
If you placed A on the road, would it be possible to figure out where B was? How?
•
How does your answer change if you change the value of []?
Scaffolding the learning
•
Is A or B closer to home? Why?
•
Suppose you put B on the line somewhere. Where would you put A?
What’s the point of this task?
Although this problem can be solved using multiplication of fractions by students who already have those
skills, the problem can be solved using simpler fraction understandings. Even if students know how to
multiply fractions, they will first have to recognise that this is a multiplication of fractions problem.
Students should come to realise that C is between home and A and A is between C and B.
There was a deliberate choice to use
2
3
as the second fraction so that students will think about the notion
that
2
3
of 3 ___ths (e.g. 3 fourths, 3 fifths, etc.) is 2 ___ths. Allowing students to select the denominator
allows for a generalisation; students will see that the result is
2
[ ]
, no matter what value is chosen for [].
That is because
2
3
x
3
[ ]
=
2
[ ]
for any chosen denominator.
Extending the learning
Students might change the fractions
3
[ ]
and
2
3
to any other fractions of their choice and try the problem.
Number