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Copyright © 3P Learning – These resources have been created in partnership with Dr. Marian Small.
For more information visit
www.mathletics.comBalancing Act
Questions to facilitate the learning
•
Could a blue box hold 10 cans? Why or why not?
•
What kinds of numbers describe what a yellow box can hold? Why those numbers?
•
What fraction of the number of cans in the blue boxes is the number in the yellow boxes?
Scaffolding the learning
•
Which colour box holds more cans? How do you know?
•
Do you think the blue box holds twice as many cans as the yellow box? Why or why not?
•
Suppose each yellow box held 6 cans. Would that help you figure out how many cans are in the
blue boxes?
What’s the point of this task?
It is essential for future development in algebra that students have an appropriate understanding of
equality—in particular, that equality represents a balance. In this case, because no numbers are given, the
students have the opportunity to come to a generalisation about the relationships between the numbers of
cans in each type of box. Coming to a generalisation is a big part of what algebraic thinking is all about.
If four yellow units match three blue units, students need to realise that the yellow unit must be 3
4 of the
blue unit. There are many ways to see this:
•
If yellow is 3
4 of blue, each blue is a yellow with an extra fourth. The three extra fourths make another
yellow, so there would be 4 yellows matching 3 blues.
•
If yellow is 3
4 of blue, the total of yellows is 3
4 + 3
4 + 3
4 + 3
4 blues = 12
4 (or 3) blues.
•
If each yellow box held 3 cans, there would be a total of 12 cans. If 12 cans were shared among the 3
blue boxes, each blue would hold 4 cans and 3 is 3
4 of 4. A similar thing would happen if the yellow box
held 6 cans or 9 cans.
Students are essentially solving a multiplication problem: How can three times one amount be the same
as four times another?
Extending the learning
Students might consider different combinations of yellow and blue boxes on each side of the balance and
figure out how the numbers of cans in those two kinds of boxes would be related.
Pattern