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Copyright © 3P Learning – These resources have been created in partnership with Dr. Marian Small.
For more information visit
www.mathletics.comQuestions to facilitate the learning
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Is it possible to have the same three numbers of dots on each side of the triangle? How?
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Is it possible to have 1 dot in the white circle? How about 4 dots?
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Once you figured out one possibility, how could you figure out other possibilities?
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Are there more possibilities for answers using even more dots or probably not? Why?
Scaffolding the learning
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What happens if you put 3 dots in the white circle, 2 in the yellow and 3 in the red? What do you know
about the green and orange circle dots?
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Suppose you want each side to use 6 dots. How could you arrange those dots into three groups?
What’s the point of this task?
The task is designed to provide students with an opportunity to practice simple addition, subtraction and
decomposition of numbers. For example, a student who uses 1 dot in the white circle, 2 dots in the yellow
circle and 5 dots in the red circle can either investigate other decompositions of 8 that involve 1 or 2 or 5
or can subtract one of those numbers from 8 to figure out what to put in other circles.
Some students will stop with one possibility, but they should be encouraged to look for others. Many
students will not realise that once a particular solution works, the same number of dots could be added to
each circle to generate another solution, but some might. Others will consider orientation and realise that
‘turning the triangle’, e.g. putting the red circle on top yields what could be considered a different solution.
Extending the learning
Students might be challenged to use exactly 24 dots in total or to have the total of dots on a single side
be 10.
Six Circles
Number and Algebra