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Questions to facilitate the learning
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Is there always a way to sort numbers so that any two can go together? Explain.
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Is there anything that was true about only three of the numbers? How would that help you solve the problem?
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Was there a different way that you found to split the numbers into two equal groups?
Scaffolding the learning
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Is it possible for 40 and 12 to go together? In what way are they alike?
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Is it possible for 40 and 31 to go together? In what way are they alike?
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Would thinking about the sizes of the numbers help sort them?
What’s the point of this task?
Students frequently gather data and then display it in a graph. In this particular case, the graph is pre-
made so that students need to figure out how to make the numbers sortable to fit the pre-made graphs.
They have to consider the attributes of numbers they might use, such as size, whether they are even or
odd, how many base ten blocks it takes to display them, etc. They also might use some combination of
attributes. For example, one category could be even numbers less than 400 and the other, the rest of
the numbers.
To make it mathematically richer, the task involves sorting numbers rather than everyday objects.
Extending the learning
Students might create a random set of 10 numbers and look at all the possible sort splits that would lead
to two bars.
Data