Rich Learning Tasks

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Questions to facilitate the learning
• What was the least number of objects you could have in total? How do you know?
• Is it possible to get both small numbers of objects and large numbers of objects?
• Once you got one possible answer, did it help you get other answers? How?
• Could the total number of objects be odd or even or both? How do you know?
• Do you predict it would be possible to get 60 objects or not? Why?
Scaffolding the learning
• Suppose you started with just one object. What would you end up with?
• Do you think you could end up with 4 objects? Work backward to try to find out.
What’s the point of this task?
This task informally introduces students to an important number principle: that 1 of a group + 2 of that
group = 3 of that group, no matter what the group size. Although this is not met formally until later grades,
experiences like this will help students make sense of that property (the distributive property) when they
meet it.
Asking students both what a number can be and what a number cannot be is an important part of
helping them learn to conjecture.
The task allows for differentiation since some students are more comfortable than others with greater
numbers, even though using actual objects should help students who struggle.
Extending the learning
Students might explore what numbers are possible or impossible if what is added is not 2 sets of the
original items, but 3 sets.
Number