Even this far into the unit, your students will still benefit from experiences that connect new ideas to the concrete and sensory ideas they've been developing since they were very young.
For example, consider starting Puzzling It Out by sharing this image.
Instead of asking students to start calculating areas right away, consider asking them questions like:
Which rectangle is the biggest? Which is the smallest?
Can you rank them from biggest to smallest?
Can you estimate the number of unit squares they each take up?
Consider that students may get into a debate—either with themselves or a classmate—about which has more area: A or D.
By starting with their senses before moving to calculation, you can strengthen both. If students (incorrectly) calculate areas for A and D that are very different, their previous estimates may help them check their answers. If they (correctly) calculate areas that are equal, they'll have even more confidence in the accuracy of their work.
That's the value of starting with student senses before moving to logic, abstraction, and calculation. You're likely to strengthen both kinds of knowledge, along with the student's sense of themself as someone with something to offer math.
Dan & the Desmos Classroom Team
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