It often helps students to know that the ideas we offer them aren't just new, but necessary for pushing past the limitations of their older ideas. Math is an aspirin rather than a vitamin. So I encourage you to invite student thinking in Garden Bricks by creating a headache. Here's one way!
Create a headache.
In Activity 1 of Garden Bricks, we ask students to divide three gardens by the width of three different bricks.
Notice how it's possible to answer the first example using visual imagination or some mental math. Drawing a picture can serve a student very well in the second example. Both examples yield whole number results.
But the third example is much harder to answer using either of those methods. It's result is a fractional value, creating the need for tape diagrams and other methods we're introducing in this unit.
Consider making this difficulty explicit to students by asking them, "Why is this third question harder than the other two?" After that conversation, your students are much more likely to experience the help you offer as pain relief, as necessary and urgent.
Dan & the Desmos Classroom Team
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