Lots o' Plots
How it works
We want to cover a garden with carrots, which must always be planted in 1 x 2 or 2 x 1 rectangles. Can we completely cover a 2 x 2 garden with carrots? What about a 3 x 3 garden? If we can't cover the entire garden with carrots, what if we can use a rock to cover a single square? Does it matter where we place the rock?
In this activity, students start by figuring out which gardens can and can't be covered by carrots. For gardens that can't be completely covered by carrots, try placing a rock in one of the squares and covering the rest of the garden with carrots. They determine where they can (and can't) place the rock so that this is possible. They also explore using more than one rock.
Why we like this activity
- It’s fun! Students enjoy trying to cover the gardens with carrots and figuring out where they can and can't place the rock.
- It helps students to develop spatial reasoning.
- It helps students to develop numerical reasoning.
It requires students to engage in mathematical habits of mind:
Making observations / comparing and contrasting / looking for patterns / making and testing predictions / finding and using strategies / understanding and explaining when trying to figure out which gardens can and can't be completely covered with carrots.
Making observations / comparing and contrasting / looking for patterns / making and testing predictions / finding and using strategies / understanding and explaining when trying to figure out where you can and can't place a rock (or rocks) so the rest of the garden can be completely covered with carrots.
- It has a low floor and a high ceiling: It's easy for students to start trying to cover gardens with carrots and rocks by trial and error, but efficiently figuring out where you can and can't place a rock (or rocks) so the rest of the garden can be completely covered with carrots requires more advanced strategies.
This activity was developed in collaboration with the Julia Robinson Mathematics Festival.