Students will learn how to find the intersections of lines, circles, and parabolas, in various combinations. Students will solve word problems and mathematical ones.
Conclude by giving your students these challenges:
- Square Flower by NRICH
- 2014 AMC 8, Problem 12
- 2000 AMC 8, Problem 16
- Apples and Oranges by Pierce School: Problem / Solution
In the figure below, \(\overline{AB} = 9.\) Mentally determine the area of the purple figure.
Here's the solution: First notice that \(\triangle DFC\) is a 3-4-5 triangle. We know \(AECD\) forms a rectangle, so \(\overline{DC} = \overline{AE} = 5.\) From this, and the fact that \(\overline{AB} = 9,\) we know \(\overline{EB} = 4,\) thus \(\triangle CEB\) is also a 3-4-5 triangle. Relocating \(\triangle CEB\) to \(\triangle DFC,\), the purple figure becomes a rectangle, the area of which, is \(\overline{AE} \cdot \overline{AD} = 15.\)