Additional Materials
Materials Required
Estimated Time Needed
(Times are approximate and will depend on the needs of the students.)
If you have a short lesson, or you find the lesson is progressing at a slower pace than anticipated, we suggest you end the lesson after the paired work, "Preparing to Play Give Us a Clue!", and continue in a second lesson.
To help students keep track of each clue, you may want to use a different color marker for each inequality.
In order to answer these two questions, it is helpful to test the inequality with specific pairs of coordinates. These are sometimes called test points.
(0,0) is usually a good choice for a test point, since it makes the arithmetic easy, but if the line itself goes through the origin, then another point should be chosen:
Since 2(0) − 0 ≤ 8 is true, the origin is included in the region 2x − y ≤ 8. This region is to the left of the line.
The purpose of this structured paired work is to make each student engage with their partner's explanations and to take responsibility for their partner's understanding.
You have two tasks during the paired work: to note aspects of the task students find difficult, and support student reasoning.
Note aspects of the task students find difficult.
For example, are students having difficulties using a test point? Do they understand the difference between inequality symbols?
You can use information about particular difficulties to focus whole-class discussion toward the end of the lesson.
Support student reasoning.
Try not to make suggestions that move students towards a particular answer. Instead, ask questions to help students to reason together. For students struggling to understand the symbols, it may help if they put the inequalities into words.
It is important that students cannot see each other's graphs. They could use a book or folder to hide the graph from their partner.
If they are not the same, encourage them to work together to identify mistakes made. The mini-whiteboard listing the clues may help sort out disagreements. This should be seen as a collaborative rather than a competitive activity.
In the summary discussion, you can explore the best strategy for giving a clue, while revising the main math concepts in the lesson. Students should use their mini-whiteboards to respond to your questions.
It will be a point on a line. For example, when the target point is (8,4), the clues could be y ≤ 4 and x + 2y ≥ 16.