M3.9.3 For the adult
Shapes on a grid
If I slide a shape across a page, or flip it over, where do its corners go?
What this chapter teaches
A shape on a grid is its corners. The midpoint of two points is halfway in each number. A translation adds the same two numbers to every corner. A reflection in the x axis flips the sign of each up number, and in the y axis it flips the sign of each across number.
Three questions to ask
There is no one right wording. Listen for the idea.
- How do you find the midpoint of (2, 6) and (8, 2)?
- What happens to the coordinates of a point when you move it 3 left and 2 up?
- Why does the point (3, 2) go to (−3, 2) in the y axis, and not to (−3, −2)?
After the chapter, the learner can
- Find the midpoint of a line between two points
- Move a shape on a grid by a translation
- Reflect a shape in the x axis or the y axis
What they copy into their notebook
Midpoint: add the two numbers and halve, for across and for up. Translation: add the same numbers to every corner. Reflection in the x axis: up changes sign. In the y axis: across changes sign.