Translate a Point Lesson Plan

What is the same? What is different?

Display the first slide of the slide show and give students a few minutes to absorb. We want them to consider what is the same and what is different about the two stars. Students might be a bit confused at first, because the stars look the same! That’s the point!

Once you start discussing, students might say things like:

• The stars are the same color.
• The stars are the same size.
• The stars are the same orientation.
• The stars are in different places on the screen.

Focus in on the fact that the stars being in different positions on the screen is the only difference! Tell students that today we’ll be learning about translations. In a translation, the figure slides. It does not change size or orientation. It is the same figure, just in a different spot!

Changes in `x` and `y`

The next slide is a good reference for students as we move onto graphing and identifying translations. Give students a few minutes to copy this slide in their notes as you explain. Talk about how changes in an `x`-value cause movements to the left and right. If we move right, we add to the `x`-value and if we move left, we subtract. Then discuss how changes in `y`-values cause movements up and down. If we move up, we add to the `y`-value and if we move down, we subtract.

Student notesheet

Give each student a copy of the student notesheet so they can plot points and write in their answers as you go through `4` different types of examples as a class.

Translate a point on the coordinate plane

This first example will be pretty easy for students to plot. They’ll follow the instructions and count `2` units to the left, then `3` units up and plot a new point. As you go through this example on the board, be sure to label the new point with the letter `N`. To extend this example, we’ll write the translation rule. Start by showing students that this looks a little like how we write coordinates in the form `(x, y)` but we’ll also write in what changes. Ask students, “when we moved left, which value changes?” Students should recognize that this is a change in the `x` value, and that it would subtract from the `x`. Write the first part of the rule as “`x-2`”. Ask similar questions for the `y`-value and fill in the rule. Afterwards, you should have the translation rule written as `(x-2, y + 3)`.

Identify translations on the coordinate plane

For the next example, students are again given a coordinate plane, but this time they’re given both points and are looking to identify the translation both in words, and as the formal translation rule. Start students off by pointing out that we should start at Point `B`. We should count the translation for `x` first, so show how we count `4` units left. Then we need to count `14` units down to reach Point `C`. Finally guide students to write the translation rule as `(x-4, y-14)`.

Translate a point given coordinates

In example `3`, we’re no longer given a coordinate grid. However, at this point, students should be familiar with how to write the translation rule from a description in words. Then, help them to find the coordinates of Point `B` by showing that we can plug the original coordinates into the translation rule, like this:

`(``x` `+ 4, ``y` `- 1)`

`(``-3` `+ 4, ``4` `-1)`

After simplifying, we find that Point `B` is at `(1, 3)`.

Identify translation given coordinates

Move onto example `4`, which is the last type of translation problem we’ll work on during this lesson. It’s helpful to tell students to first focus on the `x` value, to figure out how far left or right the point moved. You can ask, “from `9` to `2`, what happened to the `x`-value?” Students might respond that `7` was subtracted, or that the point moved left `7`. Depending on how students answer, write in the words, or the part of the rule. You can ask a similar question for the `y`-value.