After you master the challenge on page 1, you can try the slightly harder challenge on page 2.
✏️ What do you notice? What do you wonder?
2 Reflect Dance 1
Work with a partner to perform two short reflect dances, moving as if there is a mirror between you. To locate the mirror, put a piece of tape on the floor, with a dance guide paper in the middle of the mirror like this:
For the first dance, flip a coin to identify one person as the independent dancer and the other as the dependent dancer. You will switch roles for the second dance.
Independent Dancer: Always look at your partner, and take steps according to the directions below. As you dance, you can do any other body movement that’s both safe and simple enough that your partner can mirror it. Start one step back from the middle of the mirror.
Dependent Dancer: Mirror your partner’s movements, staying exactly across the mirror from your partner and the same distance away from the mirror.First Dance:
✏️ Draw a diagram to show the path that each of you followed.
✏️ Did both of you move in the same direction?Second Dance: (after switching roles)
Begin with the three-part dance routine below and finish by improvising your own dance pattern. If possible, ask a classmate to video your dance.
✏️ When did you both move in the same direction? When did you move in opposite directions?
✏️ How does this video relate to the reflect dance you just did?
4 Construct Reflect Functions
You and your partner should each take a turn making a design of your own, and you should each submit a drawing of your traces to your teacher.
5 Match the Traces
Each page of this sketch has a faint background image showing traces left by an independent variable x and its reflected image `r_j(x)`. But the mirror is hidden!
Construct your own reflect function and adjust it so you can drag x to make the same pattern as the one shown faintly in the background.
✏️ Try each of the two mirror tools. Which did you find more useful? Why?
✏️ What did you learn as you solved these challenges? Describe your method so another student could use it.
✏️ Why do you think there’s an extra tool at the bottom of the toolbox?
6 Reflect Games
Each of these three games has a different purpose:
For each game play a few times at easier levels, and work your way up to level 5. (Once you start a game at one level, you must press Reset to change to a different level.)
✏️ For each game, how many hits can you score in ten tries at level 5?
✏️ What methods did you invent to make it easier to get a high score?
7 Reflect Shapes
With this sketch, you can reflect a variety of shapes.
Note that the Reflect tool in this sketch constructs three things: the independent variable `x`, the mirror, and the dependent variable `r_j(x)`.
8 Find the Mirror
This sketch challenges you to find the hidden mirror(s). On pages 1, 2, and 3, your job is to find the mirror so that if you animate `x` on the domain, `r_j(x)` will move around the range. Pages 4 and 5 povide slightly different challenges.
✏️ What did you notice, and what did you wonder, as you constructed these reflect functions?.
9 Reflect Dance 2
In a group of four or five students, tape a dance guide paper on the classroom floor to mark two perpendicular mirrors. Invent a reflect-family dance that uses both mirrors.
Dancer `x` is the independent variable and dancer `r_j(x)` is the reflected image, across mirror `j`, of `x`. Dancer `r_k(x)` is the reflected image across mirror `k` of `x`. Decide among yourselves how the fourth dancer should move. As you create and practice your dance, check to be sure the dancers are correctly positioned relative to the mirror.
As you choreograph and practice your dance, take turns so everyone in the group has a chance to be the independent dancer. When you’re ready to perform your dance, ask someone from another group to video your group dance.
✏️ As you created your dance, how did you decide the fourth dancer should move?
✏️ In what direction must each of the other dancers move when `x` moves at 0°? at 90°? at 180°? at 270°?
✏️ What else did you notice, and what did you wonder, about the reflect functions that connect your dancers to each other?
✏️ How could you use function notation to describe the fourth dancer?
This page supports the Reflect Family lesson from the Introducing Geometric Transformations as Functions unit. You will construct reflect functions, manipulate and observe them, and learn how this function family behaves.
By the end of this lesson, you’ll be able to perform these actions and answer these questions:
The Fine Print
Record every major revision, in reverse chronological order