Coordinate Moves
5 min
Teacher Prep
Setup
Narrative
The purpose of this Warm-up is to connect (x,y) coordinates with transformations.
There are many ways to express a translation because a translation is determined by two points P and Q once we know that P is translated to Q. There are many pairs of points that express the same translation. This is different from reflections which are determined by a unique line and rotations which have a unique center and a specific angle of rotation.
Launch
Ask students how they describe a translation. Is there more than one way to describe the same translation? After they have thought about this for a minute, give them 2 minutes of quiet work time followed by a whole-class discussion.
Student Task
Select all of the translations that take Triangle T to Triangle U. There may be more than one correct answer.
A. Translate (-3,0) to (1,2).
B. Translate (2,1) to (-2,-1).
C. Translate (-4,-3) to (0,-1).
D. Translate (1,2) to (2,1).
Sample Response
A and C both take Triangle T to Triangle U.
Activity Synthesis (Teacher Notes)
Remind students that once you name a starting point and an ending point, that completely determines a translation because it specifies a distance and direction for all points in the plane. Appealing to their experiences with tracing paper may help. In this case, we might describe that distance and direction by saying “all points go up 2 units and to the right 4 units.” Draw the arrow for the two correct descriptions and a third one not in the list, like this:
Point out that each arrow does, in fact, go up 2 and 4 to the right.
Anticipated Misconceptions
Students may think that they need more information to determine the translation. Remind them that specifying one point can determine the distance and direction all of the other points move in a translation.
Standards
- 8.G.1·Verify experimentally the properties of rotations, reflections, and translations:
- 8.G.A.1·Verify experimentally the properties of rotations, reflections, and translations:
- 8.G.3·Describe the effect of dilations, translations, rotations, and reflections on two-dimensional figures using coordinates.
- 8.G.A.3·Describe the effect of dilations, translations, rotations, and reflections on two-dimensional figures using coordinates.
15 min
15 min
Knowledge Components
All skills for this lesson
No KCs tagged for this lesson
Coordinate Moves
5 min
Teacher Prep
Setup
Narrative
The purpose of this Warm-up is to connect (x,y) coordinates with transformations.
There are many ways to express a translation because a translation is determined by two points P and Q once we know that P is translated to Q. There are many pairs of points that express the same translation. This is different from reflections which are determined by a unique line and rotations which have a unique center and a specific angle of rotation.
Launch
Ask students how they describe a translation. Is there more than one way to describe the same translation? After they have thought about this for a minute, give them 2 minutes of quiet work time followed by a whole-class discussion.
Student Task
Select all of the translations that take Triangle T to Triangle U. There may be more than one correct answer.
A. Translate (-3,0) to (1,2).
B. Translate (2,1) to (-2,-1).
C. Translate (-4,-3) to (0,-1).
D. Translate (1,2) to (2,1).
Sample Response
A and C both take Triangle T to Triangle U.
Activity Synthesis (Teacher Notes)
Remind students that once you name a starting point and an ending point, that completely determines a translation because it specifies a distance and direction for all points in the plane. Appealing to their experiences with tracing paper may help. In this case, we might describe that distance and direction by saying “all points go up 2 units and to the right 4 units.” Draw the arrow for the two correct descriptions and a third one not in the list, like this:
Point out that each arrow does, in fact, go up 2 and 4 to the right.
Anticipated Misconceptions
Students may think that they need more information to determine the translation. Remind them that specifying one point can determine the distance and direction all of the other points move in a translation.
Standards
- 8.G.1·Verify experimentally the properties of rotations, reflections, and translations:
- 8.G.A.1·Verify experimentally the properties of rotations, reflections, and translations:
- 8.G.3·Describe the effect of dilations, translations, rotations, and reflections on two-dimensional figures using coordinates.
- 8.G.A.3·Describe the effect of dilations, translations, rotations, and reflections on two-dimensional figures using coordinates.