Sequences of Moves

Several transformations, one journey.

10 problems · about 19 minutes · 8.G.A.2

What this lesson teaches

The child applies a sequence of rigid motions and finds a sequence carrying one figure onto another.

Rigid motions can be applied one after another.
The result is still congruent to the original.
Two figures are congruent exactly when some sequence carries one onto the other.

From earlier lessons. Loosen up before the new work.

3 problems

Review — What a Transformation Does to Coordinates: (6, −2) translated 3 left. What is the new x?
Answer 3
Why (3, −2).
Review — Congruence: Congruent shapes, one side is 15. The matching side?
Answer 15
Why 15.
Review — Moving a Shape Without Changing It: (2, 9) reflected across the vertical axis. New first coordinate?
Answer -2
Why (−2, 9).

Straightforward practice. Get the method working first.

3 problems

Rotated 90° three times. Total turn in degrees?
Answer 270
Why 270°.
Do rigid motions keep side lengths the same? 1 for yes, 0 for no.
Answer 1
Why Rigid means unchanged.
Translated 5 right then 2 left. Net movement right?
Answer 3
Why 5 − 2.

The same ideas with more to keep track of.

2 problems

Are two figures congruent if a sequence of rigid motions maps one to the other? 1 for yes, 0 for no.
Answer 1
Why That is the definition.
Rotated 90° then 90° again. Total turn in degrees?
Answer 180
Why 90 + 90.

Mixed problems. Work out what kind of question it is before you start.

2 problems

Two Moves: A shape is translated 3 right, then 4 right. How far right in total?
Answer 7
Why 7 units.
Two Reflections: A shape is reflected across the same line twice. How many units from its start?
Answer 0
Why Back where it began.