## Exploring Flips and Slides

This lesson builds on the previous two lessons and encourages students to explore the geometric transformations of reflection and translation. Students create a design then, using flips and slides, make a four-part paper "mini-quilt" using that design as the basis. While the formal terms are reflection and translation, the more informal terms slide and flip are used at this stage. The experience focuses students’ attention on the changes these geometric transformations make in a student-designed quilt square.

To set the stage for this lesson, you may wish to read another of the books listed in the Paper Quilts Bibliography, such as *Sam Johnson and the Blue Ribbon Quilt*,
calling attention to quilt squares which show flips and slides. While
students remain seated, give each child four white squares (or to save
time, four copies of the chosen quilt square) and crayons or markers.
Then display a quilt square and ask them to copy it four times in any
color they wish, using the same colors each time. Some simple designs
include:

To help focus discussion, you might display a model square on the chalkboard or overhead.

Provide students with a 6" × 6" square workmat divided into four equal parts. Have them label the small squares starting from the top left and going clockwise. The top positions, therefore, are numbered 1 and 2, position 3 will be under position 2, and position 4 will be under position 1.

Now ask children to place one of the colored 3" × 3" squares in position 1 and then to place an identical model square face up on top of it so that like parts are touching. Then have them slide the top square down to position 4 so that it is directly under the square in position 1. [The squares in positions 1 and 4 will look the same.] Now have them place a third identical square on top of the square in position 1 so that sections colored alike are touching, then slide it into position 2, directly to the right of the square in position 1. Encourage students to find as many ways as they can of how they can slide a square into position 3. Then have them compare the 4 squares. [They will all look alike.]

Next ask children to place one of the colored 3" × 3" squares in position 1 and then to place an identical model square face up on top of it so that like parts are touching. Then have them flip the top square down to position 4 so that it is directly under the square in position 1. [The square in position 4 will be flipped over to the side without a design.] Now have them place a third identical square on top of the square in position 1 so that sections colored alike are touching, then flip it into position 2. [The square in position 2 will also be showing the side without a design.] Next have them align the fourth square with the square in position 1, then slide it down into position 4 then across into position 3. Now ask them to compare the four squares. [Squares in positions 1 and 3 will look alike, as will the squares in positions 2 and 4.]

Then ask the students to put the 4 squares into a pile, place one of the squares in position 1, then explore several ways they can slide and flip the four squares to make Four Patch designs. You may wish the students to record one of the ways they found by gluing the four small squares on a sheet of paper and describing how the Four Patch square was created.

When the children are ready, call them together to share designs and describe how each of the squares is related to the other three squares. You may wish to reinforce the vocabulary they use by modeling it with demonstration squares. You may wish to ask the students to describe the results of the reflection and translations in written form.

- Paper Quilts Bibliography
- White, 3-Inch Squares (4 per student)
- Crayons or Markers
- 6-Inch Square Work Mat, divided into 4 equal parts (1 per student)

**Assessments**

- At this stage of the unit, it is important for students to know:
- transformation terms
- how to distinguish between slides and flips
- how to follow a sequence of directions concerning transformations
- if students can determine what transformation has been used when shown the starting position and the ending position

- The guiding questions may assist you in understanding the students’ level of knowledge in this area, but others may seem appropriate as your dialogue with the students progresses.
- Collect students' written responses from the conclusion of the lesson.

**Extensions**

Samples of other quilt squares in which flipping and sliding are evident can be seen on various websites. Students can search for such websites. You may wish to encourage children to describe orally or in writing the transformations that have been used to create one or more of these patterns.

**Questions for Students**

- What type of moves did you use? Can you show us?
- How can we tell the square was slid? Was flipped?
- What is alike between the squares on the top and those on the bottom? How did that happen?
- What is alike between the squares on the right and those on the left? How did that happen?
- Suppose you slid a square and then flipped it. What would happen?
- Would you get the same thing if you flipped it and then slid it?

**Teacher Reflection**

- Which students met all the objectives of this lesson? What extension activities are appropriate for these students? What evidence did you collect to document achievement of the learning targets?
- Which students did not meet the objectives of this lesson? What instructional experiences do they need next? What mathematical ideas need clarification? What misconceptions did they demonstrate? What evidence did you collect to document lack of achievement of the learning targets?
- What adjustments would you make the next time you teach this lesson?

### Parts of a Square

### Describing Designs

### Exploring Turns

### Analyzing Designs

### Planning and Making a Mini-Quilt

### Learning Objectives

- Explore the results of sliding a square into a new position
- Explore the results of flipping a square
- Name, using informal language, the geometric transformation used to create a given design