## Exploring Flips and Slides

3-5
1

This lesson builds on the previous two lessons and encourages students to explore the geometric transformations of reflections and translations. Students create a design. Then, using flips and slides, students make a four-part paper "mini-quilt." 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. A simple design, such as the following, would conserve time:

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

Now, provide students with a large enough work-mat to fit all four squares.

Ask students to place one of the colored 3" × 3" squares in to top left-hand corner of their work-mat. Then, ask them to place a second quilt square on top of the first, so that sections colored alike are touching. Walk around the room and make sure that students are not rotating their second square. Then, have them slide the top square down so that it is directly under the first square (edges touching). If students have trouble with their first square moving, then you can provide them with a small piece of tape to help hold down their first square quilt. Now have them place a third identical square on top of the very first square so that sections colored alike are touching. Then, have students slide it directly to the right so that their edges are touching.

Now, ask students, "What do you think I will ask you to do next?" Students should reply that you will want them to place the last remaining quilt square on top of the first one and slide it to the bottom right, creating a master quilt. Encourage students to find as many ways as they can of how they can slide a square into the last position. Then have them compare the 4 squares. [They will all look alike.] Using the sample from above, the master quilt will look like this:

You may wish to take pictures of each students' quilt so that it can be reference later on.

Next ask children to reset their work-mats so that only the top left-hand square quilt is remaining (i.e. the one that was taped down).

Similar to the activity just completed, students should place a second quilt square face up on top of the first one so that like parts are touching. Now, have them flip the top square directly under the first square (edges touching). The square in the bottom left-hand corner will be without a design. Now have them place a third identical square on top of the first square [so that sections colored alike are touching], then flip it directly to the right (edges touching). This square will also be showing the side without a design. Next, have them align the last remaining quilt square with the very first square (in the top left-hand corner), then slide it directly below, then directly right.

The master quilt will now look like this:

You may wish to take pictures of each students' quilt so that it can be reference later on.

Now ask them to compare the four squares. [The top left-hand square and the bottom right-hand square will look alike, as will the squares on the top right-hand corner and bottom left-hand corner.]

Asking the students to reset their work-mats, they should now have free time to explore several ways they can slide and flip the four squares to make a master quilt. After a few minutes, have students record one of the ways they found by gluing the four small squares on a sheet of paper and describing how the master quilt was created directly below.

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.

Assessment Options

1. Use students' poster board and written/verbal demonstration to assess students. 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
2. 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.
3. Collect students' written responses from the conclusion of the lesson.

Extensions

1. 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.
2. Create a big Venn diagram on the board, labeling each circle "Flip" and "Slide." Have each student demonstrate where their master quilt should be placed on the Venn diagram. This may help facilitate conversation to help wrap up the class.
3. Move on to the next lesson, Exploring Turns.

Questions for Students

1. What type of moves did you use? Can you show us?
2. How can we tell the square was slid? Was flipped?
3. What is alike between the squares on the top and those on the bottom? How did that happen?
4. What is alike between the squares on the right and those on the left? How did that happen?
5. Suppose you slid a square and then flipped it. What would happen?
6. 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

3-5
Students investigate the ways shapes can be divided into equal pieces with one or two cuts. The lesson provides a review of the following vocabulary terms: square, triangle, and rectangle; congruent, one-half, and one-fourth. The other lessons in this unit build on this introductory lesson.

### Describing Designs

3-5
Students create designs and describe them to a classmate, using fractional and geometric terms. This lesson provides a context for using the following vocabulary terms: horizontal, vertical, square, rectangle, triangle, diagonal, one-half, and one-fourth.

### Exploring Turns

3-5
This lesson encourages students to explore the geometric transformation of rotation. Students create a design then, using turns, make a four‑part paper "mini-quilt" with that design as the basis. While the formal term is rotation, the more informal turn is used at this grade band. The experience focuses students’ attention on the changes the geometric transformations make in a student-designed quilt square.

### Analyzing Designs

3-5
This lesson encourages students to explore the geometric transformation of rotation, reflection and translation more fully. Students create a design then, using flips, turns, and slides, make a 4-part paper "mini-quilt" square with that design as the basis. This experience focuses students’ attention on both the changes produced by the geometric transformations and on line symmetry.

### Planning and Making a Mini-Quilt

3-5
Students create a quilt using the three transformations and investigate the ways shapes can be colored to show one-half and one-fourth. They locate lines of symmetry and create a set of directions for making their quilt block.

### Learning Objectives

Students will:
• 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.

### NCTM Standards and Expectations

• Describe location and movement using common language and geometric vocabulary.
• Predict and describe the results of sliding, flipping, and turning two-dimensional shapes.