Choose a quilt block from the Quilt Blocks activity sheet. (Alternatively, you can search the Web or some other source for other quilt block patterns.)
Give each child four black‑and‑white copies of the selected quilt square and crayons or markers. Then ask students to color one of the squares using any colors they wish. Next, ask students to color the other three squares in the same way. Now provide each child with a 6" × 6" work mat which has been divided into four equal parts, as was done in the previous two lessons.
Ask the children to place one of the colored squares in position 1, and then to place an identical square in the same orientation on top of it. Have students slide the identical square to position 2 and rotate it one half‑turn. (From the start, caution students to ensure that the top square is in the same orientation as the square below it. This is often where students make a mistake, which will disrupt the entire design.) Then, have them place a third square face down on top of the square in position 1 and flip it down to position 4. Finally, instruct them to turn a square that is face up in position 2 a half‑turn and place it in position 3.
The result of student designs should be a four‑square quilt with rotational symmetry, as shown below. Encourage students to discuss their resulting designs and the effects of the flips, turns, and slides.
Now give each child a small mirror and ask each to place it on the design in various places to see if the design shows in the mirror what is on the "dark" side of the mirror. Individual mirrors for each child will aid in the investigation as the children find reflections in the resulting design, but if you do not have enough mirrors for all the students, you may wish to have them work in small groups. You might ask them to focus on the squares in positions 1 and 4 or focus on those in positions 2 and 3. [They will be the upside‑down copies of each other]. Then compare the squares in positions 2 and 4 or 1 and 3. [They will be right‑left copies of each other.] Introducing the term "line symmetry," encourage the children to find as many examples of it as they can in the four‑part design they created. They may wish to glue the completed design onto a piece of paper, marking each line of symmetry with a dark crayon line.
When the children are ready, call them together to share their designs and describe how each of the squares in it can be obtained by another square using flips, slides and turns. You may wish to encourage alternate explanations. Then have students discuss the lines of symmetry they found in their designs. You may wish to ask the students to draw a sketch and reflect upon the meaning of line symmetry.
