1.2

What Can We Work Together?

Pg. 6Creating a Quilt Using Symmetry and Investigations

Today you will consider an example of how geometry is applied in the world around you. A very popular American tradition is to create quilts by sewing together remnants of cloth in intricate geometric designs. These quilts often integrate geometric shapes in repeated patterns that show symmetry. For centuries, quilts have been designed to tell stories, document special occasions, or decorate homes.

Throughout this course you will work with your team to learn new ideas, investigate, and share ideas with the class. It is important that everyone in the group participates, so no one person is left behind. It is also important to make sure everyone works together, that way one person isn't doing all of the work (and the only one learning). To ensure that everyone works to their full potential, there are roles assigned to each person in their group. Think of this like a job. You don't work, you don't get a payment (poor grade). However, work hard and the payment is worth it (good grade, recognition, high gpa)! To help you work together today, each member of your team has a specific job, assigned by your first name (or last name if team members have the same first name.)

Team Roles

Resource Manager:

•Make sure the team has all of the necessary materials, including folders.

•Ask the teacher when the entire team has a question. You might ask, “No one has an idea? Should I ask the teacher?”

•Make sure your team cleans up by delegating tasks. You could say, “I will put away the ______ while you ______ . ”

Facilitator:

•Start the team’s discussion by asking, “Who wants to read the first question?” or “Are we ready to move to the next question?”

•Make sure that all of the team members get any necessary help. You don’t have to answer all the questions yourself. A good facilitator regularly asks, “Does everyone understand?" and “Who can answer ____________’s question?”

Recorder:

•Make sure the team agrees on an answer and every paper has the approximately the same response.

•Says things like, “Do we all agree the answer is _______?”, “Your answer seems different than what the group agreed on, lets discuss this.” or “You didn’t put an answer for this question, lets make sure we all get this before moving on.”

Team Captain:

•Remind the team to stay on task and not to talk to students in other teams. You can suggest, “Let’s make sure we stay on task."

•Keep track of time. Give your team reminders, such as “I think we need to decide now so that we will have enough time to finish.”

•Make sure everyone is participating. If someone is just copying or not paying any attention, make sure to get them refocused. Say things like, “What do you think about this question?” or “Any ideas on what to do?”

Team Captain

Keeps team focused on mathAsks for clarification, explanations, and justifications.Acts as time managerSubstitutes for absent member’s jobs

Remember, no talking outside our team.We need to work on listening to each other.Let’s get back to work.We need to finish so we can have time to do the next part

1.10 – REFLECTION SYMMETRYShapes that have reflection symmetry can be folded to match up. See some examples at the right:

a. Where have you seen reflection symmetry in your life?

b. Draw your own picture below that has reflection symmetry. Can you draw a shape that has more than one line of symmetry?

1.11 – DESIGNING A QUILTHow can you use symmetry to design a quilt? Today you will work with your team to design a patch that will be combined with other team patches to make a class quilt. Be sure to utilize group roles as you work.

a. Each team member will receive four small squares. With a colored pencil or marker, shade in half of each square (one triangle) as shown below. Each team member should use a different color. Resource Managers need to get the toolboxes and one page to tape the squares to later.

YOUR COLOR HERE

b. Next each student should arrange your squares to make a larger 2-by-2 square (as shown at right) with a design that has reflection symmetry. A design has reflection symmetry if it can be folded in half so that both sides match perfectly. It doesn't matter which way you fold it, as long as the shaded colors match up when it is folded.

c. Make sure you have arranged your pieces into a different symmetrical pattern than the rest of your team. Once your team agrees, the resource manager should ask your teacher to verify that your designs are all symmetrical and unique.

d. Now create a 4-by-4 square using the designs created by each team member as shown on the Resource page. Glue (or tape) all sixteen pieces carefully to the resource page.

e. Cut along the surrounding dashed square so that you have a blank border around your 4-by-4 square.

f. Once your team has finished, the Recorder will tape your team quilt onto the whiteboard. The class will then discuss the results.

Symmetry• Which squares have only one line of

symmetry? Which direction?

• Which squares have two lines of symmetry? Which direction?

• Which squares have three lines of symmetry? Which direction?

Investigations: Team Roles

Resource Manager •Get the strips of paper and make sure area is clean when finished•Calls the teacher over for questions when teammates do not know the answerFacilitator•Start the reading in the group. Say things like, “Who wants to read part a?”•If someone doesn’t seem to understand, make sure that it is addressed in the group before moving onRecorder•Make sure each person has agreed upon answers on their paper•Don’t allow the group to move on until everyone has the answerTeam Captain•Make sure no one talks outside your team and help keep your team on-task and talking about math: "Ok, let's get back to work!", "What does the next question say?"•Encourage everyone to participate and answer questions by saying things like: “What do you think the answer is to this question?”

Resource Managers

• Resource Managers: Get 5 strips of paper

1.12 – A SIMPLE BRACELETOn a piece of paper provided by your teacher, make a “bracelet” by taping the two ends securely together. Putting tape on both sides of the bracelet will help to make sure the bracelet is secure. In the diagram of the rectangular strip shown at right, you would tape the ends together so that point A would attach to point C, and point B would attach to point D.

Now predict what you think would happen if you were to cut the bracelet down the middle, as shown in the diagram at right. Record your prediction in the table below. Once your team has recorded the prediction, make the cut. What was the result? Was it different than expected?

Experiment Prediction Result

1.12

Tape and cut bracelet in half as shown in the diagram

1.13 – A MOBIUS STRIPOn a second strip of paper, label a point A and B in the center of the strip at least one inch away from one end.

Now turn this strip into a Möbius strip by attaching the ends together securely after making one twist with tape. For the strip shown in the diagram at right, the paper would be twisted once so that point A would attach to point B. The result should look like the diagram at right.

Predict what would happen if you were to draw a line down the center of the strip from point A until you ran out of paper. Record your prediction, conduct the experiment, and record your result in the table. Once your team has recorded the prediction, draw in the line. What was the result? Was it different than expected?

Experiment Prediction Result

1.13On new paper, twist the paper once, and draw a line down the center

1.14 – CUTTING A MOBIUS STRIPWhat do you think would happen if you were to cut your Möbius strip along the central line you drew in problem 1.13? Record your prediction in your table. Cut just one of your teams Möbius strips. Record your result in your table.

Experiment Prediction Result

1.14Cut along the line in problem 1.13