Objectives:

• Students will apply problem solving procedures and skills to solve a given real life problem by manipulating felt squares to represent the possible combinations for a two color quilt, having three colors to choose from.
• Students will demonstrate inductive reasoning skills by applying what they learn from each problem to the next and by establishing a pattern in the problems.
• Students will make use of language skills in a mathematics lesson by referring to the story as a frame of reference and by reading and discussing the problems.
• Students will develop of sense of the planning, preparation, and use of mathematical knowledge that is necessary in quilt making by engaging in some practice planning of possible color choices.

Materials:

• Valerie Flournoys The Patchwork Quilt
• pencils
• small felt squares in the colors: pink, blue, white, gray, orange (enough for each child in the group to have one of each color and some for use on the felt board)
• Felt board
• Question and Recording sheets
• Dry erase board or chalk board

Procedure:

1. Read Valerie Flournoy's The Patchwork Quilt to the entire class and discuss how quilts are made from putting patches of material together. Introduce that we will be doing some practice planning for putting a quilt together during math time.
2. For activity divide into smaller groups. (grouping explained in introduction)
3. Have a student read the opening section on the worksheet and review for a moment what we have learned about quilt making from the story.
4. Introduce problem, "After making the quilt with Grandma, Tanya decided to make her own two color quilt. She had three colors to choose from: pink, blue, and white. How many two color combinations could she make from the three colors available."
5. After introducing the problem, give each student felt patches of pink, white, and blue; and let them go to work at coming up with possible solutions and recording their information. If students do not know where begin, generate one combination as a group.
6. Depending on the skill level of the groups, students could work in pairs to solve the problem or as a whole group, having students come up and place each combination on the felt board.
7. As the students solve the problem ask questions (like "Does the order of the colors matter? or What different ways can you arrange the colors?") to encourage the students' thinking and discuss issues as a group when a question arises.
8. Once the students have an answer discuss as a group how many combinations were possible and why. Use the dry erase board to have students show how they solved the problem and write word and number sentences to explain their conclusions. For example if you had five color choices your number sentence might be 4+3+2+1=10 different combinations.
9. Continue the same procedure with the following problem that adds an additional color to choose from (now having four choices). Encourage children to look for a pattern and to organize their data in a way that will make it easy for them to check what they are missing.
10. If students are very advanced they may be able to generate the algorithm for combinations, or apply what they have learned to having a large number of colors to choose from, but since this is an introductory lesson to combinations that is not expected.

Evaluation:

1. I will know that students understand what a two color combination is if they are manipulating their felt pieces into different two color combinations and recording that information.
2. I will look at students finished question sheets to see if they used logic and problem solving to come up with a reasonable answer. They will also be evaluated on their ability to explain how they got their answer, either verbally or written.
3. I will use performance assessment to evaluate students during the lesson, looking for them to be actively engaged in reasoning, discussion, and problem solving.

Extension Activities:

1. If information needs to be re-taught, use combination problems that involve another topic and vary the set-up of the lesson (i.e.: pairs, whole group etc.)
2. To extend you can continue to build on this problem by adding more color choices and to go beyond the concrete take away the felt pieces and ask students to apply the pattern they have already established. Continue building until they discover the algorithm from the pattern.
3. More ideas for quilt math involve probability, for example the following problem could be used, "Tanya could not decide what two colors to use for her quilt. She put one piece of each of the five fabrics in a bag. Then, without looking, she chose two pieces. What are the chances of her choosing a pink-blue combination?" Let the children work in pairs or groups of three to devise their own strategies for solving this problem.