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Students will learn to analyze a pattern and identify the rules for the pattern. They will also learn how to represent those rules.
For the class:
For each pair:
For each student:
When students develop an understanding of patterns, they begin to create and discover a reasoning of how patterns grow, repeat, continue, or are solved. This is when students need added encouragement to promote discovery of rules for the pattern. When a student understands how to represent the rule for the pattern, s/he begins to develop a sense that the rule can be applied several times, and in many different ways. This gives the student prior knowledge so s/he becomes a flexible problem solver and realizes that there is a solution.
2. Become mathematical problem solvers.
3. Reason mathematically.
4. Communicate mathematically.
Invitation to Learn
Choose one or both of the following activities to get students to think about patterns and how to describe them.
Whats the Rule?
Explain how to play a game called Whats the Rule?
Ordinary Marys Extraordinary Deed
Read Ordinary Marys Extraordinary Deed. As you read the book, begin to write on the board the rule for how many people are exchanging good deeds. An example of this is:
1 person = 5 deeds
5 people = 25 deeds
25 people = 125 deeds
What is the Rule? (If n = number of people, then n x 5, or 5n, = the number of deeds.)
Question: How many deeds will be exchanged with 50 people? (1,250)
When finished, determine how many good deed exchanges would take place in the classroom if each student exchanged five deeds.
1 square = 4 toothpicks
2 squares = 8 toothpicks
3 squares = 12 toothpicks
4 squares = 16 toothpicks
Ask students if they see a pattern in the numbers written on the board. Ask for explanations. The pattern they are seeing can be described with a rule. The rule is square x 4 = toothpick or n x 4 = y (use a variety of symbols to represent this rule).
Have students make triangles. Add one triangle at a time to the lower left vertex of the previous triangle. Continue until they come up with the rule.
Give each student several square, triangle, rhombus, hexagon, and trapezoid pattern blocks. Have them complete the first section of the Growing Patterns worksheet. Model how to complete the worksheet using one of the shapes and going across the row.
Have students complete the second section by making a pattern using three to five pattern blocks (e.g., square, hexagon, square, hexagon). Call on select students to tell what their pattern is.
Discuss student answers. Have them tell how they decided on the rule for their pattern.
Hand out the Whats The Rule? I worksheet to each pair of students. Have each pair solve what numbers come next in the pattern and state the rule. Students may use pattern blocks to help them visualize the growing pattern. (Answers: Steamship n + 2, Pattern Path 2x + 2, Drawbridge n - 1, Suns n x 6, Fish & Fins n x 2, and Building Flowers n x 4.)
For an extra challenge, give each student a Whats The Rule? II worksheet. Have them add, subtract, and multiply to find the missing numbers. Read Quack and Count. As the book is read, show students that numbers can be added or subtracted from each other to find a pattern.
Kagan, S. (1994). Cooperative Learning. Resources for Teachers, Inc. ISBN 1-879097-10-9.
A student who is off task and misbehaving is usually a student wanting attention. In a cooperative learning atmosphere, each student is repeatedly included in a group of students working as a team to achieve the goal of being a successful individual.