TOOTHPICK PUZZLES Name: Lesson Plan Class: Young Scholars Program, Grade 8, Lesson 1 Objectives:

1. Students will practice perseverance in problem solving by exploring solutions to open-ended problems

2. Students will focus on their ideal learning style (verbal: talking through solution methods, visual: sketching possible solutions: tactile: physically manipulating toothpicks)

3. Students will review fundamental geometry relationships (such as all squares are rectangles but not all rectangles are squares) and vocabulary (equilateral triangle, rhombus, congruence, etc.)

Needed resources:

1. Toothpick puzzle packet handout (one per student) 2. Boxes of toothpicks (optional but encouraged) for physical manipulation 3. Smartboard, ELMO, or some other form of presentation for students to share

responses Grouping: This lesson works best when students are in small groups (approximately 3 students each) to explore possible solutions to each problem. Students can either select groups or the instructor can choose to assign groups (perhaps by learning style). Instructional Sequence: 1. Ask students for examples of where they have had to solve a problem that did not have an immediate answer. Brainstorm strategies they used to solve the problem. As an example, perhaps a student had to figure out how to fix a broken video game controller. 2. Share with students that they are going to solve open-ended problems called toothpick problems today. 3. Walk students through the warmup problem as a full class. Talk through how this problem seemed impossible to start, but once viewed in a different way, had a clear answer. 4. Let students investigate the included problems. While students work, make notes about student approaches to later share as a full class. Note a solution guide is included to compare with student solutions. 5. Based on engagement level or difficulty with task, bring students together as a full class regularly to talk through solution methods for various problems. Probe for the strategy the student used to solve the problem as well as alternative methods from the class. 6. Wrap up the lesson with having students make their own puzzle and sharing with a classmate. 7. Have students reflect on the activity and collect the bottom portion to review for future instruction.

Warm-up: There are thirteen sticks below (count them to be sure!) Move four sticks to be left with ten. (How is this possible? 13 – 4 = 9??) On your paper, show how to obtain the solution to the following problems. Some problems have more than one solution! Problem 1: Remove three toothpicks to get exactly three squares. Problem 2: Move two matchsticks to make only four identical squares.

Problem 3: Move three toothpicks to get exactly four squares. Problem 4: Move two toothpicks to turn the L upside down. Problem 5: What is the minimum number of toothpicks you must move to have the fish face the other direction (to the left)? What about for the fish to face downward?

Problem 6: Move three matchsticks to make three identical squares (and nothing else). Problem 7: Move three toothpicks to make exactly five triangles. Problem 8: For the boat shown, move two toothpicks to make a rhombus and an equilateral triangle. Problem 9: Here are six toothpicks arranged to form an equilateral triangle. Can you rearrange the six matchsticks to form four equilateral triangles?

Problem 10: Arrange 12 toothpicks to form the pattern below.

a) Remove two toothpicks to leave exactly 2 squares. b) Move three toothpicks to leave exactly 3 congruent squares. c) Move four toothpicks to leave exactly 3 congruent squares. d) Move two toothpicks to make exactly seven squares. e) Move four toothpicks to make exactly ten squares.

a) b) c) d) e) Problem 11: Move four toothpicks to make exactly three squares. How many ways can you solve their problem?

There are other solutions based on where you place the smallest square in the interior.

Problem 12: Arrange 24 toothpicks to form the pattern below. a) How many total squares do you see? b) Remove eight toothpicks to leave exactly two squares. c) Remove eight toothpicks to leave exactly four squares. d) Remove four toothpicks to leave exactly five squares. e) Remove four toothpicks to leave exactly nine squares.

f)

e)

a) There are 14 total squares (9 1x1, 4 2x2, and 1 3x3) b) c) d)