Lesson 3: Patterns and Pentominoes

Grade Level: 3–8

Duration
Two class periods of at least 45 minutes

Student Objectives
Students will:

• Apply problem solving skills to solve pattern puzzles.
• Use logic and decision making to create a new puzzle challenge.

Benchmarks
Mathematics

• Uses a variety of strategies to understand problem situations

Thinking and Reasoning

• Tests a hypothesis, throws out an unsuccessful hypothesis, and formulates a new hypothesis
• Selects criteria or rules for category membership that are relevant and important

Working with Others

• Works cooperatively within a group to complete tasks, achieve goals, and solve problems

Materials

• Flashlight Readers: Chasing Vermeer Pattern Puzzles
• Printable Pentominoes (PDF)

Directions

Step 1:
Discuss how pentominoes figure into the plot of Chasing Vermeer. Be sure that students understand what pentominoes are and how pentomino puzzles are solved. Explain that completing these challenging puzzles requires sharp problem solving skills. Other logic puzzles, including the Pattern Puzzles they’ll solve, require these skills as well.

Step 2:
Have students read the directions for the activity carefully. Show them how they can access hints for any of the highlighted words. If they wish, students can use scratch paper to help visually interpret the clues as they play.

Step 3:
When they’ve solved the puzzle, students reveal a pentomino shape and receive a secret message from Petra and Calder. When everyone has completed the activity twice, discuss the activity as a class:

• Which instructions were most challenging?
• What might the secret messages truly mean?
• What letter does each of the pentominoes they revealed stand for? (Can students think of words that begin with their letters to describe the activity?)

Step 4:
Divide the students into teams of two or more. Distribute a set of Printable Pentominoes to each team.

Step 5:
Explain that each team will work together to find a solution to fitting all the pieces together. Teams should keep track of each step they take to get to their solution.

Step 6:
The team will then create written instructions (in the style of the Pattern Puzzles clues) to guide another team to mimic their solution. Instructions should be as descriptive as possible. Encourage teams to incorporate several forms of Pattern Puzzles hints, possibly including map directions, primary and non-primary colors, left and right, and diagonal.

Step 7:
Once teams have perfected their puzzles, have them swap directions with another team and attempt to solve the other team's puzzle by following the instructions. Once they have completed their task, open up a discussion about how teams successfully created exciting and challenging instructions.

Assessment & Evaluation

• Assess student participation in the completion of the pattern game online and monitor students to see if they improve on the second or subsequent tries.
• Evaluate participation and cooperation in the group activities: did everyone contribute, were ideas shared, was there communication among team members.
• Assess student’s ability to solve the logic puzzles online and the pentomino puzzle offline.

Lesson Extensions

1. Have students play the interactive pentomino game.
2. Provide examples in music or in poetry where patterns are used. Have student identify the patterns used in the creative piece. Students may then want to use the pattern to create an original work of music or poetry.
3. Calder and Tommy use a special code to communicate. Have students select a partner and write each other letters using the code from the book. Ask students if it’s easy or hard to communicate this way.
4. Twelve ends up being an important number, especially towards the end of the novel. Have students make a list of everything that comes in sets of twelve, or by the dozen in the book and then add other example from life outside the novel.
5. Tell students that your class is going to hide a treasured object and create a series of clues that other classes will need to unravel to find it. Organize several tasks around hiding the treasure and creating clues. Students will:
   • Brainstorm the treasure
   • Choose a place to hide it
   • Create a map including the area where the object is hidden
   • Write clues to lead the searchers to the treasure using the map
   • Hold a competition where classes attempt to solve the mystery