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Thursday Tool School: Critical Thinking with Pattern Blocks

Today's activity is inspired by an article in the August 2015 edition of *Teaching Children Mathematics*. It involves having students determine the cost of each element of a pattern block design given the total cost. This task provides the foundation for essential algebraic thinking skills and offers a high-level problem solving task with multiple solutions.
**Free Resource Alert:** Download a copy of this resource here.

**The Task: **
1. Present the pattern block task. Read the task together and answer any initial questions the students may have before beginning.

2. Allow student groups time to work through the questions. **Note:** Students will need more room for question #3. You may want to provide each group with poster paper so that they can illustrate and display their solutions.

3. Conduct a math talk session to discuss the students' responses. **Note:** This does not need to be lengthy; just be sure that students have an opportunity to share their work and make connections between solutions.

4. Use the following questions to encourage high-level thinking and the development of mathematical processing skills:
* How can you determine the price of each blue rhombus and the orange square?
* What process did you use to determine if there were other price combinations that would work? Are their some processes that are more efficient than others?
* How can you verify if you have found all of the possible price combinations?
* How can you represent your solutions?
* Compare your solution to another group's solution. How are they alike and different?
* Do you notice any patterns in your group's price combinations? If so, what are they? How could understanding the pattern help you find all of the price combinations?

**Extension:** Create similar tasks with additional designs. Assign a total cost and repeat the activity.
**Reference: **
Fuentes, S. Q. & Quebec, R. (2015). How much do the tiles cost? *Teaching Children Mathematics*, 22(1), 8 - 11.

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