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.