Areas of Squares on the Sides of a Triangle (Investigating Patterns)

Author:
Britton Riehm
Topic:
Pythagoras or Pythagorean Theorem

Approaches to Learning with Critical Thinking When investigating patterns, it is important to apply critical thinking skills

  • Be systematic (make changes in an consistent way)
  • Choose things to keep the same
  • Choose one to change (independent variable)
  • Choose a thing to be measured as a result of change (dependent variable)

Concept: Quantity

An amount or number of something



Question 1: Prepare When investigating patterns in the past, have you been systematic? How can you improve?

Get to know the Triangle Square Tool
  • Figure out which parts move
  • Observe how things change when you move things

Triangle - Square Tool

Question 2: Plan a Strategy You will investigate the question: When is the total area of the red squares equal to the area of the blue square? How will you be systematic and organized in your investigation? In other words

  • What will you keep the same?
  • What will you change (independent variable)?
  • How will you change the independent variable?
  • What is your dependent variable (what are you measuring as a result of the change)?
Make a plan below.

Question 3: Investigate Spend 20 minutes investigating the question: When is the total area of the red squares equal to the area of the blue square? Investigate by moving the points on the vertices of the triangle. Record your findings in your workbook in a systematic and organized investigation.

Question 4: Reflect Respond to these questions:

  • Were you successful in investigating: When is the total area of the red squares equal to the area of the blue square?
  • Self assess: Did you investigate in a systematic?

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