Solving the Pythagorean Theorem By Diagram Completed

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Learn to apply the conceptual understanding of when and why the Pythagorean Theorem is equivalent in order to solve visually for missing side lengths

Big Idea

Moving students from hands-on Pythagorean Theorem to drawing diagrams to solve for missing sides continues the concept of why and how the equality works.


20 minutes

Pass out the unit organizer sheet and spend some time reviewing critical vocabulary such as leg and hypotenuse.  Also, spend some time reviewing how students can identify the hypotenuse based on angle measures.  It is important that students begin to use this vocabulary today during collaborative discussions (Integrating math practice standard 6).

Show the  Pythagorean theorem water demo once again and ask the following question, “How is this video relative to the activity you worked through at the end of class yesterday?  I am showing this video because it directly relates to your activity page.  How does it relate?”   Script any important information on the board so students have it as a guide map throughout the class period. 

Hold another mini-wrap-up over questions 1-5 on the handout Pythagorean Theorem and script any important ideas you need the class to keep in mind for the solving questions in part six today.  Important ideas might include:  a square root is used to find the dimensions of a square when you know the area, area can be combined to create the area of the largest square or subtracted to find the area of a smaller square, the goal of the theorem is to solve for side lengths along the right triangle, you need to find the area of squares first before you begin to add or subtract anything.

Completing the Activity

30 minutes

Allow students to work in cooperative groups to complete the example problems in question 6.  As students work to finish the problems, move about the room formatively assessing students and providing feedback that moves learning forward. 

 Differentiation Strategies:

  1. If, through your formative assessment of each group, you notice that students are moving through the activity without many mistakes or questions then you may want to use a “Mission Impossible” style wrap up session. If, through your formative assessment of each group, you notice that students are really struggling to work through each problem then you could also use a “Mission Impossible” session for students to steal ideas from other groups.  You could also find or create an expert group and then have that group come to the board to present their answer and their thinking to the rest of the class in order to spark ideas.
  2. If, through your formative assessment of each group, you notice that your class is split and some groups are moving along quickly, correctly, and without questions while others are struggling to complete questions.  You could send students from the expert groups as ambassadors to the struggling groups and ask them to share their thinking with these groups.  You could also prepare an extension activity for groups that move quickly and allow them to move on while the slower groups complete the activity that their own pace and then end the class period with a typical mini-wrap up session.  If you are unfamiliar with mini-wrap ups click on the link below to watch a short video explaining the strategy: