How Can We Correct The Scarecrow?

 

 

• How can we correct the Scarecrow’s statement so it is mathematically precise?

 

These questions may be useful in helping students down the problem solving path:

• How can we determine if the Scarecrow is correct when he mentions “any two sides”?

 

This problem is a great way to introduce CCSS 8.G.6 or G-SRT.4.  If you play the clip prior to exploring the proof, students will hear the Scarecrow’s statement and have no idea what he is saying.  Then ask students, “How can we correct the Scarecrow’s statement so it is mathematically precise?”  Again, they will have no idea how to answer that question.  The whole process will take about five minutes.

From there you can use any one of a number of good strategies for exploring the proof of the Pythagorean Theorem.  Along the way students may start to make connections to the clip and realize it is related to what they are learning.  Once the exploration is complete, you can return to this problem, play the video clip again, and again ask students, “How can we correct the Scarecrow’s statement so it is mathematically precise?”

It is a great litmus test to measure whether students’ can successfully explain the proof.  Hopefully this time they will be able to answer the question.  If not, you know students need stronger understanding.

Also consider the Standards for Mathematical Practice that are used including:

• Math Practice 3 – Construct a viable argument and critique the reasoning of others.
  • What better opportunity than critiquing and correcting someone who won’t get mad at being wrong?
• Math Practice 6 – Attend to precision.
  • Students will need to determine the correct mathematical vocabulary to fix his statement.

Here are some of the Scarecrow’s errors to consider:

• He mentions “any two sides” and “remaining side” but the two sides must be the legs and the remaining side must be the hypotenuse.
• He mentions an “isosceles triangle” but while that isn’t always wrong, it is only right if it is an isosceles right triangle.
• He mentions “square root” but he must mean square (to the second power).

Am I missing any others?
 

Thanks to Andrew Stadel for a great suggestion to shorten the clip.
 

• CCSS 8.G.6 Explain a proof of the Pythagorean Theorem and its converse.
• CCSS G-SRT.4 Prove theorems about triangles. Theorems include: a line parallel to one side of a triangle divides the other two proportionally, and conversely; the Pythagorean Theorem proved using triangle similarity.

 

• Wizard of Oz