- Is there a correlation between an earthquake’s frequency and how much a building moves?
ACS (Real world applications; career connections; societal impact)
A - The Pythagorean Theorem can help people measure a missing side length quickly when creating or designing flower gardens, retaining walls, housing additions, furniture placement, etc.
C - The Pythagorean Theorem can be used by carpenters and engineers when designing houses and structures.
S - The basis for understanding nearly all geometry, there is virtually no venue of modern society that is unaffected by it. Example: Finding the distance between plates at a baseball game.
Engineering Design Process (EDP)
- Challenge - Create a building and prove that it contains a 90 degree angle by using the Pythagorean Theorem. The building should be structurally sound enough to withstand an earthquake.
- Research - Use websites to see how Pythagorean Theorem is used in construction. Also determine how the ancient Egyptians used this idea to make right angles.
- Brainstorm and Essential Questions – Look at building codes and the ancient Egyptian rope idea to figure out how they can use that to make a structure.
- Build and test for stability – Test using a shake table that would simulate an earthquake.
- Redesign – Improve upon the initial design, perhaps using bracing to see if the structure is sounder & re-test. Research the effects of bracing in buildings.
- Final Conclusion – Videotape their findings and be able to explain the findings.
8.G.6 Explain a proof of the Pythagorean Theorem and its converse.
8.G.7 Apply the Pythagorean Theorem to determine unknown side lengths in right triangles in real-world and mathematical problems in two and three dimensions.
8.G.8 Apply the Pythagorean Theorem to find the distance between two points in a coordinate system.
Earth & Space Sciences – Physical Earth -
The composition and properties of Earth’s interior are identified by the behavior of seismic waves.
Day 1: Activity 1
- Pre-test students on their prior Pythagorean Theorem Knowledge (Pre-test)
- Present students with the “hook” video on “When Not Knowing Math Can Cost You $15,000.”
- Are You Right Activity? To show students the difference between right, acute, and obtuse angles. They should be able to generate the Pythagorean Theorem from here. (Activity 1, Worksheet A)
- Pythagorean Proof Example Activity- Handout: “Showing Proof” (Activity 2) – Students should be able to “see” how the side of a squared plus b squared will equal c squared. (Activity 2, Worksheet A)
- Show a computer applet example of the Pythagorean Theorem Proof and a 3-D example with this water video
- Homework (Activity 2, Worksheet B)
Day 2: Researching the Pythagorean Theorem (Activity 3)
- Do a little Background overview and formal introduction of Pythagorean Theorem and use this slide show as a guide.
- Taco Cart Example
- Research – Complete a webquest on Pythagoras to discover his background and to understand at least one of his proofs. Students should be able to recognize and explain one proof. (Activity 3, Worksheet A)
- Triangles Triples Homework (Activity 3, Worksheet B)
Day 3: Finding the Length of Line Segments on a Grid (Activity 4)
- Finding the length of a line segment demonstration
- Treasure map activity (Activity 4, Worksheet A)
- Puzzle Proof Activity (Activity 4, Worksheet B)
Day 4: Challenge and Brainstorm (Activity 5)
- Start the Engineering Design Process
- Challenge and Brainstorm (Activity 5, Worksheet A)
- Build and Test (Activity 6)
Day 5: Redesign and Test
- Redesign Using Braces or other researched approach to improve stability (Activity 6, Worksheet A)
- Re-Test design. Students should videotape results to use for presentation of their findings.
Day 6: Conclusion and Reflection
- Conclusion/Reflection (Activity 6, Worksheet B)
- Prepare for presentations
- Presentation using videos as explanations
- Rubric (Activity 6, Worksheet C)
Where the CBL and EDP appear in the Unit
CBL - Activity 5
EDP - Activity 5 & 6
A lot of times students don’t believe the concepts that are taught in Math can be applicable to the real world. This unit will let students apply their measuring skills and the importance of the Pythagorean Theorem.
Pre-Unit Assessment Instrument
Post-Unit Assessment Instrument
Results: Evidence of Growth in Student Learning