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Problem Solving – Pythagorius

Problem Solving – Pythagorius. Fuller Computer Lab. This activity addresses the following Illinois State Goal. 9.C.3b Develop and solve problems using geometric relationships and models, with and without the use of technology.

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Problem Solving – Pythagorius

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  1. Problem Solving – Pythagorius Fuller Computer Lab

  2. This activity addresses the following Illinois State Goal. • 9.C.3b Develop and solve problems using geometric relationships and models, with and without the use of technology. • 8.D.3b Propose and solve problems using proportions, formulas and linear functions. • 8.D.3c Apply properties of powers, perfect squares and square roots. Fuller Computer Lab

  3. Rubric Fuller Computer Lab

  4. Rubric Fuller Computer Lab

  5. Rubric Fuller Computer Lab

  6. Mugs Guess and Check • She was told to make a figure with four thumbtacks, an elastic band and a piece of wood. She made the figure at the left. Her math teacher measured some of the sides of her figure and told Lisa to find the length of the side LM in mm. Can you help her? Fuller Computer Lab

  7. What do we know? • Pythagorean Theorem says A2 + B2 = C2. • We see that line LM contains the hypotenuse of two right triangles. • The sides of one are 8 cm and 6 cm. • The sides of the other are 3 cm and 4 cm. • 1 cm = 10 mm. • What do we need to find? • How long, in mm, is line LM? Fuller Computer Lab

  8. What do we do? • Compute 82 + 62, and then find the square root of the answer. • This gives us the length of the hypotenuse of the larger triangle. • Compute 32 + 42, and then find the square root of the answer. • This gives us the length of the hypotenuse of the smaller triangle. • Add the two answers. This gives us the length of Line LM. • Convert the answer we got from cm to mm. Fuller Computer Lab

  9. This is a 12 point problem • Tell what you know. • Tell what you need to find out. • Explain what you are going to do to find the answer and why that will give the answer • Show all your work. Fuller Computer Lab

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