Source: Wiggins, G., & McTighe, J. Understanding by Design. Merrill Prentice Hall: 1998.
For further information about Backward Design refer to http://www.ubdexchange.org/
Title: Problem Solving Using the Pythagorean Theorem Subject/Course: 7th grade GPS
Topic: Pythagorean Theorem
Grade(s): 7th
Designer(s): Dottie Mitcham
Stage 1 – Desired Results
Established Goals:
M8G2. Students will understand and use the Pythagorean theorem.
a. Apply properties of right triangles, including the Pythagorean theorem.
b. Recognize and interpret the Pythagorean theorem as a statement about areas of
squares on the sides of a right triangle.
Understandings:
Students will understand…
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Essential Questions:
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Concept of a right triangle
Concept of a square root
Students will know…
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Which side is the hypotenuse?
How do you simplify a square root?
Students will be able to…
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Properties of a right triangle
Properties of square roots
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Use the Pythagorean theorem to solve problems
Find the length of one side of a right triangle
given the length of the other two sides.
Identify the hypotenuse and the legs of a right
triangle.
Stage 2 – Assessment Evidence
Performance Tasks:
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Other Evidence:
David lives 33 miles due east of the
WMAT radio station. While driving due
north from his house, he was able to keep
the radio signal for about 56 miles. What is
the broadcasting range of WMAT?
A hiker leaves camp and walks 8 miles due
west and 12 miles due north. About how far
is the hiker from camp?
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Teacher observation
Quizzes
Journal entries
Performance task rubric
Stage 3 – Learning Plan
Learning Activities: from intermath
Water Stop
The rectangular field pictured has unknown dimensions. Tom and Paul are both at point A.
Tom walks straight from A to C. To get a drink, Paul walks from A to B, then from B to C. How
far does Paul walk if he travels 40 yards farther than Tom? What are the dimensions of the
field?
Squaring with Squares
One of the proofs of the Pythagorean Theorem typically uses squares constructed on each
side of a right triangle (see figure below). The area of the square constructed on the
hypotenuse (green square) is equal to the sum of the areas of the squares constructed on
each of the legs of the triangle (blue squares).
Rationalize This
rational right triangle is a triangle where all the sides are rational numbers and one of the
angles is a right angle.
Find a rational right triangle such that the length of the hypotenuse is numerically equal to
the area of the triangle, and the perimeter of the triangle is a prime integer.