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Geometry Task: Ratios, Proportions and Similar Figures

Activity/Task Variations

Blooms taxonomy level:

Understanding

Differentiation suggestions:

If students can’t get started….
Assessing Questions:

Why did you use the Pythagorean Theorem?
How did you know that you could use the Pythagorean Theorem to solve this problem?

Advancing Questions:

Draw one diagonal on the square. What does the diagonal do to the square?
Do you see any shapes other than the square in your figure?
What kind of triangle do you have?

Extension suggestions:

If students finish early….

Ask students to go back through problems 2 and 3 using the longest side instead of the shortest side of the rectangle. Do the same types of conjectures hold? Why or why not?
Ask students to compute the ratio of the length of the shortest side to the length of the longest side for each rectangle they constructed in problems 2 and 3. Do the same types of conjectures hold for this ratio? Why or why not?

Originator:

Tennessee Department of Education