# Rhombus Exploration (Fractions and Area)

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An activity involving reasoning with fractions and area--can be used before talking about area, to transition into areas of rectangles/triangles/rhombuses/kites, OR as you move into talking about equivalent fractions or what fractions mean or common denominators.

"Directions: Divide at least one of the following rhombuses into halves, at least one into thirds, at least one into fourths, at least one into sixths, at least one into eighths and at least one into twelfths. Label each divided rhombus with a fraction (½, 1/3, ¼, etc.). There are extra rhombuses so that you can pick the most convenient size for your strategy, record unsuccessful strategies that you tried, and try multiple ways.

Write: If you have parts that are all identical (or congruent), it's clear why they have the same area. If you have parts that aren't identical, how do you know or why do you think that they represent the same fraction of the rhombus?

Extension 1: If a side length of your rhombus is taken to be 12 inches, you can find the side lengths for many of the parts that you likely divided your rhombuses into. Find the side lengths you can find. Which side lengths can't you find, and why not?

Extension 2: Knowing that this is a very particular rhombus made by putting two equilateral triangle side to side means that we can likely find lots of angles of the pieces that you've broken your rhombuses into. Find the angles that you can find. Which angles can't you find, and why not?"
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2 pages
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