This task is from Tools4NCTeachers. Students determine the value of different types of pattern blocks. This is remixable. 

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The two yellow hexagons have a value of 1 whole.

Part One:

• What is the fractional value of 3 red trapezoids? What is the fractional value of 1 red trapezoid?

• If you have 3 red trapezoids, how many green triangles would it take to cover the same area? What is the fractional value of the all the green triangles? What is the fractional value of 1 green triangle?

• Write an equation expressing the relationship between the red trapezoids and the green triangles.

Solutions:

·       3 red trapezoids = ¾; 1 red trapezoid = ¼

·       It would take 9 green triangles to cover 3 red trapezoids; 9/12 is the fractional value of the all the green triangles; 1 green triangle = 1/12

·       3/4 = 9/12

Part Two:

• If two yellow hexagons have a value of 1 whole, what is the value of 4 blue rhombuses? What is the value of 1 blue rhombus?

• If you have 4 blue rhombuses how many green triangles would it take to cover the same area? What is the fractional value of all the green triangles, remembering that 2 yellow hexagons equal 1 whole? What is the value of 1 green triangle?

• Write an equation expressing the relationship between the number of blue rhombuses and the number of green triangles.

Solutions:

·       4 blue rhombuses = 2/3; 1 blue rhombus = 1/3

·       It would take 8 green triangles to cover 4 blue rhombuses; 8/12 is the fractional value of all the green triangles; 1 green triangle = 1/12

2/3 = 8/12