Georgia Department of Education

Common Core Georgia Performance Standards Framework Student Edition

Sixth Grade Mathematics · Unit 5

Name ______Date ______

Who Put the Tang in Tangram?

Find the area of the following figures.

Figure / Show your work / Area of Figure
(in square units)
Small Triangle
Medium Triangle
Large Triangle

Parallelogram
Trapezoid
Two small and one medium triangles
Rectangle

Who Put the Tang in Tangram?

Figure
Sketch it below / Show your work / Area of Figure
(in square units)
Triangle congruent to a large triangle (Do not use the square)
Trapezoid (Different from the one page 1)
Parellelogram (Different from the one on page 1)
Pentagon
Square using all 7 pieces

Name ______Date ______

Who Put the Tang in Tangram?

Part 1: Deriving Formulas

  1. On your geoboard, make a square with an area of nine square units. Draw it on the geoboard given below.
  2. Determine its length and its width.______
  3. Write a formula for the area of the square.

______

  1. Divide the square in half by drawing a diagonal in the square.
  1. What two congruent shapes have you made?

______

  1. What is the area of one triangle? ______

Explain how you found the area of one triangle.

______

  1. Make a rectangle of a different size on your geoboard. Draw it on the geoboard below.
  2. Determine its length and its width.______
  3. Write a formula for the area of the rectangle.

______

  1. Divide the rectangle in half by drawing a diagonal.
  1. What two congruent shapes have you made?

______

  1. What is the area of one triangle? ______

Explain how you found the area of one triangle. If possible, show it on the geoboard.

______

  1. Make another rectangle on your geoboard, and draw it here. à

Cut it in half with a diagonal line. What is the area of one of the triangles? Explain how you found the area of the triangle. ______

  1. What do you notice about finding the area of a triangle?

______

  1. What is a formula you can use to find the area of a triangle?

______

  1. Use the formula to find the area of the triangles below. Show your work.

Check your answers by visually estimating the areas of the triangles.

7. Area is always measured in “square” units. Why do you think this is true? ______

Name ______Date ______

Who Put the Tang in Tangram?

Part 2: Deriving Formulas

  1. Use a straight edge to draw a parallelogram in one of the grids at the bottom of the page.
  2. Carefully cut out your parallelogram.
  3. Follow a line on the graph paper to cut off a triangle from one end of your parallelogram. See the diagram below.
  1. Slide the triangle to the opposite side of your parallelogram.

What shape is formed? ______

  1. What are the dimensions of the shape? Length =______Width =______
  2. What is the area? ______
  3. Do you think this will always work with a parallelogram? ______
  4. Test your answer to #7 by using the second grid paper below to draw a different parallelogram. Find the area of the parallelogram.
  5. What is the formula for finding the area of a parallelogram? ______

Who Put the Tang in Tangram?

Part 3: Understanding Decomposition

A tangram is an ancient Chinese puzzle. It is made of a square that is broken into 7 smaller shapes: a square, a parallelogram, and 5 different-sized triangles. The object is to form other shapes and pictures from the seven pieces, such as a rocket, a bunny, a runner, a cat, and more.

2.6 cm

2 cm

4 cm

4 cm

2 cm

4 cm 2 cm

Using the knowledge you have of area, determine the total area represented by the cat tangram. Show all work!! J

A. We know that formulas exist to find the area of triangles, rectangles, etc. Is there a formula for “area of a cat”? J Yes No

B. How do you determine the area of the cat picture above?______

______

______

C. What is the total area of the cat picture? ______

D. If the same tangram pieces are rearranged to make another picture, how will the area change? Explain your reasoning. ______

______

______