OLD VERSION: IM 6.1.2 Lesson
You may recall the term area tells us something about the number of squares inside a two-dimensional shape.
Below are four drawings that each show squares inside a shape. Select all drawings whose squares could be used to find the area of the shape. Be prepared to explain your reasoning.
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Write a definition of area that includes all the information that you think is important:
This app has one square and some small, medium, and large right triangles. Click on a shape and drag to move it. Grab the point at the vertex and drag to turn it.The area of the square is 1 square unit.
Notice that you can put together two small triangles to make a square. What is the area of the square composed of two small triangles? Explain your reasoning.
Use these shapes to create a new shape with an area of 1 square unit that is not a square. Place this shape near the bottom of this app.
Use your shapes to create a new shape with an area of 2 square units. Place this shape near the bottom of this app.
Use your shapes to create a DIFFERENT SHAPE with an area of 2 square units. Place this shape near the bottom of this app.
Use your shapes to create a new shape with an area of 4 square units. Place this shape near the bottom of this app.
Are you ready for more? Find a way to use all of your pieces to compose a single large square.
What is the area of the large square you created in the app above?
Recall that the area of the square is 1 square unit. Use this app to help illustrate your answers to your questions below.
The area of the small triangle is ____________ square units. I know this because____________________.
The area of the medium triangle is ____________ square units. I know this because____________________.
The area of the large triangle is ____________ square units. I know this because____________________.
This rectangle has been decomposed along its diagonal. Recompose the two pieces to make a different shape.
How does the area of this new shape compare to the area of the original rectangle? Explain how you know.
Priya decomposed a square into 16 smaller, equal-size squares and then cut out 4 of the small squares and attached them around the outside of original square to make a new figure.
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The area of the square is 1 square unit. Two small triangles can be put together to make a square or to make a medium triangle.
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A student said, “We can’t find the area of the shaded region because the shape has many different measurements, instead of just a length and a width that we could multiply.”
Use this app to help illustrate your typed explanation above.
The area of a rectangular playground is 78 square meters. If the length of the playground is 13 meters, what is its width?