Scaling and Area

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Building Patterns of Blocks.

Use the three applets to explore the pattern blocks. Then, answer the corresponding questions. You can add a grid in the background if you need help.

  • Click the + sign to add a figure.
  • Click thesign to remove a figure.

Rhombus Blocks

(1). How many blue rhombus blocks does it take to build a scaled copy of Figure A where each side is twice as long?

(2). How many blue rhombus blocks does it take to build a scaled copy of Figure A where each side is 3 times as long?

(3). How many blue rhombus blocks does it take to build a scaled copy of Figure A where each side is 4 times as long?

Triangle Blocks

(1). How many green triangle blocks does it take to build a scaled copy of Figure B where each side is twice as long?

(2). How many green triangle blocks does it take to build a scaled copy of Figure B where each side is 3 times as long?

(3). How many green triangle blocks does it take to build a scaled copy of Figure B where each side is 4 times as long?

Trapezoid Blocks

(1). How many red trapezoid blocks does it take to build a scaled copy of Figure C using a scale factor of 2?

(2). How many red trapezoid blocks does it take to build a scaled copy of Figure C using a scale factor of 3?

(3). How many red trapezoid blocks does it take to build a scaled copy of Figure C using a scale factor of 4?

Make a prediction: How many blocks would it take to build scaled copies of these shapes using a scale factor of 5? Using a scale factor of 6? Explain your reasoning.

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Investigating How Many Blocks form a Scaled Copy.

  • Use the slider to change the scale factor.
  • You can add on a grid in the background if you need help.

(1). Move the slider to see a scaled copy of the shape, using a scale factor of 2. How many blocks did it take?

(2). Move the slider to see a scaled copy of the shape using a scale factor of 3. How many blocks did it take?

(1). Move the slider to see a scaled copy of the shape, using a scale factor of 2. How many blocks did it take?

(2). Move the slider to see a scaled copy of the shape, using a scale factor of 3. How many blocks did it take?

(1). Move the slider to see a scaled copy of the shape, using a scale factor of 2. How many blocks did it take?

(2). How is the pattern in this activity #2 the same as the pattern you saw in the activity #1? How is it different?

(3). How many blocks do you think it would take to build a scaled copy of one yellow hexagon where each side is twice as long? Three times as long?

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Investigating Scaled Effect on Area of a Figure.

Consider the follwing figures with measurements in centimeters.

What is the area of each figure? How do you know?

Choose one figure and draw scaled copies using each scale factor in the table below.

Complete the table with the measurements of your scaled copies.

If you drew scaled copies of your figure with the following scale factors, what would their areas be? Explain your thinking.

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On the grid below, draw a scaled copy of Polygon Q using a scale factor of 2.

Compare the perimeter and area of the new polygon to those of Q.

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A right triangle has an area of 36 square units.

If you draw scaled copies of this triangle using the scale factors in the table, what will the areas of these scaled copies be? Explain or show your reasoning in the applet below.