Scaling and Area

Warmup

Activity #1

Build 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 in the applet to add a figure.
• Click the – sign 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 or Trapezium 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?

(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.

Activity #2

How Many Blocks of the Rhombus Below will Tile a Scaled Complex Structure.

In the applet below, you are going to build the figure in the center using the original tiles. Note how many tiles you use to build the shape at different scale factors. Click and drag the block to move it. Use the circle to rotate the block,

• If your scale factor is already at 2, start building the figure with the original-size blocks to match it.
• Stop when you can tell for sure how many blocks it would take.
• Record your answer.
• Change the scale factor to 3 and repeat the steps.

(1.) How many blocks did it take to build the shape with scale factor 2?

(2.) How many blocks did it take to build the shape with scale factor 3?

(3.) How many blocks did it take to build the shape with scale factor 1?

(4.) Do you see a pattern that can be used to make a prediction?

• If your scale factor is already at 2, start building the figure with the original-size blocks to match it.
• Stop when you can tell for sure how many blocks it would take.
• Record your answer.
• Change the scale factor to 3 and repeat the steps.

(1.) How many blocks did it take to build the shape with scale factor 2?

(2.) How many blocks did it take to build the shape with scale factor 3?

(3.) How many blocks did it take to build the shape with scale factor 1?

(4.) Do you see a pattern that can be used to make a prediction?

• If your scale factor is already at 2, start building the figure with the original-size blocks to match it.
• Stop when you can tell for sure how many blocks it would take.
• Record your answer.
• Change the scale factor to 3 and repeat the steps.

(1). 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?

Activity #3

Investigate Scaled Effect on Area of a Figure.

• Examine the figures below carefully and answer the questions that follow.

Consider the follwing figures with measurements in centimeters.

(1.) What is the area of each figure? How do you know?

• Choose one of the two figures and draw scaled copies using each scale factor in the table below.

• Complete the table with the measurements of your scaled copies.

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

Challenge #1

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.

Challenge #2

Select one answer for each question. You may use the graph at the bottom of the page to help you. 

Challenge #3

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.

Quiz Time