To maximize student learning, certain prerequisites are necessary to use this activity. Thus, it would be appropriate to include this activity as part of a more fully developed Standards-based lesson, but it should not be used as a complete stand-alone lesson.
Discuss with the whole class the concepts of ratio, proportions, proportional, proportional shapes. Ask students to briefly answer the following questions:
- Why is it important for models that represent real structures to be in proportion to the actual structures?
- If two or more things are in proportion, which dimensions are affected?
Discuss student responses as a class.
Distribute the Blue Squares activity sheet to each student.
Students should open the Side Length and Area of Similar Figures Applet.
When the applet opens two blue rectangles appear on both grids A and B. Beneath the grids there are ratios for width A : width B, height A : height B, and area A : area B.
Guiding Questions to Ask Students:
- What do you notice about the ratios?
- Why are the ratios 1:1?
Using the slide bars, students should create a new Rectangle A. They should record the dimensions and the ratios of Rectangle A and Rectangle B in Chart 1 on the Blue Squares activity sheet.
Below is a chart that will be used for the next several steps.
|
Rectangle A |
Rectangle B |
Ratios |
|
Width: |
Width: |
Width A ÷ Width B: |
|
Height: |
Height: |
Height A ÷ Height B: |
|
Area: |
Area: |
Area A ÷ Area B: |
Students should now change Square B into a rectangle similar to Rectangle A. Once again, they should record the dimensions and the ratios of Rectangle A and Rectangle B in Chart 2 on the Blue Squares activity sheet.
Next, students will change Rectangle B so it is not similar to Rectangle A. They will record the dimensions and the ratios of Rectangle A and Rectangle B in Chart 3 on the Blue Squares activity sheet.
Students should change Rectangle A to a new figure of any size. Change Rectangle B to a figure out of proportion to Figure A. As previously, students should record the dimensions and the ratios of Rectangle A and Rectangle B in Chart 4 on the Blue Squares activity sheet.
Once the students have created similar figures, use the ratios on the Blue Squares activity sheet charts to verify similarity. Repeat the
procedure from above using various dimensions and figures.
Students should now change Figure A to a 3 x 4 rectangle and multiply both width and height by 2 to determine dimensions to create rectangle B.
Guiding Questions to Ask Students:
- Are these two shapes proportional? How can you tell by looking? How can you tell mathematically?
- What factor was used to determine the dimensions for Rectangle B?
- What is the scale factor of these two rectangles?
- If Rectangle A is 2 x 3 and Rectangle B is 16 x 24, what is the scale factor? (Students may need
to act out more examples using the applet before answering this question.)
Students should now choose a scale factor to create rectangles too large to fit on the screen. They should record the dimensions of these rectangles in Chart 5 on the Blue Squares activity sheet.
Next, students should create a new Rectangle A and record the dimensions and the number of squares it covers in Chart 6 on the Blue Squares Activity Sheet. Repeat for Rectangle B.
Students should now create a set of two similar rectangles and record the dimensions and area of each, labeling each correctly. They should record the ratios in Chart 7 on the Blue Squares activity sheet.
Finally, students should reate four more sets of similar rectangles, recording the dimensions and area of each set in Chart 7 on the Blue Squares activity sheet.
