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.
Blue Squares Activity Sheet
Side Length and Area of Similar Figures Applet
Students should open the Side Length and Area of Similar Figures Applet.
When
the applet opens two rectangles appear. Click on the "measures" tab to see the 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 create four more sets of similar
rectangles, recording the dimensions and area of each set in Chart 7 on
the Blue Squares activity sheet.