Scaling and Proportions (lesson)

[Sharma]

Note: See attached document for full lesson w/handouts

Materials:
1 sheet of graph paper per student.

Pass out graph paper to each student. Instruct the students to draw rectangles that are 1 by 1, 2 by 2, 3by 3, 4 by 4 and 10 by 10. Have students label the rectangles with the base, height and area. Discuss the term “Scale Factor”, showing them, on the document camera, that you are “scaling” the 1 by 1 rectangle 2 times (to get the 2 by 2), 3 times (to get the 3 by 3), four times (to get the 4 by 4) and 10 times (to get the 10 by 10).

Have the students complete the table on page 1.

Give the students 2 minutes to study the table silently, and then record observations for question #1. Have them discuss observations using roundtable in their group (each person shares 1 idea and rotates taking turns sharing an idea). Note: Do not worry about the “x” row yet (but if students see the pattern, GREAT! We’ll go back to the x row near the end).

Pose the question for #2, “When we scale a figure, do the dimensions grow proportionally?” Give 30 seconds for students to think about the question and then use thumbs up/down to have them vote. Walk them through the example using proportions to verify and encourage them to show at least 2 more proportions.

Come back as a class and agree that the side lengths are proportional (this should be confirmation of what was learned in similar figures in the first unit this year).

Pose the question for #3, “When we scale a figure, does the area grow proportionally?” Give 30 seconds for students to think about the question and then use thumbs up/down to have them vote. Walk them through the example to show that the ratios are NOT equal and encourage them try this out for at least 2 more proportions. NOTE: If the only example students look at is the “double”, then the area does appear to be proportional, as 2 •2 = 2-squared.

Come back as a class and agree that the area is NOT proportional.

Direct the students’ attention to question 4. Ask them why we are graphing data to determine proportionality (connect this idea to unit 1 definition of proportional). Make sure students understand the variables they need to graph and give them time to complete both graphs. Once they have graphed, ask them if the data is proportional. Use thumbs up/down to have them vote for each graph. Call on students to explain why the base vs. height IS proportional and the base vs. area is NOT proportional.

Finally, have the students go back to the table and see if they can complete the “x” row. Give them a few minutes to do the conclusions, discuss with a partner and then share with the class.

Source: http://auhsdmath.pbworks.com/

Attachments:

1. ScalingandProportions.docx

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