Similar Figures and Scale

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Mathematics · Geometry
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Page 2
Similar Figures and Scale
Mathematics · Geometry · Grades 9-10 · 50 minutes
Time needed
50 minutes (one class period)
Prep
Copy the 2-page worksheet (one per student). Write the scale-factor facts on the board.
Technology
None. A basic calculator is optional.
Student
independence
High. Students work alone, with a quick partner check at the end.
Copies to make
One 2-page worksheet per student
Materials
Pencils, Worksheet, Whiteboard or chalkboard, Calculators (optional)
Goal for today: Students will use scale factors and proportions to find missing measurements in similar figures and
will describe how perimeter, area and volume change with scale.
Before the bell
☐ Copy the worksheet, one per student (2 pages).
☐ Write on the board: Similar figures have the same shape and equal angles, and matching sides are in
proportion. Scale factor k = new length ÷ original length. If the scale factor is k: lengths × k, areas × k²,
volumes × k³.
☐ Keep the answer key on your desk. You do not need to solve anything yourself.
Say this to start
Good morning! Today’s geometry practice is about similar figures, which means shapes that are enlarged or shrunk
copies of each other. Students will use a scale factor or a proportion to find missing lengths in maps, models and
shadow problems. The key ideas are on the board, and the worksheet describes every figure in words.
Run of show
Minutes
What you do
What students do
0–5
Take attendance. Hand out the worksheet face down.
Settle in and take out a pencil.
5–13
Read the facts on the board aloud. Then read this example:
Triangle A has sides 2, 3 and 4. Triangle B is similar and its
shortest side is 6. The scale factor is 6 ÷ 2 = 3, so the
other sides are 9 and 12.
Follow along and copy the example.
13–36
Tell students to work questions 1–10. Walk the room. If
students are stuck, ask them to write a ratio “new over
old” or “big over small” and keep it the same way every
time.
Write a proportion or a scale factor, then
solve.
36–42
Tell students to answer question 11 and fill in the Scale
Factor Table. Partners may compare.
Fill in the perimeter, area and volume
ratios.
42–50
Read the answers aloud from the key while students check.
Collect all worksheets.
Check their work and hand in the
worksheet.


SubstitutePlans.com
Mathematics · Geometry
SP-GEOM-009  ·  Free to print and use in your classroom  ·  substituteplans.com
Page 3
If things go wrong
• If students set up a proportion upside down, tell them to keep the same shape on top on both sides (small
over big, or big over small).
• If students have trouble with the map problems, tell them to write “1 inch = 25 miles” and multiply or divide
by that amount.
• If a student asks about units, remind them to convert everything to the same unit first (question 6 uses
inches).
• If the class is noisy, remind them this is independent work.
Early finishers
• A square has a side of 3 and a perimeter of 12. Find the perimeter and area of a similar square with scale
factor 5.
• Explain why a model that is half as tall has only one eighth the volume.
• Make up your own map-scale problem and trade with a neighbor.
Support and challenge
• Support: Allow calculators and have students complete questions 1, 2, 4, 5 and 7 only.
• Challenge: Ask students to find the scale factor between two similar figures if their areas are 9 and 49
(answer: 3/7 or 7/3).
Notes for the teacher (you fill this in)
Jot a few lines before you leave. A full Daily Sub Report is in the free Sub Survival Kit at SubstitutePlans.com.
How far the class got / what to pick up next:
Students who were especially helpful:
Anything the teacher should know: