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The Arizona STEM Acceleration Project

Scale Factor

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Scale Factor

A 7-9th Grade STEM Lesson

Susin Hall

January 22, 2024

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Notes for Teachers

My classes are about 50

minutes long. We do bellwork,

some type of notes and/or

classwork and a closure each

day. So this lesson took a

couple days to get through.

Depending on your setup may

take less or more time.

I used this lesson for my 8th

grade Geometry class.

List of Materials

Copy Paper/Scratch Paper
Pencil
Colored Pencil (Optional)
3 Act Math Task Recording Sheet Link
Book: Your Place in the Universe by Jason Chin (available in paperback on Amazon for $8.89)

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Standards

Mathematics:

7.G.A Solve problems involving scale drawings of geometric figures, such as computing actual lengths and areas from a scale drawing and reproducing a scale drawing at a different scale.

G.G-SRT.A.1

Verify experimentally the properties of dilations given by a center and a scale factor.

Earth Science:

5.E2U1.7 Develop, revise, and use models based on evidence to construct explanations about the movement of the Earth and Moon within our solar system.

Science and Engineering Practices:

(a dimension of the Arizona Science Standards)

ask questions and define problems
develop and use models
plan and carry out investigations
analyze and interpret data
use mathematical and computational thinking
construct explanations and design solutions

Standards for Mathematical Practices (MP):

*Model with mathematics.

*Use appropriate tools strategically.

*Attend to precision.

*Look for and make use of structure.

Educational Technology:

6-8.5.c. Students break problems into component parts, identify key pieces, and use that information to solve problems.

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Objectives:

Students will be able to

understand the definition of a scale factor.
recognize scale factors in different situations
calculate scale factors

Key Vocabulary: Scale factor (k), dilation, projection lines, enlargement, reduction, similarity

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Agenda

Sample day

Bellwork (10-25 minutes - depends how much discussion) 3 Act Math Task

Classwork (20-35 minutes)

DESMOS - Intro to Dilation (technology activity)

Closure (5 minutes) turn and talk to a neighbor; asked a question based on how far we got on the DESMOS activity.

Depending on your time and how much you are spending on scale factor my agenda stays basically the same. Bellwork, Classwork and closure.

I spent two days on the DESMOS activity since I used the pacing feature and we had discussion as we went.

Final day of just scale factor was when I did the literature connection.

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Intro/Driving Question/Opening - 3 ACT Math task

BIG CHEQUES

HOW MANY TIMES BIGGER IS THE PRINTED CHEQUE VS. THE ORIGINAL?

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ACT 1

Big Cheques - ACT 1 Introducing the Problem

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What do you notice? What do you wonder?

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Main Question: How many times bigger is the printed cheque vs. the original?

Write down a low estimate, a high estimate and YOUR best guess!

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ACT 2

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Safety Slide :)

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ACT 3

THE BIG REVEAL

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Classwork

DESMOS: Intro to Dilations

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Hands-on Activity Instructions

(Literature Connection)

Hand each student a piece of copy paper (I used scratch paper - old worksheets).
Starting in portrait, I had students draw a tiny stick figure in the lower right corner. Label the figure 8-year old, 50 cm. This is a starting image.
Then as you read the book, students sketch an image of what you read.
For example, the opening part states the 8 year old is 5 times as big as the book. Students draw to the left of the figure a pic of a book. We had a talk about what height the book was and the scale factor. Students record “k=#” with an arrow to indicate which way this scale factor is.

Sample pages from the book.

The book does a good job of showing various scales as well. This page was comparing the heights of various trees. We used this page to talk about projection lines and scale.

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Hands-on Activity Instructions

(Literature Connection)

Listening to the students on how they can sketch each image was fun.
We also did predictions of what the item would be. For example, “But even these soaring skyscraper are tiny compared to…” Next page reveals “the highest peak on earth”. Then I asked what is that peak. We also discussed at this point how all of these are in relation to the ground since really there is a peak higher in Hawaii but because most of it is under water (also stated in the book!).
Students really got into the drawing each item in proportion. Some used 2-4 pieces of paper to show the comparisons of each item.

You can see where the students were adding in arrows and putting the scale factor.

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More Student Examples

5 pieces of paper!!

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Extra Notes

My students really enjoyed this lesson and even shared a video with me after the lesson was over. Here is the video that was sent!!!

There is also one page in the book that talks about how many earths it would take to get from here to there. We related that back to dilating a figure and the segments showing the scale factor.

You Are The Center of The Universe (Literally)