2. Warm-Up #25 What is a scale factor? 𝑥−6 42 = 2𝑥−14 77
If ABCDE is similar to RSTUV, find the missing lengths for both shapes.

3. Summary – Similar shapes
To calculate missing sides, we first of all need the scale factor
We then either multiply or divide by the scale factor
To show that 2 shapes are similar we can either show that all of the sides are connected by the scale factor or show that matching angles are the same

4. Scale Factor and Area of Polygons

5. Scale A scale is a ratio between two sets of measurements. Examples:
Drawings: ¼ inch = 1 foot
Maps: 1 inch = 250 miles

6. Scale Factor
A scale factor is a ratio used to enlarge or reduce similar figures.
Examples: enlarging a piece of candy for a drawing…or the Willy Wonka Factory…

7. BAIP Instructional Support Version 2
6/27/2018
Scale Factor
The scale factor of the pool is
1” to 20 yards. Or
𝑖𝑛𝑐ℎ𝑒𝑠 𝑦𝑎𝑟𝑑𝑠 = 1 20
What is a Scale Factor?(PowerPoint #1)
Teacher prompt: Show students a picture of a competition swimming pool.
(See Teacher’s Guide)
Teacher prompt: Tell students that the dimensions of this the picture of the pool have a scale factor of 1 in. to 20 yards.
Teacher prompt: Explain to students that the scale factor will help us find the actual dimensions of the diagram of the pool. A scale factor is a ratio of measurements in a scale drawing to the actual measurement of the real-world object.
Teacher prompt: Ask students, “If 1 in. = 20 yards and the pool’s length is 100 yards, what is the length of the picture of the pool?
Student response: If 1 inch equals 20 yards, then 100 ÷ 20 equals 5 inches. The length of the diagram will be 5 inches.
Teacher prompt: Yes that is correct.
Teacher prompt: Using the same scale factor, find the width of the diagram if the pool’s width is 75 yards.
Student response: Using the scale factor of 1 inch to 20 yards I divided the 75 yards by 20 yards. The width of the picture is 3 ¾ inches because 75 ÷ 20 = 3.75 or 3 ¾ inches.
Teacher prompt: Using the dimensions you just found, make a diagram of the swimming pool.
Student response: The diagram should be a 5” by 3 ¾” rectangle.

8. BAIP Instructional Support Version 2
6/27/2018
Setting up Proportions
Keep like
units in the same fraction.
Inches = yards
Inches yards
(3.) Teaching Concept 2: Use a Scale Factor to Set up Proportions to Solve Real-World Problems (PowerPoint #2)
Teacher prompt: Another way to solve the competition pool problem is to set up a proportion.
Teacher prompt: When setting up a proportion, make sure you keep like units in the same fraction.
Teacher prompt: Let us set up a proportion using the previous dimensions.
Teacher prompt: Start with the length first. Set up the proportion with the inches in the first fraction and the yards in the second fraction. Once your proportion is set up, solve for the missing length.
Student response: Length: 1inch = 20 yards
x inch yards
20x = 100
Length: x = 5 inches
Width: inch = 20 yards
x inches 75 yards
20x = 75
Width: x = 3 3/4 inches
Teacher prompt: Good job.

9. Scale Drawing (Model)
A scale drawing (model) is a drawing that uses a scale to make an object smaller than (reduction) or larger than (enlargement) the real object.
The lengths and widths of objects of a scale drawing or model are proportional to the lengths and widths of the actual object.

10. What are scale drawings? Scale drawings are everywhere!
On Maps
Footprints of houses
Vehicle design
Can you think of any more?

11. Scale in everyday life: kitchen design
Purpose:
To share Move On with you and outline what the Project can offer, to you and to learners
To give you a brief taste of the National Tests
To give you an opportunity to action plan how you will adopt the Move On approach and adapt it to your setting
Workshop outline:
Presentation covering these aspects of Move On and the National Tests
Questions
Quiz using National Test questions that you can take away and copy to use with teachers and students in your own organisation
Table-talk to explore action you will take and what support you would like from the Move On Project team
Action Planning
Is there anything else you would like me to include?
Scale 1 cm = 1 m
6cm
Length of units = 6 m 5

12. Scale in everyday life: plans
decking
path
pool
Purpose:
To share Move On with you and outline what the Project can offer, to you and to learners
To give you a brief taste of the National Tests
To give you an opportunity to action plan how you will adopt the Move On approach and adapt it to your setting
Workshop outline:
Presentation covering these aspects of Move On and the National Tests
Questions
Quiz using National Test questions that you can take away and copy to use with teachers and students in your own organisation
Table-talk to explore action you will take and what support you would like from the Move On Project team
Action Planning
Is there anything else you would like me to include?
Scale 2 cm = 1 m 7

13. BAIP Instructional Support Version 2
6/27/2018
Using A Scale Drawing
Use a Scale Drawing to Find the Actual Dimensions of the Object (PowerPoint #3)
Teacher prompt: Look at the following drawing of a Science lab. The blueprint has a scale factor of ½ in. to 1 yard. (See Teacher’s Guide)
Teacher prompt: Let x = width of the room in yards. Set up a proportion to find the width of the room and simplify if necessary.
Student response: The width is 1½ inches and the scale factor is ½ inch to 1 yard. The proportion is set up as follows:
½ inch = 1 yard
1½ inch x
½ x = 1½
Multiply ½ by its reciprocal of 2/1 to get 1x. Then multiply the right side by that same 2/1.
1x = 3/2 ● 2/1
1x = 6/2 or 3
1x = 3 yards
The width of the room is 3 yards.
Teacher prompt: Excellent. Now find the length of the science lab.
Student prompt:
5 inches x
½ x = 5
1x = 5 ● 2/1
1x = 10/1 or 10
1x = 10 yards
The length of the room is 10 yards.

14. If you have ever seen Jurassic
Park, you saw how big the
dinosaurs were compared to the
people. Pretend that they made
a large Human to watch over the
animals. What would be the scale
factor if a 64 inch person was
made to be 160 feet?

15. The scale factor tells you how many times bigger than
“normal” that person really is.
You must make all units of
measure the same….
64 inches
64 inches
64 inches = =
160 feet
1920 inches
160 x 12

16. Now take the:
64 inches
And simplify
1920 inches
1/30 inches
This means that the person
was created 30 times his
normal size.

17. A set of landscape plans shows a flower bed that is 6. 5 inches wide
A set of landscape plans shows a flower bed that is 6.5 inches wide. The scale on the plans is 1 inch = 4 feet.
What is the width of the actual flower bed?
What is the scale factor?
26 feet
1/48

18. What is the scale factor?
The central chamber of the Lincoln memorial, which features a marble statue of Abraham Lincoln, has a height of 60 feet. Suppose a scale model of the chamber has a height of 4 inches. What is the scale of the model?
Write a ratio of the height of the model to the actual height of the statue?
What is the scale factor?
60ft
4in
15ft
1in
1 inch = 15 feet
1/180

19. Antonio is designing a room that is 20 feet long and 12 feet wide
Antonio is designing a room that is 20 feet long and 12 feet wide. Make a scale drawing of the room. Use the scale 0.25 inches = 4 feet.
STEP 1: Find the room’s length on the drawing (let x = length)
STEP 2: Find the room’s width on the drawing (let w = width) 20 x 4
.25
Length = 1.25 inches = 12 x 4
.25
Width = .75 inches =

20. AREA SCALE FACTOR AREA SCALE FACTOR = 4 40cm² 10cm² 2cm 5cm
ENLARGE rectangle
Scale Factor 2
40cm²
4 cm
10 cm
AREA SCALE FACTOR = 4

21. AREA SCALE FACTOR AREA SCALE FACTOR = 9 90cm² 10cm² 2cm 5cm
ENLARGE rectangle
Scale Factor 3
90cm²
6 cm
15 cm
AREA SCALE FACTOR = 9

22. ASF = LSF² AREA SCALE FACTORS 2 4 3 9 Reflect the Length Scale Factor2² 3²
AREA SCALE FACTOR = LENGTH SCALE FACTOR SQUARED
ASF = LSF²

23. Example Questions - AREA
Calculate the unknown areas Q1 Q2
5 cm
10 cm²
40 cm²
4 cm
12 cm²
8 cm Q3
15 cm
9 cm²
4 cm²
108 cm²
2 cm
3 cm

24. Example Questions - SIDES
Calculate the unknown lengths Q1 Q2
3 cm
10 cm²
250 cm²
2 cm
12 cm² y
10 cm Q3
6 cm x
18 cm²
8 cm²
48 cm²
2 cm
3 cm z

25. VOLUME SCALE FACTOR VOLUME SCALE FACTOR = 27 = 3³ 162 cm³ 1 cm 3 cm
ENLARGE cuboid
Scale Factor 3
6 cm
9 cm
VOLUME SCALE FACTOR = 27
= 3³

26. VSF = LSF³ VOLUME SCALE FACTOR 64cm³ Volume Scale Factor = 2³
ENLARGE cylinder
Scale Factor 2
Volume Scale Factor = 2³
VOLUME SCALE FACTOR = LENGTH SCALE FACTOR CUBED
VSF = LSF³

27. Example Questions - VOLUME
5 cm³
2 cm
8 cm³
3 cm
27 cm³
4.5 cm
135 cm³
6 cm Q3
40 cm³
5 cm³
4 cm
2 cm

28. Example Questions - SIDES
5 cm³
2 cm
6 cm³
1.5 cm
384 cm³
4 cm a
6 cm b
40 cm³ Q3
120 cm³
15 cm³
3.6 cm
1.8 cm c