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### Rates, Unit Rates, Similar Figures, and Scale Drawings

Number Sense 2.2

Number Sense 1.2

By: Mr. Menjivar

09/09/11

Observe,

Question,

Comment

Rates, Similar Figures, and Scale

Drawings

Rates, Similar Figures, and

Scale Drawings Reflection

Standard:

9L

9R

CA Content Standards

- Measurement and Geometry 1.1: Compare units within and between measurement systems
- Measurement and Geometry 1.2: Construct and read drawings and models made to scale.
- Measurement and Geometry 1.3: Use measures expressed as rates to solve problems.

09/09/11

Observe,

Question,

Comment

Rates, Similar Figures, and Scale

Drawings

Rates, Similar Figures, and

Scale Drawings Reflection

Standard:

Objectives:

9L

9R

Objectives

- To find rates and unit rates
- To use measures expressed as rates and products to solve problems
- To solve problems that involve similar figures and scale drawings

09/09/11

Observe,

Question,

Comment

Rates, Similar Figures, and Scale

Drawings

Rates, Similar Figures, and

Scale Drawings Reflection

Standard:

Objectives:

Vocabulary:

9L

9R

VocabularyRatio

- A comparison of two quantities by division

VocabularyRate

- A ratio that compares quantities in different units
- Note: a unit rate is a rate that has a denominator of 1

VocabularySimilar Drawings

- Have the same shape, but not necessarily the same size

09/09/11

Observe,

Question,

Comment

Rates, Similar Figures, and Scale

Drawings

Rates, Similar Figures, and

Scale Drawings Reflection

Standard:

Objectives:

Vocabulary:

Notes/Examples:

9L

9R

Ratios

- A ratio is a comparison between two numbers by division.
- It can be written in three different ways:

5 to 2

5 : 2

5

2

Equal Ratios

- When two ratios name the same number, they are equal. It’s like writing an equivalent fraction.

20 : 30

Equal Ratios:

80 : 120

2 : 3

10 : 15

Ratios in Simplest Form

- Ratios can be written in simplest form.
- Divide both terms in the ratio by their GCF.

Example: 12 to 8

3 to 2

Find the Unit Rate

Amy can read 90 pages in 4 hours. What is the unit rate? (How many pages can she read per hour?)

Using Unit Rates

- You can find the missing terms of equal ratios.
- Use the unit rate, and set it equal to another ratio.
- Solve for what is missing by dividing or multiplying.

Example

Joe’s car goes 25 miles per gallon of gasoline. How far can it go on 8 gallons of gasoline?

Comparing Unit Prices

- Use division to find the unit prices of the two products in question.
- The unit rate that is smaller (costs less) is the better value.

Example

Juice is sold in two different sizes. A 48-fluid ounce bottle costs $2.07. A 32-fluid ounce bottle costs $1.64. Which is the better buy?

$2.07

$0.04 per fl.oz.

0.043125

48 fl.oz.

$1.64

$0.05 per fl.oz.

0.05125

32 fl.oz.

The 48 fl.oz. bottle is the better value.

09/09/11

Observe,

Question,

Comment

Rates, Similar Figures, and Scale

Drawings

Rates, Similar Figures, and

Scale Drawings Reflection

Classwork #1:

Standard:

Objectives:

Vocabulary:

Notes/Examples:

9L

9R

09/09/11

Observe,

Question,

Comment

Rates, Similar Figures, and Scale

Drawings

Rates, Similar Figures, and

Scale Drawings Reflection

Classwork #1:

Standard:

Homework:

Objectives:

Vocabulary:

Notes/Examples:

9L

9R

Homework

- Pg. 335 [1-9 all and 19]
- Pg. 337 [10-19 all]

09/09/11

Observe,

Question,

Comment

Rates, Similar Figures, and Scale

Drawings

Rates, Similar Figures, and

Scale Drawings Reflection

Classwork #1:

Standard:

Homework:

Objectives:

Warm-Up:

Vocabulary:

Notes/Examples:

9L

9R

Warm-UpSolve Each Proportions

09/09/11

Observe,

Question,

Comment

Rates, Similar Figures, and Scale

Drawings

Rates, Similar Figures, and

Scale Drawings Reflection

Classwork #1:

Standard:

Homework:

Objectives:

Warm-Up:

Vocabulary:

Notes/Examples:

Back to the Notes

9L

9R

4

=

1:3 = 3:9

2

8

ProportionsWhat are proportions?

- If two ratios are equal, they form a proportion. Proportions can be used in geometry when working with similar figures.

What do we mean by similar?

- Similar describes things which have the same shape but are not the same size.

4 ft

=

2 ft

4 ft

ExamplesThese two stick figures are similar. As you can see both are the same shape. However, the bigger stick figure’s dimensions are exactly twice the smaller.

So the ratio of the smaller figure to the larger figure is 1:2 (said “one to two”). This can also be written as a fraction of ½.

A proportion can be made relating the height and the width of the smaller figure to the larger figure:

8 feet

4 feet

2 feet

4 feet

Try One Yourself

Knowing these two stick figures are similar to each other, what is the ratio between the smaller figure to the larger figure?

Set up a proportion. What is the width of the larger stick figure?

8 feet

12 feet

4 feet

x feet

Similar Shapes

In geometry similar shapes are very important. This is because if we know the dimensions of one shape and one of the dimensions of another shape similar to it, we can figure out the unknown dimensions.

09/09/11

Observe,

Question,

Comment

Rates, Similar Figures, and Scale

Drawings

Rates, Similar Figures, and

Scale Drawings Reflection

Classwork #1:

Standard:

Homework:

Objectives:

Warm-Up:

Vocabulary:

Interactive Practice:

Notes/Examples:

9L

9R

09/09/11

Observe,

Question,

Comment

Rates, Similar Figures, and Scale

Drawings

Rates, Similar Figures, and

Scale Drawings Reflection

Classwork #1:

Standard:

Homework:

Objectives:

Warm-Up:

Vocabulary:

Interactive Practice:

Notes/Examples:

Classwork #2:

9L

9R

09/09/11

Observe,

Question,

Comment

Rates, Similar Figures, and Scale

Drawings

Rates, Similar Figures, and

Scale Drawings Reflection

Classwork #1:

Standard:

Homework:

Objectives:

Warm-Up:

Vocabulary:

Interactive Practice:

Notes/Examples:

Classwork #2:

Homework:

9L

9R

Homework

- Pg. 338 [1-9 all]
- Pg. 339 [7-14 all]

Exit SlipFind “h” using similar figures

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