Unit 1 Test Part 2 First Name and Last Name Period Date Mr. Menjivar/Pre-Algebra StandardScore NS 1.2 NS 2.2

Number Sense 2.2Number Sense 1.2

By: Mr. Menjivar

Rates, Similar Figures, and Scale Drawings 9R 9L 09/09/11 Rates, Similar Figures, and Scale Drawings Reflection 09/09/11 Observe, Question, Comment Standard:

 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.

Rates, Similar Figures, and Scale Drawings 9R 9L Rates, Similar Figures, and Scale Drawings Reflection Observe, Question, Comment Standard: Objectives: 09/09/11

 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

Rates, Similar Figures, and Scale Drawings 9R 9L Rates, Similar Figures, and Scale Drawings Reflection Observe, Question, Comment Standard: Objectives: Vocabulary: 09/09/11

 A comparison of two quantities by division

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

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

Rates, Similar Figures, and Scale Drawings 9R 9L Rates, Similar Figures, and Scale Drawings Reflection Observe, Question, Comment Standard: Objectives: Vocabulary: Notes/Examples: 09/09/11

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: 10 : 15 2 : 3 80 : 120

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

Examples Rate: 150 heartbeats 2 minutes Find The Unit Rate

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? $ fl.oz $0.04 per fl.oz. $ fl.oz $0.05 per fl.oz. The 48 fl.oz. bottle is the better value.

Rates, Similar Figures, and Scale Drawings 9R 9L Rates, Similar Figures, and Scale Drawings Reflection Observe, Question, Comment Standard: Objectives: Vocabulary: Notes/Examples: Classwork #1: 09/09/11

Rates, Similar Figures, and Scale Drawings 9R 9L Rates, Similar Figures, and Scale Drawings Reflection Observe, Question, Comment Standard: Objectives: Vocabulary: Notes/Examples: Classwork #1: 09/09/11 Homework:

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

Rates, Similar Figures, and Scale Drawings 9R 9L Rates, Similar Figures, and Scale Drawings Reflection Observe, Question, Comment Standard: Objectives: Vocabulary: Notes/Examples: Classwork #1: 09/09/11 Homework: Warm-Up:

Rates, Similar Figures, and Scale Drawings 9R 9L Rates, Similar Figures, and Scale Drawings Reflection Observe, Question, Comment Standard: Objectives: Vocabulary: Notes/Examples: Back to the Notes Classwork #1: 09/09/11 Homework: Warm-Up:

Proportions What 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 = 1:3 = 3:9

Examples These 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: 2 feet 4 feet 8 feet 4 feet 4 ft 2 ft = 8 ft 4 ft

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? 4 feet 8 feet 12 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.

Proportions and Triangles What are the unknown values on these triangles? 16 m 20 m 4 m 3 m x m y m

Rates, Similar Figures, and Scale Drawings 9R 9L Rates, Similar Figures, and Scale Drawings Reflection Observe, Question, Comment Standard: Objectives: Vocabulary: Notes/Examples: Classwork #1: 09/09/11 Homework: Warm-Up: Interactive Practice:

Parts of the body Measurements in Inches Height Right arm Left arm Head Parts of the body Measurements in Inches Height120 inches Right arm Left arm Head Current MeasurementsAdjusted Measurements

Rates, Similar Figures, and Scale Drawings 9R 9L Rates, Similar Figures, and Scale Drawings Reflection Observe, Question, Comment Standard: Objectives: Vocabulary: Notes/Examples: Classwork #1: 09/09/11 Homework: Warm-Up: Interactive Practice: Classwork #2:

Rates, Similar Figures, and Scale Drawings 9R 9L Rates, Similar Figures, and Scale Drawings Reflection Observe, Question, Comment Standard: Objectives: Vocabulary: Notes/Examples: Classwork #1: 09/09/11 Homework: Warm-Up: Interactive Practice: Classwork #2: Homework:

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