Standard NS 1.2 NS 2.2 Score First Name and Last Name Period Date Mr. Menjivar/Pre-Algebra Unit 1 Test Part 2 Number Sense 2.2 Number Sense 1.2 9 1) 16 5 4) − 24 + 1 2) 1 2 1 3) 4 3 4 − − 1 3 4 2 5 5 5) 6 ⋅ 15 6) 19 ÷ 7 12 3 −1 10 ÷ 15 19 By: Mr. Menjivar Observe, Question, Comment 09/09/11 Rates, Similar Figures, and Scale Drawings Reflection 09/09/11 Rates, Similar Figures, and Scale Drawings Standard: 9L 9R 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. Observe, Question, Comment 09/09/11 Rates, Similar Figures, and Scale Drawings Reflection 09/09/11 Rates, Similar Figures, and Scale Drawings Standard: Objectives: 9L 9R 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 Observe, Question, Comment 09/09/11 Rates, Similar Figures, and Scale Drawings Reflection 09/09/11 Rates, Similar Figures, and Scale Drawings Standard: Objectives: Vocabulary: 9L 9R 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 Observe, Question, Comment 09/09/11 Rates, Similar Figures, and Scale Drawings Reflection 09/09/11 Rates, Similar Figures, and Scale Drawings 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: 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? $2.07 48 fl.oz. $1.64 32 fl.oz. 0.043125 0.05125 The 48 fl.oz. bottle is the better value. $0.04 per fl.oz. $0.05 per fl.oz. Observe, Question, Comment 09/09/11 Rates, Similar Figures, and Scale Drawings Reflection Classwork #1: 09/09/11 Rates, Similar Figures, and Scale Drawings Standard: Objectives: Vocabulary: Notes/Examples: 9L 9R Observe, Question, Comment 09/09/11 Rates, Similar Figures, and Scale Drawings Reflection 09/09/11 Rates, Similar Figures, and Scale Drawings Classwork #1: Standard: Homework: Objectives: Vocabulary: Notes/Examples: 9L 9R Pg. 335 [1-9 all and 19] Pg. 337 [10-19 all] Observe, Question, Comment 09/09/11 Rates, Similar Figures, and Scale Drawings Reflection 09/09/11 Rates, Similar Figures, and Scale Drawings Classwork #1: Standard: Homework: Objectives: Warm-Up: Vocabulary: Notes/Examples: 9L 9R 2 1) 𝑥 3 2) 6 = 1 8 3 3) 4 = 7 𝑥 4 4) 11 = 21 𝑥 = 𝑥 22 Observe, Question, Comment 09/09/11 Rates, Similar Figures, and Scale Drawings Reflection 09/09/11 Rates, Similar Figures, and Scale Drawings Classwork #1: Standard: Homework: Objectives: Warm-Up: Vocabulary: Notes/Examples: Back to the Notes 9L 9R Proportions What are proportions? - If two ratios are equal, they form a proportion. Proportions can be used in geometry when working with similar figures. 1 4 2 = 8 1:3 = 3:9 What do we mean by similar? - Similar describes things which have the same shape but are not the same size. 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. 8 feet 4 feet 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. 2 feet A proportion can be made relating the height and the width of the smaller figure to the larger figure: 4 ft 2 ft = 8 ft 4 ft 4 feet Try One Yourself 8 feet Knowing these two stick figures are similar to each other, what is the ratio between the smaller figure to the larger figure? 12 feet 4 feet x feet Set up a proportion. What is the width of the larger stick figure? 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? 20 m 16 m xm ym 4m 3m Observe, Question, Comment 09/09/11 Rates, Similar Figures, and Scale Drawings Reflection 09/09/11 Rates, Similar Figures, and Scale Drawings Classwork #1: Standard: Homework: Objectives: Warm-Up: Vocabulary: Interactive Practice: Notes/Examples: 9L 9R Current Measurements Parts of the body Measurements in Inches Adjusted Measurements Parts of the body Measurements in Inches Height Height 120 inches Right arm Right arm Left arm Left arm Head Head Observe, Question, Comment 09/09/11 Rates, Similar Figures, and Scale Drawings Reflection 09/09/11 Rates, Similar Figures, and Scale Drawings Classwork #1: Standard: Homework: Objectives: Warm-Up: Vocabulary: Interactive Practice: Notes/Examples: Classwork #2: 9L 9R Observe, Question, Comment 09/09/11 Rates, Similar Figures, and Scale Drawings Reflection 09/09/11 Rates, Similar Figures, and Scale Drawings Classwork #1: Standard: Homework: Objectives: Warm-Up: Vocabulary: Interactive Practice: Notes/Examples: Classwork #2: Homework: 9L 9R Pg. 338 [1-9 all] Pg. 339 [7-14 all]