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Changes for 2 nd Semester: 1.Two separate interactive notebooks (Notes & Scholar Work) 2.No intervention/reteach week 3.Retakes will be taken after school on determined dates. All assignments & notes must be complete 4.Crunchymath.weebly.com

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Opening Activity 1. A tight end scored 6 touchdowns in 14 games. Find the ratio of touchdowns per game. 2. In a schedule of 6 classes, Marta has 2 elective classes. What is the ratio of elective to non-elective classes in Marta’s schedule. 3. An artist in Portland, Oregon, makes bronze sculptures of dogs. The ratio of the height of a sculpture to the actual height of the dog is 2:3. If the height of the sculpture is 14 inches, find the height of the dog.

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D. N. A. Solve the following equations.

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SlidesSkills PracticePractice 1, 2, 7, 8, 91-51-3 11, 12, 136-114-9 1512-1510-12 1713-15

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Geometry Chapter 7: Proportions and Similarity Chapter 7 Test on Friday 1/18 Retake 2/7 or 2/8 Chapter 7-1: Proportions

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Lesson 1 MI/Vocab ratio proportion cross products extremes means Write ratios. Use properties of proportions. Reinforcement of CA Standard 6NS1.3 Use proportions to solve problems (e.g., determine the value of N if 4/7 = N/21, find the length of a side of a polygon similar to a known polygon). Use cross-multiplication as a method for solving such problems, understanding it as the multiplication of both sides of an equation by a multiplicative inverse. (Key)

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Prerequisite Algebra Review Solve the following equation: Multiply both sides by the reciprocal of the fraction.

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Prerequisite Algebra Review (cont.) Solve the following equation: 5 2

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Prerequisite Algebra Review (cont.) Solve the following equation: 5

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Ratios A comparison of two quantities using division. Example: The ratio of 5 and 7 can be written as 5:7 or as the fraction and we say the ratio is “five to seven”.

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Example # 2: Gary has a bag with 4 marbles, 3 books, 5 pencils, and 2 erasers. a. What is the ratio of pencils to books? 5:3 b. What is the ratio of marbles to the total number of items in the bag? 4:14 2:7 (Must be reduced!)

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Lesson 1 Ex1 Write a Ratio SCHOOL The total number of students who participate in sports programs at Central High School is 500. The total number of students in the school is 2000. Find the athlete-to-student ratio to the nearest tenth. To find this ratio, divide the number of athletes by the total number of students. Answer: The athlete-to-student ratio is 1:4.

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1.A tight end scored 6 touchdowns in 14 games. Find the ratio of touchdowns per game. 2.In a schedule of 6 classes, Marta has 2 elective classes. What is the ratio of elective to non- elective classes in Marta’s schedule. 3.An artist in Portland, Oregon, makes bronze sculptures of dogs. The ratio of the height of a sculpture to the actual height of the dog is 2:3. If the height of the sculpture is 14 inches, find the height of the dog.

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Proportions If two ratios are equal, they can be written as a proportion. Extremes Means

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Proportion Practice Which proportions are not correct? 48 = 48 24 96 48 = 48 32 72 48 = 48

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Proportion Practice Solve the following proportions Check your answer!

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Solve each proportion.

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Using Ratios Example #1 The Perimeter of a rectangle is 60 cm. The ratio of AB:BC is 3:2. Find the length and width of the rectangle. A D C B 3:2 is in lowest terms. AB:BC could be 3:2, 6:4, 9:6, 12:8, etc. AB = 3x BC = 2x Perimeter = l + w+ l + w 60 = 3x + 2x + 3x + 2x 60 = 10x x = 6 L = 3(6) = 18 W = 2(6) = 12

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Find the measures of the sides of each triangle. 12. The ratio of the measures of the sides of a triangle is 3:5:7, and its perimeter is 450 centimeters. 13. The ratio of the measures of the sides of a triangle is 5:6:9, and its perimeter is 220 meters. 14. The ratio of the measures of the sides of a triangle is 4:6:8, and its perimeter is 126 feet. Find the measures of the angles in each triangle. 15) The ratio of the measures of the angles is 4:5:6.

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m A+ m B+ m C = 180 o Triangle Sum Thm. 2x + 3x + 4x = 180 o 9x = 180 o x = 20 o m A = 40 o m B = 60 o m C = 80 o The angle measures in ABC are in the extended ratio of 2:3:4. Find the measure of the three angles. Using Ratios Example #2 A C B 2x 3x 4x

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The ratio of the measures of the three side lengths of a ABC are, and the perimeter is 19 m. Find the measure of each side of the triangle. Using Ratios Example #3 Change the fractions into common denominators? Multiply everything by the common denominator.

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Lesson 1 Ex2 In a triangle, the ratio of the measures of three sides is 5:12:13, and the perimeter is 90 centimeters. Find the measure of the shortest side of the triangle. A 13 cm B 15 cm C 38 cm D 39 cm Extended Ratios in Triangles The shortest side is 15 centimeters. The answer is B. Check Add the lengths of the sides to make sure that the perimeter is 90.

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Lesson 1 CYP2 A.10.5 ft B.14 ft C.17.5 ft D.37 ft In a triangle, the ratio of the measures of three sides is 3:4:5, and the perimeter is 42 feet. Find the measure of the longest side of the triangle.

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Proportion Properties (The names are not important, the ideas are!!!) Cross Product Property—The product of the means equals the product of the extremes.

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Lesson 1 Ex3 B. Answer: –2 Solve Proportions by Using Cross Products Cross products Simplify. Add 30 to each side. Divide each side by 24.

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Lesson 1 CYP3 A.0.65 B.4.5 C.–14.5 D.147 A.

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1.A 2.B 3.C 4.D Lesson 1 CYP3 A.9 B.8.9 C.3 D.1.8 B.

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Lesson 1 Ex4 TRAINS A boxcar on a train has a length of 40 feet and a width of 9 feet. A scale model is made with a length of 16 inches. Find the width of the model. Solve Problems Using Proportions Answer: The width of the model is 3.6 inches. Substitution Cross products Multiply. Divide each side by 40.

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Lesson 1 Ex4 Answer: The width of the model is 3.6 inches. Solve Problems Using Proportions Substitution Cross products Multiply. Divide each side by 40.

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Proportion Practice #2 A picture of a tree is shown, the actual tree is 84 in. tall. How wide is the tree?

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Lesson 1 CYP4 A.0.6 m B.2.24 m C.2.52 m D.28.57 m Two large cylindrical containers are in proportion. The height of the larger container is 25 meters with a diameter of 8 meters. The height of the smaller container is 7 meters. Find the diameter of the smaller container.

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Homework Chapter 8.1 Pg 383: 2 – 9, 12 – 26, 56 – 61, 63, 64

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