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Mixture Problems Teacher Notes Notes: Grades are mixture problems students relate to. Organizer: Contains an organizer to structure these problems 10/27/11 ©Evergreen Public Schools 2010 1 Learning Target Solve Equations Target 3a I can write an equation to solve a problem. Solve Equations Target 3b I can show the algebraic steps I used to find a solution to a multi-step equation. What kind of problems have we already solved? ©Evergreen Public Schools 2010 2 Launch In Miss Payne’s class grades are based only on test grades. Aramis got an F on the Unit 1 test and an A on the Unit 2 test. What is his grade in the class? ©Evergreen Public Schools 2010 3 Launch In Miss Payne’s class grades are based only on test grades. Aramis got an 25% on the Unit 1 test and an 75% on the Unit 2 test. What is his grade in the class? ©Evergreen Public Schools 2010 4 Launch Kitty’s answer to the question Aramis got an 25% on the Unit 1 test and an 75% on the Unit 2 test. What is his grade in the class? Was 100%. What would you say to her? ©Evergreen Public Schools 2010 5 Explore ©Evergreen Public Schools 2010 6 Calculate GPA How is your Grade Point Average, GPA, calculated? A=4 B=3 sum of all grades C=2 number of grades D=1 F=0 ©Evergreen Public Schools 2010 7 Calculate GPA Without calculating, guess the GPA. I. II. III. IV. A, A, A, F, F, F A, B, B, B, B, F B, C, C, C, C, D A, C, C, C, C, F Share your guess with your group. ©Evergreen Public Schools 2010 8 Calculate GPA Now calculate the GPA. I. A, A, A, B, C, F II. A, B, B, B, C, F III. B, B, C, C, C, D IV. A, B, B, C, D, F Did your guess match the calculation? Share with your group. ©Evergreen Public Schools 2010 9 Math Class Grade At Mountain View HS, grades are 20% Assignments & 80% Assessments Kimberly has 120 out of 150 assignment points and 120 out of 150 assessment points. What is her percent in the class? ©Evergreen Public Schools 2010 10 20% Assign & 80% Assess I. Faith has 130 out of 150 assignment points and 120 out of 150 assessment points. II. Hope has 120 out of 150 assignment points and 130 out of 150 assessment points. Who has a higher percent in class? Faith? Hope? Are their percents the same? ©Evergreen Public Schools 2010 11 Mixture Problems You have been solving mixture problems. Here’s an organizer you can use for these problems. Ingredient 1 Ingredient 2 Total Mix Concentration Or Cost Amount ©Evergreen Public Schools 2010 12 Mixture Problems Equation: Concentration 1 Amount 1 + Concentration 2 Amount 2 = Total Concentration 1 Total Amount For short: C1A1 + C2A2 = CtotalAtotal ©Evergreen Public Schools 2010 13 Mixture Problems Faith has 130 out of 150 assignment Why points and 120 out of 150 1.00? assessment points. Ingredient 1 Ingredient 2 Total Mix assign assess Concentration Or Cost .20 .80 1.00 Amount 130/150 120/150 x ©Evergreen Public Schools 2010 14 Mixture Problems Equation: C1A1 + C2A2 = CtotalAtotal .20130 /150 .80120 /150 1.00 x .20.87 .80.80 1.00 x 0.174 0.64 x 0.814 x Ingredient 1 Ingredient 2 Total Mix assign assess Concentration Or Cost .20 .80 1.00 Amount 130/150 120/150 x ©Evergreen Public Schools 2010 15 Mixture Problems Equation: C1A1 + C2A2 = CtotalAtotal .20130 /150 .80120 /150 1.00 x .20.87 .80.80 1.00 x 0.174 0.64 x 0.814 x Faith’s percent is 81.4% ©Evergreen Public Schools 2010 16 20% Assignments & 80% Assessments Hope has 120 out of 150 assignment points and 130 out of 150 assessment points. Use the same procedure to calculate Hope’s grade. Who has a higher percent in class? Faith? Hope? Are their percents the same? ©Evergreen Public Schools 2010 17 20% Assignments & 80% Assessments Todd said both girls percents should be the same because they both have 150 out of 300 points. What would you say to Todd? ©Evergreen Public Schools 2010 18 Mixture Problems Krystal’s Red Hot Peanuts was made by What with goes combining 6 kg of peanuts which cost $1/kg here? 3 kg of spices which cost $4/kg. Find the cost of the mixture. Ingredient 2 Total Mix peanuts 1 Ingredient spices Concentration Or Cost $1/kg $4/kg ? Amount 6 kg 3 kg 9 kg ©Evergreen Public Schools 2010 19 Mixture Problems 16 4 3 x 9 Equation: 6 12 9x 18 9x 2x C 1 A 1 + C 2A 2 = CtotalAtotal Ingredient 2 Total Mix peanuts 1 Ingredient spices Concentration Or Cost $1/kg $4/kg ?x Amount 6 kg 3 kg 9 kg ©Evergreen Public Schools 2010 20 Mixture Problems Krystal’s mixture costs $2 per pound. Ingredient 2 Total Mix peanuts 1 Ingredient spices Concentration Or Cost $1/kg $4/kg Amount 6 kg 3 kg ©Evergreen Public Schools 2010 x?= 2 9 kg 21 Placemat Name 2 Explain how to use the short cut C1A1 + C2A2 = CtotalAtotal to write an equation to solve a mixture problem. Name 3 Name 4 ©Evergreen Public Schools 2010 22 Learning Target Did you hit the target? 3a I can write an equation to solve a problem. 3b I can show the algebraic steps I used to find a solution to a multi-step equation. ©Evergreen Public Schools 2010 1 2 3 4 5 23 Practice Practice 2.6D Mixture Problems ©Evergreen Public Schools 2010 24