2. Find the value of y that makes the equation true. 3. Solve for t. 5(t-3) = 2t

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1 Instructional Week 2: January ISTEP + 10 Mathematics Focus Topic: Linear Equations and Inequalities with Real-World Application Paced Standards: AI.L.1: Understand that the steps taken when solving linear equations create new equations that have the same solution as the original. Solve fluently linear equations and inequalities in one variable with integers, fractions, and decimals as coefficients. Explain and justify each step in solving an equation, starting from the assumption that the original equation has a solution. Justify the choice of a solution method. + AI.L.2: Represent real-world problems using linear equations and inequalities in one variable and solve such problems. Interpret the solution and determine whether it is reasonable. + AI.L.7: Represent real-world problems using linear inequalities in two variables and solve such problems; interpret the solution set and determine whether it is reasonable. Solve other linear inequalities in two variables by graphing. PS: 1, 2, 3, 4, 5, 6, 7, and 8 + Key Vocabulary Coefficient the numerical factor a tern that contains a variable. Fluently - efficient and accurate Teacher Background: Sample Problems for AI.L.1 1. Solve for x. 3x 7 = 8x Find the value of y that makes the equation true. 3y 8 y Solve for t. 5(t-3) = 2t 4. Find the values of m that makes the inequality true. 2.5m 7(m 3) > Solve for p. 1 ( 14) 10 5 p p 6. Justin s Work Samuel s Work 6(y-2) = 9y +15 6( y -2 ) = 9y y 2 = 9y y 12 = 9y = 3y -3y = 27-17/3 = y y = -9 Justin and Samuel are study partners and they are preparing for their Solving Linear Equations Unit Test. When they begin to compare their solutions they have differing opinions on how to solve the problem above. Decide who is correct, Justin or Samuel, and justify your reasoning. Samuel is correct. Justin did not correctly distribute the 6 to (y-2).

2 Teacher Background: Sample Problems for AI.L.2 1. A teacher is taking her students to visit a museum. The admission fee is $8 for the teacher and $4 for each student. If the total cost for the group s admission fee to the museum is $92, how many students is the teacher taking to the museum? 8 + 4x = 92 solve for x 2. Jenny starts a scarf knitting business. She spends $160 on supplies to start the business, and she spends $4.50 to make each scarf. She sells each scarf for $12. Write an inequality that can be used to determine the number of scarves Jenny must sell in order to make a profit. What is the minimum number of scarves Jenny must sell in order to make a profit? x < 12x 3. A checking account is set up with an initial balance of $4,800, and $400 is removed from the account each month for rent (no other transactions occur on the account). Write an equation whose solution is the number of months, m, it takes for the account balance to reach $2,000. How long will it take for the account to reach $2,000? m = Bernardo and Silvia play the following game. An integer between 0 and 999, inclusive, is selected and given to Bernardo. Whenever Bernardo receives a number, he doubles it and passes the result to Silvia. Whenever Silvia receives a number, she adds 50 to it and pass the result to Bernardo. The winner is the last person who produces a number less than What is the smallest initial number that results in a win for Bernardo? Work Backwards - Round 1: 2n + 50 > 1000 ; n = 475 Round 2: 2n + 50 > 475; n = 213 Round 3: 2n + 50 > 213; n = 82 Round 4: 2n + 50 > 82; n = 16 The smallest initial number is 16 for Bernardo to win 5. Michael bought total of 42 pens and markers. He spent $24.50 on markers and $1.25 for each pen. He spent a total of $ Write an equation to represent the number of pens Michael bought. How many pens did he buy? x = 59.5 Teacher Background: Sample Problems for AI.L.7 1. At a high school football game, tickets cost $7 per adult and $4 per student. Write a linear inequality to determine the number of adults and student tickets that need to be sold, so that the amount of money taken in at the gate is at least $280. Be sure to define your variables. Then, graph the inequality and describe three possible solutions. a = number of adult tickets, s = number of student tickets 7a + 4s > 280

3 Process Standards to Emphasize with all standards PS.1: Make sense of problems and persevere in solving them. PS.2: Reason abstractly and quantitatively. PS.3: Construct a viable argument and critique the reasoning of others. PS.4: Model with mathematics. PS.5: Use appropriate tools strategically. PS.6: Attend to precision. PS.7: Look for and make use of structure. PS.8: Look for and express regularity in repeated reasoning.

4 Week 2 Instructional Assessment ISTEP+ Grade 10 Name (Al.L.1) 1. Solve for y. -4 ( y + 3) + 7 = 6 ( y -2) 1. (AI.L.1) 2. Which equation(s) is/are equivalent to 36 = -4 ( m + 6)? I. -4m = 60 II. 36 = -4m + 6 III. 36 = -4m -24 IV. 15 = m a. I only b. I and II only c. I and III only d. II, III, and IV only 2. (AI.L.2) 3. In 2015, there are 475 fish in the Butler Pond. Each year the number of fish increase by 180. Write an equation whose solution is the number of years, y, it takes for the pond to have 1,500 fish. In what year will the number of fish reach 1,500? a. Equation b. Year (AI.L.7) 4. Yutang has $147 to spend on jeans and shirts. The jeans she wants cost $49 and the shirts are on sale for $21. Write a linear inequality to determine the number of jeans and shirts Yutang can buy and not exceed $147. Be sure and define the variables. Then, graph the inequality and describe three possible solutions. a. Variables b. Inequality c. d. Possible Solutions

5 Solutions to Week 2 Instructional Assessment (AI.L.1) 1.7/10 (AI.L.1) 2. C (AI.L.2) 3.(4 points) Each part is worth 2 point. Use the ISTEP+ Constructed Response Rubric. a y = 1500 b (AI.L.7) 4. (8 points) Each part is worth 2 point. Use the ISTEP+ Constructed Response Rubric. a. Variables: j = number of jeans; choices may v s = number of shirts b. Inequality: 49j + 21s < 147 c. d. Possible solutions may vary All constructed response problems will be graded using the ISTEP+ Content Rubric.