Name Date Class 7.EE.1 SELECTED RESPONSE Select the correct answer. 1. What property allows the expression.7x + 10. + 15.3x 8.x + 15.6 to be simplified to the equivalent expression 0x + 10. 8.x + 15.6? Additive inverse property Associative property of addition Commutative property of addition Commutative property of multiplication. Which of the following correctly uses the additive inverse property? 3 x 3 x 5 y = 0 5 y 5(x 3) = 5x 15 7 x 1 y + 1 y = 7 x + 0 1 3 x + 5 y + 3 y = 1 3 x + 5 y + 3 y Select all correct answers. 3. Which of the following uses the associative property of addition to simplify? 5 3 x + 8 5 x 3 5 x = 5 3 x + x 1 (x 11) = 1 x 11 0.y + (3.6y 0.6) = y 0.6 5 i 5 x + 1 5 = x + 1 5 7.8x 1.3 1.8x = 6x 1.3. Which properties are used to simplify 5 y + 3 5 x + 7 5 y to 5y + 6 5 x? Associative property of addition Associative property of multiplication Commutative property of addition Commutative property of multiplication Distributive property CONSTRUCTED RESPONSE 5. Explain how the properties of operations are used to show that 1 x + 3 5 y + 7 5 x and 1 x + 1 (3y + 7x) are equivalent. 5 6. Nadine and Walt are delivering the local newspaper throughout the town. Nadine is paid $15 per week plus $9.50 per hour, and Walt is paid $1 per week plus $10.5 per hour. a. Write expressions that represent how much Nadine and Walt are paid each week using h as the number of hours worked. b. Add both expressions to represent how much the local newspaper is paying Nadine and Walt each week to deliver the newspapers. Explain how the properties of operations are used to simplify the expression. Grade 7 7 Common Core Assessment Readiness
Name Date Class 7. Jamie is selling tickets for a whale watch at a local beach. The tickets cost $.0 for an adult and $1.50 for a child. Jamie earns a 30% commission on all ticket sales. Write an expression that uses parentheses to represent how much Jamie earns from selling tickets, where a is the number of adult tickets sold and c is the number of children s tickets sold. Use the distributive property to simplify the expression. 10. Explain how the properties of operations are used to simplify 5 (a + b) + 3 (a + c). 5 11. Marlyce s garden is surrounded by a fence. A diagram of the fence is shown. 8. Is 1 x + 6 7 7 x 7 equivalent to x +? Use the properties of 7 operations to justify your answer. 9. Write a linear expression with all rational coefficients such that simplifying the expression requires using the associative property of addition, the commutative property of addition, the distributive property, the additive inverse property, and the additive identity property. Show your work and explain how your expression simplifies. a. Write an expression that represents the perimeter of the fence as the sum of the side lengths. b. Show how the properties of operations are used to simplify the expression from part a. c. Suppose you know the perimeter of the fence is 10 feet. Find the lengths of the sides. Show your work. Grade 7 8 Common Core Assessment Readiness
Name Date Class 7.EE. SELECTED RESPONSE Select the correct answer. 1. Which of the following equations represents that y decreased by 35% is the same as 0.65 times y? y 0.35y = 0.65y y 0.35y = 0.65y y + 0.65y = 0.35y y + 0.35y = 0.65y. Which of the situations described below can be modeled by the equation n + 0.5n 0.3n = 1.n, where n is the number of nickels originally in the jar? Amanda takes out 50% of the nickels in the jar on Friday and adds a number of nickels that is equal to 30% of the remaining number of nickels in the jar on Monday. There are 0% fewer nickels in the jar after Monday than before Friday. Amanda takes out 50% of the nickels in the jar on Friday and adds a number of nickels that is equal to 30% of the original number of nickels in the jar on Monday. There are 0% fewer nickels in the jar after Monday than before Friday. Amanda adds 50% of the original number of nickels to the jar on Friday. The number of nickels Amanda takes out on Monday is equal to 30% of the new number of nickels. There are 0% more nickels in the jar after Monday than before Friday. Amanda adds 50% of the original number of nickels to the jar on Friday. The number of nickels Amanda takes out on Monday is equal to 30% of the original number of nickels. There are 0% more nickels in the jar after Monday than before Friday. 3. Which of the equations shown correctly rewrites an expression that represents the cost for a pair of shoes that is marked down 0% of the regular price r when the sales tax is 5% of the markdown price? 1.05(0.r) = 0.1r 1.05(r 0.0r) = 0.8r 1.05r 0.0r = 0.85r 1.05(r + 0.0r) = 1.6r Select all correct answers.. Which of the following expressions represent the sum of the areas of the triangles shown? 6 i 1 (x + ) + (x ) 6 1 (x + ) + (x ) 3[(x + ) + (x )] 3(x + ) 1x + 1 CONSTRUCTED RESPONSE 5. Does the expression 1.016x represent a percent increase greater than 1% if the original amount is x? Rewrite the expression as a sum of two terms to explain why or why not. Grade 7 9 Common Core Assessment Readiness
Name Date Class 6. A rectangle has a base b and a height h. Another rectangle has a base that is 1 3 of the length of the base of the first rectangle and a height that is 1 of the height of the first rectangle. Devin writes the area of the smaller rectangle as the product 1 3 b 1 h. Tracy rewrites this as 1 bh. Which student s expression makes 6 it easier to see how the areas of the rectangles are related? Explain. 7. A square pool with side length s is surrounded by tiles that form a border 5 feet wide all around the pool. a. Draw a sketch of the pool and the border. Label the side lengths. 8. Andre s house, the middle school, and the library are along the same street. The middle school is between Andre s house and the library. The distance between Andre s house and the middle school is x + 3, and the distance between the middle school and the library is x + 1. a. Write and simplify an expression for the distance between Andre s house and the library. b. Rewrite your expression from part a so that it describes how many times farther the library is from Andre s house than the middle school is from Andre s house. Explain. 9. The formula for the area of a rectangle is A = w, where A is the area, is the length, and w is the width. Rewrite the equation so it is solved for w. If the length of the rectangle increases, but the area stays the same, how does the width change? b. Write an expression for the perimeter of the pool and another expression for the perimeter of the outside of the tile border. Simplify the expressions. c. Compare the outside perimeter of the tile border and the perimeter of the pool. 10. Christopher, Jack, and Tamara collect s seashells. Christopher takes 30% of the seashells, and then Tamara takes 0% of the remaining shells. a. Write a subtraction expression that represents the number of shells that are left for Jack. Justify your answer. b. Simplify the result from part a so it is a single term with a single coefficient. Show your work. Use the simplified expression to interpret what percent of the collection of shells Jack gets. Grade 7 30 Common Core Assessment Readiness
Name Date Class 7.EE.3 SELECTED RESPONSE Select the correct answer. 1. A rectangle has a length of 8 feet and a width of 6 feet. If its length and width increase by 50% each, what is the area of the new rectangle? square feet 8 square feet 7 square feet 108 square feet. A hot air balloon is at an elevation of 3,800 feet. If the balloon falls 0 feet per minute, how long would it take for the balloon to reach,000 feet? 5 minutes 50 minutes 95 minutes 15 minutes 3. An airplane takes off 1.5 miles south of a city and flies due north at a constant speed of 170 miles per hour. What is the plane s position relative to the city after 5 minutes? 115 miles south 115 miles north 10 miles south 10 miles north. A bridge currently has 975 vehicles traveling on it per hour during peak time. A traffic engineer estimates that there will be 3.% more vehicles traveling on the bridge each year for years. How many more cars will travel on the bridge per hour during peak time in years than are traveling on it now? Round your final answer to the nearest whole vehicle. 33 vehicles 66 vehicles 67 vehicles 1,0 vehicles Select all correct answers. 5. Don is planning to mount a television on a wall and wants to center it. The wall is 88 3 inches and he wants to have at least 1 inches on each side of the television for external speakers. Don has researched the lengths for five different televisions. Which of the following lengths would fit? Television A: length of 36 1 inches Television B: length of 38 1 inches Television C: length of 39 3 inches Television D: length of 0 5 8 inches Television E: length of 1 8 inches Select the correct answer for each lettered part. 6. Each employee is getting a raise after a review. Determine if each employee will now earn at least $600 per week. a. Amanda made $1.50 per Yes hour, gets a 10% raise, and No works 38 hours per week. b. Bertram made $16.0 per Yes hour, gets a 5% raise, and No works 30 hours per week. c. Chuck made $13.90 per Yes hour, gets a 1% raise, and No works 0 hours per week. d. Emma made $17.00 per Yes hour, gets an 8% raise, and No works 35 hours per week. e. Judy made $18.30 per hour, Yes gets a 6% raise, and works No 8 hours per week. Grade 7 31 Common Core Assessment Readiness
Name Date Class CONSTRUCTED RESPONSE 7. Liz wants to hang a painting on her wall so that it is centered. The wall is 110 5 8 inches long and the painting is 8 3 inches wide. Determine how far the edges of the painting have to be from the ends of the wall. Show your work. Convert fractions to decimals for intermediate calculations and give your answer as a mixed number. 8. Two trains are both traveling at a constant speed toward each other on neighboring tracks. The trains are 5 miles apart when they start traveling. They pass each other 1 hours later. One of the trains is traveling at 5 3 miles per hour. a. Use estimation to find the speed of the other train. b. Find the speed of the other train. Show your work and convert all fractions to decimals. Write the speed of the other train as a mixed number. c. Is your answer from part b reasonable? Explain. 9. A new car typically loses 0% of its initial value during the first year. During the second year, the car loses 15% of its value after the first year. a. Estimate the value of a $18,600 car after the first and after the second year by rounding its initial value to the nearest ten thousand. Show your work. b. Find the value of the car after the first year and after the second year. Show your work. c. Did the car lose 35% of its initial value during the years? Explain without calculating. 10. A company s website advertises that it serves 9 customers per minute non-stop and that it serves 130,000 customers per week. a. Verify that the company s claim is inaccurate by using mental math and estimation. Show your work. b. How many customers should the company advertise that it serves per week based on the rate per minute that is currently on its website? Explain. c. In order for the company to reach its advertised weekly rate currently on its website, how many customers should it serve per minute? Explain. Grade 7 3 Common Core Assessment Readiness
Name Date Class 7.EE.a SELECTED RESPONSE Select the correct answer. 1. A fence forms a rectangle and uses 6 meters of fencing. If the width of the enclosed area is 13 meters, what is the length? 19 meters 38 meters 51 meters 15 meters. What is a correct method of solving the equation x 6 = 9 for x? 3 First subtract 6 from both sides of the equation, and then divide both sides of the equation by 3. First add 6 to both sides of the equation, and then divide both sides of the equation by 3. First subtract 6 from both sides of the equation, and then multiply both sides of the equation by 3. First add 6 to both sides of the equation, and then multiply both sides of the equation by 3. Select all correct answers. 3. Which of the following equations have a solution that is negative? 5x 11 = 7 x 3 + 7 3 = 13 3 3 x 9 = 39 8 6x 5 = 0 3 x 19 = 73 Select the correct answer for each lettered part.. Is the solution of the equation an integer? a. 5 x 13 3 = 10 Yes No 3 b. 3 x + 11 = 5 c. 5 6 x 17 = 55 1 Yes Yes No No d. 5 3 (x + ) = 35 Yes No e. 9(x + 7) = 39 Yes No CONSTRUCTED RESPONSE 5. Solve the equation 1 y 1 = 35 for y. Identify the sequence of operations used to solve the equation. 6. Cathy earns $13.50 per hour for the first 0 hours worked in a week and $0.5 per hour for hours over 0. If she earns $661.50 one week, how many hours does she work? Show your work using a variable that represents the time, in hours, that Cathy works over 0 hours. 7. Kevin is selling 7 identical alternators and a car wheel for scrap. He knows the wheel weighs 19.5 pounds. He puts all the items on a scale at the scrap yard and the total weight is 11.5 pounds. Find the weight of each alternator a, in pounds, algebraically. Show your work. Grade 7 33 Common Core Assessment Readiness
Name Date Class 8. The formula for the area of a trapezoid is A = h(b + b ) 1, where A is the area of the trapezoid, h is the height, and b 1 and b are the lengths of the bases. Use the formula to find b 1 if h is 7 meters, b is 10.5 meters, and A is 96.5 square meters. Show your work. 9. Tabitha uses a recipe that calls for sugar. She decides to make four times as much as the recipe produces, but she cuts 1 cup of sugar overall. Tabitha uses 5 3 cups of sugar. Find how much sugar the original recipe calls for using arithmetic. 10. Becky buys a notebook for $1.59 and pens for $0.9 each. She spends $5.07. Assume there is no sales tax where Becky lives. a. Define a variable that can be used for this situation. b. Write an equation using the variable from part a. c. Solve the equation from part b. Show your work. What does the solution of the equation mean? 11. The sum of two consecutive even integers is 11. Find the two integers by writing and solving an equation using n to represent the smaller of the two integers. Explain your reasoning and show your work. 1. Wally buys two books at a bookstore. He spends $.5 after 6% sales tax is applied, but the clerk does not provide him with a receipt. He knows that book A costs $17.50 before sales tax, but he is not sure how much book B costs. a. Use an arithmetic solution to find the cost of book B. b. Determine how the cost of book B can be represented in an equation. Write an equation using the distributive property that represents this situation. c. Use the equation from part b to find the cost of book B. Show your work. d. Explain how finding the cost of book B using the arithmetic solution compares to finding the cost of book B using the algebraic solution. Grade 7 3 Common Core Assessment Readiness
Name Date Class 7.EE.b SELECTED RESPONSE Select the correct answer. 1. Which of the following inequalities has a solution set described by the graph on the number line below?. Which of the following graphs describes the solution set of 5 x 13 5 9? 5x + 19 59 5 3 x 8 3 > 8 3 6x 17 79 5 x + 1 5 5. Your middle school is having a carnival. Admission into the carnival is $8, and each game inside the carnival costs $0.50. Which of the following inequalities represents the possible number of games g that can be played with $0? 8g + 0.50 0 8g + 0.50 0 0.50g + 8 0 0.50g + 8 0 3. Which of the following inequalities represents a solution set that has the variable x being greater than or equal to some number? Select all correct answers. 5. Which of the following inequalities has the set of positive numbers as part of its solution set? x + 15 < 1 5 3 x + 17 3 < 9 1 x 16 > 18 3 x 11 31 8 3 x + 5 9 Select the correct answer for each lettered part. 6. Determine whether the following inequalities have a solution set of x 6. 3 x +17 53 8 5 x + 7 5 > 5 5 7 x 16 7 39 7 9 x + 3 3 8 a. 7x 5 3 131 3 b. 5 x + 3 c. 3 x + 19 3 31 3 d. 7 x 7 15 Yes Yes Yes Yes No No No No e. 6 7 x + 5 7 11 7 Yes No Grade 7 35 Common Core Assessment Readiness
Name Date Class CONSTRUCTED RESPONSE 7. Reese has enough money to buy 115 cm of framing. He wants the frame to be 8.5 cm long. a. Use the perimeter of a rectangle formula, P = + w to write an inequality that determines how wide the framing can be. b. Solve the inequality from part a. c. Graph the solution on the number line. What is the interpretation of the solution? 8. Erin is training for a marathon and wants to run at least 1 1 miles. She has already run 3 7 miles and starts to jog at 8 a steady rate of 8 1 miles per hour. Write an inequality using the time t, in hours, to find the possible amounts of time remaining for her jog. Show your work. 9. Cliff earns a base pay of $75 per week plus an 8% commission on all of his sales. Write an inequality that represents the minimum amount of sales s, in dollars, Cliff must make to earn at least $560 per week. What is the interpretation of the solution set? 10. Allison is having a birthday party at a reception hall. She is willing to spend no more than $00 to rent the hall. The hall charges a flat fee of $10 plus $ per invited person. a. Determine how the number of people invited can be represented by an inequality. Write an inequality that represents this situation. b. Solve the inequality from part a. Show your work. c. Would you use a ray or a set of points for this solution on a number line? Explain. d. Graph the solution set on the number line below. 11. Tim is making a fence in the shape of a triangle for his livestock. He wants one side of the triangle to be two times as long as another side and the third side to be 1 m long. Tim wants the perimeter of the triangle to be more than m and less than 8 m. a. How can the lengths of the unknown sides be represented by variables? b. Write two inequalities that represent this situation. One inequality represents the minimum perimeter, and the other inequality represents the maximum perimeter. c. Solve the inequalities from part b. Grade 7 36 Common Core Assessment Readiness
7.EE.1 Answers 1. C. C 3. A, C. C, E 5. Use the associative property of addition to rewrite 1 x + 3 5 y + 7 5 x as 1 x + 3 5 y + 7 5 x. Then use the distributive property to rewrite 1 x + 3 5 y + 7 5 x as 1 x + 1 (3y + 7x). 5 1 point for using associative property; 1 point for using distributive property 6. a. Nadine: 9.50h + 15; Walt: 10.5h + 1 b. 9.50h + 15 + 10.5h + 1 = 9.50h + 10.5h + 15 + 1 = 19.75h + 7 The commutative property of addition allows 15 and 10.5h to be switched. This allows 9.50h and 10.5h to be added together and 15 and 1 to be added together. The distributive property is used to add the terms with the variable: 9.50h + 10.5h = (9.50 + 10.5)h = 19.75h. a. 1 point for each expression b. 1 point for answer; 1 point for explanation of properties used 7. 0.3(.0a + 1.50c); 0.3(.0a + 1.50c) = 0.3(.0a) + 0.3(1.50c) = 7.3a +.35c 1 point for expression with parentheses; 1 point for using distributive property; 1 point for simplified expression 8. No. 1 x + 6 7 7 x 7 is equal to 1 x + 6 7 + 7 x 7 because subtracting is adding the opposite. Distribute the negative sign to each term in the parentheses. 1 x + 6 7 + 7 x 7 = 1 x + 6 7 + 7 x + 7 Drop the parentheses and use the commutative property of addition to move 7 x to the left of 6 7. 1 x + 6 7 + 7 x + 7 = 1 x + 7 x + 6 7 + 7 Combine like terms and simplify. 1 x + 7 x + 6 7 + 7 = 8 x + 10 7 = x + 10 7 So, 1 x + 6 7 7 x 7 is equivalent to x + 10 7, not x + 7. 1 point for answer; 1 point for using distributive property; 1 point for using commutative property of addition; 1 point for simplified expression Grade 7 Teacher Guide 5 Common Core Assessment Readiness
9. Possible answer: 5 8 9 y + 3 (3y 5) 3 8 = 5 8 9 y + 9 y 15 3 8 = 5 8 + 9 y + 9 y 15 3 8 = 5 8 + 0 15 3 8 = 5 8 15 3 8 = 5 8 3 8 15 = 7 Distributive property Associative property of addition Additive inverse property Additive identity property Commutative property of addition Simplify. = 3 1 1 point for writing an expression that requires all five properties; 1 point for each property used in simplifying; 1 point for correctly simplifying result 10. Possible answer: 5 (a + b) + 3 5 (a + c) = 5 a + 5 b + 3 5 a + 3 c 5 Distributive property = 5 a + 3 5 a + 5 b + 3 c 5 Commutative property of addition = a 5 + 3 5 + 5 b + 3 5 c Distributive property = a(1) + 5 b + 3 5 c Simplify. = a + 5 b + 3 c Multiplicative identity property 5 1 point for each property used; 1 point for simplified result Grade 7 Teacher Guide 6 Common Core Assessment Readiness
11. a. 5a + 3a + 1 + (a 6) + 10 b. Possible answer: 5a + 3a +1 + (a 6) +10 = 5a + 3a +1 + a +10 Distributive property = 5a + 3a + a +1 +10 Commutative prop. of addition = 5a + 3a + a +1 +10 Commutative prop. of addition = 5a + 3a + a + Simplify. = 5a + 3a + a + 0 Additive inverse property = 5a + 3a + a Additive identity property = (5 + 3 + )a Distributive property = 1a Simplify. c. One side is 10 feet long. Since 1a = 10, a = 10. Substitute 10 for a for each of the unknown sides. 5a = 5(10) = 50 The side that has length 5a is 50 feet long. 3a + 1 = 3(10) + 1 = 30 + 1 = The side that has length 3a + 1 is feet long. (a 6) = (10 6) = () = 16 The side that has length (a 6) is 16 feet long. a. 1 point b. points for showing properties used; 1 point for correct simplified expression c. 1 point for side lengths; 1 point for showing work Grade 7 Teacher Guide 7 Common Core Assessment Readiness
7.EE. Answers 1. B. D 3. B. A, C, D 5. No, because the expression 1.016x can be rewritten as x + 0.016x, and 0.016x means a 1.6% increase of x, which is less than 1%. 1 point for answer; 1 point for rewriting expression; 1 point for explanation 6. Tracy s expression makes it easier to see how the areas of rectangles are related because the area of the larger rectangle is bh. Since the area of the smaller rectangle is 1 bh, the area of the 6 smaller rectangle is 1 the area of the 6 larger rectangle. 1 point for answer; points for explanation 7. a. Possible sketch: b. Perimeter of pool: s Perimeter of the outside of the tile border: (s + 10) or s + 0 c. The perimeter of the tile border, s + 0, is 0 feet longer than the perimeter of the pool, s. a. 1 point b. 1 point for each expression c. 1 point 8. a. x + 3 + x +1 = x + x + 3 +1 = 5x +15 b. 5x + 15 = 5(x + 3) The distance from Andre s house to the middle school is x + 3, and the distance from Andre s house to the library is 5(x + 3). This shows that the library is 5 times farther from Andre s house than the middle school is. a. 1 point for writing expression; 1 point for simplifying expression b. 1 point for rewriting expression; 1 point for explanation Grade 7 Teacher Guide 8 Common Core Assessment Readiness
9. A = w A = w The width gets shorter when the area stays the same and the length gets longer because when the numerator stays the same in a fraction, and the denominator gets larger, the value of the fraction gets smaller. 1 point for solving for w; points for stating the relationship between the length and the width 10. a. Possible answer: s 0.3s 0.(s 0.3s); Since Christopher is taking 30% of the seashells, he takes 0.3s seashells. So, there are s 0.3s seashells remaining. Tamara is taking 0% of those remaining seashells, so the expression 0.(s 0.3s) represents the number of seashells Tamara takes. So, there are s 0.3s 0.(s 0.3s) seashells for Jack. b. s 0.3s 0.(s 0.3s) = s 0.3s + 0.(s 0.3s) = s 0.3s 0.s + 0.1s = (1 0.3 0. + 0.1)s = 0.s Jack gets % of the seashells the group collects. a. 1 point for expression; 1 point for explanation b. 1 point for simplified expression; 1 point for interpretation Grade 7 Teacher Guide 9 Common Core Assessment Readiness
7.EE.3 Answers 1. D. A 3. B. C 5. A, B, C 6. a. Yes b. No c. Yes d. Yes e. No 7. Convert the mixed numbers to decimals. 110 5 8 = 110.65 ; 8 3 8 = 8.375 Subtract 8.375 from 110.65 to determine the length of the wall that is not covered by the painting. 110.65 8.375 = 8.5 Since the painting is centered on the wall, the length from the end of the wall to the edge of the painting for each side is the same. Divide 8.5 by. 8.5 = 1.15 Convert 1.15 to a fraction. 1.15 = 1 15 1000 = 11 8 The edges of the painting have to be 1 1 inches away from each end of 8 the wall. 1 point for converting fractions to decimals; 1 point for showing work; 1 point for correct mixed number answer 8. a. Possible answer: Round 5 to 300, 5 3 to 5, and 1 to 5. The first train travels 5 5 = 15 miles. So, the second train travels 300 15 = 175 miles and, thus, the second train travels 175 = 35 miles 5 per hour. (Accept answers that use different rounding, such as rounding 5 to 50 and 5 3 to 30.) b. The speed of the other train is 30 1 miles per hour. Convert 5 3 and 1 5 3 = 5.75 ; 1 =.5 to decimals. The first train travels 5.75.5 = 115.875 miles. So, the second train travels 5 115.875 = 136.15 miles. Divide 136.15 by.5. 136.15 = 30.5.5 Convert 30.5 to a mixed number. 30.5 = 30 1 c. Yes, because the answer from part b, 30 1, is close to the estimate of 35. a. points b. 1 point for answer; 1 point for showing work; 1 point for converting all fractions to decimals c. 0.5 point for answer; 0.5 point for explanation Grade 7 Teacher Guide 30 Common Core Assessment Readiness
9. a. Round 18,600 to 0,000. Subtract the product of 0,000 and 0. from 0,000. 0,000 0,000 0. = 16,000 The value of the car is about $16,000 after the first year. Subtract the product of 16,000 and 0.15 from 16,000. 16,000 16,000 0.15 = 13,600 The value of the car is $13,600 after the second year. b. Subtract the product of 18,600 and 0. from 18,600. 18,600 18,600 0. = 1,880 The value of the car is $1,880 after the first year. Subtract the product of 1,880 and 0.15 from 1,880. 1,880 1,880 0.15 = 1,68 The value of the car is $1,68 after the second year. c. No, because the car did not lose 0% of its initial value in the first year and then lose 15% of its initial value in the second year. The car s value lost 15% of a lower amount in the second year, so the car s value lost less than 35% of its initial value during the years. a. 1 point for answer; 0.5 point for rounding; 0.5 point for showing work b. 0.5 point for value after first year; 0.5 point for value after second year; 1 point for showing work c. 1 point for answer; 1 point for explanation 10. a. Possible answer: The expression 9 60 7 represents the number of customers that the company serves per week. Notice that 9 60 7 is less than 10 60 7, which is also less than 10 60 5 8. Notice that 5 8 equals 50. 10 60 5 8 = 10 60 50 = 10 60 00 = 10,000 Since 130,000 is greater than 10,000 and 10,000 is greater than the customers served per week, the company s claim is inaccurate. b. Possible answer: Since 9 60 7 = 90,70, the company should claim that it serves 90,000 customers per week. c. Possible answer: The company should serve about 13 customers per minute so it can advertise that it serves 130,000 customers per week. First, find how many minutes there are in a week. 60 7 = 1,0 7 = 10,080 Then, divide 130,000 by 10,080 to find how many customers should be served per minute. Round up. 130,000 1.90 13 10,080 a. points b. 1 point for answer; 1 point for explanation c. 1 point for answer; 1 point for explanation Grade 7 Teacher Guide 31 Common Core Assessment Readiness
7.EE.a Answers 1. A. D 3. B, C, E. a. No b. Yes c. Yes d. No e. No 5. y = 7; Add 1 to both sides of the equation. 1 y 1 + 1 = 35 + 1 1 y = 1 Multiply both sides of the equation by. 1 y i = 1 i y = 8 y = 7 1 point for solution; 1 point for adding 1 to both sides of the equation; 1 point for multiplying both sides of the equation by 6. Let t be the time, in hours, Cathy works over 0 hours. An equation that represents this situation is 13.50 i 0 + 0.5t = 661.50, which simplifies to 50 + 0.5t = 661.50. Subtract 50 from both sides of the equation. 50 50 + 0.5t = 661.50 50 0.5t = 11.50 0.5t 0.5 = 11.50 0.5 t = 6 Since 6 is the number of hours Cathy works over 0 hours, she works 0 + 6 = 6 hours that week. 1 point for equation; 1 point for solution; 1 point for interpretation 7. Each alternator weighs 13.5 pounds. An equation that represents this situation is 7a + 19.5 = 11.5. Solve the equation for a. 7a +19.5 19.5 = 11.5 19.5 7a = 9.75 7a 7 = 9.75 7 a = 13.5 1 point for answer; 1 point for equation; 1 point for showing work 8. 96.5 = 7(b +10.5) 1 7 i 96.5 = 7 i 7(b +10.5) 1 7.5 = b 1 +10.5 7.5 10.5 = b 1 +10.5 10.5 17 = b 1 Thus, b 1 is 17 meters. 1 point for answer; 1 point for showing work 9. Add 1 to 5 3 to find the amount of sugar needed for four recipes. 5 3 + 1 = 6 Divide 6 by to find the amount of sugar in the original recipe. 6 = 3 = 11 The original recipe calls for 1 1 cups of sugar. 1 point for answer; 1 point for using arithmetic Grade 7 Teacher Guide 3 Common Core Assessment Readiness
10. a. The variable p is used to represent the number of pens Becky buys. b. 0.9p + 1.59 = 5.07 c. 0.9p +1.59 = 5.07 0.9p +1.59 1.59 = 5.07 1.59 0.9p = 3.8 p = 3.8 0.9 p = 1 The solution of the equation is p = 1, and it means that Becky buys 1 pens. a. 1 point b. 1 point c. 0.5 point for solution; 0.5 point for showing work; 1 point for meaning of solution 11. The difference between consecutive even integers is. Since n is the smaller consecutive even integer, n + is the larger consecutive even integer. An equation that represents two consecutive even integers whose sum is 11 is n + (n + ) = 11, or n + = 11. Solve the equation for n. n + = 11 n = 11 n = 11 n = 56 Since n = 56, 56 is the smaller consecutive even integer and the larger consecutive even integer is 56 +, or 58. The two consecutive even integers are 56 and 58. 1 point for equation; 0.5 point for each consecutive even integer; 1 point for explanation; 1 point for showing work 1. a. A 6% sales tax increases the price of the two books by 6% and can be represented as multiplying by 1.06. So, divide the total cost, $.5, by 1.06. $.5 1.06 = $.00 Subtract the cost of book A, $17.50, from $.00 to find the cost of book B. $.00 $17.50 = $.50 The cost of book B is $.50. b. The cost of book B can be represented as the variable b in an equation. An equation that represents this situation is 1.06(b + 17.50) =.5. c. 1.06(b + 17.50) =.5 1.06 1.06 b +17.50 =.00 b +17.50 17.50 =.00 17.50 b =.50 The cost of book B is $.50. d. The arithmetic solution divides $.5 by 1.06 and subtracts $17.50 from the quotient. The algebraic solution divides both sides of the equation by 1.06 and subtracts 17.50 from both sides of the equation. The two solutions use the same operations in the same order. a. 1 point b. 1 point for representing the cost of book B in an equation; 1 point for equation c. 1 point for answer; 1 point for showing work d. 1 point Grade 7 Teacher Guide 33 Common Core Assessment Readiness
7.EE.b Answers 1. C. C 3. D. A 5. B, C, E 6. a. Yes b. No c. No d. Yes e. No 7. a. P + w 115 (8.5) + w 115 57 + w b. 115 57 57 57 + w 58 w 58 w 9 w c. The solution means that the width of the frame is greater than 0 cm but at most 9 cm. a. 1 point b. 1 point c. 1 point for number line; 1 point for interpretation 8. 8 1 t + 3 7 8 1 1 ; Rewrite 8 1, 3 7 8, and 1 1 as improper fractions and solve for t. 17 t + 31 8 9 17 t + 31 8 31 8 116 8 31 8 17 t 85 8 17 i 17 t 17 i 85 8 t 5 Erin needs to run at least another hour and fifteen minutes to meet her goal. 1 point for inequality; 1 point for solution; 1 point for showing work 9. 0.08s + 75 560; 0.08s + 75 75 560 75 0.08s 85 0.08s 0.08 85 0.08 s 3,56.5 Cliff must have at least $3,56.50 in sales per week in order for him to earn at least $560 per week. 1 point for inequality; 1 point for solution set; 1 point for interpretation Grade 7 Teacher Guide 3 Common Core Assessment Readiness
10. a. The variable p can be used to represent the number of people invited to Allison s party. p + 10 00 b. p +10 10 00 10 p 80 p 80 p 35 3 p 11 3 c. I would use a set of points because only whole numbers of people can be invited. The solution set is integers from 0 to 11 because Allison can invite no more than 11 people and a 3 negative number of people cannot be invited. d. a. 1 point for using a variable to represent the number of invited people; 1 point for inequality b. 1 point for solution; 1 point for showing work c. 0.5 point for stating a set of points should be used; 0.5 point for explanation d. 1 point 11. a. Possible answer: The variable s can be used to represent the length of the shorter unknown side, and s can be used to represent the length of the longer unknown side. b. To write an inequality that represents the minimum perimeter, add s, s, and 1 and set it greater than. s + s + 1> 3s + 1> To write an inequality that represents the maximum perimeter, add s, s, and 1 and set it less than 8. s + s + 1< 8 3s + 1< 8 c. 3s + 1 1> 1 3s 3 > 1 3 s > 7 3s + 1 1< 8 1 3s 3 < 63 3 s < 1 The length of the shorter unknown side is greater than 7 m and less than 1 m. a. 1 point b. 1 point for each inequality c. 1 point for each solution Grade 7 Teacher Guide 35 Common Core Assessment Readiness