6.NS.1. SELECTED RESPONSE Select the correct answer. CONSTRUCTED RESPONSE. 4. Divide You have 7 cup of sour cream to make

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1 Name Date Class 6.NS. SELECTED RESPONSE Select the correct answer.. You have 7 cup of sour cream to make 8 tacos. If each taco requires cup of 6 sour cream, how many tacos can you make? 4. Divide Nima uses 2 cup peanuts, 2 cup cashews, 4 cup pecans, and some raisins in a recipe that makes 2 4 cups of taco 4 tacos taco 5 tacos 2. How many -cup servings are there in cup of peanut butter? Carl wants to plant a garden that is 2 yards long and has an area of square yards. How wide should the 2 garden be? 7 yard 2 yards 2 yards 5 4 yards trail mix. How many cups of peanuts are there per cup of trail mix? Jerry is tiling the wall behind his sink. The tiles he s using are square with sides that measure 4 inches. If the area of wall he s tiling is 42 inches long and 29 4 inches high, how many tiles will he need? CONSTRUCTED RESPONSE 7. The following division is being performed using multiplication by the reciprocal. Find the missing numbers. 5 2? = 5 2 i? 0 =? Grade 6 Common Core Assessment Readiness

2 Name Date Class 8. Ida is cutting a -foot wooden board 2 into -foot sections to do some detail 6 work on a model she is building. How many whole -foot sections are there in 6 the -foot wooden board? Explain your 2 answer and show your work. 9. Baruka has gallon of milk left in the 2 fridge. a. How many 5 -gallon (0-ounce) 64 servings of milk does she have left? Show your work. b. If she drinks 0 ounces of milk a day, how many days of milk does she have left? Explain. 0. Juan was presented with the following problem on a math test: Divide 4 by 5 7. Show your work. His work is shown below. What was Juan s error? Correct his work and state the correct quotient = 5 7 i 4 = Consider the division statement a. Describe a real world situation that might involve this expression. b. Find the quotient. c. Interpret the quotient in terms of the situation you described in part a. Grade 6 4 Common Core Assessment Readiness

3 Name Date Class 6.NS.2 SELECTED RESPONSE Select the correct answer.. Divide R27 7 R 7 2. Divide R4 4 4 R. An art teacher has 92 containers of paint for 7 students. If the teacher wants to provide each student with an equal number of containers, how many containers will be left over? A local theater can seat 2,254 people. The seats are arranged into 98 rows. Each row has the same number of seats. How many seats are there in each row? Select all correct answers. 5. The event staff for a local concert hall has 7 tickets to sell. If they sell all of the tickets at the same price, they will have $48. Which of the following people have enough money to buy a ticket? Celia has $4.50. Louis has $7.00. Jan has $6.50. Nicola has $6.00. Chuck has $5.00. CONSTRUCTED RESPONSE 6. A skyscraper with 02 floors is,26 feet tall. Each floor is the same height. How tall is each floor? Show your work. 7. An apple orchard harvested,584 apples and separated them evenly into 2 bags. a. How many apples are in each bag? b. If 56 apples were placed in each bag instead, how many bags would be left over? 8. A movie streaming service charges its customers $5 a month. Martina has $98 saved up. Will she have any money left over if she pays for the maximum amount of months she can afford? Explain. Grade 6 5 Common Core Assessment Readiness

4 Name Date Class 9. Maurice says that is 6 with a remainder of 87. a. Without seeing his work, how can you tell Maurice divided incorrectly? b. Maurice is correct about this fact: = 079. Explain how you can use that fact to find the correct quotient and remainder for without actually dividing. Then find the quotient. 0. The administrator of the school is dividing 42 students into 8 groups to do a teambuilding exercise. One of the guidance counselors says that the exercise will be most effective if there are 7 or fewer students in a group. a. Explain why the administrator s plan is not as effective as it can be. b. How many groups should there be? Will all the groups have the same number of students? Explain.. a. Find 7, 8, and 9. b. Without dividing, what is the quotient of 20? Use the pattern you found in the first three problems to explain you answer. c. According to the pattern, 0 should be 9 with a remainder of. Explain why that is incorrect and find the correct quotient. Grade 6 6 Common Core Assessment Readiness

5 Name Date Class 6.NS. SELECTED RESPONSE Select the correct answer.. Add Subtract Multiply , Divide ,425 Match each multiplication expression with its product A 76, , CONSTRUCTED RESPONSE B 7,62.6 C,762.6 D E F.7626 G H Elsa has $45.78 in her savings account and $2.8 in her wallet. a. How much money does Elsa have? b. If Elsa puts half of the money in her wallet in the bank, how much money will she have in her savings account? Grade 6 7 Common Core Assessment Readiness

6 Name Date Class 4. Mariposa needs a number of 0.25-inch strips of wood for a model she is building. How many of these strips can she get from a inch wooden board? Show your work. 5. Jean-Paul incorrectly states that = His work is shown below. Explain Jean-Paul s mistake and correct his work At a local gas station, regular gasoline sells for $.499 per gallon, while premium gasoline sells for $.879 per gallon. a. Find the difference in price between the two types of gasoline. b. How much does a person save on 5.25 gallons of gas by buying regular instead of premium? Show your work, and round your answer to the nearest whole cent. 7. Shen earns $9.60 per hour at his part-time job. Last month, he worked 7.25 hours the first week, 8.75 hours the second week, 5.5 hours the third week, and 6.75 hours the fourth week. Shen puts half of his paycheck in the bank every other week starting with the first. a. How much money did Shen earn each week? b. How much money did he have in the bank at the end of last month? Show your work. c. How much money did Shen have to spend from his 4 paychecks? Show your work. 8. Pablo wants to buy a steak at the grocery store. He has two options. The first is.7 pounds and costs $9.59. The second is.75 pounds and costs $0.85. Which is the better buy? Explain. Grade 6 8 Common Core Assessment Readiness

7 Name Date Class 6.NS.4 SELECTED RESPONSE Select the correct answer.. Find the greatest common factor of 2 and Find the least common multiple of 8 and Find the greatest common factor of 7 and Find the least common multiple of 6 and Factor out the greatest common factor of the expression below using the distributive property ( + 2) 0(9 + 6) 5(6 + 4) 6(5 + 0) CONSTRUCTED RESPONSE 6. Is it possible to use the distributive property to rewrite as a product of a whole number greater than and a sum of two whole numbers? Explain your answer. 7. Charlie and Dasha are roommates, and they have a dog. If neither of them is home, they hire someone to watch the dog. Charlie must go on business trips every 6 months, while Dasha must go on business trips every 9 months. If they both just got back from business trips, how many months will it be before they need to hire someone to look after the dog again? Explain your answer. 8. Salvatore is making some party favors for his birthday party. He has 96 pencils and 80 boxes of raisins. He wants each party favor to be the same, and he wants to use all of the pencils and raisins. Find the GCF of 96 and 80 to figure out how many party favors he can make. How many pencils and boxes of raisins will be in each one? Grade 6 9 Common Core Assessment Readiness

8 Name Date Class 9. a. What is the LCM of two numbers when one number is a multiple of the other? Give an example. b. What is the LCM of two numbers that have no common factors greater than? Give an example. 0. a. Find the greatest common factor of and 5. b. Find the greatest common factor of and. c. Use your results from parts a and b to make a conjecture about the GCF of any pair of prime numbers.. Consider the sum a. Use the distributive property to rewrite the sum as the product of a whole number other than and a sum of two whole numbers. b. Write the sum as the product of a whole number different from the one you chose in part a and a sum of two whole numbers. c. Can this be done in more than two ways? Explain. 2. A baker has 72 vanilla cupcakes and 80 chocolate cupcakes. She wants to make platters for a party that have both kinds of cupcakes and the same total number of cupcakes on each platter. a. Can the baker make 0 platters of cupcakes with no cupcakes left over? Explain why or why not. b. What is the greatest number of platters she can make? How many of each kind of cupcake will be on each platter? Grade 6 20 Common Core Assessment Readiness

9 Name Date Class 6.NS.5 SELECTED RESPONSE Select the correct answer.. Carlos deposited $28.50 into his bank account after making a $20.00 withdrawal to pay for some school supplies. Represent these situations as signed numbers , , , , In Barrow, Alaska, the northernmost town in the United States, the record high temperature is 79 F, recorded on July, 99. The record low is 56 F below zero, recorded on February, 924. Represent these situations as signed numbers. 79, 56 79, 56 79, 56 79, 56. While on vacation in Australia, Brent and Giselle decide to explore the Great Barrier Reef. Brent decides to go snorkeling near the surface at a depth of 5 feet below sea level. Giselle is an experienced scuba diver and decides to explore a little deeper at 80 feet below sea level. Represent these situations as signed numbers. 5, 80 5, 80 5, 80 5, 80 Select all correct answers. 4. Choose all the situations that can be described with a negative number. The Titanic rests at a depth of about 2,000 feet. The temperature of the photosphere of the Sun is approximately 5,505 C. The height of the Taipei 0 skyscraper in Taiwan is,67 feet. The average high temperature in Antarctica in January is 5 F below zero. The world record for deepest scuba dive is,08 feet. The world record for highest base jump from a building is 2,205 feet above sea level. CONSTRUCTED RESPONSE 5. An object s elevation is its height above some fixed point. The most commonly used point is sea level. The word altitude is used to describe an object s position above sea level, whereas the word depth is used to describe an object s position below sea level. Express each of the following situations as a signed number or zero. a. An airplane at an altitude of 0,000 feet b. A submarine at a depth of,200 feet c. A boat on the surface of the ocean Grade 6 2 Common Core Assessment Readiness

10 Name Date Class 6. In golf, par is the number of strokes an average player should need to complete a particular hole. If a golfer scores under par, the score is reported as a negative number representing the number of strokes less than par. If a golfer scores over par, the score is reported as a positive number. Scoring par exactly is represented by 0. Express each of the following scores as a signed number or zero. a. Margaret completed 8 holes with an overall score of 9 under par. b. Anika completed the last hole with a score of over par. c. Johan completed 9 holes on par. d. Seamus completed the first hole of the tournament with a score of 2 under par. 7. In a standard savings account, the term credit is used to describe a deposit of money into the account. The term debit is used to describe a withdrawal of money from the account. Describe what a positive number, a negative number, and zero mean in this context. 8. Use a signed number to represent each of the following situations. Then describe what 0 represents in the same situation. a. Salazar dives to a depth of 7 feet. b. Nu deposits $6.78 into her bank account. c. Overnight, the temperature drops by 5 F. 9. Write two situations that could be described by each of the following numbers. a. 50 b. 50 Grade 6 22 Common Core Assessment Readiness

11 Name Date Class 6.NS.6a, 6.NS.6b SELECTED RESPONSE Select the correct answer.. Describe the locations of and with respect to 0 on a number line. is to the right of 0, and is to the right of 0. is to the left of 0, and is to the left of 0. is to the left of 0, and is to the right of 0. is to the right of 0, and is to the left of What is the opposite of 2? In which quadrant is, 4 5? Quadrant I Quadrant II Quadrant III Quadrant IV 4. If the point (.9, 2) is reflected across the x-axis, which quadrant will it be in? Quadrant I Quadrant II Quadrant III Quadrant IV 5. Choose the correct sign description of a point in Quadrant I. (+, +) (, ) (+, ) (, +) Select all correct answers. 6. Which pairs of numbers lie on opposite sides of 0 on a number line? 8, 7 0, 0 4, 9 8, 5 2, 2 2, 200 CONSTRUCTED RESPONSE 7. Graph 5, 0, 2, and 4 on the number line. Then, graph their opposites on the same number line Elevation is measured as a distance above or below sea level. Sea level has an elevation of 0 feet. Johanna is standing on a hillside 5 feet above sea level, and Marcus is exploring a cave at an elevation that is the opposite of Johanna s elevation. What is Marcus s elevation? 9. The point (.25, 987) is in Quadrant IV. What kind of reflection would move this point from Quadrant IV to Quadrant III? Which coordinate(s) would change signs? Grade 6 2 Common Core Assessment Readiness

12 Name Date Class 0. To celebrate the 00th anniversary of the opening of their school, the teachers organize a treasure hunt for the students. One of the clues states, Think of the main office as 0 on a number line. You will find the next clue in the room that is the opposite of the teachers lounge. Use the diagram below to determine where the students should go to find the next clue. Explain.. The following graph shows the point ( 4, ). It also shows the points that result when ( 4, ) is reflected across the x-axis and the y-axis. Gym Teachers' Lounge Boys' Room Main Office Girls' Room Science Lab Classroom a. Find the opposites of 8,, and 7. b. Find the opposites of the opposites from part a. c. What do you notice about a number and the opposite of its opposite? 2 2. Consider the ordered pair, y. Find a value of y that places the ordered pair in each quadrant. If it is not possible for the ordered pair to be in a certain quadrant, explain why. a. The point ( 4, ) reflected across the x-axis is ( 4, ). What do you notice about the signs of the coordinates? b. The point ( 4, ) reflected across the y-axis is (4, ). What do you notice about the signs of the coordinates? c. What do you think would happen to the signs of the coordinates of ( 4, ) if it were reflected across the x-axis and then the result was reflected across the y-axis? Explain your answer and provide the resulting point. Grade 6 24 Common Core Assessment Readiness

13 Name Date Class 6.NS.6c SELECTED RESPONSE Select the correct answer.. Where is 2 on a number line? Between and 2 Between and 0 Between 0 and Between 2 and 2. Identify the point on the number line. 4. Describe the process of graphing on a coordinate plane. 4, 5 Starting at the origin, move 4 unit in 5 the positive x-direction. Then, move unit in the positive y-direction. Starting at the origin, move 4 unit in 5 the negative x-direction. Then, move unit in the negative y-direction Starting at the origin, move 4 unit in 5 the positive x-direction. Then, move unit in the negative y-direction.. Identify the coordinates of the point. Starting at the origin, move 4 5 unit in the negative x-direction. Then, move unit in the positive y-direction. Select all correct answers. 5. What numbers are graphed on the vertical number line? ( 2, 4) ( 4, 2) ( 4, 2) (2, 4) Grade 6 25 Common Core Assessment Readiness

14 Name Date Class CONSTRUCTED RESPONSE 6. Graph and label (0.75,.25), (.5, 2), ( 0.25,.75), and (, 0.75). 8. Below is a map showing various places in relation to Carlos s house at the origin. Find the coordinates of the library, the school, the bike shop, and the baseball field. 7. A group of students is participating in a tug-of-war contest. The rope is laid out in a straight line with a knot in the middle. The students are positioned according to the following diagram. The object of the game for both teams is to pull the knot 2 units in their direction. The first team to do so wins the contest. Assume that each team pulls in a straight line. If Holden s side wins, find the final positions of Holden and Marishka. Explain your answers using a number line. 9. a. Graph and label the point ( 2, 8). b. Find the point that represents a reflection of ( 2, 8) across the x-axis. Graph and label the result. c. Find the point that represents a reflection of the result from part b across the y-axis. Graph and label the result. Grade 6 26 Common Core Assessment Readiness

15 Name Date Class 6.NS.7a SELECTED RESPONSE Select the correct answer.. If > 7 and > 7, where are and relative to 7 on a number line? and are both to the right of 7. and are both to the left of 7. is to the right of 7 and is to the left of 7. is to the left of 7 and is to the right of If 4 > 5 and 2 < 5, where are 4 and 2 relative to on a number line? 5 4 and 2 are both to the right of 5. 4 and 2 are both to the left of 5. 4 is to the right of 5, and is to 2 the left of 5. 4 is to the left of 5, and 2 right of 5. is to the. A number x is to the left of 0.2 on a number line. Which inequality describes this situation? x > 0.2 x < < x x < On a number line, a number p is to the right of 8. Which of the following choices describes this situation? 8 > p p < 8 8 > p p > 8 Select all correct answers. 5. Which statements are equivalent to the inequality 2.5 < 8? 2.5 is to the left of 8 on a number line. 8 is to the right of 2.5 on a number line. 8 is to the left of 2.5 on a number line. 2.5 is less than is to the right of 8 on a number line. 8 < > is less than 2.5. CONSTRUCTED RESPONSE 6. Describe the positions of 0 and 7 relative to each other on a number line in two different ways, given that 7 > < x and x < 0,000. Is x between 0.00 and 0,000, to the left of 0.00, or to the right of 0,000? Explain your reasoning. Grade 6 27 Common Core Assessment Readiness

16 Name Date Class 8. Look at the following inequalities.,000,000 > 7 2,0< 7 2,22> 7 2,,000 < 7 2, 8 9 < 7 2, 7 2 > 0.2, 7 2 < 2, 7 2 < 4 6 a. Which of the numbers above are to 0. Matthias says that the inequality > 2.2 is true because is to the right of 2.2 on a number line. Helga says that the inequality is true because 2.2 is to the left of on a number line. Who is correct? Explain your answer by graphing and 2.2 on a number line and interpreting the result. the right of 7 2 on a number line? b. Which of the numbers above are to the left of 7 2 on a number line? 9. Consider the three points on the number line. a. Pick any two of the points and write an inequality statement. Explain your answer using the positions of the two numbers relative to each other on the number line. b. Could the relationship between the two numbers you chose be represented in a different way? If so, write the inequality.. Consider the inequality 5.5 < 4. a. Graph the two numbers on a number line. b. Describe the positions of 5.5 and 4 relative to each other on a number line in two different ways. c. Write an inequality using 5.5 and a number to the left of 5.5 on the number line. d. Write an inequality using 4 and a number to the right of 4 on the number line. Grade 6 28 Common Core Assessment Readiness

17 Name Date Class 6.NS.7b SELECTED RESPONSE Select the correct answer.. The thermometer at Bruce s house shows a temperature of 2 F. The thermometer at Zan s house reads 5 F. Which inequality represents this situation? Whose thermometer shows a warmer temperature? 2 F < 5 F; Bruce s thermometer shows a warmer temperature. 2 F < 5 F; Zan s thermometer shows a warmer temperature. 2 F > 5 F; Bruce s thermometer shows a warmer temperature. 2 F > 5 F; Zan s thermometer shows a warmer temperature. 2. Marco and Randy decide to have a foot race on a local field. Marco can maintain a speed of 8 miles per hour, while Randy runs at 6 miles per hour. Which inequality represents this situation? Who is faster? 8 mph > 6 mph; Marco is faster. 8 mph > 6 mph; Randy is faster. 8 mph < 6 mph; Marco is faster. 8 mph < 6 mph; Randy is faster.. In a cooking class, each student needs 2 cup of sugar for a recipe. Zach has cup of sugar at his cooking station, 4 while Suzanne has cup at her cooking 2 station. Who has enough sugar to make the recipe? Zach has enough sugar. Suzanne has enough sugar. Zach and Suzanne both have enough sugar. Neither Zach nor Suzanne has enough sugar. 4. Anthony has $5.4 in his savings account, Maxine has $54.78, Rodolfo has $54.98, and Nicola has $5.29. Who has saved the most money? Who has saved the least? Maxine has saved the most money, and Anthony has saved the least. Maxine has saved the most money, and Nicola has saved the least. Rodolfo has saved the most money, and Nicola has saved the least. Rodolfo has saved the most money, and Anthony has saved the least. Select all correct answers. 5. Jack needs a piece of wood at least inch long for some detail work on a 6 project he is working on. Which of the following lengths of wood would meet his requirements? 2 inch 7 8 inch 4 inch 27 2 inch 5 8 inch CONSTRUCTED RESPONSE 6. A recipe calls for 2 cup strawberries, 4 cup sugar, 2 cup walnuts, and 4 cup flour. Order the amounts from least to greatest. Which ingredient does the recipe require the least amount of? Grade 6 29 Common Core Assessment Readiness

18 Name Date Class 7. While climbing a mountain, Chuck and Marissa decided to take separate trails and meet at the peak. Chuck took the easier trail and was at an elevation of about 425 feet after an hour. Marissa took the more advanced trail and made it to 550 feet in an hour. Marissa started to get tired and was only able to climb 50 more feet in the next hour. Since Chuck took the easier trail, he was able to climb an additional 50 feet in the second hour. Write inequalities that express their locations on the mountain after hour and after 2 hours. Who was at a higher elevation after 2 hours? 8. Sally plants four flowers in her garden and measures their heights (Height ). One month later, she measures their heights again (Height 2). Which flower grew the most? Show your work. Flower Height Height in. 7 4 in in in in. 8 4 in. 9 6 in. 7 2 in. 9. The record low temperatures for three towns in Alaska are given in the table below. Write three inequalities using three different pairs of temperatures. Which of the three towns has the highest record low? Town Record Low Anchorage 4 F Barrow 56 F Juneau 22 F 0. Sam and Nima have part-time jobs for the summer. Over the last three weeks, Sam has made deposits of $40.25, $58.50, and $28.40 into his savings account. During the same time, his sister Nima has deposited $60.85, $20.00, and $62. into her savings account. a. Write an inequality that compares Sam s total deposits with Nima s total deposits. Who deposited more money? b. Sam and Nima both make withdrawals from their accounts. Nima withdraws $7.28. After the withdrawals, Sam has more money in his account than Nima does. What is the largest amount Sam could have withdrawn for this to be true? Explain your reasoning. Grade 6 0 Common Core Assessment Readiness

19 Name Date Class 6.NS.7c, 6.NS.7d SELECTED RESPONSE Select the correct answer.. Marlene is about to write a check for $0.48 to pay for groceries. When she subtracts the amount of the check from her account balance, she sees that the new balance would be $ Rather than overdraw her checking account, Marlene asks the cashier to remove some items. For Marlene to be able to pay by check without overdrawing her account, what is the minimum value of the items the cashier must remove? $0.48 $28.80 $28.80 $ Which of the following pairs of numbers have the same absolute value?, 0., 2 2 0, 4, 40. How do the numbers and 2 compare? How do their absolute values compare? is greater than 2, but 2 has the greater absolute value. 2 is greater than, but has the greater absolute value. is greater than 2, and has the greater absolute value. 2 is greater than, and 2 has the greater absolute value Which is greater, or 2? Which number has the greater absolute value? is greater than, but has the greater absolute value is greater than, but has the greater absolute value is greater than, and has the greater absolute value is greater than, and has the greater absolute value. Select all correct answers. 5. Which numbers have an absolute value of 2? CONSTRUCTED RESPONSE 6. Identify the pairs of numbers on the number line that have the same absolute value Grade 6 Common Core Assessment Readiness

20 Name Date Class 7. Both Vince and Betty use their debit cards to make purchases. After their purchases, Vince s checking account balance shows a transaction of $25.00, while Betty s shows $8.25. Who spent more money? Justify your answer by writing an inequality. 0. In a town, Talbot Street is the main commercial center. The number line shown represents Talbot Street, where each unit represents 00 feet. 8. Find two numbers a and b with the following properties. a. a > b, a > b b. a > b, a < b c. a > b, a = b 9. Monica is hiking in California s Death Valley. Along her route, she sees a sign that says 282 feet below sea level. Elevation is the height above or below a fixed point. Positive elevations indicate heights above the point, and negative elevations indicate heights below the point. a. What is the elevation of the sign relative to sea level? Explain. b. How far up or down must Monica hike from the sign to reach sea level? Explain. a. Yvette and Naomi are at the intersection of Second Street and Talbot Street. If Yvette goes to the grocery store and Naomi goes to the fruit stand, who travels farther from Second Street? Justify your answer. b. Anzelm is at the intersection of First Street and Talbot Street. How many feet is Anzelm from Second Street? Justify your answer.. Suppose a and b are two negative numbers. If a > b, is it possible that a > b? Explain your answer, using a number line and examples as needed. Grade 6 2 Common Core Assessment Readiness

21 Name Date Class 6.NS.8 SELECTED RESPONSE Select the correct answer.. On a coordinate plane, point A is located at ( 5, ). To get to point B, move 8 units to the right, 6 units down, and unit to the left. What are the coordinates of point B? CONSTRUCTED RESPONSE 4. Jerry and Meena are riding their bicycles through the city to meet at the park, as shown on the coordinate plane. On the coordinate plane, north is in the positive y-direction, and unit represents city block. Jerry starts at the point (2, 5) and rides north toward the park at the point (2, ). Meena starts at east of the park at the point (5, ) and rides west toward the park. How far does each person travel to reach the park? ( 2, 9) ( 2, ) (2, ) (2, 9) 2. What is the distance between point A at ( 7, 5) and point B at (2, 5)? North is the positive y-direction on a coordinate plane, and unit on the plane represents foot. A soccer ball is kicked directly east from point (, 4). The ball travels a horizontal distance of 2 feet through the air and rolls an extra 4 feet. Where does the ball stop? (4, 4) ( 40, 4) (20, 4) (, 4) 5. Point A is located at (, ), point B is located at (, 4), and point C is located at (, ) on a coordinate plane. a. What is the distance between points A and B? b. What is the distance between points A and C? Grade 6 Common Core Assessment Readiness

22 Name Date Class 6. Ravel wants to build a fence around his garden. The shape of his garden is shown on the coordinate plane, where each unit represents foot. Use absolute values to find the length of each section of fence. How many feet of fence does Ravel need? Show your work. 7. Jamie s house is in the center of town, at point (0, 0). He is doing some errands in town and stops at the other four labeled points on the coordinate plane. One unit on the coordinate plane represents block. He travels 4 blocks to his first stop. His second stop is 7 blocks from his first stop. He can only travel on the sidewalks, which are represented by the grid lines. a. Where did Jamie go first? List all possible answers. Justify your answers. b. Where did Jamie go second? List all possible answers. Justify your answers. Grade 6 4 Common Core Assessment Readiness

23 6.NS. Answers. C 2. D. C 4. B 5. C 6. C 7. 0,, 8 point for each number 8. There are 4 whole -foot sections = 2 i 6 = 76 6 = is not a whole number. However, 9 since 44 9 = 4 8, there are 4 whole 9 -foot sections, with some left over that 6 Ida cannot use. point for answer; point for work; point for explanation 9. a = 2 i 64 5 = 64 0 = 2 5 = servings b. Since 2 5 = 6 2, she has enough milk 5 for 6 full days. a. point for answer; point for work b. point for answer; point for explanation 0. Juan set up the problem incorrectly as In the problem, is the dividend 4 and 5 is the divisor. The correct work is = 4 i 7 5 = The quotient is points for error description; point for corrected work; point for quotient. a. Possible answer: Sally requires several rectangular pieces of construction paper for an art project. The pieces need to have an area of square inch. She has several strips 4 of paper left from the last art project that are each 7 inch wide. How long 6 should each piece be cut to meet her requirements for this project? b = 4 i 6 7 = 4 7 c. Possible answer: Sally should cut the strips into lengths of 4 7 inch. a. 2 points for reasonable situation b. point c. point for correct interpretation of answer according to part a Grade 6 Teacher Guide 7 Common Core Assessment Readiness

24 6.NS.2 Answers. D 2. B. B 4. C 5. B, C, D The floors are feet tall. point for work; point for answer 7. a. 2 apples b. 48 bags a. point b. 2 points 8. Yes; Martina has enough money to pay for 6 months of the service. She will have $8 left over. point for the answer; point for explaining the remainder in the context of the problem; point for explaining the quotient in the context of the problem 9. a. The remainder, 87, is larger than the divisor, 62, so 6 is not the maximum number of times 62 can go into 079. b. Maurice found a quotient that is too small, so increase 6 by in the expression , subtract 62 from 87, and see if that gives a remainder of less than 62. If you multiply 62 by 7, you get 054, which is 25 less than the dividend of 079. The correct quotient is 7 with a remainder of 25. point for the error; point for the correct answer; points for explaining an appropriate method that doesn t involve division 0. a. The administrator s plan will not be as effective because there will be 42 8 = 9 students on each team. This is more than 7 students per team. b. Divide the number of students by There will be 49 teams. The teams will not all have the same number of students because there will be 48 teams of 7 students and team of 6 students. a. 2 points b. point for stating there will be 49 teams; point for stating the teams do not all have the same number of students; point for stating why Grade 6 Teacher Guide 8 Common Core Assessment Readiness

25 . a b. 20 will be 9 with a remainder of. In each of the three quotients, the remainder increased by every time the dividend increased by. c. The remainder cannot be the same as the divisor. The correct quotient is 0. : a. point for each quotient; b. point for the quotient of 20 ; point for explaining the pattern c. point for explaining the error; point for correct quotient Grade 6 Teacher Guide 9 Common Core Assessment Readiness

26 6.NS. Answers. D 2. A. A 4. B 5. F 6. H 7. D 8. B 9. E 0. A. C 2. G. a. $67.6 b. $56.47 a. point b. point ,25 56,250. 8,25 56,250, ,000 25,000 0 Mariposa can get eighteen 0.25-inch strips from the inch wooden board. point for work; point for answer 5. Jean-Paul did not line the numbers up by place value when adding. The easiest way to do this is to line up the decimal points = point for error; 2 points for corrected work; point for answer 6. a. The difference in price is $0.8 per gallon. b. $ = $5.795 $5.80 a. point b. point for answer; point for work 7. a. Shen earned $69.60 the first week, $84.00 the second week, $52.80 the third week, and $64.80 the fourth week. b. Shen had = $6.20 in the bank at the end of last month. c. Shen had earned $ $ $ = $27.20 for the month. He put $6.20 in the bank, so he has $27.20 $6.20 = $20.00 to spend at the end of last month. a. 0.5 point for each amount b. point for answer; point for work c. point for answer; point for work 8. The second steak is the better buy. The first steak costs $7.00 per pound and the second costs $6.20 per pound. point for answer; 2 points for an explanation that includes the prices per pound Grade 6 Teacher Guide 0 Common Core Assessment Readiness

27 6.NS.4 Answers. D 2. B. A 4. B 5. A 6. No, the greatest common factor of 85 and 99 is. The only way to rewrite using the distributive property is to write ( ). point for answer; 2 points for explanation 7. The LCM of 6 and 9 is 8. Therefore, Charlie and Dasha will both be traveling on business trips in 8 months, and so will need to hire someone then. point for answer; point for explanation 8. The GCF of 96 and 80 is 6, so Salvatore can make 6 party favors. Each one will have 6 pencils and 5 boxes of raisins. point for using the GCF to find the number of party favors; point for number of pencils per party favor; point for number of boxes of raisins per party favor 9. Possible answers: a. The LCM is the greater of the two numbers. For example, the LCM of and 9 is 9. b. The LCM is the product of the two numbers. For example, the LCM of 5 and 9 is 45. a. point for answer; point for valid example b. point for answer; point for valid example 0. a. b. c. The only factors of a prime number are and itself, so the greatest common factor of two prime numbers is always. a. point b. point c. 2 points. Possible answer: a = (2 + 5) b = 9(4 + 5) c. This cannot be done in more than two ways because and 9 are the only common factors of 6 and 45 other than. a. point b. point c. point for stating that it cannot be done in more than two ways; point for explanation 2. a. No, she cannot make 0 platters of cupcakes; 72 is not divisible by 0. b. The GCF of 72 and 80 is 8, so she can make 8 platters. Each platter will have 9 vanilla cupcakes and 0 chocolate cupcakes. a. point for answer; point for explanation b. point for number of platters; point for number of vanilla and chocolate cupcakes Grade 6 Teacher Guide Common Core Assessment Readiness

28 6.NS.5 Answers. C 2. C. B 4. A, D, E 5. a. 0,000 b.,200 c. 0 point for each part 6. a. 9 b. c. 0 d. 2 point for each part 7. A positive number indicates money being deposited, so it is a credit to the account. A negative number indicates money being withdrawn, so it is a debit to the account. Zero means that money is neither being deposited nor withdrawn, so there is no change. point for positive number interpretation; point for negative number interpretation; 2 points for interpretation of zero 8. a. 7; 0 represents sea level b. 6.78; 0 represents no deposit or withdrawal c. 5; 0 represents no change in termperature a. point for signed number; point for interpreting 0 b. point for signed number; point for interpreting 0 c. point for signed number; point for interpreting 0 9. a. Possible answers: climbing to a height of 50 feet; depositing $50 into a bank account b. Possible answers: diving to a depth of 50 feet; withdrawing $50 from a bank account a. point for each reasonable answer b. point for each reasonable answer Grade 6 Teacher Guide 2 Common Core Assessment Readiness

29 6.NS.6a, 6.NS.6b Answers. D 2. A. D 4. B 5. A 6. B, C, E 7. The opposite of 5 is 5. The opposite of 0 is 0. The opposite of 2 is 2. The opposite of 4 is point for each nonzero point; point for zero and its opposite (they are the same point) 8. 5 feet point for the correct number; point for including units 9. A reflection across the y-axis would move the point to Quadrant III. The x-coordinate would change from positive to negative. point for identifying the transformation; point for identifying sign change 0. The students should go to the science lab. The teachers lounge is represented by 2 on the number line. The opposite of 2 is 2, so the next clue is in the room represented by 2 on the number line, the science lab. 2 points for answer; 2 points for the explanation. a. 8,, and 7 b. 8,, and 7 c. The opposite of the opposite of a number is the same as the original number. a. 0.5 point for each opposite b. 0.5 point for each opposite c. point 2. Quadrant I: Possible answer: y = Quadrant IV: Possible answer: y = 2 The ordered pair, y cannot be in Quadrant II or Quadrant III because the x-coordinate is positive. point for Quadrant I value; point for Quadrant IV value; point for stating the point cannot be in Quadrant II or Quadrant III; point for explanation. a. The y-coordinate of the point ( 4, ) has the opposite sign of the y-coordinate of ( 4, ). b. The x-coordinate of the point (4, ) has the opposite sign of the x-coordinate of ( 4, ). c. A reflection across the x- and then the y-axis would result in a change to the signs of both coordinates. If ( 4, ) were reflected across the x-axis and then that point was reflected across the y-axis, the resulting point would be (4, ). a. point for noting the sign change b. point for noting the sign change c. point for noting the sign changes; point for the coordinates of the result Grade 6 Teacher Guide Common Core Assessment Readiness

30 6.NS.6c Answers. C 2. B. D 4. A 5. B, D, F, G The coordinates of the library are ( 4, ). The coordinates of the school are (, 4). The coordinates of the bike shop are (4, ). The coordinates of the baseball field are (, ). point for each ordered pair 9. The points are graphed and labeled below. point for each graphed and labeled point 7. Holden will be at 5 and Marishka will be at. Holden s side pulls the knot 2 units in the negative direction, so all the students move 2 units in the negative direction, as shown on the number line. a. point for graphed and labeled point b. point for coordinates of point; point for graphed and labeled point c. point for coordinates of point; point for graphed and labeled point point for Holden s position; point for Marishka s position; 2 points for correct number line and labels Grade 6 Teacher Guide 4 Common Core Assessment Readiness

31 6.NS.7a Answers. A 2. C. B 4. D 5. A, B, D, G 6. 0 is to the left of 7 on a number line. 7 is to the right of 0 on a number line. point for each answer 7. x is between 0.00 and 0,000. Since 0.00 < x, x is to the right of 0.00 on a number line. Since x < 0,000, x is to the left of 0,000. Since x is to the right of 0.00 and to the left of 0,000, x is between the two numbers. point for answer; 2 points for explanation 8. a., 2 b.,000, 4, 22, and,000, , 0, and a. 0.5 point per number b. 0.5 point per number 9. a. Possible answer: 2.25 < 2; 2.25 is to the left of 2 on the number line, so 2.25 is less than 2. b. Yes; Possible answer: 2 > 2.25 a. point for correct inequality; point for explanation b. point for correct answer; point for inequality 0. They are both correct. As shown on the number line, is to the right of 2.2. It is also correct to say that 2.2 is to the left of. point for the answer; point for the explanation; point for each graphed number. a. b. 5.5 is to the left of 4; 4 is to the right of 5.5. c. Possible answer: 6 < 5.5 d. Possible answer: 4 < a. 0.5 point for each graphed number b. 0.5 point for each description c. point d. point Grade 6 Teacher Guide 5 Common Core Assessment Readiness

32 6.NS.7b Answers. C 2. A. A 4. C 5. B, D 6. 4 cup, 2 cup, 2 cup, 4 cup The recipe requires a smaller amount of sugar than the other ingredients. 2 points for correctly ordered list of values; point for stating the recipe requires the least amount of sugar 7. Possible answer: hour: 425 ft < 550 ft; 2 hours: 775 ft > 700 ft Chuck was at a higher elevation after 2 hours. point for each inequality; point for who was at a higher elevation after 2 hours 8. Flower change in height: in Possible answer: 4 F < 22 F, 4 F > 56 F, 22 F > 56 F Juneau has the highest record low. point for each inequality; point for stating Juneau has the highest record low 0. a. Sam deposited $27.5 and Nima deposited $ An inequality that compares these total deposits is $27.5 < $42.98 (or $42.98 > $27.5). Nima deposited more money. b. Nima withdrew $7.28, so she has a total of $42.98 $7.28 = $ If Sam has more money in his account, he must have at least $05.7. That means the largest withdrawal he could make is $27.5 $05.7 = $2.44. a. point for the total deposits, point for a correct inequality b. point for correct answer; 2 points for appropriate explanation Flower 2 change in height: 2 in. Flower change in height: Flower 4 change in height: 5 in. 6 in. 6 From least growth to most growth, the order is Flower 2, Flower 4, Flower, and Flower. Flower grew the most in one month. 0.5 point for each height difference; 2 points for ordered list; 0.5 point for answer Grade 6 Teacher Guide 6 Common Core Assessment Readiness

33 6.NS.7c, 6.NS.7d Answers. C 2. B. B 4. D 5. B, F and 2.25 and point for each pair of numbers 7. Vince spent more money; $25.00 > $8.25. point for correct answer; point for inequality 8. a. Possible answer: a = 2, b = b. Possible answer: a = 2, b = c. Possible answer: a = 2, b = 2 point for each part 9. a. Since the sign is 282 feet below sea level, the elevation of the sign relative to sea level is 282 feet. b. Since the sign is 282 feet below sea level and the elevation of sea level is 0 feet, Monica must hike up 282 feet to reach sea level. a. point for answer; point for a reasonable explanation b. point for answer; point for a reasonable explanation 0. a. Yvette travels farther from Second Street. The grocery store is = units from 0, and the fruit stand is = unit from 0. Thus, Yvette travels farther from Second Street to the grocery store than Naomi travels from Second Street to the fruit stand. b. On the number line, the location of First Street is 4. Since Second Street is represented by 0 on the number line, the absolute value of the location is the distance. First Street is 4 = 4 units from 0. Since each unit represents 00 feet, Anzelm is 4 00 feet = 400 feet from Second Street. a. point for answer; 2 points for justification b. point for answer; 2 points for justification. If a > b and a and b are both negative, it is not possible for a > b. Since a > b, a is to the right of b on a number line. Since a and b are negative numbers, both a and b are to the left of 0 on a number line. Since the distance from a to 0 must be less than the distance from b to 0 on a number line, a < b.so a > b is not possible. point for answer; points for a reasonable explanation Grade 6 Teacher Guide 7 Common Core Assessment Readiness

34 6.NS.8 Answers. C 2. C. A 4. Meena travels 5 2 = blocks, and Jerry travels 5 = 6 blocks. point for each distance 5. a. ( 4) = 5 units b. = 6 units a. point b. point 6. Starting at point (, 4) and moving clockwise to find each side length: The distance between (, 4) and (4, 4) is 4 = 5 = 5. The length of this section is 5 feet. The distance between (4, 4) and (4, 5) is 4 ( 5) = 9 = 9. The length of this section is 9 feet. The distance between (4, 5) and ( 4, 5) is 4 ( 4) = 8 = 8. The length of this section is 8 feet. The distance between ( 4, 5) and ( 4, ) is 5 ( ) = 4 = 4. The length of this section is 4 feet. The distance between ( 4, ) and (, ) is 4 ( ) = =. The length of this section is feet. The distance between (, ) and (, 4) is 4 = 5 = 5. The length of this section is 5 feet. The perimeter of the garden is the sum of these distances, = 4 feet. Ravel needs 4 feet of fence. 2 points for the lengths of all the sections; point for reasonable work; point for answer 7. a. Jamie went to city hall first. The distance between Jamie s house and city hall is 4 blocks. The distance between Jamie s house and the grocery store is 5 blocks. The distance between Jamie s house and the mall is 5 blocks. The distance between Jamie s house and the doctor s office is 5 blocks. City hall is the only location that is 4 blocks away. b. Jamie went to either the mall or the grocery store second. The distance between city hall and the mall is 7 blocks. The distance between city hall and the grocery store is 7 blocks. The distance between city hall and the doctor s office is 9 blocks. The mall and the grocery store are both 7 blocks away. The mall and the grocery store are the only possible second stops. a. point for answer; point for explanation b. point for each answer; point for explanation Grade 6 Teacher Guide 8 Common Core Assessment Readiness