Standards: MAFS.6.RP.1.1, MAFS.6.RP.1.2 MAFS.6.RP.1.3

Transcription

1 GRADE 6 Week 1 Standards: MAFS.6.RP.1.1, MAFS.6.RP.1.2 MAFS.6.RP.1.3 Chris and Jenny are comparing two similar punch recipes. Each recipe calls for cranberry juice and ginger ale but in different amounts. The tables below show the amounts of cranberry juice and ginger ale for four different quantities of punch. Chris's Punch Cranberry Juice Ginger Ale (in cups) (in cups) Jenny's Punch Cranberry Juice Ginger Ale (in cups) (in cups) Is the proportion of the punch that is cranberry juice the same in each of Chris's recipes given in his table? Explain how you determined your answer. 2. Is the proportion of the punch that is cranberry juice the same in each of Jenny's recipes given in her table? Explain how you determined your answer. 3. Is the proportion of the punch that is cranberry juice the same in Chris's recipes as it is in Jenny s recipes? If not, whose punch is stronger, that is, contains a greater proportion of cranberry juice? Explain how you determined your answer. 4. Brenda wants to buy one of the three cereals listed below. Determine which box is the best buy. Show and explain how you determined this. A. 16 ounces of Frosted Flurries for $3.50 B ounces of Chocolate O s for $2.42 C ounces of Cinnamon Grahams for $ Carlos predicts that his math homework will take him 60 of the total of 75 minutes he has available for homework tonight. At this rate, how many minutes would Carlos spend on math homework out of a total of 100 available minutes? Explain or show your calculations.

2 1 m 2 m m GRADE 6 Week 2 Standards: MAFS.6.NS.1.1, MAFS.6.NS.2.2, MAFS.6.NS.2.3, MAFS.6.NS Jasmine wants to build a meter long garden path paved with square stones that measure 1 4 meter on each side. There will be no spaces between the stones. 1 4 m Paving Stone Garden Path Explain how the model could be used to answer the following question: How many stones are needed for the path? 7. Complete each of the following division problems without a calculator, showing all of your work.. A B Solve the following problems without the use of a calculator. A B Find the greatest common factor of 24 and 36. Show your work and explain how you found your answer. 10. Rewrite in the form a(b + c) where: a is the greatest common factor of 36 and 42 and b and c are whole numbers. Check to be sure your expression has the same value as

3 GRADE 6 Week 3 Standards: MAFS.6.NS.3.5, MAFS.6.NS.3.6, MAFS.6.NS The change in position of the ball during each play of a football game is measured in yards. A. What integer best represents a gain of 5 yards? B. What integer best represents a loss of 15 yards? 12. Part 1: Plot and label each given point. Part 2: Give the coordinates of each point on the coordinate plane. A: (5, 4) B: (-2, 3) 13. Find the coordinate (to the nearest half) of each point on the number line. 14. Death Valley is at an elevation of 282 feet and Tallahassee is at an elevation of 203 feet. A. Use an inequality symbol (> or <) to compare these two elevations. B. Use an inequality symbol to compare the absolute values of these two elevations. Explain what this tells you about Death Valley and Tallahassee. 15. A US Navy submarine, SeaWolf, is 40 feet below sea level while another, Nautilus, is 100 feet below sea level. A. Write integers that describe each submarine s position relative to sea level. SeaWolf Nautilus B. Write an inequality that compares these integers.

4 GRADE 6 Week 4 Standards: MAFS.6.EE.1.1, MAFS.6.EE.1.2, MAFS.6.EE Evaluate, without a calculator, showing every step of your work Jimmy had to list the coefficients for each term in the following expression: 15x 2 x 8 His answer was 15. Did he get it right? Explain. 18. Use the formula F = 9 C + 32 to convert 28 Celsius (C) to degrees Fahrenheit (F) Write an expression to represent each phrase below: A. Nine plus the quotient of w and four B. Seven fewer than the product of three and y 20. The triangle shown below is equilateral, that is, all sides are of equal length. The length of one side is represented by the expression x + 2 so that the perimeter of the triangle can be represented by the expression: (x + 2) + (x + 2) + (x + 2) A. Use the properties of operations to write a second expression that is equivalent to this expression. B. Explain, using properties of operations, why the two expressions are equivalent.

5 GRADE 6 Week 5 Standards: MAFS.6.EE.2.5, MAFS.6.EE.2.6, MAFS.6.EE Which value(s) from each set below make the corresponding equation or inequality true? Show how you determined your answers. A = x {5.5, 8.5, 21.3, 34.1} B. x 12 > 4 + x {12, 16, 20, 24} 22. Gavin has ten identical U.S. coins, each under $1.00, in his pocket. The total value of the coins in cents is represented by 10x. A. What does x represent? B. What are the possible values of x? 23. Justin, Nadine, and Mark were competing to see who could score the most points in their basketball game. A. Mark scored three times as many points as Justin. Write an algebraic expression to represent the number of points Mark scored. Explain the meaning of the variable. B. Nadine scored five points more than Mark. Write an algebraic expression to represent the number of points Nadine scored. Explain the meaning of the variable. 24. Melvin wants to go to the school musical. The school auditorium has 1250 seats arranged in three sections. The left section has 375 seats, and the right section has 375 seats. A. Write an equation to find the number of seats in the center section and explain why you wrote the equation the way you did. B. Solve the equation. C. What does the solution to your equation mean? 25. A solar panel generates 3 of a kilowatt of power. A warehouse wants to generate 24 5 kilowatts of power. A. Write an equation to find how many solar panels the warehouse will need on its roof to generate 24 kilowatts of power. B. Find the solution to your equation. C. What does the solution to your equation mean?

6 GRADE 6 Week 6 Standards: MAFS.6.EE.2.8, MAFS.6.EE A farmer is going to plant more than 50 acres in corn this year. If a represents the number of acres planted in corn, write an inequality to describe all possible values of a. 27. High altitude parachute jumps are usually made from an altitude that is no more than 35,000 feet to avoid frostbite from extreme cold. If h represents the height of a jumper, write an inequality to describe all possible values of h. 28. Latasha wants to save money for the purchase of an MP3 player. The equation T = 5w + 10 represents the total amount of money, in dollars, Latasha can save after w weeks. Using the equation, make a table to represent the relationship between the number of weeks and the total amount of money saved, and then graph your data. Number of Weeks (w) Total Saved (in dollars, T) Latasha s Savings 29. Lisa is going on a long-distance bike ride with her friends. They will ride at a rate of 10 miles every hour. A. Write an equation that relates the distance, D, that Lisa travels to the number of hours, h, she has ridden. B. Identify and describe the independent and dependent variables in your equation. 30. The inequality p > 15,000 feet describes the altitudes at which a civil aircraft must provide everyone with supplemental oxygen, according to the U.S. Federal Aviation Regulations. A. Graph this inequality. B. List three examples of altitudes at which oxygen use is required. C. How many values does this inequality represent in all? 10,000 20,000

7 GRADE 6 Week 7 Standards: MAFS.6.G.1.1, MAFS.6.G.1.2, MAFS.6.1.3, MAFS.6.G Find the area of the trapezoid by composing into rectangles or decomposing into triangles or other shapes as needed. Show your work neatly and completely. 10 m 16 m (not drawn to scale) 18 m 32. Mr. Moretti wants to cover the walkway around his swimming pool with tile. Determine how many square feet of tile he will need to cover the shaded portion of the diagram. Show your work neatly and completely. 33. The standard size of a construction brick is inches by 8 inches by volume of one brick and explain how you found your answer. inches. Find the 34. Amelia is making a drawing to determine the length of a fence needed to go around her garden. Using the given coordinates, draw an outline of her garden (polygon ABCDEF) and determine the total length of fencing needed. Show all work neatly and completely to justify your answer. A(6, 3) B(6, -4) C(-10, -4) D(-10, 7) E(-5, 7) F(-5, 3)

8 GRADE 6 Week 8 Standards: MAFS.6.SP.1.1, MAFS.6.SP.1.2, MAFS.6.SP.1.3, MAFS.6.SP.2.4, MAFS.6.SP For each of the following, indicate whether or not the question is a statistical question and justify your response. A. How far does our math teacher live from school? B. How far do students in our class live from school? 37. The dot plots below show the distributions of student test scores in two sixth grade math classes. A. Describe the approximate center of each distribution. B. Explain what the center of each distribution means in terms of the students scores on the math test. 38. What is the difference between measures of center and measures of variability? Explain what each tells you about a set of data. 39. The students in Mr. T s classes wrote down the number of minutes they spent doing chores at home over a one week period: 15, 20, 15, 30, 45, 60, 30, 15, 20, 30, 45, 60, 25, 30, 25 Make a dot plot to summarize the data.