Monroe Township School District Monroe Township, New Jersey Preparing for Middle School 6 th Grade *PREPARATION PACKET* **MODIFIED for RESOURCE STUDENTS** Summer 2014 ***SOLVE THESE PROBLEMS WITHOUT THE USE OF A CALCULATOR AND SHOW ALL WORK*** You will be responsible for handing in the completed packet with all work shown ON THE FIRST DAY OF SCHOOL. The problems here are very representative of the types of items you will need to have mastered BEFORE 6 th Grade Math so we strongly encourage that you include this packet in your summer festivities! Good luck and enjoy! J Name: REVIEW: COMMON CORE STATE STANDARDS (CCSS): Grade 5 Operations and Algebraic Thinking 5.OA o Write and interpret numerical expressions o Analyze patterns and relationships Number and Operations in Base Ten 5.NBT o Understand the place value system. o Perform operations with multi- digit whole numbers and with decimals to hundredths. Number and Operations Fractions 5.NF o Use equivalent fractions as a strategy to add and subtract fractions. o Apply and extend previous understandings of multiplication and division to multiply and divide fractions Measurement and Data 5.MD o Convert like measurement units within a given measurement system. o Represent and interpret data. o Geometric measurement: understand concepts of volume and relate volume to multiplication and to addition. Geometry 5.G o Graph points on the coordinate plane to solve real- world and mathematical problems o Classify two- dimensional figures into categories based on their properties. Page 1
PREVIEW: COMMON CORE STATE STANDARDS (CCSS): Grade 6 Ratios and Proportional Relationships 6.RP o Understand ratio concepts and use ratio reasoning to solve problems The Number System 6.NS o Apply and extend previous understandings of multiplication and division to divide fractions by fractions. o Compute fluently with multi- digit numbers and find common factors and multiples. o Apply and extend previous understandings of numbers to the system of rational numbers. Expressions & Equations 6.EE o o Apply and extend previous understandings of arithmetic to algebraic expressions. Reason about and solve one- variable equations and inequalities. Geometry 6.G o Solve real- world and mathematical problems involving area, surface area, and volume. Statistics and Probability 6.SP o Develop understanding of statistical variability. o Summarize and describe distributions. Page 2
Operations and Algebraic Thinking 1. Simplify the following numerical expression. (Remember PEMDAS: Parentheses, Exponents, Multiply and Divide left to right, Add and Subtract left to right) (12 4) + 2 3 2. Complete the next three terms in the pattern: 0, 17,,, ANSWER: 3. Complete the table. Write a rule for completing the table. 3 18 5 30 8 48 54 72 ANSWER: (rule) 4. Amy is 7 years younger than her brother. Her brother is 23. Write a numerical expression (math sentence) to show Amy s age and solve. Page 3
5. The table below shows the number of gallons of gasoline in the gas tank each second as it fills. If the pattern continues, how much gas will be in the tank after 6 seconds? Seconds Pumping Gasoline Gallons in the Tank 1 2 3 4 5 6 0.15 0.30 0.45 0.60 6. Which expression shows how to solve 7 63 with mental math. (Hint: Check by finding the product). A. (7 6) + (7 3) B. (7 60) + (7 3) C. (7 60) + (7 30) D. (7 6) + (7 30) 7. Bob has a certain number of books, b. The number of books Jim has is 4 times as great. Write an expression that can be used to determine the number of books Jim has? (Hint: Write a number sentence) Number and Operations in Base Ten 8. Write the number eight and twenty-eight thousandths in standard form. Page 4
9. Order the following from greatest to least. Be sure to use semicolons (;) in between each number. 27.041 27.014 27.104 27.410 10. Write the following in standard form. (3 x 100) + (7 x 10) + (2 x 1) + (.5) + (.08) 11. Write 10 4 in standard form. 12. Insert >, < or = to make the following statement true. 10.9 10.24 13. Describe the rule for the following pattern from left to right. Complete the next three terms in the sequence. 120,000; 12,000; 1,200; 120; ; ; ANSWER:_(rule) (next 3 terms) Page 5
14. Write 3,409.7 in expanded form. (Example 500 + 20 + 6 = 526) 15. Write the following words in numerals: one hundred five and twenty-nine thousandths 16. Round 273.452 to the nearest tenth 17. What is the value of the underlined digit in the number below? (Remember that value does not mean place). 57, 035, 189 18. Megan s check for lunch at the Luigi s was $13.87. She paid with a 20 dollar bill. How much change did she receive? Page 6
Find the sum, difference, product or quotient. Show all work. 19. 3,684 12 = 20. 5,906 87 = 21. 27 + 8.7 = 22. 0.39 0.07 = 23. 68.64 2.4 = 24. Use mental math to find the value of 54.6 1,000. Page 7
Number and Operations Fractions 25. On Monday Katie works 1 2 2 hours and on Wednesday she works hours. How many more hours does she work on Wednesday? Write an equation to represent the problem and use it to answer the question. 2 3 3 26. It takes 3 4 cup of ice cream and 1 cup milk to make a milkshake. How 2 many cups is that altogether? Write an equation to represent the problem and use it to answer the question. 27. Jimmy lives 5 of a mile from school. Billy lives twice as far as Jimmy. 6 How far does Billy live from school? Write an equation to represent the problem and use it to answer the question. 28. Three students shared a pizza. One student ate 1 8 of the pizza, another ate 1 4 of the pizza and the third student ate the rest. What fraction of the pizza was the third student s portion? ANSWER: Write an equation to represent the problem and use it to answer the question. Page 8
29. 1 6 of the seats in the auditorium were reserved for parents and 1 8 seats was reserved for the teachers. of the What fraction of the seats was reserved altogether? What fraction was left for general admission? Find the sum or difference. Show all work. Simplify if necessary. 30. 2 3 1 = 3 31. 1 3 + = 5 4 32. 7 2 1 = 8 3 33. 5 8 3 = 9 34. 3 2 3 + 1 = 4 3 Page 9
35. 4 1 2 1 = = 5 4 Measurement and Data 36. Leah is 52 inches tall and Carol is 4 feet 7inches tall. Which girl is taller? How much taller is she? (Remember: 12 inches = 1 foot) ANSWER(who) (by how much) 37. Mike s beach towel is 1 yard long. What measure is equivalent to 1 yard, in inches? (Remember 12 inches = 1 foot) 38. What is the volume of the rectangular prism shown below?. = 1 cubic foot 39. Dan hiked a 13-kilometer trail at Great Peak. How many meters did Dan hike? Page 10
40. Tyler has a container with 2.95 liters of laundry detergent. How many milliliters of detergent are in the container? Geometry 41. Which quadrilateral has two acute angles, two obtuse angles, and two pairs of opposite parallel sides?. A B C D E 42. Plot the following points on the coordinate plane: A (2,1) B (2,4) C (3,4) D (3,1) Page 11
43. Use the clues below to identify the figure. My figure has four sides. My figure has opposite sides that are parallel. All of my figure s sides are congruent. My figure has two obtuse angles and two acute angles. 44. A B C G D F E I H Write the letter of all the shapes above that fit into each of the categories below. (You may use a shape more than once.) Contain at least 1 right angle Parallelogram Quadrilateral Rectangle Page 12
45. The temperature in Michelle s house from 9:00 a.m. to 7:00 p.m. is recorded in the table below. Plot the points on the graph. Remember to label the graph with number increments that are reasonable. Time Temperature 9 am 65 11 am 60 1 pm 63 3 pm 68 TEMPERATURE 5pm 65 7 pm 60 TIME What was the approximate temperature in Michelle s house at 2:00 p.m.? What was the difference in temperature from 1:00 p.m. to 3:00 p.m.? Page 13