Topic 8. Numerical expressions patterns & Relationships. Name. Test Date

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1 Topic 8 Numerical expressions patterns & Relationships Name Test Date

2 1. Celia has listened to 5 of the 14 songs on her new CD. Which equation could Celia use to find s, the fraction of the songs she has left to listen to? A 5 1 s B 5 1 s C 9 1 s D 14 1 s The table below shows how far each skater in a 1-mile race has traveled. Skating Race Skater Ray Scott Theo Walt Distance (miles) If none of the skaters pass each other, which skater will win the race? A Ray B Scott C Theo D Walt 3. A dolphin swims 26 miles per hour. How far could a dolphin swim in 9 hours? A 125 miles B 184 miles C 234 miles D 269 miles Daily Common Core Review Jack needs to finish _ 5 of a school 8 project by Monday. So far he has done 3 _ 8 of the project. a. Draw a rectangle to show Jack s project. Shade the fraction that Jack has finished so far. b. What fraction of the project does Jack have left to do by Monday? Write your answer in simplest form. 5. The giant tortoise can move at speeds of up to 0.17 miles per hour. The top speed for a greyhound is miles per hour. How much greater is the greyhound s speed than the tortoise s? 6. A school needs 75 light bulbs. Bulbs come in packages of 8. How many packages should the school order? D 8 1

3 Variables and Expressions Practice 8-1 For questions 1 through 4, write a numerical expression that represents the word phrase apples divided into 12 baskets 2. 5 more than 3 times 8 3. three times the sum of 13 and nine fewer than 72 divided by 3 For 5 through 7, translate each expression into words (12 2 6) (52 8) Write two different word phrases for the expression 9. Do 5 3 and 3 5 represent the same expression? Explain. 10. Dan is 12 inches taller than Jay. Jay is 54 inches tall. Which expression shows Dan s height? A B C D Explain what the expression (5, ,250) 3 6 means. P 8 1

4 Quick Check Which shows the phrase 15 divided by 5 as a numerical expression? A B C D A teacher needs 6 craft sticks for each student in a class for a project. Which numerical expression shows the total craft sticks needed if there are 36 students? A B C D Writing to Explain There are 6 people in Susanna s family (an even number). They went to an amusement park for the day. a. Admission was $15.00 per person. Write an expression to show the cost of admission for all of them. b. They split into two equal groups while they were at the park. Write an expression to show the number of people in each group. c. All of them but three went on the rollercoaster. Write an expression to show the number of people that went on the rollercoaster. d. They saw another family that had 4 more people in their family than Susanna s family. Write an expression to show the number of people in that family. Q 8 1

5 1. Giancarlo and his friends are getting ready for a costume party. They buy 6 packages of fake noses and 8 packages of masks. Each package contains 2 sets. How many total items did they buy? A 28 B 22 C 20 D 16 Daily Common Core Review Use mental math to find the product Use the Distributive Property to fill in the blanks (400 3 ) 1 ( 3 8) Which answer shows how you can use the Distributive Property to find the product of ? A ( ) 1 (6 3 4) B ( ) 1 (16 3 4) C (16 3 3) 1 (16 3 4) D ( ) 1 (16 3 4) 3. Leslie bikes 10 miles each day for 100 days. How many miles did she bike in all? Write your answer in standard form and in exponential notation. D 8 2

6 Order of Operations Practice 8-2 Use the order of operations to evaluate each expression (8 4 2) ( ) 3 (25 4 5) (7 2 7) 1 (5 3 2) 5 7. (8 4 4) 3 (7 3 0) (6 23) (8 2 3) 5 9. Which is a true statement, or ? Explain your answer. Insert parentheses to make each statement true Insert parentheses in the expression so that: a. the expression equals 32. b. the expression equals (12 1 1) Solve (25 2 7) A 18 B 11 C 6 D Write two order-of-operation problems. Then trade with a classmate and solve the problems. P 8 2

7 Quick Check What is the value of the expression? Use the correct order of operations (6 1 1) A 15 B 69 C 119 D What is the first operation that you will perform when you evaluate this expression? 12 1 (18 2 a) A addition B subtraction C multiplication D division 3. How would you insert parentheses to make the equation true? A (6 2 2) B ( ) C ( ) 5 18 D 2 3 ( ) How can this expression be simplified? Use the correct order of operations a 1 b A 2a 1 2b 2 1 B 2a 1 2b 2 2 C 2a 2 2b 1 3 D 5a 1 2b Writing to Explain Evaluate the expression below step by step, identifying the operations that you perform and the order in which you perform them (5 2 3) Q 8 2

8 1. For the following expression, which operation is performed first? (8 4) A Addition B Division C Multiplication D Subtraction 2. Ted bought a CD for $14.95 and a ball cap for $ Then he purchased a book for $9.95. How much did he spend in all? A $41.85 B $41.95 C $42.85 D $42.95 Daily Common Core Review What is the sum of ? 5. Evaluate this expression [( ) 4 7] A 27 B 30 C 35 D Evaluate: [( ) 1 ( )] Evaluate: 40 4 [9.6 2 ( )] 3. What is the estimated sum of 3, , ,354, rounded to the nearest hundred? A 12,400 B 14,500 C 15,200 D 16,000 D 8 3

9 Evaluating Expressions Practice ( ) [( ) 2 9.5] [(12 2 4) 3 0.6] 4. [( ) 1 ( )] [8.6 2 ( )] [( ) 1 ( )] [( ) 1 ( )] [( ) 1 ( )] ( ) ( ) 11. Keisha bought a new pair of skis for $450. She put $120 down and got a student discount of $45. Her mother gave her 1_ of the 2 balance for her birthday. Which of these expressions could be used to find the amount Keisha still owes on the skis? A C ( ) 4 2 B [450 2 ( ) 4 2] D [450 2 ( )] ( ) 2 [( ) 2 ( )] Give the order of operations a student solving this problem would use to evaluate the expression. Solve. P 8 3

10 1. Evaluate the expression [( ) 2 ( )] A 9.84 B C 36.7 D 49.3 Quick Check Evaluate the expression [( ) 1 ( )]. A 41.5 B C D Which expression has a value of 66? A ( ) (8 1 64) B [( ) 3 ( )] C 16 4 [( ) 1 ( )] 1 64 D [16 4 ( ) (8 1 64)] 4. Writing to Explain Sela simplified the expression 25 3 [6 3 (25 2 8) 1 12] 4 5 and found the answer to be 770. Rudi simplified the same expression and found the answer to be 570. Which girl is correct? Explain. Rudi: Sela: 25 3 [6 3 (25 2 8) 1 12] [6 3 (25 2 8) 1 12] [6 3 (17) 1 12] [ ] [ ] [ ] [114] , , Q 8 3

11 1. Ms. Chang drew a quadrilateral on the board. Which word best describes the figure Ms. Chang drew? Daily Common Core Review Annie tutors 8 students each week. She charges each student $72 a week. How much money, in dollars, does Annie earn each week? A Rectangle B Square C Rhombus D Trapezoid 5. What fraction is modeled by the shaded circles below? Explain how you wrote the fraction. 2. What digit is in the ten thousands place in the number 34,278,915? A 1 B 3 C 5 D 7 3. While doing his math homework, Ramon used 4 6 = 24 to solve a division fact. What division fact could Ramon have been solving? A 24 4 = 6 B 12 4 = 3 C 24 3 = 8 D 18 6 = 3 D 8 4

12 Addition and Subtraction Expressions Practice 8-4 Find a rule and write the missing number for each table r a s b w n Evaluate the expression 15 n when n = Which expression stands for 32 more than a number d? A 32 d B 32 d C 32 + d D 32 d 9. Explain what the variable represents in an addition or subtraction expression. P 8 4

13 1. What is a rule for this table? x ? A x 6 B x + 6 C x 7 D x + 7 Quick Check What is a rule for this table? p ? A p + 19 B p 22 C p + 22 D p How many boys will participate in the track meet if there are 21 girls participating in the meet? Number of girls in the track meet Number of boys in the track meet A 17 B 16 C 15 D Writing to Explain Juliet s Book Shop is having a sale. What expression can Juliet write to figure out sale prices? Explain how you found the expression. Then, use the expression to find the sale prices when the regular prices are $30, $35, and $40. Regular price (p) $10 $15 $20 $25 $30 $35 $40 Sale price $8 $13 $18 $23 Q 8 4

14 1. In standard form, what is four hundred two thousand, nine hundred eighty-one? A 42,981 B 402,981 C 420,981 D 429, The parents of fourth-grade students at Mulcahey School were invited to attend an open house. The parents were put into 6 equal groups. Each group had 31 parents. How many parents attended the open house? Daily Common Core Review There are 14 students in Mrs. McGovern s club, and only half of the students returned their permission slips on time. How many students returned their permission slips on time? 5. Complete the following pattern: Write a rule for the pattern, and explain how you used the rule to complete the pattern. A 25 B 37 C 180 D What mixed number represents the shaded parts of the rectangles? A 1 3_ 8 B 1 1_ 8 C 5_ 8 D 3_ 8 D 8 5

15 Multiplication and Division Expressions Practice 8-5 Find a rule and write the missing number for each table m k z q e l s d Evaluate the expression 48 n when n = Which expression means 3 times a number h? A 3 h B 3 h C 3 + h D 3 h 11. How could you change Exercise 5 so that your rule uses the inverse operation? P 8 5

16 1. What is a rule for the table? s ? A s 28 B s 5 C s 5 D s 7 Quick Check What is a rule for the table? g ? A g + 15 B g 6 C g 6 D g Use the table to find the score a student should receive for answering 19 questions correctly. Number of questions answered correctly Score A 5 B 85 C 92 D Writing to Explain The Ramirez family s favorite snack is yogurt. Mrs. Ramirez buys yogurt in different-sized cases. Number of containers in a case How many days pass before it is all eaten How many days would it take for a case of 25 yogurts to be eaten? Explain your reasoning. Q 8 5

17 1. Which answer shows the algebraic expression for the following phrase? Six times a number plus seven A 6 + n 7 B 6 + 7n C n D 6n Evaluate the following expression. ( ) 19 A 38 B 39 C 45 D Evaluate the following expression for n = n A 17 B 18 C 20 D 22 Daily Common Core Review Molly is writing a paper for her history class. To complete the paper, Molly must spend 2 hours on research and 1 hour writing each page. Use the expression to evaluate the number of hours needed for 10 pages. Use the expression to evaluate the number of hours needed for 19 pages. 5. Evaluate the following expressions for y = y y 6y 51 D 8 6

18 Patterns: Extending Tables Practice 8-6 In 1 3, fill in the tables and find the relationship between the corresponding terms. 1. Rule A: Start with 40. Subtract 5. Rule B: Start with 63. Subtract 5. Start First Term Second Term Third Term Rule A Rule B Rule C: Start with 64. Divide by 4. Rule D: Start with 128. Divide by 4. Start First Term Second Term Third Term Rule C 64 Rule D Rule G: Start with 3. Multiply by 2. Rule H: Start with 6. Multiply by 2. Rule G Rule H Start First Term Second Term Third Term In 4 7, find the relationship between the corresponding terms in each rule. 4. Rule A: Start with 47. Subtract 3. Rule B: Start with 59. Subtract Rule A: Start with 9. Add 4. Rule B: Start with 22. Add Rule A: Start with 6. Multiply by 2. Rule B: Start with 18. Multiply by Rule A: Start with 64. Divide by 2. Rule B: Start with 256. Divide by 2. P 8 6

19 For 1 2, use the table. Quick Check 8-6 Start First Term Second Term Third Term Rule A Rule B What is the rule used for Rule B? A Start at 0. Add 2. B Start at 2. Add 6. C Start at 0. Add 6. D Start at 0. Multiply by What is the relationship between the corresponding terms in Rules A and B? A Rule B is always 4 greater than Rule A. B Rule A is always 3 times as much as Rule B. C Rule A is always 4 greater than Rule B. D Rule B is always 3 times as much as Rule A. 3. Writing to Explain Sammy is counting the number of wings on the bees in his uncle s beekeeping hive. Sammy makes a rule to help him: Start with 0. Add 2 for each bee. What rule could he use for counting the legs? Remember that bees have 6 legs. How are the corresponding terms in these sequences related? Q 8 6

20 1. Which answer shows the operation that should be done first in the following expression? 15 (16 4) (5 2) A addition B subtraction C multiplication D division 2. Using the order of operations, which answer shows the correct value of the following expression? 22 (8 5) (12 3) Daily Common Core Review Pam s suitcase can weigh up to 50 pounds. She is planning to pack 5 school books, each of which weighs 2 pounds. She will also pack 3 notebooks weighing 1 pound each, and 6 boxes of golf balls weighing 2 pounds each. Her clothing weighs a total of 16 pounds. Write and evaluate an expression to show how many pounds Pam has to pack. A 10 B 34 C 40 D 100 Will Pam s suitcase be under the 50-pound weight limit? 3. Which answer is correct? (45 16) 12 A 41 B 27 C 19 D Insert parentheses to make each statement true D 8 7

21 Problem Solving: Use Reasoning Practice Christina collects stamps. She has 47 stamps in all. She has 20 stamps from Europe. The number of African stamps is 2 times the number of Asian stamps. How many stamps from each of these three continents does she have? Use reasoning to write this as a numerical expression. 2. Write a problem that can be solved by acting it out and using reasoning. 3. A public pool opened for the summer. A total of 246 people came swimming over the first 3 days it was open. On the first day, 79 came to swim. On the second day, 104 people swam. How many people swam on the third day? 4. Marissa earned $480 in the summer. If she earned $40 a week, how many weeks did she work? A 48 B 12 C 10 D 9 5. How could you use cubes to help you write an expression and model the problem? P 8 7

22 Quick Check Mike has 15 coins in his pocket. One third of the coins are dimes and the rest are nickels. How much money does he have? You can use reasoning to solve the problem. A $0.50 B $0.75 C $1.00 D $ Linda has 50 pages in her scrapbook. She used 8 pages for things about her family. Two-thirds of the remaining pages are about her friends, and the rest are blank. How many blank pages remain? You can use reasoning to solve the problem. A 12 B 14 C 21 D A car dealership has 64 vehicles on its lot. Of the total, _ 1 are pickup trucks 4 and there are twice as many cars as there are SUVs. How many of each type of vehicle are on the lot. You can use reasoning to solve the problem. A 16 pickup trucks, 32 cars, 16 SUVs B 24 pickup trucks, 32 cars, 16 SUVs C 16 pickup trucks, 16 cars, 32 SUVs D 22 pickup trucks, 28 cars, 14 SUVs 4. Writing to Explain There are 42 houses on Main Street. Three less than half of the houses are made of brick. Of the rest of the houses, _ 3 are painted white and 4 the rest painted other colors. Explain how you could use objects to act out this problem. Then use reasoning to solve the problem and fill in the table. House Number Total 42 Brick White Other colors Q 8 7

Name. 4. Lilly completed a math project worth 200 points. She earned all but 13 points. How many points did she earn?

Name. 4. Lilly completed a math project worth 200 points. She earned all but 13 points. How many points did she earn? Daily Spiral Review 6-1 1. The model is shaded to represent a fraction. Which model below shows an equivalent fraction? A B C D 2. Jimmy s basketball team scored 35 points in the last game. There are 7