Grade Common Core Math

Transcription

1 th 5 Grade Common Core Math Operations and Algebraic Thinking Printable Review Problems

2 Standards Included: -Use parentheses, brackets, or braces in numerical expressions, and evaluate expressions with these symbols. -Write simple expressions that record calculations with numbers, and interpret numerical expressions without evaluating them. -Generate two numerical patterns using two given rules. Identify apparent relationships between corresponding terms. Form ordered pairs consisting of corresponding terms for two patterns, and graph the ordered pairs on a coordinate plane.

3 Name: 5 th Grade Common Core Math Date: Show all of your work 1.) Which expression can be used to represent the phrase: four less than a number? 2.) The expression 6n can represent which of the following phrases? A.) d 4 B.) 4 d C.) d + 4 D.) 27 4 A.) 6 times n students B.) n students divided into groups of 6 C.) 6 students divided into n groups D.) 6 less than n students 3.) If z + 7= 19, then what is the value of (z)? 4.) Evaluate the expression: 9 + (16 3) = 5.) Which rule can be used to find the output numbers in this table? Input Output A.) divide the input number by 11 B.) add 24 to the input number. C.) multiply the input number by 9 D.) divide the input number by ) Which variable expression can be used to represent: 13 more than the quotient of 6 and a number x? A.) 13 6x B.) x C.) (6 x) + 13 D.) (6 x)

4 5 th Grade Common Core Math Answer Key 1.) Which expression can be used to represent the phrase: four less than a number? 2.) The expression 6n can represent which of the following phrases? A.) d 4 B.) 4 d C.) d + 4 D.) 27 4 A.) 6 times n students B.) n students divided into groups of 6 C.) 6 students divided into n groups D.) 6 less than n students 3.) If z + 7= 19, then what is the value of (z)? 4.) Evaluate the expression: 9 + (16 3) = z = ) Which rule can be used to find the output numbers in this table? Input Output ) Which variable expression can be used to represent: 13 more than the quotient of 6 and a number x? A.) divide the input number by 11 B.) add 24 to the input number. C.) multiply the input number by 9 D.) divide the input number by A.) 13 6x B.) x C.) (6 x) + 13 D.) (6 x) a

5 Name: 5 th Grade Common Core Math Date: Show all of your work 1.) What is the value of the expression: 5 + (20 8) = 2.) Garth is giving 10 of his action figures to his brother. If (a) represents the number of action figures Garth has, write an expression that shows how many action figures Garth will have left after giving 10 to his brother? 3.) What is the value of: 8 + 2g 7, when (g) = 5? 4.) Which of the following is equal to 8? A.) 6 + (4 2) B.) (2 + 1) 3 C.) (6 + 4) D.) ( ) ) Stu bought chips, popcorn, and pretzels for a picnic. Together, he bought 15 bags. He bought 3 bags of pretzels, and 3 times as many bags of chips as popcorn. How many bags of chips did he buy? 6.) A child s ticket for a movie costs $2 less than an adult s ticket. If (a) represents the cost of an adult s ticket, which expression represents the cost of a child s ticket? A.) a 2 B.) 2 + a C.) 2a D.) 2 a 2

6 5 th Grade Common Core Math Answer Key 1.) What is the value of the expression: 5 + (20 8) = 2.) Garth is giving 10 of his action figures to his brother. If (a) represents the number of action figures Garth has, write an expression that shows how many action figures Garth will have left after giving 10 to his brother? 15 a 10 3.) What is the value of: 8 + 2g 7, when (g) = 5? 4.) Which of the following is equal to 8? A.) 6 + (4 2) B.) (2 + 1) 3 C.) (6 + 4) D.) ( ) ) Stu bought chips, popcorn, and pretzels for a picnic. Together, he bought 15 bags. He bought 3 bags of pretzels, and 3 times as many bags of chips as popcorn. How many bags of chips did he buy? 6.) A child s ticket for a movie costs $2 less than an adult s ticket. If (a) represents the cost of an adult s ticket, which expression represents the cost of a child s ticket? A.) a 2 B.) 2 + a C.) 2a D.) 2 a 9 bags 2a

7 Name: 5 th Grade Common Core Math Date: Show all of your work 1.) Brett scored 12 more points than Jason in a basketball game. If (p) represents the number of points that Jason scored, which expression represents the number of points that Brett scored? 2.) What is the value of the expression below if (y) = 5? 35 (y + 2) + 4 = A.) p 12 B.) p + 12 C.) 12p D.) 12 p 3.) Which number completes the table? n n 7 9? ) In the expression below, which operation would you perform first? 12 + (18-2) x 3 24 = A.) 10 B.) 13 C.) 16 D.) 84 5.) Solve: 10 ( ) + 3 = 6.) Write the algebraic equation, then solve to find the number: seventy-nine less than a number is 47. 3

8 5 th Grade Common Core Math Answer Key 1.) Brett scored 12 more points than Jason in a basketball game. If (p) represents the number of points that Jason scored, which expression represents the number of points that Brett scored? 2.) What is the value of the expression below if (y) = 5? 35 (y + 2) + 4 = A.) p 12 B.) p + 12 C.) 12p D.) 12 p 9 3.) Which number completes the table? n n 7 9? ) In the expression below, which operation would you perform first? 12 + (18-2) x 3 24 = A.) 10 B.) 13 C.) 16 D.) 84 subtraction in the parenthesis 5.) Solve: 10 ( ) + 3 = 6.) Write the algebraic equation, then solve to find the number: seventy-nine less than a number is x 79 = 47 x = 126 and 3a

9 Name: 5 th Grade Common Core Math Date: Show all of your work 1.) Amber made the input-output table shown below. Which rule explains how to get the output number from the input number? A.) add 5, multiply by 2 B.) add 10 C.) multiply by 5, add 2 D.) multiply by 6 Input Output ) Ryan is painting faces at the fair. It takes him 10 minutes to set up his materials. Each face takes 6 minutes to paint. Ryan wants to know how many faces (f) he can paint in 60 minutes. Which equation represents this situation? A.) 6f + 10 = 60 B.) 10f + 6 = 60 C.) 6f 10 = 60 D.) 10f 6 = 60 3.) Solve: [(6-3) x 2] 3 = 4.) Where would you insert parentheses to make the equation true? 2 x = 18 A.) 2 x 4 + (6-2) = 18 B.) (2 x 4 + 6) = 18 C.) 2 x ( ) = 18 D.) 2 x ( ) = 18 5.) Solve: [( ) x 2] 4 = 6.) Which operation would you perform first when evaluating: ? A.) division B.) multiplication C.) addition D.) subtraction 4

10 5 th Grade Common Core Math Answer Key 1.) Amber made the input-output table shown below. Which rule explains how to get the output number from the input number? A.) add 5, multiply by 2 B.) add 10 C.) multiply by 5, add 2 D.) multiply by 6 Input Output ) Ryan is painting faces at the fair. It takes him 10 minutes to set up his materials. Each face takes 6 minutes to paint. Ryan wants to know how many faces (f) he can paint in 60 minutes. Which equation represents this situation? A.) 6f + 10 = 60 B.) 10f + 6 = 60 C.) 6f 10 = 60 D.) 10f 6 = 60 3.) Solve: [(6-3) x 2] 3 = 4.) Where would you insert parentheses to make the equation true? 2 x = 18 2 A.) 2 x 4 + (6-2) = 18 B.) (2 x 4 + 6) = 18 C.) 2 x ( ) = 18 D.) 2 x ( ) = 18 5.) Solve: [( ) x 2] 4 = 6.) Which operation would you perform first when evaluating: ? A.) division B.) multiplication C.) addition D.) subtraction 11 4a

11 Name: 5 th Grade Common Core Math Date: Show all of your work 1.) Write the algebraic equation, then solve to find the number: seventy-six less than a number is ) What is a rule for this table? p ? A.). p + 19 B.) p 22 C.) p + 22 D.) p 19 3.) Louis bought packages of donuts. There were 4 donuts in each package, and Louis gave 6 donuts to his friends. Write an expression to show this situation. 4.) Brett rakes leaves to earn money. He uses the information in the table shown to find how long it would take him to rake lawns of different sizes. Write a rule that tells how the amount of time Brett takes to rake a lawn is related to the lawn's size. Size of Lawn (square ft.) Time to Rake (minutes) ) In the expression below, which operation would you perform first? 7 x 4 - (8 7) + 2 = 6.) What is the value of the expression? 9 (8 5) + 8 = 5

12 5 th Grade Common Core Math Answer Key 1.) Write the algebraic equation, then solve to find the number: seventy-six less than a number is ) What is a rule for this table? p ? A.). p + 19 B.) p 22 C.) p + 22 D.) p 19 x - 76 = 89 x = 165 and 3.) Louis bought packages of donuts. There were 4 donuts in each package, and Louis gave 6 donuts to his friends. Write an expression to show this situation. 4.) Brett rakes leaves to earn money. He uses the information in the table shown to find how long it would take him to rake lawns of different sizes. Write a rule that tells how the amount of time Brett takes to rake a lawn is related to the lawn's size. Size of Lawn (square ft.) Time to Rake (minutes) p 6 5.) In the expression below, which operation would you perform first? 7 x 4 - (8 7) + 2 = Answers may vary. Example: For every 50 square feet of lawn, it takes 10 additional minutes to rake. 6.) What is the value of the expression? 9 (8 5) + 8 = division in the parenthesis 35 5a

13 Name: 5 th Grade Common Core Math Date: Show all of your work 1.) How many boys will participate in the track meet if there are 21 girls participating in the meet? 2.) Write the algebraic equation, then solve to find the number: the sum of a number and 33 is 123. Number of girls in the track meet Number of boys in the track meet ? 3.) Solve: [ 79 - ( ) ] 2 = 4.) What is the value of: k, if (k) = 4? 5.) The girls in Karen s family own a total of 46 t-shirts. The oldest, Heidi, has 18 t-shirts. Karen has 6 times as many t-shirts as her little sister, June. How many t-shirts does Karen own? 6.) Use the table to find the score a student should receive for answering 19 questions correctly. Number of questions answered correctly Score ? 6

14 5 th Grade Common Core Math Answer Key 1.) How many boys will participate in the track meet if there are 21 girls participating in the meet? 2.) Write the algebraic equation, then solve to find the number: the sum of a number and 33 is 123. Number of girls in the track meet Number of boys in the track meet ? 3.) Solve: 17 boys [ 79 - ( ) ] 2 = n + 33 = 123 n = 90 and 4.) What is the value of: k, if (k) = 4? ) The girls in Karen s family own a total of 46 t-shirts. The oldest, Heidi, has 18 t-shirts. Karen has 6 times as many t-shirts as her little sister, June. How many t-shirts does Karen own? 6.) Use the table to find the score a student should receive for answering 19 questions correctly. Number of questions answered correctly Score ? 24 t-shirts 95 6a

15 Name: 5 th Grade Common Core Math Date: Show all of your work 1.) Solve: 1 ( ) = 2.) Solve: 5 ( ) = 3.) Solve: (12 4) 2 = 4.) Evaluate x + 5y, if (x) = 12 and (y) = 9. 5.) What is the rule for the table below? s k ) Kyle has a total of 36 unmatched socks that are either red, black, or brown. There are 11 unmatched red socks, and 4 times as many unmatched black socks as brown socks. How many unmatched black socks does Kyle have? 7

16 5 th Grade Common Core Math Answer Key 1.) Solve: 1 ( ) = 2.) Solve: 5 ( ) = ) Solve: (12 4) 2 = 4.) Evaluate x + 5y, if (x) = 12 and (y) = ) What is the rule for the table below? s k ) Kyle has a total of 36 unmatched socks that are either red, black, or brown. There are 11 unmatched red socks, and 4 times as many unmatched black socks as brown socks. How many unmatched black socks does Kyle have? s 5 = k 20 socks 7a

17 Name: 5 th Grade Common Core Math Date: Show all of your work 1.) Which is the rule for the table below? 2.) Solve: x ? ( ) = A.) x 6 B.) x + 6 C.) x 7 D.) x ) Evaluate 47 + d, if (d) = 30 4.) An electrician charges $45 per hour and spends $20 a day on gasoline. Write an expression to represent his earnings for one day. 5.) Solve: 6 2 x 4 + [(9 x 3) ] = 6.) Solve: [74 (5 + 4)] 2 = 8

18 5 th Grade Common Core Math Answer Key 1.) Which is the rule for the table below? 2.) Solve: x ? ( ) = A.) x 6 B.) x + 6 C.) x 7 D.) x + 7 6,480 3.) Evaluate 47 + d, if (d) = 30 4.) An electrician charges $45 per hour and spends $20 a day on gasoline. Write an expression to represent his earnings for one day. 77 $45x - $20 5.) Solve: 6 2 x 4 + [(9 x 3) ] = 6.) Solve: [74 (5 + 4)] 2 = a

19 Name: 5 th Grade Common Core Math Date: Show all of your work 1.) Write the algebraic equation, then solve to find the number: a number increased by 55 is ) Solve: ( ) + 4 = 3.) Solve: = 4.) Write the rule, then fill in the empty box. Input Output ? 5.) Which expression has a value of 66? A.) (16 3.2) x x ( ) B.) [(16 3.2) x ( )] x C.) 16 [(3.2 x 2) + (0.2 x 8)] D.) [16 (3.2 x 2) x ( ) 6.) If an expression had all of the operations listed below, which operation would you perform last? A.) parentheses B.) addition C.) division D.) multiplication 9

20 5 th Grade Common Core Math Answer Key 1.) Write the algebraic equation, then solve to find the number: a number increased by 55 is ) Solve: ( ) + 4 = n + 55 = 92 n = 37 and 71 3.) Solve: = 4.) Write the rule, then fill in the empty box. Input Output ? 8.3 Rule: multiply by 4? = ) Which expression has a value of 66? A.) (16 3.2) x x ( ) B.) [(16 3.2) x ( )] x C.) 16 [(3.2 x 2) + (0.2 x 8)] D.) [16 (3.2 x 2) x ( ) 6.) If an expression had all of the operations listed below, which operation would you perform last? A.) parentheses B.) addition C.) division D.) multiplication 9a

21 Name: 5 th Grade Common Core Math Date: Show all of your work 1.) What is the rule used for B? Start 1 st Term 2 nd Term 3 rd Term A 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 6 2.) Use the input-output table from question #1 to answer this question: What is the relationship between the corresponding terms in A and B? A.) B is always 4 greater than A. B.) A is always 3 times as much as B. C.) A is always 4 greater than B. D.) B is always 3 times as much as A. 3.) Evaluate p 10, if (p) = ) Which expression represents a number decreased by 9? A.) 9 c B.) c 9 C.) 9 c D.) c 9 5.) Solve: 6.) Solve: 7 (7 4) + 6 = [ 90 (6 x 4 9) ] x 5 = 10

22 5 th Grade Common Core Math Answer Key 1.) What is the rule used for B? Start 1 st Term 2 nd Term 3 rd Term A 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 6 2.) Use the input-output table from question #1 to answer this question: What is the relationship between the corresponding terms in A and B? A.) B is always 4 greater than A. B.) A is always 3 times as much as B. C.) A is always 4 greater than B. D.) B is always 3 times as much as A. 3.) Evaluate p 10, if (p) = ) Which expression represents a number decreased by 9? A.) 9 c B.) c 9 C.) 9 c D.) c ) Solve: 6.) Solve: 7 (7 4) + 6 = [ 90 (6 x 4 9) ] x 5 = a

23 Name: 5 th Grade Common Core Math Date: Show all of your work 1.) Write the rule, then fill in the empty box. 2.) Write the algebraic expression for (n) rows of chairs with 6 chairs in each row. Input Output ? ) Solve: 1.6 ( ) = 4.) Write the algebraic expression for Stephanie walked (k) miles, then walked 6 more. 5,) Solve: 3 x ( ) + 2 = 6.) Solve: [(12 x 2.4) - ( )] = 11

24 5 th Grade Common Core Math Answer Key 1.) Write the rule, then fill in the empty box. Input Output 2.) Write the algebraic expression for (n) rows of chairs with 6 chairs in each row ? ) Solve: Rule: subtract 7.8? = ( ) = 6n 4.) Write the algebraic expression for Stephanie walked (k) miles, then walked 6 more. 0.4 k + 6 5,) Solve: 3 x ( ) + 2 = 6.) Solve: [(12 x 2.4) - ( )] = a

25 Name: 5 th Grade Common Core Math Date: Show all of your work 1.) Cassie has $12. She buys a balloon that costs (b). Which expression shows how much money Cassie has left? 2.) Solve for (h): h + 9 = 21. A.) b + 12 B.) 12 - b C.) 12b D.) b 12 3.) Solve: [(6 x 5) (45 5)] + 5 = 4.) Write the rule, then fill in the empty box. Input Output ? ) Write the algebraic equation for: twenty more than twice a number is ) Solve: 99 9 x [4 + (11-5)] = 12

26 5 th Grade Common Core Math Answer Key 1.) Cassie has $12. She buys a balloon that costs (b). Which expression shows how much money Cassie has left? 2.) Solve for (h): h + 9 = 21. A.) b + 12 B.) 12 - b C.) 12b D.) b ) Solve: [(6 x 5) (45 5)] + 5 = 4.) Write the rule, then fill in the empty box. Input Output ? Rule: add 9.5? = ) Write the algebraic equation for: twenty more than twice a number is ) Solve: 99 9 x [4 + (11-5)] = 2x + 20 = a

27 Name: 5 th Grade Common Core Math Date: Show all of your work 1.) Solve: (12 3) 2 = 2.) Write the algebraic expression for: twice a number (k). 3.) Which expression shows the number of wheels (w) on 2 cars? A.) 2w B.) 2 + w C.) w 2 D.) w 2 4.) Solve: 10 x (8-6) = 5.) Solve: 4.6 x ( ) = 6.) Write the rule, then fill in the empty box. Input Output ?

28 5 th Grade Common Core Math Answer Key 1.) Solve: (12 3) 2 = 2.) Write the algebraic expression for: twice a number (k). 16 2k 3.) Which expression shows the number of wheels (w) on 2 cars? A.) 2w B.) 2 + w C.) w 2 D.) w 2 4.) Solve: 10 x (8-6) = 20 5.) Solve: 4.6 x ( ) = 6.) Write the rule, then fill in the empty box. Input Output ? Rule: add 3.8? = a

29 Name: 5 th Grade Common Core Math Date: Show all of your work 1.) Solve the equation by testing these values for (k): 2, 3, 4, and 5. 2.) Write a statement for this algebraic equation: 5 + n = k = 48 A.) k = 5 B.) k = 4 C.) k = 3 D.) k = 2 3.) Solve: 4.) Solve: 4 x x (6 + 1) = = 5.) Keith and Chuck were born on the exact day, but not in the same year. Their ages are shown in the table below. Keith's Age Chuck's Age How much older is Chuck than Keith? 6.) Use the table from question #5 to answer these questions: Which choice best explains the rule for this table? A.) Add 3 to Chuck's Age to find Keith's age. B.) Subtract 4 from Chuck's Age to find Keith's age. C.) Subtract 3 from Keith's Age to find Chuck's age. D.) Add 3 to Keith's Age to find Chuck's age. When Keith is 35, how old will Chuck be? 14

30 5 th Grade Common Core Math Answer Key 1.) Solve the equation by testing these values for (k): 2, 3, 4, and 5. 2.) Write a statement for this algebraic equation: 5 + n = k = 48 A.) k = 5 B.) k = 4 C.) k = 3 D.) k = 2 Answers may vary. Example: n more than 5 is 12 3.) Solve: 4.) Solve: 4 x x (6 + 1) = = ) Keith and Chuck were born on the exact day, but not in the same year. Their ages are shown in the table below. Keith's Age Chuck's Age How much older is Chuck than Keith? 6.) Use the table from question #5 to answer these questions: Which choice best explains the rule for this table? A.) Add 3 to Chuck's Age to find Keith's age. B.) Subtract 4 from Chuck's Age to find Keith's age. C.) Subtract 3 from Keith's Age to find Chuck's age. D.) Add 3 to Keith's Age to find Chuck's age. When Keith is 35, how old will Chuck be? 3 years older 38 14a

31 Name: 5 th Grade Common Core Math Date: Show all of your work 1.) Write the rule, then fill in the empty box. 2.) What is the value of G 6 when (G) is equal to 48? Input Output ? A.) 9 B.) 8 C.) 288 D.) 6 3.) Solve: (8-7) x (2 + 1) + 1 = 4.) Solve: 9 (9 2 4) 9 = 5.) Miss Nannini sells homemade bread at the farmer's market. She sold 35 loaves during the first hour and 85 loaves during the second hour. Write an algebraic expression to show the number of loaves Miss Nannini has left to sell. 6.) Solve: 4 + ( ) 2 = 15

32 5 th Grade Common Core Math Answer Key 1.) Write the rule, then fill in the empty box. Input Output ? 2.) What is the value of G 6 when (G) is equal to 48? A.) 9 B.) 8 C.) 288 D.) 6 Rule: divide by 6? = 45 3.) Solve: (8-7) x (2 + 1) + 1 = 4.) Solve: 9 (9 2 4) 9 = ) Miss Nannini sells homemade bread at the farmer's market. She sold 35 loaves during the first hour and 85 loaves during the second hour. Write an algebraic expression to show the number of loaves Miss Nannini has left to sell. 6.) Solve: 4 + ( ) 2 = x a

33 Name: 5 th Grade Common Core Math Date: Show all of your work 1.) Write the algebraic expression for: the sum of a number (r) and ) The Fox Theater has main floor and box seating. The main floor can seat 12 people in each row. Another 30 people can sit in the box seats. If (r) represents the number rows, on the main floor, which expression shows how many people can be seated in the theater? A.) 30r - 12 B.) 30r + 13 C.) 12r - 30 D.) 12r ) Ty had 48 more hits during the baseball season than Sean (s) who had 24. Evaluate the expression s + 48, if (s) = 24. Then, explain what your answer represents. 4.) What is the rule for the table? g ? ) Write the algebraic expression for: 60 people separated into (n) vans. 6.) Write the algebraic expression for: 24 divided by a number (f). 16

34 5 th Grade Common Core Math Answer Key 1.) Write the algebraic expression for: the sum of a number (r) and ) The Fox Theater has main floor and box seating. The main floor can seat 12 people in each row. Another 30 people can sit in the box seats. If (r) represents the number rows, on the main floor, which expression shows how many people can be seated in the theater? r A.) 30r - 12 B.) 30r + 13 C.) 12r - 30 D.) 12r ) Ty had 48 more hits during the baseball season than Sean (s) who had 24. Evaluate the expression s + 48, if (s) = 24. Then, explain what your answer represents. 4.) What is the rule for the table? g ? The answer represents the total number of hits for Ty. (g)6 (g times 6) 5.) Write the algebraic expression for: 60 people separated into (n) vans. 6.) Write the algebraic expression for: 24 divided by a number (f). 60 n 24 f 16a

35 Name: 5 th Grade Common Core Math Date: Show all of your work 1.) Solve: (8 3) ) Write the rule, then fill in the empty box. Input Output 10? ) Write the algebraic equation for: the length of a football field (L) is 30 yards more than its width. Express the length of the field in terms of its width (w). 4.) Write the algebraic expression for: 9 more than a number (k). 5.) Write the algebraic expression for: 21 fewer kids than two times a number (h). 6.) Solve: 9 x (2 3 4 x 5) = 17

36 5 th Grade Common Core Math Answer Key 1.) Solve: (8 3) ) Write the rule, then fill in the empty box. Input Output 10? Rule: multiply by 7? = 70 3.) Write the algebraic equation for: the length of a football field (L) is 30 yards more than its width. Express the length of the field in terms of its width (w). 4.) Write the algebraic expression for: 9 more than a number (k). w + 30 = L k ) Write the algebraic expression for: 21 fewer kids than two times a number (h). 6.) Solve: 9 x (2 3 4 x 5) = 2h a

37 Get the complete 5 th Grade Common Core Math Review Problems Products **With Answer Keys! Click the pictures below! Operations and Algebraic Thinking Measurement and Data Geometry and Coordinate Graphing Numbers and Operations in Base Ten Numbers and Operations Fractions

38 All of the 5 th Grade Review Problems have been bundled into one document! Click the picture below to check it out!

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