7 th Grade Common Core Name (s) Class Date ERROR ANALYSIS EXPRESSIONS WORD PROBLEMS Includes: * Evaluating Expressions * Writing Expressions * Sequences * Simplifying Expressions * Adding & Subtracting Linear Expressions * Factoring Linear Expressions Question # 0
An online application charges $1.25 to download a song and $10.99 membership fee. Write an expression that gives the total cost in dollars to download s songs. Then find the cost of downloading 6 songs. 1.25s + 10.99s =12.24s expression 12.24(6) 6 songs =73.44 The expression for the total cost to download songs is 12.24s. It will cost $73.44 to download 6 songs. Question # 1
Robin records the height of her plant for three months. If the pattern continues, what algebraic expression can Robin use to find the plant s height for any month? What will be the plants height at 12 months? Month 1 2 3 Height 4 8 12 n= month n + 4 plant height for any month =12 + 4 =16 The expression is n+ 4. The plant will be 16 inches tall at 12 months. Question # 2
cc Name (s) Class Date Write an expression to represent the total number of legs on c cats and b birds. How many legs are there in 4 cats and 6 birds? c + b 4 + 6 = 10 The expression is c + b. There are a total of 10 legs. Question # 3
Sean buys some T-shirts for $12 each and the same number of belts for $7.50 each. Write an expression in simplest form that represents the total amount spent. n = number of t-shirts and belts 12n + 7.50 An expression that represents the total amount spent is 12n + 7.50. Question # 4
Theodore goes to a baseball game and buys 3 waters that cost x dollars each and a bag of popcorn for $4.50. Write an expression in simplest form that represents the total amount of money Theodore spent. 3x + 4.50x =(3 + 4.50)x = 7.50x The expression to find the total amount of money Theodore is spent 7.50x. Question # 5
A rectangle has side lengths (x +5) feet and (2x 3) feet. Write a linear expression in simplest form to represent the perimeter. Find the perimeter if the value of x is 6 feet. (x + 5) + (2x 3) (x + 2x) + (5 + ( 3)) 3x + 2 expression 3(6) + 2 18 + 2 = 20 A linear expression to represent the perimeter is 3x + 2. If x = 6, the perimeter is 20 square units. Question # 6
Tanya has 6m + 1 pencils and Michael has 4m 4 pencils. Write an expression in simplest form to show how many pencils Tanya and Michael have all together. Find the total pencils if m = 2. (6m + 1) + (4m 4) 7m = 10m 3 =7(2) = 7m =14 The expression 7m can be used to find the total pencils Tanya and Michael have. If m=2, Tanya and Michael have 14 pencils all together. Question # 7
Then share a strategy this student could use to prevent the same error in the 25future. The number of points scored by the home team at a basketball game is represented by (x+6). The number of points scored by the visiting team is represented by (3x 6). Write an expression to find how many more runs the home team scored than the visiting team. Then evaluate the expression if the value of x is 5. (x + 6) - (3x-6) 4(5) + 12 x + 6 + 3x + 6 20 + 12 = 32 x + 3x + 12 4x + 12 The expression is 4x +12. If x=6, the home team scored 32 more runs than the visiting team. Question # 8
The perimeter of the classroom shown is 6x + 3. Find the length of the missing side. (6x + 3)+ (3x +1) + x + x 6x + 3x + x +x +3 + 1 11x + 4 The length of the missing side is 11x + 4. Question # 9
The area of a rectangular patio is (9x + 18) square units. Factor 9x + 18 to find the possible dimensions of the porch. 9x + 18 9x = 3 3 x 18 = 2 3 3 GCF = 9 9(x + 18) The possible dimensions of the patio is 9 square units and (x +18) square units. Question # 10
Answer Key Error Correct Sample Work Correct Answer 1. The membership fee, $10.99, is a constant and should not be multiplied to s. 1.25s + 10.99 1.25(6) + 10.99 7.50 + 10.99 18.49 The expression for the total cost to download songs is 1.25s + 10.99. It will cost $18.49 to download 6 songs. 2. The height for each month is the value of the month times 4. So the formula is 4n. 4n 4(12) 48 inches The expression is 4n. The plant will be 48 inches tall at 12 months. 3. Each cat has 4 legs and each bird has 2 legs. To find the total you need to add the total number of cat legs with the total number of bird legs. 4. The variable n represents the number of t-shirts and the number of belts. So n needs to be multiplied to the cost of t- shirts and the cost of belts. 5. Theodore only bought 1 bag of popcorn and for $4.50. This is a constant and should not be multiplied to x. 4c + 2b 4(4) + 2(6) 16 + 12 28 legs 12n + 7.50n 19.50n 3x + 4.50 The expression is 4c + 2b. There are a total of 28 legs. An expression that represents the total amount spent is 19.50n. The expression to find the total amount of money Theodore is spent 3x + 4.50. Question # 11
6. The rectangle has 2 sides with lengths (x+5) feet and 2 sides with lengths (2x-3) feet. To find the perimeter all 4 sides must be added. 7. 10m and 3 are unlike terms and therefore cannot be combined. 8. When subtracting linear expressions you can add the additive inverse. The additive inverse of (3x+ 6) is ( 3x 6). 2(x + 5) + 2(2x 3) 2x + 10 + 4x + ( 6) 6x + 4 6x + 4 = 6(6) +4 = 36 +4 = 40 (6m + 1) + (4m 4) 10m 3 10m 3 10(2) 3 20 3 = 17 (x + 6) - (3x-6) x + 6 + ( 3x) + 6 x + ( 3x) + 12 2x + 12 A linear expression to represent the perimeter is 6x + 4. If x = 6, the perimeter is 40 square units. The expression 10m 3 can be used to find the total pencils Tanya and Michael have. If m=2, Tanya and Michael have 17 pencils all together. The expression is 2x + 12. If x=6, the home team scored 2 more runs than the visiting team. 9. The perimeter (6x + 3) is the sum of all the sides. To find the missing side, the sum of the missing sides should be subtracted from the perimeter. 2(5) + 12 10 + 12 = 2 (3x +1) + x + x 5x + 1 (6x + 3) (5x + 1) 6x + 3 + ( 5x) 1 6x + ( 5x) + 3 1 x + 2 10. 9x and 18 should be divided by the GCF. 9x + 18 9x = 3 3 x 18 = 2 3 3 The length of the missing side is x+2. The possible dimensions of the patio is 9 square units and (x +2) square units. 9(x + 2) Question # 12
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