Notes & Practice. Aligned to the Common Core State Standards 7.EE.B.4. Grades th Grade Math Curriculum

Transcription

1 Unit Section 3 Solving Two-Step Equations Notes & Practice Aligned to the Common Core State Standards 7.EE.B.4 8th Grade Math Curriculum Grades 6-9

2 Teacher s Guide CCSS 7.EE.B.4 Use variables to represent quantities in a real-world or mathematical problem, and construct simple equations and inequalities to solve problems by reasoning about the quantities. a. Solve word problems leading to equations of the form px + q = r and p(x q) = r, where p, q, and r are specikic rational numbers. Solve equations of these forms Kluently. Compare an algebraic solution to an arithmetic solution, identifying the sequence of the operations used in each approach. For example, the perimeter of a rectangle is 54 cm. Its length is 6 cm. What is its width Objective Students will be able to solve two-step equations. Students will be able to solve world problems involving two-step equations. Differentiated Notes v Traditional Notes These are basic skeletal notes. Students Kill in the examples with you and do the try problems independently. r Modi/ied Notes These cut down on the amount of writing that students are required to do. All examples are Killed in, but practice problems are left blank for student completion. (Excellent for IEP and 504 accommodations involving difkiculties with hearing, handwriting, etc.) f Teacher Notes These are completely Killed in for teacher reference. These notes are also great for students who have been absent.

3 Differentiated Practice (Homework) v Advanced Practice Perfect challenge for your high Klyers! Many problems overlap with Basic Practice, but this worksheet skips some of the basic problems and replaces them with more advanced practice. r Basic Practice The majority of your students will complete this onlevel assignment. f Modi/ied Practice Great option for students requiring a modikied amount of homework per an IEP or 504. This is a cut down version of the Basic Practice assignment (one page only).

4 Name: Class: Date: v Solving Two-Step Equations Steps for Solving a Two-Step Equation: 1) ) Example 1: Solve each equation. Show your work. a) b) 3 b + 7 = v = 1 m c) 9 = 5 d) 4 f 3 6 =.5 Try: a) b) 4 g =1 7w + = 19 c) 1 d d) 4 = 7 p +.4 = 3.5

5 v Example : Use the Five-Step Method to solve each word problem. a) Jamie picks out a blouse to purchase. It is on sale for 5% off plus she has a $10 off coupon. She pays $3 for the blouse. Determine the original price. D E S Five-Step Method A C b) Michael is collecting sea glass from the beach. He begins with 14 pieces in his collection and adds 3 new pieces per day. Determine how many days it will take Michael to have 80 pieces of sea glass in his collection. Try: a) Kayla is given a monthly allowance. She puts 40% of the money directly into her savings account. She spends $15 at the movies with her friends. At the end of the month, she has $3 left. How much is her monthly allowance b) Juan has already run 6 miles this month. He plans to run an additional.5 miles per day. At this rate, how long will take Juan to run 41 miles

6 Name: Class: Date: r Solving Two-Step Equations Steps for Solving a Two-Step Equation: 1) Use reverse order of operations to undo one operation. (This is usually addition or subtraction.) ) Use the inverse operation to undo the second operation. Example 1: Solve each equation. Show your work. a) b) 3 b + 7 = b = ( 8) 3 b = 1 c) m 9 = 5 d) m = ( 4)4 4 m =16 Try: a) b) 4 g = v = v = v = 3 f 3 6 =.5 6 f 3 = (.5)6 6 f 3 = f =18 7w + = 19 c) 1 d d) 4 = 7 p +.4 = 3.5

7 r Example : Use the Five-Step Method to solve each word problem. a) Jamie picks out a blouse to purchase. It is on sale for 5% off plus she has a $10 off coupon. She pays $3 for the blouse. Determine the original price. p=original price 0.75p-10=3 p=44 The original price of the blouse is $ (44)-10=3 3=3 Five-Step Method D Define the variable. E Write the equation. S Solve the equation. A Answer the question. C Check your solution. b) Michael is collecting sea glass from the beach. He begins with 14 pieces in his collection and adds 3 new pieces per day. Determine how many days it will take Michael to have 80 pieces of sea glass in his collection. d=days 14+3()= d=80 80=80 d= It will take days to have 80 pieces of sea glass. Try: a) Kayla is given a monthly allowance. She puts 40% of the money directly into her savings account. She spends $15 at the movies with her friends. At the end of the month, she has $3 left. How much is her monthly allowance b) Juan has already run 6 miles this month. He plans to run an additional.5 miles per day. At this rate, how long will take Juan to run 41 miles

8 Name: Class: Date: -3 Steps for Solving a Two-Step Equation: Solving Two-Step Equations 1) Use reverse order of operations to undo one operation. (This is usually addition or subtraction.) ) Use the inverse operation to undo the second operation. Example 1: Solve each equation. Show your work. a) 3 b + 7 = 1 b) b = ( 8) b = 1 c) m 9 = 5 4 d) m = ( 4)4 4 m =16 Try: a) g =1 b) g = ( 5) 5 g = v = v = v = 3 f 3 6 =.5 6 f 3 = (.5)6 6 f 3 = f =18 7w + = 19 7w = w = 3 f c) 1 d d) 4 = d = ( 8) ( 4) 4 d = 3 p +.4 = 3.5 p +.4 = ( 3.5) p +.4 = p = 4.6

9 Example : Use the Five-Step Method to solve each word problem. a) Jamie picks out a blouse to purchase. It is on sale for 5% off plus she has a $10 off coupon. She pays $3 for the blouse. Determine the original price. p=original price 0.75p-10=3 p=44 The original price of the blouse is $ (44)-10=3 3=3 Five-Step Method D Define the variable. E Write the equation. S Solve the equation. A Answer the question. C Check your solution. b) Michael is collecting sea glass from the beach. He begins with 14 pieces in his collection and adds 3 new pieces per day. Determine how many days it will take Michael to have 80 pieces of sea glass in his collection. d=days 14+3()= d=80 80=80 d= It will take days to have 80 pieces of sea glass. Try: a) Kayla is given a monthly allowance. She puts 40% of the money directly into her savings account. She spends $15 at the movies with her friends. At the end of the month, she has $3 left. How much is her monthly allowance a=monthly allowance 0.6(30)-15=3 0.6a-15=3 3=3 a=30 Kayla s monthly allowance is $30. f b) Juan has already run 6 miles this month. He plans to run an additional.5 miles per day. At this rate, how long will take Juan to run 41 miles d=days 6+.5d=41 d=14 It will take Juan 14 days to run 41 miles. 6+.5(14)=41 41=41

10 Name: Class: Date: v For 1-1, solve each two-step equation. Solving Two-Step Equations Practice 1) 3a +.3 =11.6 ) d 9 = 1 3) 3 j 3 ( 1 ) = 0 4e 4) 5) 6) b =18 ( ) = 11 9c + ( 4) = 4 k m 7) 8) 9).5 = 3 = 0 5 f + 1 =11 ( ) g n + 10) 11) =1 1) = h 1 =1. 4

11 For 13-14, use the Five-Step Method. v 13) Landon earns about $60 per week mowing lawns in the summer and shoveling driveways in the winter. He invested $0 in equipment. How long will it take him to earn $860 14) Mary is thinking of a mystery number. She reduces it by 15% then subtracts 5. The result is 9. Determine the mystery number. 15) Select the equation that does not belong. a. 3 x 7 = 4 b. c. p =1 d. c 5 = 0 4k = 10 16) Identify and correct error: 3.5x +1. = ( 3.5x ) = ( 10.5)3.5 x = 36.75

12 Name: Class: Date: r For 1-1, solve each two-step equation. Solving Two-Step Equations Practice 1) 3a + =11 ) d 9 = 1 3) 3 j 3 ( 1 ) = 0 4e 4) 1 = 9 5) 6 + 4b =18 6) 9c ( ) = 4 k m 7) = 8) 9) 3 = 0 5 f + 1 =11 ( ) g n + 10) 11) =1 1) + 4 = 3 5 h 1 =1. 4

13 For 13-14, use the Five-Step Method. r 13) Landon earns about $60 per week mowing lawns in the summer and shoveling driveways in the winter. He invested $0 in equipment. How long will it take him to earn $860 14) Meaghan is thinking of a mystery number. She cuts it in half then adds 5. The result is 4. Determine the mystery number. 15) Select the equation that does not belong. a. 3 x 7 = 4 b. c. p =1 d. c 5 = 0 4k = 10 16) Identify and correct error: 3.5x +1. = ( 3.5x ) = ( 10.5)3.5 x = 36.75

14 Name: Class: Date: f For 1-9, solve each two-step equation. Solving Two-Step Equations Practice 1) 3a + =11 ) d 9 = 1 3) 3 j 3 ( 1 ) = 0 4e 4) 1 = 9 5) 6 + 4b =18 6) 9c ( ) = 4 k m 7) = 8) 9) 3 = 0 5 f + 1 =11 10) Use the Five-Step Method: Landon earns about $60 per week mowing lawns in the summer and shoveling driveways in the winter. He invested $0 in equipment. How long will it take him to earn $860

15 v Name: Class: Date: -3 For 1-1, solve each two-step equation. Solving Two-Step Equations Practice (Answer Key) 1) 3a +.3 =11.6 ) d 9 = 1 3) 3 j 3 ( 1 ) = 0 a = 3.1 d =1 j = 36 4e 4) 5) 6) b =18 ( ) = 11 9c + ( 4) = 4 e = 5 = 1 1 b = 16 3 = c = 0 k m 7) 8) 9).5 = 3 = 0 5 f + 1 =11 k = 5 m = 5 f = ( ) g n + 10) 11) =1 1) = h 1 =1. 4 g = 5 n = 7 h = 8.8

16 For 13-14, use the Five-Step Method. v 13) Landon earns about $60 per week mowing lawns in the summer and shoveling driveways in the winter. He invested $0 in equipment. How long will it take him to earn $860 w=weeks 60w-0=860 w=18 It will take Landon 18 weeks to earn $ (18)-0= =860 14) Mary is thinking of a mystery number. She reduces it by 15% then subtracts 5. The result is 9. Determine the mystery number. m=mystery number 0.85m-5=9 m=40 The mystery number is (40)-5=9 9=9 15) Select the equation that does not belong. a. 3 x 7 = 4 b. c. p =1 d. c 5 = 0 4k = 10 The solution is -. In all others, the solution is. 16) Identify and correct error: 3.5x +1. = ( 3.5x ) = ( 10.5)3.5 x = They should have divided by 3.5. The correct answer is x=3.

17 r Name: Class: Date: -3 For 1-1, solve each two-step equation. Solving Two-Step Equations Practice (Answer Key) 1) 3a + =11 ) d 9 = 1 3) 3 j 3 ( 1 ) = 0 a = 3 d =1 j = 36 4e 4) 1 = 9 5) 6 + 4b =18 6) 9c e = 10 b = 6 c = 0 ( ) = 4 k m 7) = 8) 9) 3 = 0 5 f + 1 =11 k = 6 m = 5 f = ( ) g n + 10) 11) =1 1) + 4 = 3 5 h 1 =1. 4 g = 14 n = 7 h = 8.8

18 For 13-14, use the Five-Step Method. r 13) Landon earns about $60 per week mowing lawns in the summer and shoveling driveways in the winter. He invested $0 in equipment. How long will it take him to earn $860 w=weeks 60w-0=860 w=18 It will take Landon 18 weeks to earn $ (18)-0= =860 14) Meaghan is thinking of a mystery number. She cuts it in half then adds 5. The result is 4. Determine the mystery number. m=mystery number 0.5m+5=4 m=38 The mystery number is (38)+5=4 4=4 15) Select the equation that does not belong. a. 3 x 7 = 4 b. c. p =1 d. c 5 = 0 4k = 10 The solution is -. In all others, the solution is. 16) Identify and correct error: 3.5x +1. = ( 3.5x ) = ( 10.5)3.5 x = They should have divided by 3.5. The correct answer is x=3.

19 Name: Class: Date: -3 For 1-9, solve each two-step equation. Solving Two-Step Equations Practice (Answer Key) 1) 3a + =11 ) d 9 = 1 3) 3 j 3 ( 1 ) = 0 a = 3 d =1 j = 36 4e 4) 1 = 9 5) 6 + 4b =18 6) 9c e = 10 b = 6 c = 0 ( ) = 4 k m 7) = 8) 9) 3 = 0 5 f + 1 =11 k = 6 m = 5 f = 10) Use the Five-Step Method: Landon earns about $60 per week mowing lawns in the summer and shoveling driveways in the winter. He invested $0 in equipment. How long will it take him to earn $860 f w=weeks 60w-0=860 w=18 It will take Landon 18 weeks to earn $ (18)-0= =860

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