Moving with Algebra Sampler

27 Lesson Plans 261 ©MathTeachersPress, Inc. Reproductionbyanymeans isstrictly prohibited. 47 Solve. 1. 3 n – 1 = 5 n = ________ 4. 10 n – 20 = 0 n = ________ 7. +3 = 5 x = ________ 10. +5 = 8 n = ________ 13. 16 = 4 +3 x x = ________ 2. 2 n + 8 = 12 n = ________ 5. 3 + 5 n = 18 n = ________ 8. –4 = 1 x = ________ 11. 7 = +3 n = ________ 14. 2 = – 3 n = ________ 3. 4 x – 3 = 25 x = ________ 6. 15 = 5 x + 5 x = ________ 9. +4 = 7 x = ________ 12. 9 = 5 + n = ________ 15. – 1 = 2 n = ________ n __ 10 n __ 8 x __ 4 n __ 5 n __ 2 x __ 2 n __ 3 x __ 4 16. 3 n +2 n +5 = 20 19. 8 = 5 n + 2 n – 6 22. 5 n – 4 + 2 n = 17 17. 5 n – 8 + n = 4 20. 4 n +3 – 2 n – 6 = 5 23. 14 + 2 n +5 = 39 18. 3 n – n +7 = 13 21. 7 n – 4 +9 n = 28 24. 2 n +8 +( – 4) = 10 Combine like terms.Solve. Solving Two-Step Equations 25. Bernice said,“I am thinking of a number.If I multiply it by 3 and subtract 5 from the result, I get 40.” What was Bernice’s number? ________ 26. Paul said,“I am thinking of a number.If I multiply it by 10 and add 5 to the result, I get 65.”What was Paul’s number? ________ 2 2 7 2 3 2 8 10 12 9 8 32 4 25 30 5 n =15 6 n =12 2 n =6 n =3 n =2 n =3 14=7 n 2 n =8 16 n =32 n =2 n =4 n =2 7 n =21 2 n =20 2 n =6 n =3 n =10 n =3 n =15 n =6 You can solve equations with more than one step by using the properties of equality.First undo the addition and subtraction.Then undo the multiplication and division. 2 n 5 7 2 n 5 5 7 5 2 n 12 n 6 12 2 2 n 2 2 n 5 7 1. Undo the addition or subtraction. 2. Undo the multiplication or division. Objective: To solve two-step equations using inverse operations. Materials: Black and white cubes (or positive and negative integer squares, Master 19, or Algebra Tiles), brown paper bags (or envelopes), small paper plates Two-Step Equations Write on the board or overhead: (Student’s name) thought of a number. He divided it by 2 and subtracted 5 from the quotient. The result was 1. What was the number? Ask a student to suggest the related number sentence. – 5 = 1 Model the solution with rods, cubes (or squares) and bags (or envelopes). You will need 2 paper plates for the second step when 12 black cubes are shared or divided on 2 paper plates. Ask students to draw a picture of the solution and solve the problem with pencil. Drawing: Solution with paper and pencil: – 5 = 1 2 n – 5 + 5 = 1 + 5 = 6 2 • = 6 • 2 n = 12 n 2 n 2 n 2 n 2 Read the explanation together. Relate the pattern of undoing to using the inverse operation. In the first step, 5 was subtracted from the variable, so we add 5 to both sides of the equation to undo the operation. In the second step, the variable is multiplied by 2, so we divide both sides by 2. The odd-numbered problems may be worked with a partner. Have students complete the even- numbered problems independently. Checking by Substitution Have students check their answers using substitution. Creating Puzzles Have students make up their own two-step number puzzles. Collect the problems and redistribute copies to other class members. Example: If I multiply my age by 2 and subtract 6, the answer is 20. How old am I? Skill Builders pp. 217, 218, 245 Positive and Negative Integers Algebra Adding positive and negative integers Sample Lesson Algebra & Functions Unit 5