1. Solving Equations using Mental Math Core Focus on Introductory Algebra Lesson 3.2

2. Copy and complete each table. Determine if each number in the table is a solution of the equation. x 7x = 42Solution? 6 7 8 x 26 − x = 15Solution? 10 11 12 Warm-Up 7(6) = 42YES 7(7)  42 NO 7(8)  42 NO 26 − 10  15 NO 26 − 11 = 15YES 26 − 12  15 NO

3. Solving Equations Using Mental Math Solve one-step equations using mental math. Lesson 3.2

4. Good to Know! In this lesson, you will learn a problem-solving strategy to solve equations using mental math. You will be given equations and asked to find the solution to each equation. The steps to mentally solve an equation are: GUESSCHECKREVISE

5. Use the Guess, Check and Revise method to solve the equation. a.y + 7 = 15 GUESS  CHECK  REVISE  CHECK y = 99 + 7 = 15y = 88 + 7 = 15 16  15 15 = 15 Example 1 Too high. Pick a lower number. y = 8 is the solution.

6. Use the Guess, Check and Revise method to solve the equation. b.6x = 30 GUESS  CHECK x = 56(5) = 30 30 = 30 Example 1 Continued… The first guess worked. x = 5

7. Two sisters, Kylie and Sara, went shopping for school clothes. Sara spent $105.11 and Kylie wasn’t sure how much she spent. The sisters spent a total of $187.68. Write an equation and use it to estimate how much Kylie spent on clothes. Let k stand for the amount Kylie spent. Kylie’s Clothes + Sara’s Clothes= Total Cost k + 105.11 = 187.68 Round to the nearest whole number.k + 105 = 188 Example 2 GUESS  CHECK  REVISE  CHECK k = 8080 + 105 = 188k = 8383 + 105 = 188 185  188 188 = 188

8. Step 1Helen grew her fingernails out so each nail is 24.2 cm long. The longest fingernail on record is 76.7 cm. Write an addition equation and use it to estimate how much longer Helen’s nails need to be to tie the record. Step 2John Evans balanced a 352 pound car on his head. Ryan worked his way up to balancing a 151 pound car on his head. Write an addition equation and use it to determine how many more pounds Ryan needs to balance on his head to tie the record. Step 3A Japanese pig named Kotetsu has the record for the highest jump by a pig. His jump measured 27.5 inches. An American pig jumped 12.2 inches. Write an addition equation and use it to estimate how many more inches the American pig needs to tie the record. Step 4Mac gathered 1,498 people for an Irish Dance. This is about 6,100 people fewer than the record set in Cork, Ireland on September 10, 2005. Write a subtraction equation and use it to estimate how many people attended the Irish Dance in Ireland in 2005.

9. How do you use the Guess, Check and Revise method to solve an equation? Communication Prompt

10. Solve each equation using the Guess, Check and Revise method. 1.4 + y = 13 2.8x = 48 3.21 − m = 3 4. Exit Problems y = 9 x = 6 m = 18 d = 24