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2. Lesson Menu Objectives Vocabulary Example 1 Example 2 Quick Quiz

3. Objectives To extend the techniques of solving balance puzzles to equation-solving techniques that are independent of the model To provide experience in assigning variables and translating problems into algebraic sentences To develop strategies for solving equations through operations with the balance model

4. Vocabulary model

5. Example 1 Write an equation that fits the balance puzzle. On the left side of the balance there are 4 bags of blocks and 4 single blocks. If n stands for the number of blocks in each bag, then the number of blocks in “four bags and four blocks” is 4n + 4. On the right side of the balance there are 2 bags and 6 single blocks. The number of blocks in “two bags and six blocks” is 2n + 6.

6. Example 1 Since the sides balance, the number of blocks on the left, 4n + 4, is equal to the number of blocks on the right, 2n + 6. This can be expressed with the equation 4n + 4 = 2n + 6. Answer: 4n + 4 = 2n + 6

7. 1.A 2.B 3.C 4.D Example 1 Find the equation that matches the balance puzzle. A.3n + 6 = 5n + 3 B.4n + 3 = 3n + 5 C.3n + 6 = 3n + 5 D.4n + 3 = 5n + 3

8. Example 2 Write an equation that fits the balance puzzle. On the left side of the balance there are 3 bags of blocks and 1 single block. If n stands for the number of blocks in each bag, then the number of blocks in “three bags and one block” is 3n + 1. On the right side of the balance there are 2 bags and 9 single blocks. The number of blocks in “two bags and nine blocks” is 2n + 9.

9. Example 2 Since the sides balance, the number of blocks on the left, 3n + 1, is equal to the number of blocks on the right, 2n + 9. This can be expressed with the equation 3n + 1 = 2n + 9. Answer: 3n + 1 = 2n + 9

10. 1.A 2.B 3.C 4.D Example 2 Find the equation that matches the balance puzzle. A.3n + 6 = 4n + 9 B.3n + 6 = 9n + 4 C.6n + 3 = 9n + 4 D.6n + 3 = 4n + 9

11. 1.A 2.B 3.C 4.D Quick Quiz 1A A. Three bags and 7 blocks are in balance with one bag and 12 blocks. Select the equation for this situation. A.3 + 7 = 1 + 12 B.4b = 19 C.3b + 7 = b + 12 D.3b + 7 = 1 + 12

12. 1.A 2.B 3.C 4.D Quick Quiz 1B B. Three bags and 7 blocks are in balance with one bag and 12 blocks. Solve the equation by using balance operations. A.b = 15 B.b = 2.5 C.b = 5 D.b = 19

13. 1.A 2.B 3.C 4.D Quick Quiz 2A A. Find the equation that matches the balance puzzle. A.2n + 8 = 5n + 2 B.8n + 5 = 2n + 5 C.13n = 7n D.10n = 10

14. 1.A 2.B 3.C 4.D Quick Quiz 2B B. Solve 2n + 8 = 5n + 2. A.n = 4 B.n = 1 C.n = 3 D.n = 2

15. 1.A 2.B 3.C 4.D Quick Quiz 3 CHALLENGE Complete the equation 2x + 3 = ___ so that it describes a balance puzzle that has an answer of 5.5 blocks. A.2x + 3 = 14 B.2x + 3 = 13 C.2x + 3 = 33 D.2x + 3 = 5.5

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17. Resources Image Bank Math Tools Multilingual e-Glossary Solving Equations Using Algebra Tiles Spreadsheets Solving EquationsTwo-Step Equations

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