Objectives Vocabulary Example 1 Example 2 Quick Quiz

• To develop strategies for solving equations through operations with the balance model • 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

• model

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 4 n + 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 2 n + 6.

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

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

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 3 n + 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 2 n + 9.

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

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

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. 4 b = 19 C. 3 b + 7 = b + 12 D. 3 b + 7 = 1 + 12 1. 2. 3. 4. A B C D

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 1. 2. 3. 4. A B C D

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

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

CHALLENGE Complete the equation 2 x + 3 = ___ so that it describes a balance puzzle that has an answer of 5. 5 blocks. A. 2 x + 3 = 14 B. 2 x + 3 = 13 C. 2 x + 3 = 33 D. 2 x + 3 = 5. 5 1. 2. 3. 4. A B C D

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