Teaching Compensation for Addition (558 + 79)

### 3.2 Teaching the Method of Compensation to Calculate 558 + 79 The method of compensation is a mental math strategy that simplifies calculations by making one number more "friendly" (easier to work with) and then adjusting the result accordingly. Here's how you can teach this method for adding 558 and 79: 1. **Identify the Numbers**: Start by writing down the problem: 558 + 79. 2. **Adjust One Number**: Explain that it would be easier if we rounded 79 to a more whole number, like 80, because adding 80 is simpler. So, we will adjust 79 to 80. - \( 79 + 1 = 80 \) 3. **Adjust Calculation**: Since you added 1 to 79 to make it 80, you also need to subtract 1 from the final result to compensate for this change. - Calculate: \( 558 + 80 = 638 \) 4. **Compensate for the Adjustment**: Since we added an extra 1, we need to subtract that 1 from 638 to get the final correct answer. - \( 638 - 1 = 637 \) 5. **Final Result**: Thus, \( 558 + 79 = 637 \). Here's how you present it step-by-step to your students: - Add 1 to 79 to get 80 (a friendly number). - Add 80 to 558 to get 638. - Subtract 1 from 638 to get 637. ### 3.3 Teaching the Method of Compensation to Subtract 365 – 28 Compensation can also be used for subtraction to simplify calculations: 1. **Identify the Numbers**: Write down the subtraction problem: 365 - 28. 2. **Adjust One Number**: Explain that it would be easier if we rounded 28 to a friendly number, like 30, because subtracting 30 is simpler. So, we will adjust 28 to 30. - \( 28 + 2 = 30 \) 3. **Adjust Calculation**: Since you added 2 to 28 to make it 30, you also need to add this 2 to the final result to compensate for the initial rounding. - Calculate: \( 365 - 30 = 335 \) 4. **Compensate for the Adjustment**: Since we subtracted an extra 2, we need to add that 2 back to 335 to get the correct result. - \( 335 + 2 = 337 \) 5. **Final Result**: Thus, \( 365 - 28 = 337 \). Here's how you present it step-by-step to your students: - Add 2 to 28 to make it 30 (a friendly number). - Subtract 30 from 365 to get 335. - Add 2 to 335 to get 337. By using these steps, you help students see how compensation works by simplifying the arithmetic and then adjusting for those changes to get the accurate solution.