2. Everyday Mathematics Partial-Differences Subtraction

3. Partial-Differences Subtraction Partial-differences subtraction involves: Thinking about numbers in expanded notation; Using place value to determine partial differences; and Adding partial differences. Everyday Mathematics

4. Partial-Differences Subtraction Solve: 471 – 293 We begin by thinking about each number in expanded notation. 471 = 400 + 70 + 1 293 = 200 + 90 + 3 We can subtract in any place- value order. Everyday Mathematics 471 – 293

5. Partial-Differences Subtraction Solve: 471 – 293 Everyday Mathematics 471 – 293 Let’s start with the hundreds place. 471 = 400 + 70 + 1 293 = 200 + 90 + 3 400 – 200 = 200

6. Partial-Differences Subtraction Solve: 471 – 293 Everyday Mathematics 471 – 293 Now we subtract the tens. Since we are subtracting a larger 400 – 200 = 200 number from a smaller number, the difference is negative. 471 = 400 + 70 + 1 293 = 200 + 90 + 3 70 – 90 = –20

7. Partial-Differences Subtraction Solve: 471 – 293 471 – 293 400 – 200 = 200 70 – 90 = –20 Everyday Mathematics Finally, we subtract the ones. 471 = 400 + 70 + 1 293 = 200 + 90 + 3 Since we are subtracting a larger number from a smaller number, the difference is negative. 1 – 3 = –2

8. Partial-Differences Subtraction Solve: 471 – 293 Everyday Mathematics 471 – 293 We add the partial-differences to find the total. 200 –20 + –2 178 471 – 293 = 178

9. Partial-Differences Subtraction When children use partial-differences subtraction they practice Everyday Mathematics a variety of skills related to number sense and algebraic reasoning. For example: Thinking about numbers in expanded notation; Using place value to determine partial differences; and Adding positive and negative numbers. If children start with the largest place value, which is generally their inclination, they begin the problem-solving process with a reasonable estimate of what the final answer should be.