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Partial-Differences Subtraction Partial-differences subtraction builds on a skill most people use daily: reading from left to right. The person using this algorithm begins at the far-left side of the problem and subtracts the subtrahend (the lesser number) from the minuend (the greater number) one place-value column at a time until the final difference between the two numbers is reached. Most students find it helpful to see the subtrahend expressed in expanded notation, and many students find it natural to move from left to right when performing mathematical operations. Build Understanding Subtraction Review expanded notation: Write 2,638 on the board and explain how to write the number in expanded form (2,000 + 600 + 30 + 8). Have students expand the following numbers at their desks: 318; 1,967; 8,049. Ask volunteers to write the answers on the board, and, if necessary, model a few of the numbers using base-10 blocks. Note: If students seem confused when one or more of the place values are zero, explain two different ways they can handle the situation: Using 8,049 as an example, students can expand the number either as 8,000 + 0 + 40 + 9 or as 8,000 + 40 + 9. Using page 31, explain that with this method of subtracting, students will begin on the far-left side of the problem and subtract one place-value column at a time until they find the final difference between the minuend (the top number) and the subtrahend (the bottom number). Use questions like the following to guide students through the example (and through other examples you provide): • Which number will be broken down into its individual place values? (the subtrahend) • What is the greatest place value in the subtrahend? • How will you subtract the second-greatest place value in the subtrahend? (Write it in expanded notation and then subtract it from the minuend.) 1. 223 • What is the final difference between the minuend and the subtrahend? Error Alert Make sure students understand that the second subtracted number (100 in the example on page 31) has been “pulled out” from the original subtrahend. If necessary, have students write each subtrahend in expanded notation and then draw an arrow from each part of the expanded notation to its counterpart in the recorded algorithm (the “solution column”). 2. 566 3. 361 Check Understanding 4. 211 Write 213 − 148 on the board. Have three volunteers take turns solving each step of the problem to help emphasize the fact that three place values are being subtracted, one at a time, in sequence. Work through as many problems in this way as necessary until you are reasonably certain that most of your students understand the algorithm. Then assign the “Check Your Understanding” exercises at the bottom of page 31. (See answers in margin.) 5. 6,568 6. 768 7. 42,179 Copyright © Wright Group/McGraw-Hill Page 31 Answer Key 8. 4,449 30 Teacher Notes EM3_ALRH_Part 1_004-082_PDF.indd30 30 9/15/08 PDF Pages 2:44:55 PM Name Date Time Partial-Differences Subtraction Subtract left to right, one column at a time. In some cases, the larger number is on the bottom. When this happens and you subtract, the difference is a negative number. Example 9,328 - 5,170 First, write or think of 5,170 as 5,000 + 100 + 70 + 0. (minuend) (subtrahend) 9,328 - 5,170 Find the total. → (4,000 + 200 − 50 + 8) → Copyright © Wright Group/McGraw-Hill (9,000 (300 (20 (8 − − − 5,000) 100) 70) 0) → 4,000 200 → 50 → 8 → Multiplication Subtract the hundreds. Subtract the tens. Subtract the ones. → → → → Subtract the thousands. 4,158 Check Your Understanding Solve the following problems. 1. 317 − 94 2. 582 − 16 3. 640 − 279 4. 835 − 624 5. 7,104 − 536 6. 2,952 − 2,184 7. 43,870 − 1,691 8. 15,033 − 10,584 Write your answers on a separate sheet of paper. EM3_ALRH_Part 1_004-082_PDF.indd31 31 Student Practice 31 9/15/08 PDF Pages 2:44:55 PM