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FOCUS ALGORITHM Partial-Sums Addition for Decimals Addition Just as they do with whole numbers, problem solvers add decimals by adding values of digits one place-value column at a time—whether tens or tenths, hundreds or hundredths, and so on. The partial-sums algorithm and the column-addition algorithm used for adding multidigit whole numbers can easily be applied to decimal addition as long as the problem solver is careful to keep track of the place values—both whole-number and decimal place values. Students will feel empowered as they discover that they can apply their number sense and understanding of whole-number addition to decimal situations. The key, as with whole-number addition, is to pay attention to the place values, and consequently the decimal point, in each of the addends. Build Understanding Discuss equivalent decimals like 7.3, 7.30, and 7.300. Then have students annex zeros to find equivalent decimals for 6.7, 0.4, 0.023, and 9. You may also want to review the whole-number versions of this algorithm on pages 4–7. As you work through Example 1 on page 17, point out that the partial sums should be written with the same number of decimal places as the addend with the greater (or greatest) number of decimal places. Use questions like the following to guide students through the examples: • Does it matter which place-value column you add first? (no) • In Example 1, why are 6 ones written as 6.000? (Zeros are added to show the same number of decimal places as the addend with the greater number of decimal places. In this example, both 4.658 and 2.761 happen to have the same number of decimal places—three.) Error Alert Watch for students who do not write all the partial sums and the answer with the same number of decimal places. If students have difficulty with this, they may first need to review place value. Check Understanding 1. 6.166 Write 5.298 + 3.44 on the board. Have a volunteer work the problem using the partial-sums algorithm. Encourage the student to “ narrate” his or her thought process. Encourage the class to ask questions, and guide the volunteer in answering as necessary. When you are reasonably certain that most of your students understand the algorithm, assign the “Check Your Understanding” exercises at the bottom of page 17. (See answers in margin.) 2. 67.84 3. 1.002 4. 0.034 5. 6.291 Copyright © Wright Group/McGraw-Hill Page 17 Answer Key 6. 18.029 7. 102.02 8. 5.914 16 Teacher Notes EM3_ALRH_Part 1_004-082_PDF.indd16 16 9/15/08 PDF Pages 2:44:49 PM Name Date Time FOCUS ALGORITHM Partial-Sums Addition for Decimals Use what you already know about adding whole numbers. Add one place-value column at a time. → → → → → 4.658 + 2.761 6.000 1.300 0.110 + 0.009 7.419 → → → → → 9.682 + 1.506 10.000 1.100 0.080 + 0.008 11.188 Example 1 Add Add Add Add Add the the the the the ones. tenths. hundredths. thousandths. partial sums. → → → → → (4.000 + 2.000) (0.600 + 0.700) (0.050 + 0.060) (0.008 + 0.001) (6.000 + 1.300 + 0.110 + 0.009) Copyright © Wright Group/McGraw-Hill Example 2 Add Add Add Add Add the the the the the ones. tenths. hundredths. thousandths. partial sums. → → → → → (9.000 + 1.000) (0.600 + 0.500) (0.080 + 0) (0.002 + 0.006) (10.000 + 1.100 + 0.080 + 0.008) Addition Remember to pay attention to the place values of the addends to record the decimal point in the sum. Check Your Understanding Solve the following problems. 1. 3.441 + 2.725 2. 60.45 + 7.39 3. 0.906 + 0.096 4. 0.006 + 0.028 5. 2.4 + 3.891 6. 12.34 + 5.689 7. 89.22 + 12.8 8. 5 + 0.034 + 0.88 Write your answers on a separate sheet of paper. EM3_ALRH_Part 1_004-082_PDF.indd17 17 Student Practice 17 9/15/08 PDF Pages 2:44:49 PM