What are we going to do?

1. Learning Objective We will add and subtract multi-digit decimals. What are we going to do? CFU Activate Prior Knowledge • A decimal numberincludes place values lower than the ones place. • Digits to the right of the decimal point represent values less than one. Subtract the decimal numbers. Add the decimal numbers. Decimal Point Hundredths Hundreds 1 Tenths Ones Tens 2 . . 1 1 5 6 7 1 5 3 7 2 5 4 3 1 . . Students, you already know how to add and subtract numbers with decimals. Now, we will add and subtract multi-digit numbers with decimals. Make Connection + - Place Value 9 3 2 8 1 8 . . 2 4 9 9 7 1 9

2. Concept Development • To add and subtract decimals, the numbers must be lined up by place value. • A quick way to line up decimal numbers by place value is to line up their decimal points. 14.5 = 14.500 Additional zeroes are used when needed. CFU Which problem below has the decimal places lined up correctly? How do you know? A B In your own words, how do you add and subtract decimals? “Adding and subtracting decimals is done by __________.” Adding and Subtracting Decimals Tom and his grandfather went fishing. They both caught a fish. Tom’s fish weighed 8.123 pounds and his grandfather’s weighed 14.5 pounds. Place Value How many pounds of fish do they have altogether? How much less does Tom’s fish weigh than his grandfather’s? Thousands Hundreds Tens Ones Tenths Hundredths Thousandths Ten Thousands Decimal Point Hundred Thousands 14.5 + 8.123 = ? 14.5 – 8.123 = ? . , 7 8 2 2 5 4 1 3 3 They have 22.623 pounds of fish altogether. Tom’s fish weighs 6.377 fewer pounds.

3. Skill Development/Guided Practice • To add and subtract decimals, the numbers must be lined up by place value. • A quick way to line up decimal numbers by place value is to line up their decimal points. How did I/you line up the numbers? How did I/you interpret the sum or difference? CFU Add and subtract multi-digit numbers 2 Read the problem and identify1 the values being added or subtracted, if needed. Line up the numbers by the place value of their digits. Add or subtract the numbers. Hint: Start at the lowest place value. Interpret2 the sum or difference. Hint: Answer the question. 1 4 2 3 4 1. 1,244.602 + 20,327.5 = ? 2. 10,167.27 – 3,621.561 = ? 1 1 0 9 6 6 1,244.602 1 1 1 1 10,167.270 - + - + 20,327.500 3,621.561 2 1, 5 7 2 1 0 2 . 6, 4 5 7 0 9 5 . 3. 781,164.01 – 363,065.003 = ? 4. 432,562.713 + 13,252.53 = ? 1 1 432,562.713 7 0 5 0 1 1 1 1 781,164.010 13,252.530 363,065.003 1 find (synonym) 2 explain the meaning of Vocabulary 4 4 5, 8 1 5. 2 4 3 4 1 8, 0 9 9. 0 0 7

4. Skill Development/Guided Practice (continued) How did I/you determine what the question is asking? How did I/you determine the math concept required? How did I/you determine the relevant information? How did I/you solve and interpret the problem? How did I/you check the reasonableness of the answer? CFU 1 2 3 4 Anita and her father went panning3 for gold. They both found some gold! Her father’s nugget was 3.221 grams. Anita’s nugget was 12.04 grams. 5 + - 5. How much gold did they find altogether? 6. How much larger is Anita’s nugget than her father’s? 1 3 1 1 12.040 12.040 3.221 3.221 1 5. 2 6 1 8. 1 1 9 Anita and her father found a total of 15.261 grams of gold. Anita’s nugget was 8.119 grams larger than her father’s. 3 looking for valuables in a river bed using a small pan Vocabulary

5. Skill Development/Guided Practice (continued) CFU How did I/you determine what the question is asking? How did I/you determine the math concept required? How did I/you determine the relevant information? How did I/you solve and interpret the problem? How did I/you check the reasonableness of the answer? 1 2 3 4 7. Mr. James was measuring out chemicals for a science experiment for his classes. He has already measured out 1,356.078 grams of sulfur. He needs a total of 10.475 kilograms (10,475 grams). How much more sulfur does he need? 5 + - 6 4 9 9 1 1 1 1 10,475.000 1,356.078 Mr. James needs 9,118.922 more grams of sulfur. 9, 1 1 8. 9 2 2 8. If each of Mr. James’ students need to dissolve 26.332 grams of sulfur into 12.6 liters of water (12,600 grams). How much will the solution weigh altogether? 26.332 12,600.000 The solution will weigh 12,626.332 grams altogether. 1 2, 6 2 6. 3 3 2

6. Relevance • To add and subtract decimals, the numbers must be lined up by place value. • A quick way to line up decimal numbers by place value is to line up their decimal points. Adding and subtracting multi-digit decimals will help you in real life. 1 Emil bought a drink for $1.68 and paid for it with a $20.00 bill. His waiter was not paying attention when he did the math and only gave him $0.32 back! The waiter did not line up the decimal points 20.0 1.68 0.32 Adding and subtracting multi-digit decimals will help you do well on tests. 2 - Sample Test Question: 99. Which of the following problems is/are correct? A 1,237.123 + 321.25 = 1,558.373 B 532,125.62 – 193,365.324 = 338,760.296 C D CFU Does anyone else have another reason why it is relevant to add and subtract multi-digit decimals? (Pair-Share) Why is it relevant to add and subtract multi-digit decimals? You may give one of my reasons or one of your own. Which reason is more relevant to you? Why? Yes Yes Yes Yes No No No No

7. To add and subtract decimals, the numbers must be lined up by place value. • A quick way to line up decimal numbers by place value is to line up their decimal points. Skill Closure Add and subtract multi-digit numbers Read the problem and identify the values being added or subtracted, if needed. Line up the numbers by the place value of their digits. Add or subtract the numbers. Hint: Start at the lowest place value. Interpret the sum or difference. Hint: Answer the question. 1 2 3 4 Word Bank Word Bank 2. James jogs every morning. Last week, he ran a total of 23.65 miles. This week he ran 17.324 miles. How much further did he run last week? 1. 1,244.602 + 20,327.5 = ? addition subtraction decimals place value multi-digit decimal point + - 1 1 1,244.602 20,327.500 1 4 James ran 6.326 miles further last week. 1 1 23.650 2 1, 5 7 2. 1 0 2 17.324 0 6. 3 2 6 Access Common Core Anita thinks that the answer to question 2 above is 40.976 miles. Explain the mistake that she made. Anita added the two distances instead of subtracting them. Summary Closure What did you learn today about adding and subtracting multi-digit numbers? (Pair-Share) Use words from the word bank.

8. Independent Practice • To add and subtract decimals, the numbers must be lined up by place value. • A quick way to line up decimal numbers by place value is to line up their decimal points. Add and subtract multi-digit numbers Read the problem and identify the values being added or subtracted, if needed. Line up the numbers by the place value of their digits. Add or subtract the numbers. Hint: Start at the lowest place value. Interpret the sum or difference. Hint: Answer the question. 1 2 3 4 1. 17,578.786 + 865,952.46 = ? 2. 307,167.27 – 13,352.361 = ? 2 6 6 6 1 1 1 1 1 1 1 1 1 1 307,167.270 17,578.786 + - + - 13,352.361 865,952.460 2 9 3, 8 1 4. 9 0 9 8 8 3, 5 3 1. 2 4 6 3. 853,325.8 – 462,156.035 = ? 4. 523,621.312 + 141,658.214 = ? 1 7 2 1 7 9 1 1 1 1 1 523,621.312 853,325.800 141,658.214 462,156.035 6 6 5, 2 7 9. 5 2 6 3 9 1, 1 6 9. 7 6 5

9. Independent Practice (continued) Helga and Julio were weighing their backpacks with all their books in them. Helga’s backpack weighed 12,465.27 grams. Julio’s backpack weighed 16,147.931 grams. - + 5. How much less does Helga’s backpack weigh than Julio’s? 6. Julio has to carry his oboe for music class that weighs 1292.738 grams. How much will Julio have to carry to school? 5 0 8 1 1 1 1 1 1 16,147.931 16,147.931 12,465.270 1,292.738 0 3, 6 8 2. 6 6 1 1 7, 4 4 0. 6 6 9 Helga’s backpack weighs 3,682.661 grams less than Julio’s. Julio has to carry 17,440.669 grams to school.

10. Periodic Review 1 Sven and Shan are working on their science fair project about growing different bean plants. The first plant has grown 1,234.659 millimeters. The second plant has grown 2,149.53 millimeters. 1. How much longer is the second plant? 2. After another week, the first plant had grown another 1,198.3 millimeters. How long is the first plant now? 1 8 4 2 1 1 1 1 2,149.530 1 1 1,234.659 1,234.659 1,198.300 0 9 1 4. 8 7 1 2, 4 3 2. 9 5 9 The first plant is 914.871 millimeters longer. The first plant is now 2,432.959 millimeters long. - +

11. Access Common Core Before completing the problems below, identify the addition problems that will need composing and the subtraction problems that will need decomposing. In which place value is composing/decomposing needed? Explain how you know whether an addition problem will need composing. 661,856.054 910,291.000 986,432.321 All of these problems will need composing. They all have at least one set of digits that will add up to 10 or more. - - - + + + Explain how you know whether a subtraction problem will need decomposing. 852,367.010 782,311.421 325,721.051 921,164.320 781,362.356 69,816.067 134,065.311 336,135.003 316,555.457 23,065.403 128,928.644 1,245.951 465,755.964 898,098.917 68,575.116 All of these problems will need composing. They all have at least one set of digits where a larger digit is being subtracted from a smaller one.

12. Periodic Review 2 The state of Michigan is resurfacing the highway between Flint and Grand Rapids. The highway is 183,465 meters. They have already resurfaced 92,436.35 meters. 1. How many more meters do they have left to do? 2. If they finish another 138.635 meters tomorrow, how much will they have done? 5 4 9 1 1 1 1 183,465.00 92,436.350 92,436.35 138.635 9 1, 0 2 8. 6 5 9 2, 5 7 4. 9 8 5 + -

13. Access Common Core 1. Describe and correct the error made in each of the addition problems. 1a. 1b. 1c. There should have been regrouping in the hundredths place. The answer should be 833,877.873 There should have been regrouping in the hundredths and the thousands place. The answer should be 826,059.300 The tenths place was added incorrectly. The answer should be 1,054,809.744. + - - + - + 2. Describe and correct the error made in each of the subtraction problems. 2a. 2b. 2c. 310,346.887 735,252.818 457,810.989 936,866.59 453,430.357 924,481.807 596,998.755 147,757.404 372,628.943 5,905.268 528,208.393 573,531.086 1,054,809.844 995,919.27 825,059.290 588,595.414 396,273.414 883,877.863 The place values were incorrectly lined up. The answer should be 930,961.322. This answer is correct. Starting at the thousands place, regrouping was done without subtracting from the top digits. The correct answer is 587,495.414

14. Periodic Review 3 Walker would like to hang several banners side by side on the wall of his store. They are 10,475.8 millimeters; 13,175.33 millimeters; and 9,476.039 millimeters long. 1. How much space on his wall will be needed to hang them all side by side? 2. The section of wall that Walker wants to hang the banners on is 34.5 meters (34,500 millimeters) long. Will he have enough space to hang them? How much space will be left over, or how much more room will be needed? 1 1 2 1 1 10,475.800 13,175.330 9,476.039 4 9 9 9 9 1 1 1 1 1 34,500.000 millimeters will be needed 3 3, 1 2 7. 1 6 9 33,127.169 + - meters will be left over 0 1, 3 7 2. 8 3 Access Common Core Helena spilled White-Out on her math homework. Help Helena fix her homework by filling in the missing numbers. Explain how you knew which numbers were missing. 3 9 9 3. 6 3 4 9 0 2 8 3 2 5 0 1 4 9,

15. EDI – Cognitive, Teaching, and English Learner Strategies Cognitive Strategies Teaching Strategies Language Strategies Content Access Strategies