Objective: Add decimals using place value strategies, and relate those strategies to a written method.

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1 NYS COMMON CORE MATHEMATICS CURRICULUM Lesson Lesson 9 Objective: Add decimals using place value strategies, and relate those strategies to a written method. Suggested Lesson Structure Fluency Practice Application Problem Concept Development Student Debrief Total Time (14 minutes) (5 minutes) (31 minutes) (10 minutes) (60 minutes) Fluency Practice (14 minutes) Sprint: Round to the Nearest One 5.NBT.4 Decompose the Unit 5.NBT.1 Round to Different Place Values 5.NBT.4 One Unit More 5.NBT.7 (8 minutes) (2 minutes) (2 minutes) (2 minutes) Sprint: Round to the Nearest One (8 minutes) Materials: (S) Round to the Nearest One Sprint Note: This Sprint helps students build mastery of rounding to the nearest whole number. Decompose the Unit (2 minutes) Materials: (S) Personal white board Note: Decomposing common units as decimals strengthens student understanding of place value. T: (Project ) Say the number. S: 6 and 358 thousandths. T: How many tenths are in 6.358? S: 63 tenths. T: (Write = 63 tenths thousandths.) On your boards, write the number separating the tenths. S: (Write = 63 tenths 58 thousandths.) Repeat the process for hundredths. Follow the same process for to a written method. 140

3 NYS COMMON CORE MATHEMATICS CURRICULUM Lesson Concept Development (31 minutes) Materials: (S) Hundreds to thousandths place value chart (Lesson 7 Template), personal white board Problems tenths + 6 tenths 2 ones 3 thousandths + 6 ones 1 thousandth 2 tenths 5 thousandths + 6 hundredths T: (Write 2 tenths + 6 tenths on the board.) Solve 2 tenths plus 6 tenths using disks on your place value chart. S: (Solve.) T: Say the sentence using unit form. S: 2 tenths + 6 tenths = 8 tenths. T: How is this addition problem the same as a wholenumber addition problem? Turn and share with your partner. S: In order to find the sum, I added like units tenths with tenths. 2 tenths plus 6 tenths equals 8 tenths, just like 2 apples plus 6 apples equals 8 apples. Since the sum is 8 tenths, we don t need to bundle or regroup. T: (On the board, write Problems 2 and 3.) Work with your partner, and solve the next two problems with place value disks on your place value chart. NOTES ON MULTIPLE MEANS OF REPRESENTATION: Understanding the meaning of tenths, hundredths, and thousandths is essential. Proportional manipulatives, such as base ten blocks, can be used to ensure understanding of the vocabulary. Students should eventually move to concrete place value disks or drawing, which are more efficient. S: (Solve.) T: Let s record our last problem vertically. (Write and the plus sign underneath on the board.) What do I need to think about when I write my second addend? Lead students to see that the vertical written method mirrors the placement of disks on the chart. Like units should be aligned with like units. Avoid procedural language like line up the decimals. Students should justify alignment of digits based on place value units. to a written method. 142

7 NYS COMMON CORE MATHEMATICS CURRICULUM Lesson 9 Sprint 5 1 A Round to the Nearest One Number Correct: to a written method. 146

8 NYS COMMON CORE MATHEMATICS CURRICULUM Lesson 9 Sprint 5 1 B Round to the Nearest One Number Correct: Improvement: [KEY] to a written method. 147

9 NYS COMMON CORE MATHEMATICS CURRICULUM Lesson 9 Problem Set 5 1 Name Date 1. Solve, and then write the sum in standard form. Use a place value chart if necessary. a. 1 tenth + 2 tenths = tenths = b. 14 tenths + 9 tenths = tenths = one(s) tenth(s) = c. 1 hundredth + 2 hundredths = hundredths = d. 27 hundredths + 5 hundredths = hundredths = tenths hundredths = e. 1 thousandth + 2 thousandths = thousandths = f. 35 thousandths + 8 thousandths = thousandths = hundredths thousandths = g. 6 tenths + 3 thousandths = thousandths = h. 7 ones 2 tenths + 4 tenths = tenths = i. 2 thousandths + 9 ones 5 thousandths = thousandths = 2. Solve using the standard algorithm. a = b = c = d = to a written method. 148

10 NYS COMMON CORE MATHEMATICS CURRICULUM Lesson 9 Problem Set 5 1 e = f = 3. Van Cortlandt Park s walking trail is 1.02 km longer than Marine Park s. Central Park s walking trail is km longer than Van Cortlandt s. a. Fill in the missing information in the chart below. New York City Walking Trails Central Park Marine Park Van Cortlandt Park km 1.28 km km b. If a tourist walked all 3 trails in a day, how many kilometers would he or she have walked? 4. Meyer has 0.64 GB of space remaining on his ipod. He wants to download a pedometer app (0.24 GB), a photo app (0.403 GB), and a math app (0.3 GB). Which combinations of apps can he download? Explain your thinking. to a written method. 149

11 NYS COMMON CORE MATHEMATICS CURRICULUM Lesson 9 Exit Ticket 5 1 Name Date 1. Solve. a. 4 hundredths + 8 hundredths = hundredths = tenth(s) hundredths b. 64 hundredths + 8 hundredths = hundredths = tenths hundredths 2. Solve using the standard algorithm. a = b = to a written method. 150

12 NYS COMMON CORE MATHEMATICS CURRICULUM Lesson 9 Homework 5 1 Name Date 1. Solve. a. 3 tenths + 4 tenths = tenths b. 12 tenths + 9 tenths = tenths = one(s) tenth(s) c. 3 hundredths + 4 hundredths = hundredths d. 27 hundredths + 7 hundredths = hundredths = tenths hundredths e. 4 thousandths + 3 thousandths = thousandths f. 39 thousandths + 5 thousandths = thousandths = hundredths thousandths g. 5 tenths + 7 thousandths = thousandths h. 4 ones 4 tenths + 4 tenths = tenths i. 8 thousandths + 6 ones 8 thousandths = thousandths 2. Solve using the standard algorithm. a = b = c = d = to a written method. 151

13 NYS COMMON CORE MATHEMATICS CURRICULUM Lesson 9 Homework 5 1 e = f = 3. Walkway Over the Hudson, a bridge that crosses the Hudson River in Poughkeepsie, is kilometers long. Anping Bridge, which was built in China 850 years ago, is 2.07 kilometers long. a. What is the total span of both bridges? Show your thinking. b. Leah likes to walk her dog on the Walkway Over the Hudson. If she walks across and back, how far will she and her dog walk? 4. For his parents anniversary, Danny spends \$5.87 on a photo. He also buys a balloon for \$2.49 and a box of strawberries for \$4.50. How much money does he spend all together? to a written method. 152

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