Engage NY Module 1 LESSON 9 Objective: Add decimals using place value strategies and relate those strategies to a written method.

ROUND TO THE NEAREST ONE (SPRINT) This sprint will help build mastery of rounding to the nearest whole number.

Decompose the Unit Read this number: 6.358 How many tenths are in 6.358? 63 tenths 6.358 = 63 tenths and ____ thousandths 63 tenths and 58 thousandths

Decompose the Unit Read this number: 7.354 How many tenths are in 7.354? 73 tenths 7.354 = 73 tenths and ____ thousandths 73 tenths and 54 thousandths

Round to Different Place Values Say this number: 2.475 Round this number to the nearest tenth. 2.475 ≈ 2.5 Round 2.475 to the nearest hundredth. 2.475 ≈ 2.48 Say this number: 2.987 2.987 ≈ 3.0 Round 2.987 to the nearest hundredth. 2.987 ≈ 2.99

One Unit More Say the decimal that is one unit more than 5 tenths. Say the decimal that is one hundredth more than 5 hundredths. 0.06 = 6 hundredths Say the decimal that is one thousandth more than 5 thousandths. 0.006 = 6 thousandths Say the decimal that is one hundredth more than 8 hundredths. 0.09 = 9 hundredths

One Unit More Say the decimal that is one tenth more than 3 tenths. Say the decimal that is one thousandth more than 2 thousandths. 0.003 = 3 thousandths In your math journal write one more thousandth than 0.052. 0.052 + 0.001 = 0.053 = 53 thousandths In your math journal write one tenth more than 35 hundredths. 0.35 + 0.1 = 0.45 = 45 hundredths

One Unit More In your math journal write one thousandth more than 35 hundredths. 0.35 + 0.001 = 0.351 = 351 thousandths In your math journal write one hundredth more than 438 thousandths. 0.438 + 0.01 = 0.448 = 448 thousandths

APPLICATION PROBLEM Ten baseballs weigh 1,417.4 grams. About how much does 1 baseball weigh? Round your answer to the nearest tenth of a gram. Round your answer to the nearest gram. If someone asked you, “About how much does a baseball weigh?” which answer would you give? Why? Use a statement of solution to record your answers. One baseball weighs = _____ Rounded to the nearest tenth of a gram weight = _______ Rounded to the nearest gram weight = _______

Concept Development - Problem 1 Solve 2 tenths plus 6 tenths using disks on your place value chart. (2 tenths + 6 tenths = ______) Say the sentence in words. 2 tenths + 6 tenths = 8 tenths How is this addition problem the same as a whole number addition problem?

Concept Development - Problem 2 Solve 2 tenths 5 thousandths plus 6 hundredths using disks on your place value chart. (2 tenths 5 thousandths + 6 hundredths = ______) Say the sentence in words. 2 tenths 5 thousandths + 6 hundredths = 265 thousandths Let’s record our problem vertically. What do I need to think about when I write my second addend? 0.205 +0.060 0.265

Concept Development - Problem 3 Solve 2 ones 3 thousandths plus 6 ones 1 thousandth using disks on your place value chart. (2 ones 3 thousandths + 6 ones 1 thousandth = ______) Say the sentence in words. 2 ones 3 thousandths + 6 ones 1 thousandth = 8 and 4 thousandths Let’s record our problem vertically. What do I need to think about when I write my second addend? 2.003 +6.001 8.004

Concept Development - Problem 4 Use your place value chart and disks to show the addends of our next problem. 1.8 + 13 tenths = ______ Tell how you represented these addends. (Did you represent 13 tenths using 13 tenth disks or 1 one disk and 3 tenths disks? Did you represent 1.8 using mixed units or only tenths? Which way of composing these addends requires the least amount of drawing? Why? Will your choice of units in your drawing affect your sum? Add. Share your thinking with a partner. Let’s record what we did on our charts. Ones Tenths Hundredths 1.8 +1.3 3.1 3 1

Concept Development - Problems 5-6 In your math journal, draw a place value chart to show how to add these problems. Show your regrouping then check your answers using vertical column addition. 1 hundred 8 hundredths + 2 ones 4 hundredths = ______ 100.08 + 2.04 102.12 148 thousandths + 7 ones 13 thousandths = _______ .148 + 7.013 7.161

Concept Development - Problem 7 Use your place value chart and disks to find the sum of 0.74 and 0.59. 0.74 + 0.59 = ______ How is this problem like others we’ve solved? How was it different? We still need to combine like units – ones with ones, tenths with tenths, hundredths with hundredths but this time we have to bundle in two place value units. We still record our thinking the same way we do with whole numbers – aligning like units. Ones Tenths Hundredths 1 3 3 0.74 +0.59 1.33

Concept Development - Problems 8-9 In your math journal, solve these two problems using the written method (line up your digits according to place value). You may use a place value mat if needed. 7.048 + 5.196 = ______ 7.048 +5.196 12.244 7.44 + 0.774 = _______ 7.44 + 0.774 8.214

Problem Set, Debriefing, Exit Ticket, and Homework Complete Problem Set in small groups. Check answers and discuss difficulties. Handout Exit Ticket and independently. Handout Homework.