Engage NY Module 1 LESSON 7 Objective: Round a given decimal to any place using place value understanding and the vertical number line.

FIND THE MIDPOINT (SPRINT) Review finding the halfway point between a few numbers then pass out the “sprint” exercises to the students.

Compare decimal fractions Compare these numbers using the greater than, less than, or equal sign. 12.57 ____ 12.75 328.2 _____328.099 12.57 < 12.75 328.2 > 328.099 0.67 _____ 𝟔𝟕 𝟏𝟎𝟎 4.07 _____ forty-seven tenths 4.07 < forty-seven tenths 0.67 = 𝟔𝟕 𝟏𝟎𝟎 Twenty-four and 9 thousandths ___ 3 tens 𝟖𝟑 𝟏𝟎𝟎 _____ 0.084 Twenty-four and 9 thousandths < 3 tens 𝟖𝟑 𝟏𝟎𝟎 > 0.084

Rename the units 1.5 = ____ tenths 27.5 = ____ tenths

APPLICATION PROBLEM Craig, Randy, Charlie, and Sam ran a 5K race on Saturday. They were the top 4 finishers. Here are their race times: Craig: 25.9 minutes Randy: 32.2 minutes Charlie: 32.28 minutes Sam: 25.85 minutes Who won first ? Who won second ? Third? Fourth? Give a statement of solution for your answers.

Concept development problem 1 Work with your neighbor to name 155 using as many hundreds as possible. Then name it using as many tens as possible, and then using as many ones as possible. Record your ideas in your place value chart. Hundreds Tens Ones Tenths Hundredths Thousandths 1 hundred 5 tens 5 ones 15 tens 5 ones 155 ones Strategically decompose 155 using multiple units to round to the nearest ten and nearest hundred.

Concept development problem 1 Hundreds Tens Ones Tenths Hundredths Thousandths 1 hundred 5 tens 5 ones 15 tens 5 ones 155 ones Which of these decompositions of 155 helps you round this number to the nearest 10? Talk with your table. Record each of these numbers on your number line. Circle the figure that rounds 155 to the nearest 10. 16 tens = 160 15 tens + 5 ones = 155 15 tens = 150

Concept development problem 1 Hundreds Tens Ones Tenths Hundredths Thousandths 1 hundred 5 tens 5 ones 15 tens 5 ones 155 ones Using your chart, which of these representations help you round 155 to the nearest 100? Label your number line with the nearest multiples and circle your rounded number. 2 hundreds = 200 155 1 hundred + 5 tens = 150 1 hundred = 100

Concept development problem 2 Strategically decompose 1.57 to round to the nearest whole and nearest tenth. Use your place value chart to name 1.57 using as many ones, tenths, and hundredths as possible. Record your ideas on your place value chart. Hundreds Tens Ones Tenths Hundredths Thousandths 1 one 5 tenths 7 hundredths 15 tenths 7 hundredths 157 hundredths 16 tenths = 1.60 Notice this problem shows the relationship between meters and centimeters as different units are being used to name the same quantity. That is 1.57 meters = 157 centimeters. 15 tenths + 7 hundredths = 1.57 15 tenths + 5 hundredths 15 tenths = 1.50

Concept development problem 3 Strategically decompose to round 4.381 to the nearest ten, one, tenth, and hundredth. Use your place value chart and decompose 4.381 using as many tens, ones, tenths, and hundredths as possible. Record your work. Hundreds Tens Ones Tenths Hundredths Thousandths 4 ones 3 tenths 8 hundredths 1 thousandth 43 tenths 8 hundredths 1 thousandth 438 hundredths 1 thousandth 4381 thousandths

Concept development problem 3 Strategically decompose to round 4.381 to the nearest ten, one, tenth, and hundredth. Hundreds Tens Ones Tenths Hundredths Thousandths 4 ones 3 tenths 8 hundredths 1 thousandth 1 thousandth 43 tenths 8 hundredths 438 hundredths 1 thousandth 4381 thousandths We want to round this number to the nearest 10 first. How many tens did you need to make this number? Between what two multiples of ten will we place this number on the number line? Draw your number line and circle your rounded number. Round 4.381 to the nearest one, tenth, and hundredth. Mark these on your number line. 1 ten = 10 5 ones = 5 4 ones + 381 4 ones = 4 0 tens = 0

Concept development problem 4 Strategically decompose to round 9.975 to the nearest ten, one, tenth, and hundredth. Use your place value chart and decompose 9.975 using as many tens, ones, tenths, and hundredths as possible. Record your work. Hundreds Tens Ones Tenths Hundredths Thousandths 0 tens 9 ones 9 tenths 7 hundredths 5 thousandths 99 tenths 7 hundredths 5 thousandths 997 hundredths 5 thousandths 9975 thousandths

Concept development problem 4 Strategically decompose to round 9.975 to the nearest ten, one, tenth, and hundredth. Hundreds Tens Ones Tenths Hundredths Thousandths 0 tens 9 ones 9 tenths 7 hundredths 5 thousandths 99 tenths 7 hundredths 5 thousandths 997 hundredths 5 thousandths 9975 thousandths tens tenths hundredths ones 10 ones = 10 1 ten = 10 100 tenths = 10 998 hundredths 9.975 9.975 9.975 9.5 9.5 9.95 9.975 9 ones = 9 0 tens 99 tenths = 9.9 997 hundredths

Concept development problem 4 Repeat the sequence to strategically decompose to round 99.799 to the nearest ten, one, tenth, and hundredth. Hundreds Tens Ones Tenths Hundredths Thousandths tens tenths hundredths ones

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.