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

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

3. Compare decimal fractions
Compare these numbers using the greater than, less than, or equal sign.
12.57 ____
328.2 _____
12.57 < 12.75
328.2 >
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

4. Rename the units 1.5 = ____ tenths 27.5 = ____ tenths

5. 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: minutes
Randy: minutes
Charlie: minutes
Sam: minutes
Who won first ? Who won second ? Third? Fourth? Give a statement of solution for your answers.

6. 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.

7. 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

8. 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

9. 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

10. Concept development problem 3
Strategically decompose to round to the nearest ten, one, tenth, and hundredth.
Use your place value chart and decompose 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

11. Concept development problem 3
Strategically decompose to round 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 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

12. Concept development problem 4
Strategically decompose to round to the nearest ten, one, tenth, and hundredth.
Use your place value chart and decompose 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

13. Concept development problem 4
Strategically decompose to round 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

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

15. 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.