Rounding Decimals

Eureka Math

Place Value and
Decimal Fractions

Do Now
White Board

Directions: Express the numbers in the missing forms below.

Unit Form

Expanded Form

Standard Form

4 ones and 8 tenths 3 thousandths

3 thousandths and 8 tenths

3 hundredths

9 ones and 3 tenth 8 thousandths

4 hundredths and 1 tenth

8 thousandths

SWBAT round a given decimal to any place using place value understanding and the vertical number line.

Learning Objective:

SWBAT round a given decimal to any place using place value

understanding and the vertical number line.

Demonstration of Learning:

Given problems, I will round a given decimal to any place using place

value understanding and the vertical number line.

Module1 | TopicC | Lesson7

TEKS: 5.2C Rounddecimalstotenthsorhundredths

Place Value and Decimal Fractions

Decimal fractions

Tenths

Hundreths

Lesson Vocabulary

SWBAT round a given decimal to any place using place value understanding and the vertical number line.

4.87

4.87

4.87 = 4 87
100

Round to Different

Place Values

Round to Different Place Values

Oral/choral response

SWBAT round a given decimal to any place using place value understanding and the vertical number line.

8 ones

9 ones

8.5 = 85 tenths

87 tenths

8.735

Write the number sentence, when rounded to the nearest one.

8.735 ≈ __________

Round to Different Place Values

Whiteboard

SWBAT round a given decimal to any place using place value understanding and the vertical number line.

Write the number sentence, when rounded to the nearest tenth.

8.735 ≈ __________

87
tenths

88
tenths

875 hundredths = 8.75

8.735

873 hundredths

Round to Different Place Values

Whiteboard

SWBAT round a given decimal to any place using place value understanding and the vertical number line.

Write the number sentence, when rounded to the nearest
hundredth.

8.735 ≈ __________

873 hundredths

874 hundredths

8735 thousandths = 8.735

8.735

Round to Different Place Values

Oral/choral response

SWBAT round a given decimal to any place using place value understanding and the vertical number line.

7 ones

8 ones

7.5 = 75 tenths

74 tenths

7.458

Write the number sentence, when rounded to the nearest one.

7.458 ≈ __________

Round to Different Place Values

Whiteboard

SWBAT round a given decimal to any place using place value understanding and the vertical number line.

75
tenths

745 hundredths = 74.5

7.458

Write the number sentence, when rounded to the nearest tenth.

7.458 ≈ __________

74
tenths

Round to Different Place Values

Whiteboard

SWBAT round a given decimal to any place using place value understanding and the vertical number line.

Write the number sentence, when rounded to the nearest hundredth.

7.458 ≈ __________

745 hundredths

746 hundredths

7.458

7458 thousandths = 745.5

Application Problem

Learn Book page 49

Application Problem

Turn and Talk / Whiteboard

Organic whole wheat flour sells in bags weighing 2.915 kilograms.

A. How much flour is this when rounded to the nearest tenth?

B. How much flour is this when rounded to the nearest one?

Use a place value chart and number line to explain your

thinking.

SWBAT round a given decimal to any place using place value understanding and the vertical number line.

Extension: What is the difference of the two answers?

Application Problem

Turn and Talk / Whiteboard

Organic whole wheat flour sells in bags weighing 2.915
kilograms.

A.

How much flour is this when rounded to the

nearest tenth?

B.

How much flour is this when rounded to the

nearest one?

Use a place value chart and number line to
explain your thinking.

SWBAT round a given decimal to any place using place value understanding and the vertical number line.

Extension: What is the difference of the two answers?

Concept Development

Concept Development

Think-Pair-Share

Ms. Lisa asked her students to Decompose 49.67

Round 49.67 to the nearest ten.

SWBAT round a given decimal to any place using place value understanding and the vertical number line.

Tens

Ones

Tenths

Hundredths

6

9

4

7

49

6

7

496

7

4967

4 tens

5 tens

49.5 ones = 49

49.67

Ms. Lisa asked her student to round 49.67 to the nearest one.

SWBAT round a given decimal to any place using place value understanding and the vertical number line.

Tens

Ones

Tenths

Hundredths

4

9

6

7

49

6

7

496

7

4967

Concept Development

Think-Pair-Share

9 ones

10 ones

496 tenths = 49.65

49.67

Ms. Lisa asked her student to round 49.67 to the nearest tenth.

SWBAT round a given decimal to any place using place value understanding and the vertical number line.

Concept Development

Think-Pair-Share

Tens

Ones

Tenths

Hundredths

4

9

6

7

49

6

7

496

7

4967

6 tenths

7 tenths

4967 hundredths = 4967.5

49.67

Mr. Karma asked his students to Decompose 9.949.

SWBAT round a given decimal to any place using place value understanding and the vertical number line.

Ones

Tenths

Hundredths

Thousandths

Concept Development

Think-Pair-Share

4

9

9

9

99

4

9

994

9

9949

Round 9.949 to the nearest tenth.

Show your work on a number line.

SWBAT round a given decimal to any place using place value understanding and the vertical number line.

Ones

Tenths

Hundredths

Thousandths

9

9

4

9

99

4

9

994

9

9949

Concept Development

Think-Pair-Share

9 tenths

10 tenths

9.95 hundredths

9.949

Round 9.949 to the nearest hundredth.

Show your work on a number line.

SWBAT round a given decimal to any place using place value understanding and the vertical number line.

Concept Development

Think-Pair-Share

Ones

Tenths

Hundredths

Thousandths

9

9

4

9

99

4

9

994

9

9949

9 hundredths

10 hundredths

9.500 thousandths

9.949

A decimal number has 1 digit to the right of the
decimal point. If we round this number to the
nearest whole number, the result is 27. What
are the maximum and minimum possible
values of these two numbers?

Use a number line to show your reasoning.
Include the midpoint on the number line.

SWBAT round a given decimal to any place using place value understanding and the vertical number line.

Concept Development

Think-Pair-Share

27

27.5

28

27.4

SWBAT round a given decimal to any place using place value understanding and the vertical number line.

Concept Development

Think-Pair-Share

A decimal number has 1 digit to the right of the
decimal point. If we round this number to the
nearest whole number, the result is 27. What
are the maximum and minimum possible
values of these two numbers?

Use a number line to show your reasoning.
Include the midpoint on the number line.

26

26.5

27

Problem 3: Extension (Optional)

What if our number had exactly 2 digits
to the right of the decimal point? Could I
find a number larger than 27.4 that
would still round down to 27?

What is the largest possible value it could
have?

SWBAT round a given decimal to any place using place value understanding and the vertical number line.

Concept Development

Oral/ choral response

Student Guide Activity

Problem Set

Learn Book Page 51-52

#1, #2

Student Debrief

Student Debrief

●Compare our approach to rounding in today’s lesson and in Lesson 7. How are they
alike? How are they different? (Students will likely offer many accurate responses. Lead
the discussion, however, toward the notion of only choosing specific decompositions to
round in today’s lesson as opposed to naming every decomposition in Lesson 7. Explore
which units, or place values, are worthy of attention and which are not when rounding
to a specific place value. Are there patterns to these choices?)

●Once a number rounds up at one place value, does it follow then that every place value
will round up? Why or why not? (Encourage students to reference their Problem Sets as
evidence of their reasoning. Problem 1(b) provides an example of differing unit choices
resulting in differences in rounding up and down.)

●How does the place value chart help organize your thinking when rounding?

●Finding the maximum and minimum values poses a significant increase in cognitive load
and an opportunity to build excitement! Make time to deeply discuss ways of reasoning
about these tasks, as they are sure to be many and varied. Consider a discussion of
Problem 3 that mirrors the one in the lesson. What if our number has exactly 3 digits to the
right of the decimal? Can we find a value larger than 13.74 that would round down to
13.7? (13.749.) What about 4 places or 5 places to the right of the decimal? (13.7499,
13.74999.) Encourage students to generalize that we can get infinitely close to 13.5 with a
decimal that has an infinite number of nines, yet that decimal will still round down to 13.7.
We can find points on the number line as close as we like, and yet they will not be equal to
13.75. Follow the discussion with the discovery that this is not true for our minimum value.
There is nothing less than 13.750 that will round up to 13.8. Math journals offer a venue for
students to continue to explore maximum and minimum tasks beyond today’s lesson.

SWBAT round a given decimal to any place using place value understanding and the vertical number line.

Demonstration of Learning

Given problems, I will round a given decimal to any place using place

value understanding and the vertical number line.

LS1S2AE