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INEQUALITY 5.NBT.4
Rounding Decimals and Mixed Decimals
Purpose:
To illustrate rounding decimals and mixed decimals
Materials:
Decimal Squares and Mixed Decimal Place Value Tables (attached)
TEACHER MODELING/STUDENT COMMUNICATION
Activity 1 Rounding to the nearest whole number
Decimal
Squares
1a. Spread the squares face down. Select any square and write its
decimal. Is your square less than half shaded, half shaded, or greater
than half shaded? (The square shown here is more than half shaded.)
.7
pencils
and paper
b. Is the decimal for your square closer to 0, closer to 1, or half way between? (.7 is
closer to 1 that to 0.)
c. The closest whole number, 0 or 1, is the value of your decimal rounded to the
nearest whole number. If the square is half shaded, we will round the decimal to 1.
Ask for a show of hands for students whose decimals round to 1; to 0.
2a. Select any square, place it face up, and use the
backs of two more squares of the same color to
illustrate a mixed decimal. Write the mixed decimal
for your three squares.
2.85
b. Is the shaded amount of your face-up square less than, equal to, or greater than half
shaded? (The square for .85 is greater than half shaded.)
c. If the face-up square for your decimal rounds to 1, the mixed decimal is rounded
up to the next whole number. If the decimal for your face-up square rounds to 0, the
mixed decimal is rounded to the whole number part, that is, the decimal part is
dropped off. (In the above example, 2.85 is rounded up to 3.)
3. Round the following numbers to the nearest whole number. It may help you to think
about whether the square for the decimal part is less than, equal to, or greater than half
shaded to determine if the decimal part rounds down to 0 or up to 1.
a. .52 (1)
b. 4.3 (4)
c. .725 (1)
d. 2.06 (2)
e. 3.5 (4)
Activity 2 Rounding to the nearest tenth
Decimal
Squares
pencils
and paper
1a. Select any green square and write its decimal. How many full
columns are shaded? (For the square shown here, 3 full columns are
shaded.) Is the next column of your square less than, equal to, or
greater than half shaded? (The next column shown here is more than
half shaded.)
f. .275 (0)
b. If the next column of your square after the full columns is less than half shaded or has no
shading, the decimal for the square rounds down to the tenths digit, that is, the partial column
is not used. If the next column is more than half shaded, the decimal for the square rounds up
to the next tenth. (For the above square, .36 rounds up to .4, but the decimal .34 would round
down to .3.)
c. What do you think the decimal for your square should round to, if the next column is
half shaded? (Discuss this situation. It is customary to round up to the next tenth.)
d. Ask for student examples of rounding decimals to the tenths place.
2. Select any yellow square and write its decimal. Determine if its
next column is less than, half shaded, or greater than half shaded
and round the decimal for the square to the nearest tenth. (Discuss
a few examples. The decimal .625 rounds down to .6)
3. Round the following decimals to the nearest tenth.
a. .67 (.7)
Mixed
Decimal
Place
Value
Tables
b. .483 (.5)
c. .07 (.1)
d. .318 (.3)
e. .042 (0)
Activity 3 Rule for rounding decimals and mixed decimals
1. Write the digits for 23.684 in a place value table.
b. What is 23.684 rounded to the nearest whole number? (24, the tenths digit is > 5)
c. What is 23.684 rounded to the nearest tenth? (23.7, the hundredths digit is > 5)
d. What is 23.684 rounded to the nearest hundredth? (23.68, the thousandths digit is < 5)
2. Write a rule for rounding a decimal or mixed decimal to any place value. (To round
to a given place value, check the digit to its right. If this digit is greater than or
equal to 5, round up; and if the digit is less than 5, round down.)
3. Write the following numbers in a place value table and round them to the given place
value. (Note: It may help students to first place an arrow above the given place value as
shown below and then consider the digit to its right.
a. 12.46 (to nearest whole number, 12)
c. 45.813 (to nearest whole number, 46)
b. 9.372 (to nearest tenth, 9.4)
d. .317 (to nearest tenth, .3)
INDEPENDENT PRACTICE and ASSESSMENT
Worksheets 5.NBT.4 #1 and #2
Mixed Decimal Place Value Tables Name:
Date:
.