Building Decimals Workmat Reproducible
Decimal Place Value Bars
This Really Good Stuff® product includes:
• Decimal Place Value Bars
• This Really Good Stuff® Activity Guide
students an opportunity to practice reading the values
on each Bar.
Congratulations on your purchase of the Really Good
Stuff® Decimal Place Value Bars—helpful tools to foster
students’ understanding of decimal place value.
Meeting Common Core State Standards
The Really Good Stuff® Decimal Place Value Bars are
aligned with the following Common Core State Standards
for Mathematics:
Number and Operations in Base Ten
5.Overview
• Understand the place value system.
• Perform operations with multi-digit whole numbers and with
decimals to hundredths.
Number and Operations—Fractions
4.Overview
• Understand decimal notation for fractions, and compare
decimal fractions.
Displaying and Preparing the Decimal Place Value Bars
Before introducing the Decimal Place Value Bars, make
copies of this Really Good Stuff® Activity Guide, and file
them for future use. Or, download another copy of it from
our Web site at www.reallygoodstuff.com. Divide the Bars
into sets for each student or group.
Introducing the Decimal Place Value Bars
Indicate to students that the Decimal Place Value Bars
will help them think about the parts of numbers that are
written as decimals. Show students a sample of each
Bar. Arrange the Bars in order from smallest in size to
largest in size with the .1 Bar at the top and the .001
Bar at the bottom. Ask students to notice that each
Bar is a different color; that each Bar has a different
value; that the size of the Bar increases as the decimal
value gets smaller; and that there is an additional zero
between the decimal point and the one. Make connections
to the fraction values and the number of zeros after the
decimal point that each Bar represents (.1 = 1/10, .01 =
1/100, .001 = 1/1,000). Help students understand that
even though the values look large, they are working with
very small numbers between the numbers 0 and 1. Give
Building Decimal Numbers
Copy and distribute the Building Decimals Workmat
Reproducible. Explain to students that they are to use
the Decimal Place Value Bars to show different numbers.
Model building the number 0.32 by counting 3 tenths
(0.1, 0.2, 0.3) and 2 hundredths (0.01, 0.02,). Explain
that the 3 in the tenths place told you how many tenths
you needed and the 2 in the hundredths place told you
how many hundredths you needed. Write in expanded
form as 0.3 + 0.02. Allow students to build several
decimal numbers, such as 0.43 and 0.65. Encourage
students to count up to the given number as they move
the Decimal Place Value Bars and to write the number
in expanded form.
Model building the number .245 by counting 2 tenths
(0.1, 0.2), 4 hundredths (0.01, 0.02, 0.03, 0.04), and
5 thousandths (0.001, 0.002, 0.003, 0.004, 0.005).
Explain that the 2 in the tenths place told you how
many tenths you needed, the 4 in the hundredths
place told you how many hundredths you needed, and
the 5 in the thousandths place told you how many
thousandths you needed. Remind students that looking
at the place value of each number helped you to figure
out how many of each of the Decimal Place Value
Bars you needed. Allow students to write the number
in expanded form, for example: 0.2 + 0.04 + 0.005 or
0.200 + 0.040 + 0.005. Allow students to build
several numbers, such as 0.254 and 0.642.
Give students an opportunity to build additional numbers
on the reproducible. Instruct them to manipulate the
Decimal Place Value Bars in the place value chart at
the top, and then write the number in expanded form in
the number sentence below. Remind students to place
a comma between the digit in the hundredths and the
thousandths place in their answers.
Variation: Have students write the decimal numbers as
fractions. For example, show students that they can
write 0.2 + 0.04 + 0.005 = 0.245 as 2/10 + 4/100 +
5/1,000 = 245/1,000.
All activity guides can be found online.
Helping Teachers Make A
Difference®
© 2014 Really Good Stuff 1-800-366-1920 www.reallygoodstuff.com Made in China #162278
®
Helping Teachers Make A
Difference®
© 2014 Really Good Stuff 1-800-366-1920 www.reallygoodstuff.com Made in China #162278
®
Decimal Place Value Bars Reproducible
Decimal Place Value Bars
Exploring the Decimal Place Value Bars
Separate the Decimal Place Value Bars into piles of each
value. Review together how the Decimal Place Value Bars
will help students see how each place value is connected.
Count the thousandths as you move them into the
thousandths column of a place value chart. Explain
that when students get to 10, when counting, they can
trade the 10 thousandths in for 1 hundredth. Model this
trade, removing the 10 thousandths and replacing with
1 hundredth in the hundredth column. Move hundredths
into the hundredths column until you get to 10
hundredths. Ask students what you should do now that
you have 10 hundredths. Model this trade. Encourage
students to notice that each place value is 10 times
greater than the place to the right. Make connections
to what students know about whole numbers. Write a
multiplication expression for each place value:
Hundredths 0.001 x 10 = 0.01
Tenths 0.01 x 10 = 0.1
Ones 0.1 x 10 = 1
Tens 1 x 10 = 10
Hundreds 10 x 10 = 100
combinations. Model combinations as addition
sentences, such as:
• If I have 2 tenths, how many more tenths do I need
to get to the number 1? (0.2 + 0.8 = 1)
• If I have 4 hundredths, how many more do I need to
get to the number 0.1? (0.04 + 0.06 = 0.1)
Explain that when they use the Decimal Place Value
Bars, they may have to trade 10 Bars for another
Bar of equal value.
Comparing Decimals
Encourage students to use the Decimal Place Value
Bars to compare decimal numbers and tell which number
is greater. Display the number sentence 0.23 _______
0.35 and model building each decimal number: There are
2 tenths in 0.23 and 3 tenths in 0.35, so I can know
that 0.23 is less than 0.35. Ask students to complete
the number sentence 0.23 < 0.35. Copy and distribute
the Decimal Place Value Bars Reproducible for students
to practice comparing numbers, and to keep in their math
folders for later use.
Display the problem 0.45 − 0.16. Remind students that
when they subtract, they are taking numbers away from
each other. Model building 0.45 with 4 tenths and 5
hundredths. Emphasize that you are not building 0.16
because this needs to come from the 0.45. Think aloud
as you trade the Decimal Place Value Bars, and model
the problem on a place value chart.
Answers (Comparing Decimals): 1) <, 2) <, 3) >, 4) <, 5) >, 6) <, 7) =, 8) >
Recognizing Combinations of 10 in Decimal Numbers
Remind students how they used combinations of
the number 10 in addition. (If they have 3, they will
need 7 more to make 10.) Ask them to identify other
combinations of 10. Show students how to apply
complements of 10 to decimals with combinations, such
as 0.4 + 0.6 = 1, which is the same as 4 tenths plus 6
tenths. Encourage students to think about the number
of Decimal Place Value Bars as they consider the
Helping Teachers Make A Difference®
© 2014 Really Good Stuff® 1-800-366-1920 www.reallygoodstuff.com Made in China #162278
Helping Teachers Make A Difference®
Adding and Subtracting Decimal Numbers
Explain to students that they can use Decimal Place
Value Bars to model addition and subtraction of
decimal numbers <1.0. Display the problem 0.34 + 0.27.
Model building 0.34 and 0.27. Remind students that
when they add, they are putting numbers together.
Combine the tenths in one area and the hundredths
in another area. Show students how to count to find
the total. Tell students that the total is 5 tenths
and 11 hundredths. Model physically trading 10 of the
hundredths in for 1 tenth, so the answer is 6 tenths
and 1 hundredth or 0.61.
Display the problem 0.56 − 0.324. Model building
0.56 with 5 tenths and 6 hundredths. In this problem,
explain that you need to take away 4 thousandths,
but no thousandth are shown in 0.56. Model trading 1
hundredth for 10 thousandths with the Decimal Place
Value Bars, and record on a place value chart.
Ask students to practice both addition and subtraction
problems on their Decimal Place Value Bars Repoducible.
Encourage them to consider whether their answers are
reasonable by estimating the answer to a problem.
Answers (Adding and Subtracting Decimals): 1) 0.72, 2)
0.424, 3) 0.933, 4) 0.816, 5) 0.819, 6) 1.049, 7) 0.03,
8) 0.44, 9) 0.23, 10) 0.074, 11) 0.127, 12) 0.438
© 2014 Really Good Stuff® 1-800-366-1920 www.reallygoodstuff.com Made in China #162278
Building Decimals Workmat Reproducible
Decimal Place Value Bars
This Really Good Stuff® product includes:
• Decimal Place Value Bars
• This Really Good Stuff® Activity Guide
students an opportunity to practice reading the values
on each Bar.
Congratulations on your purchase of the Really Good
Stuff® Decimal Place Value Bars—helpful tools to foster
students’ understanding of decimal place value.
Meeting Common Core State Standards
The Really Good Stuff® Decimal Place Value Bars are
aligned with the following Common Core State Standards
for Mathematics:
Number and Operations in Base Ten
5.Overview
• Understand the place value system.
• Perform operations with multi-digit whole numbers and with
decimals to hundredths.
Number and Operations—Fractions
4.Overview
• Understand decimal notation for fractions, and compare
decimal fractions.
Displaying and Preparing the Decimal Place Value Bars
Before introducing the Decimal Place Value Bars, make
copies of this Really Good Stuff® Activity Guide, and file
them for future use. Or, download another copy of it from
our Web site at www.reallygoodstuff.com. Divide the Bars
into sets for each student or group.
Introducing the Decimal Place Value Bars
Indicate to students that the Decimal Place Value Bars
will help them think about the parts of numbers that are
written as decimals. Show students a sample of each
Bar. Arrange the Bars in order from smallest in size to
largest in size with the .1 Bar at the top and the .001
Bar at the bottom. Ask students to notice that each
Bar is a different color; that each Bar has a different
value; that the size of the Bar increases as the decimal
value gets smaller; and that there is an additional zero
between the decimal point and the one. Make connections
to the fraction values and the number of zeros after the
decimal point that each Bar represents (.1 = 1/10, .01 =
1/100, .001 = 1/1,000). Help students understand that
even though the values look large, they are working with
very small numbers between the numbers 0 and 1. Give
Building Decimal Numbers
Copy and distribute the Building Decimals Workmat
Reproducible. Explain to students that they are to use
the Decimal Place Value Bars to show different numbers.
Model building the number 0.32 by counting 3 tenths
(0.1, 0.2, 0.3) and 2 hundredths (0.01, 0.02,). Explain
that the 3 in the tenths place told you how many tenths
you needed and the 2 in the hundredths place told you
how many hundredths you needed. Write in expanded
form as 0.3 + 0.02. Allow students to build several
decimal numbers, such as 0.43 and 0.65. Encourage
students to count up to the given number as they move
the Decimal Place Value Bars and to write the number
in expanded form.
Model building the number .245 by counting 2 tenths
(0.1, 0.2), 4 hundredths (0.01, 0.02, 0.03, 0.04), and
5 thousandths (0.001, 0.002, 0.003, 0.004, 0.005).
Explain that the 2 in the tenths place told you how
many tenths you needed, the 4 in the hundredths
place told you how many hundredths you needed, and
the 5 in the thousandths place told you how many
thousandths you needed. Remind students that looking
at the place value of each number helped you to figure
out how many of each of the Decimal Place Value
Bars you needed. Allow students to write the number
in expanded form, for example: 0.2 + 0.04 + 0.005 or
0.200 + 0.040 + 0.005. Allow students to build
several numbers, such as 0.254 and 0.642.
Give students an opportunity to build additional numbers
on the reproducible. Instruct them to manipulate the
Decimal Place Value Bars in the place value chart at
the top, and then write the number in expanded form in
the number sentence below. Remind students to place
a comma between the digit in the hundredths and the
thousandths place in their answers.
Variation: Have students write the decimal numbers as
fractions. For example, show students that they can
write 0.2 + 0.04 + 0.005 = 0.245 as 2/10 + 4/100 +
5/1,000 = 245/1,000.
All activity guides can be found online.
Helping Teachers Make A
Difference®
© 2014 Really Good Stuff 1-800-366-1920 www.reallygoodstuff.com Made in China #162278
®
Helping Teachers Make A
Difference®
© 2014 Really Good Stuff 1-800-366-1920 www.reallygoodstuff.com Made in China #162278
®
Decimal Place Value Bars Reproducible
Decimal Place Value Bars
Exploring the Decimal Place Value Bars
Separate the Decimal Place Value Bars into piles of each
value. Review together how the Decimal Place Value Bars
will help students see how each place value is connected.
Count the thousandths as you move them into the
thousandths column of a place value chart. Explain
that when students get to 10, when counting, they can
trade the 10 thousandths in for 1 hundredth. Model this
trade, removing the 10 thousandths and replacing with
1 hundredth in the hundredth column. Move hundredths
into the hundredths column until you get to 10
hundredths. Ask students what you should do now that
you have 10 hundredths. Model this trade. Encourage
students to notice that each place value is 10 times
greater than the place to the right. Make connections
to what students know about whole numbers. Write a
multiplication expression for each place value:
Hundredths 0.001 x 10 = 0.01
Tenths 0.01 x 10 = 0.1
Ones 0.1 x 10 = 1
Tens 1 x 10 = 10
Hundreds 10 x 10 = 100
combinations. Model combinations as addition
sentences, such as:
• If I have 2 tenths, how many more tenths do I need
to get to the number 1? (0.2 + 0.8 = 1)
• If I have 4 hundredths, how many more do I need to
get to the number 0.1? (0.04 + 0.06 = 0.1)
Explain that when they use the Decimal Place Value
Bars, they may have to trade 10 Bars for another
Bar of equal value.
Comparing Decimals
Encourage students to use the Decimal Place Value
Bars to compare decimal numbers and tell which number
is greater. Display the number sentence 0.23 _______
0.35 and model building each decimal number: There are
2 tenths in 0.23 and 3 tenths in 0.35, so I can know
that 0.23 is less than 0.35. Ask students to complete
the number sentence 0.23 < 0.35. Copy and distribute
the Decimal Place Value Bars Reproducible for students
to practice comparing numbers, and to keep in their math
folders for later use.
Display the problem 0.45 − 0.16. Remind students that
when they subtract, they are taking numbers away from
each other. Model building 0.45 with 4 tenths and 5
hundredths. Emphasize that you are not building 0.16
because this needs to come from the 0.45. Think aloud
as you trade the Decimal Place Value Bars, and model
the problem on a place value chart.
Answers (Comparing Decimals): 1) <, 2) <, 3) >, 4) <, 5) >, 6) <, 7) =, 8) >
Recognizing Combinations of 10 in Decimal Numbers
Remind students how they used combinations of
the number 10 in addition. (If they have 3, they will
need 7 more to make 10.) Ask them to identify other
combinations of 10. Show students how to apply
complements of 10 to decimals with combinations, such
as 0.4 + 0.6 = 1, which is the same as 4 tenths plus 6
tenths. Encourage students to think about the number
of Decimal Place Value Bars as they consider the
Helping Teachers Make A Difference®
© 2014 Really Good Stuff® 1-800-366-1920 www.reallygoodstuff.com Made in China #162278
Helping Teachers Make A Difference®
Adding and Subtracting Decimal Numbers
Explain to students that they can use Decimal Place
Value Bars to model addition and subtraction of
decimal numbers <1.0. Display the problem 0.34 + 0.27.
Model building 0.34 and 0.27. Remind students that
when they add, they are putting numbers together.
Combine the tenths in one area and the hundredths
in another area. Show students how to count to find
the total. Tell students that the total is 5 tenths
and 11 hundredths. Model physically trading 10 of the
hundredths in for 1 tenth, so the answer is 6 tenths
and 1 hundredth or 0.61.
Display the problem 0.56 − 0.324. Model building
0.56 with 5 tenths and 6 hundredths. In this problem,
explain that you need to take away 4 thousandths,
but no thousandth are shown in 0.56. Model trading 1
hundredth for 10 thousandths with the Decimal Place
Value Bars, and record on a place value chart.
Ask students to practice both addition and subtraction
problems on their Decimal Place Value Bars Repoducible.
Encourage them to consider whether their answers are
reasonable by estimating the answer to a problem.
Answers (Adding and Subtracting Decimals): 1) 0.72, 2)
0.424, 3) 0.933, 4) 0.816, 5) 0.819, 6) 1.049, 7) 0.03,
8) 0.44, 9) 0.23, 10) 0.074, 11) 0.127, 12) 0.438
© 2014 Really Good Stuff® 1-800-366-1920 www.reallygoodstuff.com Made in China #162278