Workmat Reproducible
Place Value Bars
This Really Good Stuff® product includes
• Place Value Bars
• This Really Good Stuff® Activity Guide
Congratulations on your purchase of these Really
Good Stuff® Place Value Bars—helpful tools to foster
students’ understanding of place value.
Meeting Common Core State Standards
The Really Good Stuff® Place Value Bars are aligned
with the following Common Core State Standards
for Mathematics:
Number and Operations in Base Ten
1.Overview
• Understand place value.
• Use place value understanding and properties of operations
to add and subtract.
2.Overview
• Understand place value.
• Use place value understanding and properties of operations
to add and subtract.
3.Overview Use place value understanding and properties of
operations to perform multi-digit arithmetic.
Displaying and Preparing the Place Value Bars
Before introducing the Place Value Bars, make copies of
this Really Good Stuff® Activity Guide, and file the pages
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 Place Value Bars
Indicate to students that the Place Value Bars will help
them to think about the parts of multi-digit numbers.
Show students a sample of each Bar. Arrange the Bars
in order from smallest to largest, with the 1 Bar at the
top. Ask students what they notice about the Bars. If
necessary, lead students to notice that each Bar is a
different color; that each has a different value; that as
their value gets larger, the size of the Bar increases; and
that there is an additional zero with each new value. Have
students practice reading the values on each Bar.
Separate the Place Value Bars into piles of each value.
Review together how the Bars will help students to see
how each place value is connected. Count the ones as you
move them into the ones column of a place value chart.
Explain that when they get to 10, as they count, they
trade the 10 ones in for a ten. Model this trade, removing
the ones and replacing them with a ten in the tens
column. Count by tens as you move 10 tens into the tens
column. Ask students what you should do now that you
have 10 tens. Model this trade. Continue with hundreds
and trade in ten hundreds for 1 thousand. Encourage
students to notice that each place value is ten times
greater than the place to the right. Write a multiplication
expression for each place value:
Ones 1 x 1
Tens 10 x 1
Hundreds 10 x 10
Thousands 10 x 100
Variation: Ask students to consider how other place
values are related, such as:
• How many tens does it take to make 1,000? (100)
• How many ones does it take to make 100? (100)
Building Multi-Digit Numbers
Copy the Workmat Reproducible. Explain to students
that they are to use the Place Value Bars to show
different numbers: Model building the number 42 by
counting 4 tens (10, 20, 30, 40) and 2 ones (41, 42).
Remind students that the 4 in the tens place told you
how many tens you needed and the 2 in the ones place
told you how many ones you needed. Write in expanded
form as 40 + 2. Allow students to build several two-digit
numbers. Encourage students to count up to the given
number as they move the Bars and to write the number
in expanded form.
Model building the number 317 by counting 3 hundreds
(100, 200, 300), 1 ten (310), and 7 ones (311, 312, 313,
314, 315, 316, 317). Review that the 3 in the hundreds
place told you how many hundreds you needed, the 1
in the tens place told you how many tens you needed,
and the 7 in the ones place told you how many ones you
needed. Write in expanded form as 300 + 10 + 7. Allow
students to build several three-digit numbers and to
write the number in expanded form.
Model building the number 2,453 by counting 2
thousands (1,000, 2,000), 4 hundreds (2,100, 2,200,
2,300, 2,400), 5 tens (2,410, 2,420, 2,430, 2,440,
2,450), and 3 ones (2,451, 2,452, 2,453). Remind
students that looking at the place value of each
number helped you to figure out how many of each Bar
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 #162239
®
Helping Teachers Make A
Difference®
© 2014 Really Good Stuff 1-800-366-1920 www.reallygoodstuff.com Made in China #162239
®
Number Cards Reproducible
Place Value Bars
you needed. Allow students to build several four-digit
numbers and to write the number in expanded form.
Distribute the Workmat Reproducible. Instruct students
to manipulate the Bars on the chart at the top of the
reproducible, and then to write the expanded form of
the numbers they build in the number sentences below.
Remind student to place a comma between the digit in
the hundreds and the thousands in their answers.
Copy and distribute the Number Cards Reproducible.
Explain to students that they will work in pairs to build
the numbers written on the cards on the workmat.
Instruct students to place the number cards upside
down, then take turns choosing a card to build.
model addition and subtraction of multi-digit numbers.
Display the problem 34 + 75. Model building 34 and 75.
Remind students that when they add, they are putting
numbers together. Combine the tens in one area and the
ones in another area. Show students how you count to
find the total. Tell students that the total is 10 tens
and 9 ones. To reinforce the concept, write the problem
on a place value chart, and say, “I know 10 tens is the
same as 1 hundred, so I need to trade those 10 tens for
1 hundred.” Model physically trading the Bars. Thinking
aloud, say, “now I know 1 hundred, 0 tens, and 9 ones, so
the answer is 109.”
Thousands
Variation: Students each choose a card, build the
number on the workmat, and determine who has the
biggest number. Students write the two numbers in
a number sentence with < or >. The student with the
biggest number earns a point.
More or Less Multi-Digit Numbers
Give students multi-digit numbers, and require them
to mentally identify 10 (or 100) more or 10 (or 100)
less than a given number. With each new number, have
students manipulate their Bars to show the changes.
Recognizing Combinations of 10 in Multi-Digit Numbers
Remind students how they used combinations of 10
when thinking about small numbers; for instance, if I
have 3, I will need 7 more to make 10. Ask students to
identify other combinations of 10. Show how to apply
complements of 10 to 100 with combinations, such
as 20 + 80, which is the same as 2 tens and 8 tens.
Encourage students to think about the number of Place
Value Bars as they consider the combinations. Model
combinations as addition sentences, such as:
• If you have 800, how many more do you need to
get to 1,000? (800 + 200 = 1,000)
• If you have 40, how many more do you need to get
to 100? (40 + 60 = 100)
Note: Students may benefit from imagining a ten-frame
(5 x 2 array) as they manipulate the Bars.
Hundreds
1
Tens
Ones
3
+7
10
4
5
9
0
9
Encourage students to practice other addition problems.
Display the problem 452 – 65. Remind students that
when they subtract, they are taking numbers away from
each other. Model building 452 with 4 hundreds, 5 tens,
and 2 ones. Emphasize that you are not building 65
because this needs to come from the 452. Again, think
aloud as you trade the Place Value Bars, and model the
problem on a place value chart:
Thousands
Hundreds
Tens
Ones
4
5
–6
14
–6
8
2
5
12
–5
7
3
3
Instruct students to practice other
subtraction problems.
Note: Encourage students to consider whether their
answers are reasonable. Students can do this by
estimating the answer to a problem.
Adding and Subtracting Big Numbers
Indicate that they can also use Place Value Bars to
Helping Teachers Make A Difference®
© 2014 Really Good Stuff® 1-800-366-1920 www.reallygoodstuff.com Made in China #162239
Helping Teachers Make A Difference®
© 2014 Really Good Stuff® 1-800-366-1920 www.reallygoodstuff.com Made in China #162239
Workmat Reproducible
Place Value Bars
This Really Good Stuff® product includes
• Place Value Bars
• This Really Good Stuff® Activity Guide
Congratulations on your purchase of these Really
Good Stuff® Place Value Bars—helpful tools to foster
students’ understanding of place value.
Meeting Common Core State Standards
The Really Good Stuff® Place Value Bars are aligned
with the following Common Core State Standards
for Mathematics:
Number and Operations in Base Ten
1.Overview
• Understand place value.
• Use place value understanding and properties of operations
to add and subtract.
2.Overview
• Understand place value.
• Use place value understanding and properties of operations
to add and subtract.
3.Overview Use place value understanding and properties of
operations to perform multi-digit arithmetic.
Displaying and Preparing the Place Value Bars
Before introducing the Place Value Bars, make copies of
this Really Good Stuff® Activity Guide, and file the pages
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 Place Value Bars
Indicate to students that the Place Value Bars will help
them to think about the parts of multi-digit numbers.
Show students a sample of each Bar. Arrange the Bars
in order from smallest to largest, with the 1 Bar at the
top. Ask students what they notice about the Bars. If
necessary, lead students to notice that each Bar is a
different color; that each has a different value; that as
their value gets larger, the size of the Bar increases; and
that there is an additional zero with each new value. Have
students practice reading the values on each Bar.
Separate the Place Value Bars into piles of each value.
Review together how the Bars will help students to see
how each place value is connected. Count the ones as you
move them into the ones column of a place value chart.
Explain that when they get to 10, as they count, they
trade the 10 ones in for a ten. Model this trade, removing
the ones and replacing them with a ten in the tens
column. Count by tens as you move 10 tens into the tens
column. Ask students what you should do now that you
have 10 tens. Model this trade. Continue with hundreds
and trade in ten hundreds for 1 thousand. Encourage
students to notice that each place value is ten times
greater than the place to the right. Write a multiplication
expression for each place value:
Ones 1 x 1
Tens 10 x 1
Hundreds 10 x 10
Thousands 10 x 100
Variation: Ask students to consider how other place
values are related, such as:
• How many tens does it take to make 1,000? (100)
• How many ones does it take to make 100? (100)
Building Multi-Digit Numbers
Copy the Workmat Reproducible. Explain to students
that they are to use the Place Value Bars to show
different numbers: Model building the number 42 by
counting 4 tens (10, 20, 30, 40) and 2 ones (41, 42).
Remind students that the 4 in the tens place told you
how many tens you needed and the 2 in the ones place
told you how many ones you needed. Write in expanded
form as 40 + 2. Allow students to build several two-digit
numbers. Encourage students to count up to the given
number as they move the Bars and to write the number
in expanded form.
Model building the number 317 by counting 3 hundreds
(100, 200, 300), 1 ten (310), and 7 ones (311, 312, 313,
314, 315, 316, 317). Review that the 3 in the hundreds
place told you how many hundreds you needed, the 1
in the tens place told you how many tens you needed,
and the 7 in the ones place told you how many ones you
needed. Write in expanded form as 300 + 10 + 7. Allow
students to build several three-digit numbers and to
write the number in expanded form.
Model building the number 2,453 by counting 2
thousands (1,000, 2,000), 4 hundreds (2,100, 2,200,
2,300, 2,400), 5 tens (2,410, 2,420, 2,430, 2,440,
2,450), and 3 ones (2,451, 2,452, 2,453). Remind
students that looking at the place value of each
number helped you to figure out how many of each Bar
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 #162239
®
Helping Teachers Make A
Difference®
© 2014 Really Good Stuff 1-800-366-1920 www.reallygoodstuff.com Made in China #162239
®
Number Cards Reproducible
Place Value Bars
you needed. Allow students to build several four-digit
numbers and to write the number in expanded form.
Distribute the Workmat Reproducible. Instruct students
to manipulate the Bars on the chart at the top of the
reproducible, and then to write the expanded form of
the numbers they build in the number sentences below.
Remind student to place a comma between the digit in
the hundreds and the thousands in their answers.
Copy and distribute the Number Cards Reproducible.
Explain to students that they will work in pairs to build
the numbers written on the cards on the workmat.
Instruct students to place the number cards upside
down, then take turns choosing a card to build.
model addition and subtraction of multi-digit numbers.
Display the problem 34 + 75. Model building 34 and 75.
Remind students that when they add, they are putting
numbers together. Combine the tens in one area and the
ones in another area. Show students how you count to
find the total. Tell students that the total is 10 tens
and 9 ones. To reinforce the concept, write the problem
on a place value chart, and say, “I know 10 tens is the
same as 1 hundred, so I need to trade those 10 tens for
1 hundred.” Model physically trading the Bars. Thinking
aloud, say, “now I know 1 hundred, 0 tens, and 9 ones, so
the answer is 109.”
Thousands
Variation: Students each choose a card, build the
number on the workmat, and determine who has the
biggest number. Students write the two numbers in
a number sentence with < or >. The student with the
biggest number earns a point.
More or Less Multi-Digit Numbers
Give students multi-digit numbers, and require them
to mentally identify 10 (or 100) more or 10 (or 100)
less than a given number. With each new number, have
students manipulate their Bars to show the changes.
Recognizing Combinations of 10 in Multi-Digit Numbers
Remind students how they used combinations of 10
when thinking about small numbers; for instance, if I
have 3, I will need 7 more to make 10. Ask students to
identify other combinations of 10. Show how to apply
complements of 10 to 100 with combinations, such
as 20 + 80, which is the same as 2 tens and 8 tens.
Encourage students to think about the number of Place
Value Bars as they consider the combinations. Model
combinations as addition sentences, such as:
• If you have 800, how many more do you need to
get to 1,000? (800 + 200 = 1,000)
• If you have 40, how many more do you need to get
to 100? (40 + 60 = 100)
Note: Students may benefit from imagining a ten-frame
(5 x 2 array) as they manipulate the Bars.
Hundreds
1
Tens
Ones
3
+7
10
4
5
9
0
9
Encourage students to practice other addition problems.
Display the problem 452 – 65. Remind students that
when they subtract, they are taking numbers away from
each other. Model building 452 with 4 hundreds, 5 tens,
and 2 ones. Emphasize that you are not building 65
because this needs to come from the 452. Again, think
aloud as you trade the Place Value Bars, and model the
problem on a place value chart:
Thousands
Hundreds
Tens
Ones
4
5
–6
14
–6
8
2
5
12
–5
7
3
3
Instruct students to practice other
subtraction problems.
Note: Encourage students to consider whether their
answers are reasonable. Students can do this by
estimating the answer to a problem.
Adding and Subtracting Big Numbers
Indicate that they can also use Place Value Bars to
Helping Teachers Make A Difference®
© 2014 Really Good Stuff® 1-800-366-1920 www.reallygoodstuff.com Made in China #162239
Helping Teachers Make A Difference®
© 2014 Really Good Stuff® 1-800-366-1920 www.reallygoodstuff.com Made in China #162239