Place Value
Objectives To develop place-value concepts and connect place
value
in money with place value in base-10 blocks.
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Ongoing Learning & Practice
Key Concepts and Skills
Reviewing Ballpark Estimation
• Count by 1s, 10s, and 100s. Math Journal 2, p. 255
calculator
Children make ballpark estimates,
find the exact answers, and compare
their estimates to the exact answers.
[Number and Numeration Goal 1]
• Model and write 3- and 4-digit numbers
using base-10 blocks and money. [Number and Numeration Goal 2]
• Make exchanges with base-10 blocks
and relate that to exchanges with money. [Measurement and Reference Frames Goal 4]
Key Activities
Children identify and represent place value
and numbers using base-10 blocks, compare
the use of base-10 blocks to the use of
money to represent place value, and practice
place-value exchanges.
Math Boxes 10 8
Math Journal 2, p. 256
Children practice and maintain skills
through Math Box problems.
Curriculum
Focal Points
Differentiation Options
READINESS
Building Base-10 Structures
per group: base-10 blocks, quarter-sheets
of paper
Children build base-10 block structures
and identify their values as numbers.
EXTRA PRACTICE
Writing and Comparing Numbers
Home Link 10 8
Math Masters, pp. 322A and 322B
Children practice place value with whole
numbers.
Math Masters, p. 322
Children practice and maintain skills
through Home Link activities.
Using Base-10 Blocks for Place Value
Ongoing Assessment:
Recognizing Student Achievement
ELL SUPPORT
Children use base-10 blocks to discuss
the relationships between values.
Use Mental Math and Reflexes. [Operations and Computation Goal 3]
Ongoing Assessment:
Informing Instruction See page 766.
Key Vocabulary
flat long cube place value big cube
Materials
Math Journal 2, pp. 253 and 254
Home Link 10 7
Math Masters, pp. 320 and 321 (optional); p. 415
transparencies of Math Masters, pp. 320
and 321 (optional) base-10 blocks
(1 big cube, 9 flats, 9 longs, 9 cubes) 24 pennies, 39 dimes, thirty-nine $1 bills,
and one $10 bill per group: 1 six-sided
die, 1 ten- or twelve-sided die slate
Advance Preparation
For the Math Message, label and display a centimeter cube, a long, a flat, and a big cube for children to refer
to as they complete the problems. For a mathematics and literacy connection, obtain a copy of How Much,
How Many, How Far, How Heavy, How Long, How Tall Is 1000? by Helen Nolan (Scholastic Inc., 1995).
Teacher’s Reference Manual, Grades 1– 3 pp. 56, 57
764
Unit 10
Decimals and Place Value
Interactive
Teacher’s
Lesson Guide
Mathematical Practices
SMP1, SMP2, SMP5, SMP6, SMP7
Content Standards
Getting Started
Mental Math and Reflexes
2.NBT.1, 2.NBT.1a, 2.NBT.1b, 2.NBT.2, 2.NBT.3, 2.NBT.4, 2.NBT.8
Math Message
1 long =
Pose number stories involving estimation. Have children
record amounts on an Exit Slip (Math Masters, page
415).
10
cubes
longs = 100 cubes
1 big cube = 10 flats = 100 longs = 1,000 cubes
1 flat =
Suggestions:
About how much change should I get?
10
Home Link 10 7 Follow-Up
I bought a 6-pack of soda for $1.99. I gave the cashier a $5
bill. About $3.00
I bought a bag of potato chips for $2.39. I gave the cashier
$3.00. About 60¢
Briefly review area answers. Have children share
strategies for solving one addition or subtraction
problem.
I bought a bag of grapes for $3.23 and a bag of chips for
$0.99. I gave the cashier a $10 bill. About $5.80, or about
$6.00
Ongoing Assessment:
Recognizing Student
Mental Math
Achievement and Reflexes
1 Teaching the Lesson
Math Message Follow-Up
WHOLE-CLASS
DISCUSSION
Quickly review Math Message responses. Discuss relationships
among base-10 blocks: each is 10 times larger than the next
1
smaller one, and _
the size of the next larger one.
10
Representing 3- and 4-Digit
Use Mental Math and Reflexes to assess
children’s ability to estimate change. Children
are making adequate progress if they can
correctly estimate the first problem. Some
children may be able to do all three problems.
[Operations and Computation Goal 3]
WHOLE-CLASS
ACTIVITY
Numbers with Base-10 Blocks
(Math Masters, pp. 320 or 321)
Name
LESSON
10 8
Date
Place-Value Chart
TenThousands Hundreds
Thousands
Ask three volunteers to form a line at the front of the room. The
first child on the left, as viewed by the class, holds 3 flats for all to
see, the one in the middle holds up 5 longs, and the child on the
right holds 2 cubes. Tell children to assume that the cube is ONE.
What is the place value of each digit? 3 hundreds, 5 tens, and 2
ones Have children write the number represented by these base10 blocks on their slates. Have them say the number aloud. 352
Write 300 + 50 + 2 = 352 on the board. Explain to children that
writing a number model that shows the value of each digit in a
number is called expanded notation.
Time
Tens
Ones
Math Masters, page 320
Name
LESSON
10 8
Date
Time
Place-Value Mat
1s
293-347_EMCS_B_MM_G2_U10_576949.indd 320
3/1/11 4:29 PM
10s
Choose a fourth child to stand first in line on the left and hold a
big cube. Children write the new number and say it aloud. 1,352
Discuss the change that results from adding the big cube to the
collection. The number increases by 1,000. Write 1,000 + 300 + 50
+ 2 = 1,352 on the board.
Í dimes
important, however, for them to know that multidigit numbers can be written as a
sum of the values of each digit.
Î pennies
NOTE It is not expected that children use the term expanded notation. It is
Math Masters, page 321
Lesson 10 8
765
Student Page
Date
Time
LESSON
10 8
Repeat the activity with other 3- and 4-digit numbers less than
2,000. Then reverse the procedure: Write a 3- or 4-digit number on
the board and ask children in the line to represent the number with
base-10 blocks. Write a number model to represent the base-10
blocks on the board. Repeat with several other numbers as needed.
Money Exchange Game Directions
Materials
□ 1 six-sided die
□ 1 ten- or twelve-sided die
□ 24 pennies, 39 dimes, thirty-nine $1 bills,
and one $10 bill per player
Players
2 or 3
Skill
Make exchanges between coins and bills
Object of the Game
To be the first to trade for $10
Directions
Ongoing Assessment: Informing Instruction
1. Each player puts 12 pennies, 12 dimes, twelve $1 bills, and
one $10 bill in the bank.
Watch for children who are having difficulty recording numbers on their slates.
Have them write the numbers on a place-value chart or mat (Math Masters,
pages 320 or 321).
2. Players take turns. Players use a six-sided die to represent
pennies. Players use a ten- or twelve-sided die to represent dimes.
3. Each player
rolls the dice.
takes from the bank the number of pennies and dimes
Reviewing the Role of 0
shown on the faces of the dice.
puts the coins in the correct columns on his or her
Place-Value Mat on journal page 254.
4. Whenever possible, a player replaces 10 coins or bills
as a Placeholder
of a lower denomination with a coin or bill of the next
higher denomination.
5. The first player to trade for a $10 bill wins.
If there is a time limit, the winner is the player with the
largest number on the mat when time is up.
Math Journal 2, p. 253
229_262_EMCS_S_SMJ_G2_U10_57640X.indd 253
253
3/3/11 7:38 AM
NOTE There are many names for base-10
blocks. The following names are used in
Everyday Mathematics: cube (centimeter
cube) for the smallest cube, long for the strip
of 10 cm cubes, flat for the block consisting of
100 cm cubes. This leaves open the
possibility of using the cube, the long, or
the flat as the unit (ONE) for decimal and
fraction work.
10 8
Point out the similarities between base-10 blocks and money,
comparing cubes and pennies, longs and dimes, flats and dollars,
and so on. Discuss how both groups of materials make trades
using a 10-for-1 rule, represent larger numbers the same way,
and represent numbers in more than one way. Also discuss the
differences between base-10 blocks and money: Relationships
among base-10 blocks are reflected in the size of the blocks, but
relationships among denominations of coins and bills are not
reflected in size; money is used inside and outside of school, but
base-10 blocks are usually used only at school.
Place-Value Mat
Playing the Money
Exchange Game
Í
10s
dimes
Î
1s
pennies
SMALL-GROUP
ACTIVITY
$1 dollars
100s
$10
1,000s
(Math Journal 2, pp. 253 and 254; Math Masters, p. 321)
Explain the rules of the Money Exchange Game. You may wish to
use an overhead transparency of Math Masters, page 321 to model
the game. Then divide the class into groups of 2 or 3 players and
have children play the game.
Math Journal 2, p. 254
229_262_EMCS_S_SMJ_G2_U10_57640X.indd 254
766
WHOLE-CLASS
DISCUSSION
Base-10 Blocks and Money
Time
LESSON
Continue the routines from the previous activity, but have one or
more children in the line be empty-handed, representing the digit
0 in those places. Children write the numbers on their slates with
zeros in the appropriate places. Reverse the procedure: Write
3- or 4-digit numbers containing one or more zeros on the board
and ask children to represent those numbers with base-10 blocks.
Comparing Place Value with
Student Page
Date
WHOLE-CLASS
ACTIVITY
Unit 10 Decimals and Place Value
3/3/11 7:38 AM
Student Page
2 Ongoing Learning & Practice
Date
Time
LESSON
10 8
Ballpark Estimates
Fill in the unit box. Then, for each problem:
Unit
Make a ballpark estimate before you add.
Reviewing Ballpark Estimation
INDEPENDENT
ACTIVITY
(Math Journal 2, p. 255)
Write a number model for your estimate.
Use your calculator and solve the problem. Write the exact answer in
the box.
Compare your estimate to your answer.
Children complete this journal page by finding a ballpark estimate
for each problem. They then solve the problem using a calculator.
When most children have completed this journal page have them
compare their estimates with their exact answers and discuss any
discrepancies. If necessary, encourage children to estimate and
solve the problem again.
1. Ballpark estimate:
148 + 27
3. Ballpark estimate:
163 + 32
175
4. Ballpark estimate:
133 + 35
195
5. Ballpark estimate:
168
6. Ballpark estimate:
140 + 40 = 180 180 + 20 = 200150 + 180 = 330
143 + 41
Math Boxes 10 8
2. Ballpark estimate:
150 + 30 = 180 160 + 30 = 190 130 + 40 = 170
184 + 23
184
154 + 183
207
337
INDEPENDENT
ACTIVITY
(Math Journal 2, p. 256)
Mixed Practice Math Boxes in this lesson are linked with
Math Boxes in Lessons 10-6 and 10-10. The skill in
Problem 6 previews Unit 11 content.
Home Link 10 8
Math Journal 2, p. 255
229_262_EMCS_S_SMJ_G2_U10_57640X.indd 255
2/27/11 11:24 AM
INDEPENDENT
ACTIVITY
(Math Masters, p. 322)
Home Connection Children identify digits in specified
places in 3- and 4-digit numbers, read the numbers to
someone at home, and write 3- and 4-digit numbers
represented by sets of base-10 blocks.
Home Link Master
Student Page
Date
Time
LESSON
10 8
Name
Math Boxes
Date
10 8 Place Value
1. What number is shown by the
2. Kelly has $10. Her lunch total
blocks?
Family
Note
was $8.75. How much change
will she get?
$1.25
347
In each number:
4. Cross out the names that don’t
By afternoon, the temperature
was 75°F. How much did the
temperature rise? 13°
belong.
1
ten cents, _
10 of a dollar,
End
+13°F
$10.00, Í, ÂÂ, $0.01,
1
_
of a dollar,
75°F
Circle the digit in the hundreds place.
Underline the digit in the thousands place.
1. 4 6 2
2. 1 , 3 2 6
3. 5 , 0 0 6
4. 8 6 9
5. 2 , 3 0 4
6. 4 , 5 6 7
Read the numbers in Problems 1–6 to someone at home.
7.
100
Number model: 62 + 13 = 75
Write the numbers represented by the base-10 blocks.
1
_
2 of a dollar
88–90
6. 4 ladybugs. 5 spots on each
party hat
C
paper towel roll
D
globe
20
lady bugs spots per
lady bug
4
57
256
two hundred fifty six
5
Practice
spots
in all
Solve.
20
Sample answers: 4 × 5 = 20;
5 + 5 + 5 + 5 = 20
11. 134 + 24 =
13. 67 - 38 =
112 113
158
29
188
14. 164 + 216 = 380
12. 152 + 36 =
Math Masters, p. 322
Math Journal 2, p. 256
229_262_EMCS_S_SMJ_G2_U10_57640X.indd 256
1,204
=
10.
Fill in the diagram and write a
number model.
p
shoe box
B
g
A
1,183
=
9.
ladybug. How many spots?
py g
a cone? Circle the best answer.
247
=
8.
116–118
5. Which object is shaped like
10
Example: 9 , 3 4 2
10¢
Change
62°F
In this lesson, your child has been studying place value, or the value of digits in numbers.
Listen as your child reads the numbers in Problems 1–6. You might ask your child to pick a
few of the numbers and tell you the place value of each of the digits. For example, in 462,
the value of 4 is 400, the value of 6 is 60, and the value of 2 is 2.
Please return this Home Link to school tomorrow.
11
3. In the morning, it was 62°F.
Start
Time
HOME LINK
3/18/11 3:53 PM
293-347_EMCS_B_MM_G2_U10_576949.indd 322
2/25/11 2:29 PM
Lesson 10 8
767
Teaching Master
Name
Date
3 Differentiation Options
Time
LESSON
10 8 Place Value
Write the number for each group of base-10 blocks.
1.
READINESS
Building Base-10 Structures
346
2.
530
5–15 Min
To explore place value using a concrete model, have children build
a base-10 structure with flats, longs, and cubes. The cube is ONE.
Children work together to count the “value” of each structure and
record it on a quarter-sheet of paper. Then children arrange the
sheets in order from least to greatest value.
3.
604
4.
Copyright © Wright Group/McGraw-Hill
SMALL-GROUP
ACTIVITY
1,326
5. Circle the largest number.
EXTRA PRACTICE
Writing and Comparing Numbers
4,343
4,563
4,543
4,463
Then explain how you
know what number
is the largest.
Answers vary.
INDEPENDENT
ACTIVITY
5–15 Min
(Math Masters, pp. 322A and 322B)
To provide children additional practice with writing and
comparing numbers, have them complete Math Masters,
pages 322A and 322B.
Math Masters, p. 322A
322A-322B_EMCS_B_MM_G2_U10_576949.indd 322A
3/18/11 2:28 PM
ELL SUPPORT
Using Base-10 Blocks for
INDEPENDENT
ACTIVITY
5–15 Min
Place Value
To provide language support for place value concepts, do the
following activity. Show each of the base-10 blocks, draw a sketch
of each one on the board, and label them with their names and
values. Have children place 10 cubes on top of 1 long. Point out
that 10 cubes are the same as 1 long. 10 cubes and 1 long have
the same value. Next, place 10 longs on top of 1 flat. Point out
that 10 longs are the same as 1 flat. 10 longs and 1 flat have the
same value.
Teaching Master
Name
Date
LESSON
Place Value
10 8
Time
continued
Write in expanded form.
Example: 56
6. 63
7. 457
8. 893
9. 1,538
10. 2,341
11. 4,906
50 + 6
60 + 3
400 + 50 + 7
800 + 90 + 3
1,000 + 500 + 30 + 8
2,000 + 300 + 40 + 1
4,000 + 900 + 6
Write the number.
12. 900 + 20 + 5
13. 800 + 70 + 6
925
14. 9,000 + 20 + 4
876
15. 1,000 + 3
9,024
1,003
Do your own. Write a number. Write the number in
expanded form.
16.
Answers vary.
17.
Math Masters, p. 322B
322A-322B_EMCS_B_MM_G2_U10_576949.indd 322B
768
Unit 10 Decimals and Place Value
3/18/11 2:28 PM
Name
Date
HOME LINK
10 8
Family
Note
Time
Place Value
In this lesson, your child has been studying place value, or the value of digits in numbers.
Listen as your child reads the numbers in Problems 1–6. You might ask your child to pick a
few of the numbers and tell you the place value of each of the digits. For example, in 462,
the value of 4 is 400, the value of 6 is 60, and the value of 2 is 2.
10
Please return this Home Link to school tomorrow.
In each number:
Circle the digit in the hundreds place.
Underline the digit in the thousands place.
Example: 9 , 3 4 2
1. 4 6 2
2. 1 , 3 2 6
3. 5 , 0 0 6
4. 8 6 9
5. 2 , 3 0 4
6. 4 , 5 6 7
Read the numbers in Problems 1–6 to someone at home.
7.
Write the numbers represented by the base-10 blocks.
247
=
8.
=
9.
Copyright © Wright Group/McGraw-Hill
10.
=
Practice
Solve.
11. 134 + 24 =
12. 152 + 36 =
13. 67 - 38 =
14. 164 + 216 =
322
Name
LESSON
10 8
Date
Time
Place Value
Write the number for each group of base-10 blocks.
1.
2.
3.
Copyright © Wright Group/McGraw-Hill
4.
5. Circle the largest number.
Then explain how you
know what number
is the largest.
4,343
4,563
4,543
4,463
322A
Name
LESSON
10 8
Date
Place Value
Time
continued
Write in expanded form.
Example: 56
50 + 6
6. 63
7. 457
8. 893
9. 1,538
10. 2,341
11. 4,906
Write the number.
12. 900 + 20 + 5
13. 800 + 70 + 6
14. 9,000 + 20 + 4
15. 1,000 + 3
16.
17.
322B
Copyright © Wright Group/McGraw-Hill
Do your own. Write a number. Write the number in
expanded form.