Numeration and
Place Value
Objective To review place value in 2-digit and 3-digit numbers.
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Teaching the Lesson
Key Concepts and Skills
• Count by 1s, 10s, and 100s with base-10
blocks. [Number and Numeration Goal 1]
• Explore place-value concepts with base-10
blocks; read and write 2- and 3-digit
numbers. [Number and Numeration Goal 2]
• Build numbers with base-10 blocks
in preparation for modeling addition
strategies. [Number and Numeration Goal 2]
Key Activities
Children explore base-10 blocks, matching
numbers to them and modeling 2- and 3-digit
numbers (with and without zero).
Ongoing Assessment:
Informing Instruction See page 187.
Family
Letters
Assessment
Management
Common
Core State
Standards
Ongoing Learning & Practice
1 2
4 3
Playing the Digit Game
My Reference Book, pp. 132 and 133
per partnership: 4 each of number
cards 0–9 (from the Everything Math
Deck, if available)
Children practice forming and
comparing numbers.
Math Boxes 3 1
Math Journal 1, p. 54
Children practice and maintain skills
through Math Box problems.
Home Link 3 1
Curriculum
Focal Points
Interactive
Teacher’s
Lesson Guide
Differentiation Options
READINESS
Counting Practice
calculator base-10 blocks (10 flats,
10 longs, 10 cubes)
Children use their calculators to investigate
place value.
ENRICHMENT
Creating 3-Digit Numbers
number cards 1–9 (from the Everything Math
Deck, if available)
Children create as many numbers as
possible using three digits.
Math Masters, p. 57
Children practice and maintain skills
through Home Link activities.
Ongoing Assessment:
Recognizing Student Achievement
Use journal page 53. [Number and Numeration Goal 2]
Key Vocabulary
base-10 system
Materials
Math Journal 1, p. 53
My Reference Book, p. 11
Math Masters, p. 427
transparency of Math Masters, p. 56
(optional) base-10 blocks number cards
0–9 (from the Everything Math Deck, if
available) calculator
Advance Preparation
You may want to spend two days on this lesson. For Part 1, you and each child or partnership will need
a set of base-10 blocks (3 or 4 flats, 10 longs, and 10 cubes in bags labeled with children’s tool-kit
numbers). To display a Place-Value Mat, make an overhead transparency of Math Masters, page 56
or draw a Place-Value Mat on the board. For a mathematics and literacy connection, obtain a copy of
A Place for Zero: A Math Adventure by Angeline Sparagna LoPresti (Charlesbridge Publishing, 2003).
Teacher’s Reference Manual, Grades 1–3 pp. 30, 56, 57
184
Unit 3
Place Value, Money, and Time
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Getting Started
Mental Math and Reflexes
Math Message
Pose number stories that involve addition and subtraction facts. Suggestions:
Keisha read 8 pages of her book last night and 6 pages this morning. How
many pages did she read in all? 14 pages
Hana scored 7 points. Dakota scored 9. How many points did they score in all?
16 points
52 =
5
25 =
2
tens and
2
ones
tens and
5
ones
Austin brought 17 cupcakes to school for his birthday. He gave 8 to his
classmates. How many cupcakes does he have left? 9 cupcakes
1 Teaching the Lesson
Math Message Follow-Up
● On
WHOLE-CLASS
DISCUSSION
Briefly discuss children’s responses. Ask children to explain how
they decided which digit names the tens and which digit names
the ones. These numbers will be revisited later in the lesson.
Explain to children that in today’s lesson they will use base-10
blocks to create numbers.
Exploring a Simple Way to
Day 1 of this lesson, children should
complete the Math Message Follow-Up,
explore drawing base-10 blocks, and
begin matching numbers and displays of
base-10 blocks.
● On
Day 2 of this lesson, children should
continue matching numbers and displays
of base-10 blocks and do place-value
exercises. Then have children complete
Part 2 activities.
Interactive whiteboard-ready
ePresentations are available at
www.everydaymathonline.com to
help you teach the lesson.
WHOLE-CLASS
ACTIVITY
Draw Base-10 Blocks
(My Reference Book, p. 11)
Hold up a cube, a long, and a flat. Say: These are called base-10
blocks. Hold up a cube. Say: This is a base-10 cube. It represents
one. Then hold up a long and say: This is a long. It represents ten.
Ask children why they think a long represents ten. Because it is
made up of 10 cubes Last, hold up a flat and say: This is a flat.
It represents one hundred. Ask children why they think a flat
represents one hundred. Because it is made up of 100 cubes
Display the blocks on the overhead projector.
Remind children that our system for writing numbers is called the
base-10 system, because it is based on grouping things by tens.
Explain that base-10 blocks are useful for understanding numbers
and solving problems.
Base-10 blocks
cube
flat
Base-10 drawings
Show children the pictures in the margin as a quick and easy way
to draw base-10 blocks. Drawing pictures may be more convenient
than using the actual blocks, and pictures are often useful for
explaining and recording solutions.
Read about base-10 blocks with your class on page 11 of
My Reference Book.
long
cube
long
flat
Lesson 3 1
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NOTE Children use 10 number cards, a
Place-Value Mat, a calculator, and many base10 blocks for these activities. Before beginning
this activity, you may want to show children
how to arrange these materials on their desks.
If necessary, children can work in pairs.
NOTE To review writing 2-digit number words,
consider varying the Matching Numbers and
Displays of Base-10 Blocks activity. Have
children work in partnerships. One partner
shows a 2-digit number by placing base-10
blocks on a Place-Value Mat. The other partner
writes the number word for that number on
his or her slate. Then partners reverse the
procedure. One partner writes a 2-digit number
word on his or her slate and the other partner
forms the number with the base-10 blocks and
Place-Value Mat.
Ongoing Assessment:
Informing Instruction
Watch for children who enter 7008 on the
calculator. When representing 708
with base-10 blocks, be sure to point out that
there are three columns on the Place-Value
Mat, therefore there should only be 3 digits.
Teaching Aid Master-Name
Date
Time
ones
Place-Value Mat
Matching Numbers and
WHOLE-CLASS
ACTIVITY
Displays of Base-10 Blocks
(Math Masters, pp. 56 and 427)
Give each child or partnership a set of number cards (0–9) and a
Place-Value Mat. Display 3 flats, 5 longs, and 2 cubes on a PlaceValue Mat. (See Advance Preparation.) Have children show the
number 352 by putting cards on their Place-Value Mats. Children
show 352 by putting the card for 3 in the hundreds place, the card
for 5 in the tens place, and the card for 2 in the ones place. Ask:
How many hundreds are in this number? 3 How many tens? 5
How many ones? 2 Then ask children to read the number in
unison. Three hundred fifty-two
Repeat with other 2- and 3-digit numbers, including the numbers
52 and 25 from the Math Message. Ask children to explain what
the digits 5 and 2 mean in each number. Display the place-value
blocks at random without the mat. By doing this, children will
have to sort the blocks mentally into ones, tens, and hundreds.
Then reverse the procedure. Write a 2- or 3-digit number on the
board and ask children to show the number by placing base-10
blocks on their Place-Value Mats. Repeat with several other
2- or 3-digit numbers.
Now, repeat the previous procedures using numbers with zero in
the tens or ones place. For example, display 3 flats and 4 cubes
and ask children to use number cards to show the number on their
Place-Value Mats. Some children may put no digit card in the tens
column; others will put a zero. Point out that not including the
zero can cause problems when there is no Place-Value Mat.
Write 34 and 304 on the board and ask which number matches
the base-10 blocks. 304 Ask which digit in 304 shows that there
are no longs. The zero
Continue with a series of translations among spoken numbers,
written numbers, base-10 blocks, number cards, and calculator
displays. For example:
Say: Show the number 508 with base-10 blocks. 5 flats,
8-cubes
Say: Use cards to show the number with 4 in the ones place,
0 in the tens place, and 8 in the hundreds place. 804
tens
Ask: In 567, which number is in the ones place? 7 The tens
place? 6 The hundreds place? 5
Write 749 on the board. Say: Read the number on the board.
Seven hundred forty-nine.
hundreds
Say: Use your calculator. Enter 708. Now use base-10 blocks
to show 708. 7 flats, 8 cubes
Math Masters, p. 427
186
Unit 3 Place Value, Money, and Time
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Student Page
Using Place Value to Compare Numbers
Date
31
Write the numbers 549 and 547. Ask a volunteer to read the
numbers. Ask: Which is greater? 549 How can you tell? Answers
will vary. One possible strategy is to write the numbers one under
the other, so that same-place digits are aligned, and then compare
the values of the aligned pairs of digits starting with the first pair
on the left. (See margin.) For example: The hundreds digits are the
same; each has a value of 500. The tens digits are the same; each
has a value of 40. The ones digits are not the same; 9 is greater
than 7. So 549 is greater than 547. Write 549 > 547. Repeat with
other 3-digit numbers.
Doing Place-Value Exercises
Time
LESSON
Place Value
Write the number for each group of base-10 blocks.
547
1.
403
2.
3. Write a number with …
4.
5 in the ones place,
3 in the hundreds place, and
2 in the tens place.
>
322
How many ones?
6. 122
>
102
5
0
6
How many tens?
325
Write <, >, or =.
5. 328
506
How many hundreds?
7. 623
<
633
8. Marta wrote 24 to describe the number shown by these
INDEPENDENT
ACTIVITY
base-10 blocks:
(Math Journal 1, p. 53)
Is Marta right? Explain your answer.
Children use base-10 blocks to complete journal page 53. Then
review the answers with them. For Problem 3, make sure children
have written 325 and not 532 or 235. Ask a volunteer to explain
the answer to Problem 8. Have other children explain why they
agree or disagree with the answer. Make sure children are able to
identify each of the base-10 materials in the pictures.
Sample answer: No; the base-10 blocks
show 2 hundreds, not 2 tens.
Math Journal 1, p. 53
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5 4 9
Ongoing Assessment:
Recognizing Student Achievement
Use journal page 53, Problems 1 and 3 to assess children’s understanding of
place value. Children are making adequate progress if they can correctly answer
the problems using base-10 blocks. Some children may be able to complete the
problems that involve 0 as a placeholder.
[Number and Numeration Goal 2]
2 Ongoing Learning & Practice
Playing the Digit Game
NOTE You may wish to have children
review expanded notation, which involves a
knowledge or understanding of place value.
Expanded notation is a way of writing a
number as the sum of the values of each digit.
Student Page
Games
The Digit Game
PARTNER
ACTIVITY
(My Reference Book, pp. 132 and 133)
Have children read the rules for the Digit Game on pages 132 and
133 of My Reference Book. Explain to children that they will play
the game with 3 cards, using them to make the largest possible
3-digit number. Play several demonstration hands with the class.
Have partners play several rounds of the game.
5 4 7
Journal page 53
Problems
1 and 3
Materials ❑ number cards
0–9 (4 of each)
Players
2
Skill
Making and comparing numbers
Object of the game To collect more cards.
Directions
1. Shuffle the cards. Place the deck number-side
down on the table.
2. Each player draws 2 cards from the deck and
uses them to make the larger 2-digit number.
3. The player with the larger number takes
all 4 cards.
4. The game is over when all of the cards have
been used.
5. The player with more cards wins.
My Reference Book, p. 132
Lesson 3 1
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Student Page
Date
Time
LESSON
Math Boxes 3 1
Math Boxes
31
calculator to count by 7s.
9+7
Rule
+7
7
>
10 + 12
21
14
(Math Journal 1, p. 54)
2. Write <, >, or =.
1. Fill in the frames. Use your
7+7
13
< 26
= 5+9
Mixed Practice Math Boxes in this lesson are paired with
Math Boxes in Lesson 3-3. The skills in Problems 5 and 6
preview Unit 4 content.
42 35 28
9
98 99
3. Solve.
4. How much money? Fill in the
Unit
$21.40
B $21.45
18 + 9 =
Change
17 + 9 =
End
+10¢
16 + 9 =
?
15 + 9 =
Answer:
17 ¢
Home Connection Children continue their work with
base-10 blocks as they complete place-value exercises
similar to those on journal page 53.
D $11.40
6. Solve.
How much does he have now?
7¢
INDEPENDENT
ACTIVITY
(Math Masters, p. 57)
A
C $2.45
Start
Home Link 3 1
circle next to the best answer.
15
70 + 80 = 150
700 + 800 = 1,500
7,000 + 8,000 = 15,000
7+8=
5. Mike had 7¢. He found a dime.
INDEPENDENT
ACTIVITY
Unit
27
26
25
24
3 Differentiation Options
116
Math Journal 1, p. 54
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READINESS
Counting Practice
SMALL-GROUP
ACTIVITY
5–15 Min
To explore place value using a concrete model, have children use a
calculator and base-10 blocks in a counting activity. Begin by
reviewing how to count by 1s on the calculator. The following
program will work on any calculator: Clear the calculator.
+
+
Press 0 + 1
1
1
.… Two additional programs
for counting by 1s are given below for demonstration purposes.
Have children perform the steps on their own calculators.
Home Link Master
Name
Date
HOME LINK
31
䉬
Family
Note
For the Texas Instruments TI-108:
Time
ON/C
Place Value
1. Press
All numbers are made up of digits. The value of a digit depends on its place in the number.
In the number 704, the digit 7 means 7 hundreds, the digit 0 means 0 tens, and the digit
4 means 4 ones. This idea is called place value.
2. Press 0. This is the starting number.
Your child has been using base-10 blocks to help him or her understand the idea of place
value. Base-10 blocks are shown in Problems 1a and 1b below. A “cube” (with each side
1 unit long) represents 1. A “long” (a rod that is 10 units long) represents 10. And a “flat”
(a square with each side 10 units long) represents 100.
10 11
Please return this Home Link to school tomorrow.
3. Press
+
. This clears your calculator.
. This tells the calculator to count up.
4. Press 1. This tells the calculator to count by 1s.
1. Which number do the base-10 blocks show?
a.
374
b.
507
2. Write a number with
740
4. In 806, how
many hundreds?
How many tens?
How many ones?
1. Press
3. Write a number with
7 in the hundreds place,
0 in the ones place, and
4 in the tens place.
For the Casio SL-450:
3 in the tens place,
6 in the ones place, and
9 in the hundreds place.
. This clears your calculator.
2. Press 1. This tells the calculator to count by 1s.
936
8
0
6
5. In 231, how
many hundreds?
How many tens?
How many ones?
2
3
1
3. Press
. This tells the calculator to count up.
4. Press 0. This is the starting number.
Math Masters, p. 57
188
Unit 3 Place Value, Money, and Time
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Now the calculator is ready to start counting by 1s. Without
clearing their calculators, have children press the
key. Press
the
key repeatedly together as the class counts together by 1s
stopping at 9.
Ask children what comes next. Then have them press
once,
observing the change from 9 to 0 in the ones place and the
appearance of a 1 in the tens place. What does the 1 stand for?
1 ten
Clear the calculators and repeat the counting by 1s activity. This
time, have the children work in partnerships. One partner does
the calculator count while the other partner takes a cube each
time one more is added. Compare what happens after 9 is
displayed on the calculator (changing to 10) and the exchange of
ten single cubes for one long.
Repeat the counting activity having all children count by 10s on
the calculator from 0 to 100. Now have partnerships repeat the
count switching roles so one partner counts on the calculator and
the other partner takes longs. Repeat with 100s and flats.
If interest and time permit, change the start number and repeat
counts by 10s and 100s using both the calculator and the blocks—
for example, start at 14 (1 long, 4 cubes) and count by 10s (adding
one long each time).
ENRICHMENT
Creating 3-Digit Numbers
SMALL-GROUP
ACTIVITY
5–15 Min
To further explore 3-digit numbers, have children create as many
3-digit numbers as possible using the same three nonzero digits.
Each child selects three cards from the Everything Math Deck
(1–9). They create as many numbers as possible using the three
cards and record their answers. Try three different cards. Ask:
How many combinations are possible using three cards? 6 Have
children try four cards. How many combinations are possible using
four cards? 24
Planning Ahead
Before beginning Lesson 3-2, make an overhead transparency of
Math Masters, page 58, the Fruit and Vegetables Stand Poster.
Lesson 3 1
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