(3.1B) Number, operation, and quantitative reasoning. The student uses place value to communicate about increasingly large whole numbers in verbal and written form, including money. The student is expected to use place value to compare and order whole numbers through 9,999. Suggested Activities/Lessons: •
Lesson: Compare and Order Numbers •
Lesson: Compare and Order Using a Number Line •
Number Top-‐It •
Digit Discovery TAKS Objective:Objective 1
TEKS: 3.1 The student uses place value to communicate
about increasingly large numbers in verbal and written
form.
Student Expectation: 3.1B Compare/order whole numbers
through 9,999.
Connection to
EUS title: Constructing and Utilizing
Essential Unit
Patterns and Numbers
of Study:
Essential Questions:
* Why is it important to know different ways to represent
the value of a number?
* What are some patterns you notice in our number
system?
* How does a digit's placement in a number change the
value of the number?
* How can numbers be expressed, ordered, and compared?
Understandings:
Overview:
Materials:
* Place value is based on groups of ten.
* There are a variety of ways to break apart and put
together whole numbers.
This is a learning activity that practices the sequencing of
numbers and place value decisions. See attached
prerequisite lesson.
Place Value Tools – Base Ten Materials and student
copies of pictorial Base 10 Blocks of units, tens, hundreds
and thousands.
Student copy and a class set of expanded notation cards
(0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 00, 10, 20, 30, 40, 50, 60, 70,
80, 90, 000, 100, 200, 300, 400, 500, 600, 700, 800, 900,
1000, 2000, 3000, 4000, 5000, 6000, 7000, 8000, 9000)
See attachments
Place Value Mat to the 1000’s
Place Value Path Game Boards
Digit cards per student (2 sets of 0-9)
Vocabulary:
Procedure:
compare
digit
greater than
more than
number
numeral
less than
order
place value
valuecomparative symbols >, <, =
equivalentexpanded notation (form)
greatest
standardized notation (form)word form ones
hundreds
thousands
tens
comma
Each player has their own Place Value Path Board 100 1000. The teacher will model the game with students on
overhead with digit cards.
Game Directions: The digit cards are shuffled and placed
face down. The teacher turns over 3 cards. When the
cards are turned over, the players must decide what
number to build,and which spot to place them in on the
game board. The path must go from the smallest number
to the largest number. Once a number is written in, it
must stay in that spot. The first person to complete the
path is the winner.
The teacher draws and displays the three numerals. The
teacher says, two, nine, four.
Teacher asks,What numbers can you create with these
digits?
What is the largest number you can make?
942 = 900 + 40 + 2 9 groups of hundred, 4 groups of
ten, 2 groups of one.
What is the smallest number you can make?
249 = 200 + 40 + 9
2 groups of hundred, 4 groups of
ten, nine groups of one.
What are the other numbers you can make?
Teacher lists the numbers the students share and
continues to ask, Are there any other numbers that can
be made?
In our number, how many groups of one are there?
In our number, how many groups of ten are there?
In our number, how many groups of hundred are there?
These are the “over and over” questions that students
need to be asked in reference to the picture of the
quantity, the expanded form of the quantity, and the
standardized form of the quantity.
924 =
294 =
492 =
429 =
900 +
200 +
400 +
400 +
20 +
90 +
90 +
20 +
4
4
2
9
What makes these numbers different from one
another? Listening for … that the digit’s placement
changes the value of the number.
Teachers says, Now, let’s chose one of the possible
number choices and write it on one of spaces on the
Place Value Path game board.
Draw another three cards from the deck and read aloud.
one, seven, five
What numbers can you create with these digits?
Look at your game board. Do you want to make a
number larger than the number you just recorded or
make a smaller number?
How are you going to decide where to place your
number on the game board?
How do you know your number is larger than ______?
How do you know that your number is smaller than
______? How do you know your number is between
_____ and ______ ?
Teacher should continue to facilitate the same questioning
stated above for 3-4 rounds.
The game continues until all spots on the board are filled.
Once students seem to master the skill needed for the
game you may have the students, pair up to play in small
groups. This provides the teacher the opportunity to
continue to work with the students who still need further
guidance practicing the skill. There is a point where a
player may not be able to use the cards and would
have to skip a turn.
There are two options for the cards after they are
played. One option would be to play the game where the
cards are reshuffled back into the deck. This would keep
the probability of the deck constant. The other option
would be to remove the cards once they have been played.
Play would continue until the deck is used up and then the
cards would be reshuffled and play continued until a path
is completed. This option changes the probability of the
deck as the cards are removed.
Listen for …
 Does the student accurately read the numbers using the
proper number naming patterns?
 Does the student clearly describe a reasonablestrategy
for placing the numbers on the game board?
Does the student's strategy and explanations involve
place value?
Look for …
Can the student place numbers on the game board
accurately?
Does the student demonstrate a good grasp of the
number system and place value?
Does the student apply useful benchmark numbers when
placing the numbers on the Place Value Path game board?
Does the student successfully compare and order
numbers on the Place Value Path game board?
Does the student use place value and patterns in number
relationships to compare, order, and place numbers on
game board?
Struggling students may need to use the pictorial Base 10
blocks or expanded notation cards.
Debriefing
Questions:
Chose two numbers from your game board. What are
your numbers? (For example,
two hundred ninety-four and seven hundred fifteen.)
Can you show the value of your numbers using the
pictorial Base 10 blocks?
What number is the greater? How do you know?
What number is the least? How did you decide this?
Write two numbers in your mathematics journal and use
a number symbol (>, <, = ) to compare the two
numbers. Why did you write this symbol? (For
example, 294 < 715.)
Is there another number sentence that you can write
comparing 294 and 715? (For example, 715 > 294.)
If you add/subtract 10 to each of your numbers, how
would the new numbers compare? How do you know?
What are the new numbers?
If you add/subtract 100 to each of your numbers, how
would the new numbers compare? How do you know?
What are the new numbers?
If you add/subtract 1000 to each of your numbers,
how would the new numbers compare? How do you
know? What are the new numbers?
Listen for…How does the student determine the new
numbers? Does s/he use concrete models, count on, use
mental arithmetic, pencil and paper to find the new
numbers, or another method?
Guided
Practice:
Evidence of
Learning:
Students can replay the game using the Place Value
Path 100 – 1,000 or the Place Value Path 1,000 –
10,000 Game board
Using the digits eight, one, four and five, rearrange the
numbers to create a four-digit number.
1,548
Write 5 things about your number:
1. the digit in the hundreds place is the same number
of sides on a pentagon
2. the number is even
3. if you add up all the digits it is equal to eighteen
4. the digit in the tens place is the number of angles
and sides on a square
5. the number in the tens place 4, is half the number
in the ones place 8
Rearrange the numbers to make:
the smallest number: ____________________
the largest number: _____________________
an even number: ________________________
an odd number: ________________________
a number less than 2000: _________________
a number more than 5000: ________________
Assessment
Objective 1 TEKS 3.1B
Name _____________
Date _______
The lengths of the longest four rivers in Texas are the Rio
Grande River with 1,896 miles, the Red River with 1,360 miles,
Brazos River 1,280 miles and the Pecos River 926 miles. Using
words, write the lengths of the rivers in order from the shortest
river to the longest river. Explain your process.
The numbers below are arranged from least to greatest.
4, 174
4,628
4,873
5,047
Which of the following numbers belong in the empty pentagon?
Mark your answer.
a.
b.
c.
d.
4,874
4,761
4,627
5,050
Prior to this lesson students should have experience in building
numbers with concrete and pictorial Base 10 materials.
For example, Students have their Base 10 Tool Kit and are using
the expanded notation cards and digit cards. The expanded
notation cards (large set) are handed out to students. The
teacher calls out a number 264. The teacher then models
building the number on the overhead or document camera using
the Base 10 materials. If a student is holding a card that is part
of the value of the number, he/she comes to the front of the
room. The student with the 200 card would come up, followed by
the student who has the 60 card and the student with the 4 card
would come up. The students would be lined up to show 200 + 60
+ 4. The teacher calls out “expanded notation” or “expanded
form.” The seated students would also build their number w/
paper base ten materials as well as with the expanded form
cards. The teachers calls out “standardized notation” or
“standardized form” and students in front of the class slide their
cards together to show 264. Students manipulate their own
expanded notation cards.
Can be made on sentence strips
This strategy connects the picture of the quantity with the
abstract meaning of 200 + 60 + 4 to the use of digit cards 264
Place Value Pocket
Thousands
Hundreds
Tens
Ones
2 0 0
6 0
4
“Expanded Notation”
264
“Standardized Notation”
Continue practice with this activity using larger numbers up to
9,999 for the 3.1B lesson.
Place Value Mats and digit cards are important tools in building
number sense tools that students construct.
Place Value Questions.
The teacher can ask these questions:
 In our number, how many groups of one are there?
5 groups of one = 5
 In our number, how many groups of ten are there?
3 groups of ten = 30
 In our number, how many groups of a hundred are there?
7 groups of hundred = 700
 In our number, how many groups of a thousand are there?
2 groups of thousand = 2000
Place Value Path100
- 1000
TAKS Objective 1: The student will demonstrate an
understanding of numbers, operations, and quantitative
reasoning.
TEKS 3.1:The student uses place value to communicate
about increasingly large whole numbers in verbal and
written form, including money.
Student Expectation 3.1B:The student is expected to use
place value to compare and order whole numbers through
999,999.
Connection to
ESU title: Place Value and Money
Essential Unit Essential Questions: What are some
of Study:
patterns you notice in our number
system?
Understandings: Students will understand
that symbols are used to represent
formal math language.
Students will explore strategies for comparing and
Overview:
Materials:
Vocabulary:
Procedure:
ordering whole numbers utilizing place value and the
number line.
Decks of cards
Game sheet for Who Has More?
Dry erase boards for student responses
Compare, order, place value, hundred thousands, ten
thousands, one thousands, hundreds, tens, ones, greater
than, less than, larger than, smaller than, symbol, <, >
Today we are going to explore and use strategies to
compare and order large whole numbers.
Which number is less 503 or 350? [350]
How do you know? [3 hundreds is less than 5 hundreds;
350 comes before 503]
You used what you knew about place value to help you
compare the numbers.
What words would you say to compare the numbers?
[503 is greater than 350 or 350 is less than 503]
What math symbols could we use to show that
comparison? [< or >]
Write a sentence showing that comparison.
[350 < 503 or 503 > 350]
Read that sentence. [350 is less than 503 or 503 is
greater than 350]
How did you know which symbol to use? Talk with your
partner. [The open part of the symbol always points to
the larger number.]
How would you compare 108,464 and 97,996 using the
math symbols for greater than and less than?
[108,464 > 97,996 or 97,996 < 108,464]
What strategy did you use to compare the numbers?
Talk with a partner.
[108,464 has more digits than 97,996 so it is greater;
97,996 has less digits than 108,464 so it is less; 108,464
has a digit in the hundred thousands place while 97,996
has only a digit in the ten thousands place so it is greater;
97,996 has a digit in the ten thousands place while
108,464 has a digit in the hundred thousands place so it is
less]
What symbol, < or >, would make this sentence true?
(record on board)
673,024 ___ 692,102 [<]
How do you know? Share with a partner.
[Both numbers have 6 in the hundred thousands place.
But, the digits in the ten thousands place are different.
70,000 is less than 90,000 so 673,024 is less than
692,102.]
If we wanted to put the following numbers in order
from least to greatest, how would using a number line
help?
476
267 742
[267 would come before 476 on the number line and 476
would come before 742 on the number line. So the order
of the numbers from least to greatest would be:
267 476 742]
Debriefing
Questions:
Guided
Practice:
Evidence of
Learning:
How could you use place value to order these numbers
least to greatest?
[200 is less than 400 and 400 is less than 700]
Order these numbers from greatest to least:
25,716
25,961
25,381
[25,961
25,716 25,381]
How did you figure that out? Share with a partner
your strategy.
[All 3 numbers started the same with 25 thousand, but
the hundreds were different. 900 is more than 700 and
700 is more than 300.]
1. What math symbols or words can we use to compare
whole numbers? [< or >; greater than, more than, less than,
smaller than]
2. Explain what the symbols mean. [> means greater than; <
means less than; the mouth or open part always opens to
the greater number]
3. If you want to compare or order whole numbers, what
are some strategies you could use? [position on the
number line: if the number is to the left of the other
number or numbers then it is smaller or the smallest; use
place value to determine the value of the digits: the more
digits the larger the number, the higher the place the
greater the number; starting from the left find where
the digits in the same place are different and then
compare their value]
Play game: Who Has More?
Materials: deck of cards (0-9), game sheet for each
student pair
Players will use the cards to make 5 digit numbers and
compare them using the symbols.
Teacher checks with each group to check for accuracy or
misunderstandings.
1.Which of these numbers is less than 10,580?
a. 10,791
b. 10,601
c. 10,589
d. 10,578
2. The numbers are arranged from greatest to least.
Write a number that could belong on the empty line.
6,521 ___ 5,942 5,601 5,578
3. Use < or > to make the sentences true.
45,181 ___ 46,758
346,521 ___ 344,099
200,425 ___ 39,939
4. Academy has 8,674 tennis balls in the store. Sports
Authority has 8,903 tennis balls. Which store has more
tennis balls?
Circle the store name.
Academy
Sports Authority
Assessment for Learning Objective 1 – TEKS 3.1B Name ________________________
Date _____________
1. Which of these numbers is less than 10,580?
a. 10,791
b. 10,601
c. 10,589
d. 10,578
2. The numbers are arranged from greatest to least. Write a
number that could belong on the empty line.
6,521 ____________
5,942
5,601
5,587
3. Use < or > to make the sentences true.
45,181 ____ 46,758
346,521 ____ 344,099
200,425 ____ 39,939
4. Academy has 8,674 tennis balls for sale in their store and
Sports Authority has 8,903 tennis balls for sale. Which store
has more tennis balls?
Circle the store name.
Academy
Sports Authority
TEKS 3.1B Game Sheet
Who
Has More?
Object of game: To find which created 5 digit
number is greater than the other.
Number of Players: 2
Materials: deck of cards (0-9), game sheet per
pair
Directions:
1. Shuffle the deck of cards.
2.
Each player draws 5 cards.
3.
Player 1 turns over the cards and records
the numbers in the order turned over to
create a 5 digit number for Round 1.
4.
Player 2 does the same thing.
5.
The player with the largest number records
the symbol in the box to make the sentence
true.
6.
Play for 5 rounds.
7.
At the end of the game, each player orders
their numbers from greatest to least.
Who Has More?
Use < or >.
Player 1
Player 2
Round 1
Round 2
Round 3
Round 4
Round 5
Order your numbers from greatest to least.
Player 1
Player 2
S t r a n d s Numeration; IVIeasurement and Reference Frames
S k i l l Practice finding tine total value of coins
G a m e s K i t M a t e r i a l s Cper group]
Game Master 114 (record sheet)
16 nickels, 40 pennies
Players 2
Object of the game To have the greater amount of money.
Nickel/Penny Grab Record Sheet SiA 144
1 grabbact
I have
® and
a, Myparlnerhas
1.
Players m i x the coins together.
2.
One player grabs a handful of coins; the other player takes the
coins that are left.
3.
Players help each other count the coin collections and determine
which player has more money.
4.
The player w i t h more money wins the game.
©.
c.
Who has ma™? .
f 1 grabbed
Direct
® ai
My partner grabbed _
S t r a n d Numeration
S k i l l Practice comparing numbers
G a m e s K i t M a t e r i a l s (per group)
Nunnber Top-Zf Gameboard (or Game Masters 115 and
116,1 copy for every 2 players)
Everything Math Deck
Grade 3 ,
Grade 4
(number cards 0-9, 4 of each)
Players
2-5
228
\
Z
Grade I
204 \ J 287^
Object of the game To make the greatest 7-digit number.
Direct
128 Game Directions
1.
The dealer shuffles the cards and places the deck number-sidedown on the playing surface.
2.
The Place-Value M a t has rows of boxes. Each player uses one
row of boxes on the game mat or uses the space on the playing
surface below the gameboard.
c
I n each round, players take turns turning over the top card from
the deck and placing i t on any one of their empty boxes. Each
player takes 7 turns and places 7 cards on his or her row of the
game mat.
7-Drgit Place-Value M a t
aSI, 1 1 S W '
A t the end of each round, players read their numbers aloud and
compare them to the other players' numbers. The player w i t h
the greatest number for the round scores 1 point. The player
w i t h the next-larger number scores 2 points, and so on.
Players play 5 rounds for a game. One player shuffles the deck
between each round. The player w i t h the least number of points
at the end of 5 rounds wins the game.
=;tXAMPItTwo players finished''One;Tound of 7-6\^ Number Top-It
Here are the results.
Millions
c/.:;
•
HundredTenThousands Thousands Thousands Hundreds
4
'2
7
\
5
Tens
Ones
0
Player 1
]
0
^
2
1
Player 2
s
Player t's number is larger than Player 2's number.
So Player 1 scores 1 point for this round. Player 2 scores 2 points.
V a r i a t i o n (recommended for Grade 3)
Students can play an easier version of the game by l i m i t i n g the
numbers to 5 digits. Players do not use the Millions box or the
Hundred-Thousands box on the Place-Value Mat.
3
7-Digit P l a c e - V a l u e M a t (...tl
gS'., 116<<
5
Game Directions 129
Name
Date
Time
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7-Di'git Place-Value Mat
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7-Digit Place-Value Mat (cont.)
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Number Top-It
Game Masters 2 9 9
strand
Numeration
Skill Practice place-value skills and comparing numbers
Wlaterials Cper group)
cdlored chalk (optional)
3 sets of the number cards 0 - 9 (each set of numbers written in a
different color such as red, blue, and green)
P l a y e r s whole class
Object of the game To use clues to form 3-digit numbers.
lirections
1.
2.
3.
Use colored chalk, if available, to write the place-value names
along the top ofthe board. For example, write "hundreds" i n red,
"tens" in blue, and "ones" in green.
Mix and distribute the colored number cards so that each
student has at least one.
Give clues to summon students to the board.
Say / am the largest 3-digit number.
Students with red 9, blue 9, and green 9 come to the board and
stand under their colors, holding up their number cards.
Say I am 10 less than the number up there now.
Blue 9 sits down and is replaced by blue 8.
Say / am 500 less than the number up there now.
Red 9 sits down and is replaced by red 4.
Variation
Ask students to make up the clues.
64 Game Directions