Place Your Values
Current California Math Standards
Place Your Values (Whole Numbers)
Grade Three Number Sense
1.0 Students understand the place value of whole numbers:
1.1 Count, read, and write whole numbers to 10,000.
1.2 Compare and order whole numbers to 10,000.
1.3 Identify the place value for each digit in numbers to 10,000.
2.0 Students calculate and solve problems involving addition, subtraction, multiplication, and division:
2.1 Find the sum or difference of two whole numbers between 0 and 10,000.
Place Your Values Standards
1
Current California Math Standards
Place Your Values (Decimals)
Grade Four Number Sense
1.0 Students understand the place value of whole numbers and decimals to two decimal places and how whole
numbers and decimals relate to simple fractions. Students use the concepts of negative numbers:
1.1 Read and write whole numbers in the millions.
1.2 Order and compare whole numbers and decimals to two decimal places.
2.0 Students extend their use and understanding of whole numbers to the addition and subtraction of simple
decimals:
2.1 Estimate and compute the sum or difference of whole numbers and positive decimals to two
places.
3.0 Students solve problems involving addition, subtraction, multiplication, and division of whole numbers and
understand the relationships among the operations:
3.1 Demonstrate an understanding of, and the ability to use, standard algorithms for the addition
and subtraction of multi digit numbers.
Grade Five Number Sense
2.0 Students perform calculations and solve problems involving addition, subtraction, and simple multiplication
and division of fractions and decimals:
2.1 Add, subtract, multiply, and divide with decimals; add with negative integers; subtract positive
integers from negative integers; and verify the reasonableness of the results.
Grade Six Number Sense
1.0 Students compare and order positive and negative fractions, decimals, and mixed numbers. Students solve
problems involving fractions, ratios, proportions, and percentages:
1.1 Compare and order positive and negative fractions, decimals, and mixed numbers and place them on
a number line.
Place Your Values Standards
2
Current California Math Standards
Place Your Values (Multiplication)
Grade Three Number Sense
1.0 Students understand the place value of whole numbers:
1.1 Count, read, and write whole numbers to 10,000.
1.2 Compare and order whole numbers to 10,000.
1.3 Identify the place value for each digit in numbers to 10,000.
2.0 Students calculate and solve problems involving addition, subtraction, multiplication, and division:
2.1 Find the sum or difference of two whole numbers between 0 and 10,000.
2.2 Memorize to automaticity the multiplication table for numbers between 1 and 10.
2.4 Solve simple problems involving multiplication of multidigit numbers by one-digit numbers
(3,671 x 3 = __).
2.8 Solve problems that require two or more of the skills mentioned above.
Grade Four Number Sense
3.0 Students solve problems involving addition, subtraction, multiplication, and division of whole numbers and
understand the relationships among the operations:
3.1 Demonstrate an understanding of, and the ability to use, standard algorithms for the addition
and subtraction of multi digit numbers.
3.2 Demonstrate an understanding of, and the ability to use, standard algorithms for multiplying a
multi digit number by a two-digit number and for dividing a multi digit number by a one-digit
number; use relationships between them to simplify computations and to check results.
3.3 Solve problems involving multiplication of multi digit numbers by two-digit numbers.
Place Your Values Standards
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Place Your Values
Materials:
One deck of cards for every two players with all the tens, face cards and jokers removed (you will only use ace
through nine)
One large deck of playing cards for modeling the game on the white board (can be purchased in the Target game
section for $5.00)
One recording sheet for every student (see pages 7-11)
One Place Your Values template for every student (see pages 12-17)
Note: To save money you can make sets of digit cards using the master on page 18. You would need to make 4
sets for each pair of students if you wanted to have the same level of variety offered in a standard deck of playing
cards. You would also want to model the game using digit cards. Just enlarge the master on page 18 to 160% and
run on construction paper. Remember to run multiple copies to get a good variety of digits.
Mathematical Practice Standards:
3. Construct viable arguments and critique the reasoning of others.
7. Look for and make use of structure.
Current California Content Standards:
See pages 1-3 labeled “Place Your Values Standards”
Background Information:
This activity helps students to see the structure present in our place value system (a four placed in the hundreds
column is ten times greater than a four placed in the tens column; a four placed on the left side of the decimal is
very different than a four placed on the right side of the decimal). Students also have an opportunity to add and
subtract numbers in a context that has meaning to them. Having students make an observation after each turn is
an important part of the learning, so be sure to model this well during your demonstration.
Introduction (5 minutes):
Inform students that they are going to play a game called “Place Your Values”. In each round the players try to
create a number that is larger than the number their opponent creates. The difference between the two numbers
created is awarded as points to the person creating the largest number. The object of the game is to have the
most points at the end of four rounds. Tell them you are going to play a game against one student so everyone
can better understand the game.
Demonstration of how to play Place Your Values (15 minutes):
Put the “Place Your Values” sheet under the document camera or overhead. Draw two templates on the board
that match the game you have chosen to play. The template consists of boxes a little larger than the size of the
playing card and the value of each column labeled (see figure below).
Teacher
Hundreds
Place Your Value Lesson Plan
Tens
Student
Ones
Hundreds
Tens
Ones
4
The teacher and student take turns turning over a card and placing it in one of the columns on the template.
Once the player places their card, they make an observation. You will model a complete game by competing
against one student. An example of a classroom demonstration is depicted below and is based on the cards in the
figure below.
Teacher
Student
Hundred
s
Tens
Ones
Hundred
s
Tens
Ones
Draw One: The teacher placed the two in the ones column and said, “The number two is pretty low so I want to
put it in the ones column because I believe my next two cards will be higher than a two. The columns to the left
have a higher place value so I want to save my bigger numbers for those columns.” Once the teacher completed
her observation she said “done” and then the student flipped over a card. The student turned over a one and
placed it in the ones column. The student observed that “the one is the lowest card so I want to put it in the
column with the lowest place value. Done.”
Draw Two: The teacher placed the eight and said, “There is only one number higher than an eight, so I think I will
place the 8 in the hundreds column. Putting an eight in that column gives me 8 hundreds instead of just 8 tens.
Done.” The student drew a seven and said, “I am going to put the 7 in the tens column because if I put it in the
ones column I cannot get a number higher than you. Done.”
Draw Three: The teacher placed the two and said, “I made the number 822. The only way you can win is if you
turn over an eight or a nine. I think I am going to win Round 1. Done.” The student turned over a six and said,
“You created the larger number. I think you beat me by about 100 points. Done.”
Notice how the observations progress with each succeeding card. On the first draw the players are
looking only at the value of the card drawn. On the second draw the players are considering the
opponent’s game board, the value of the card, and the likelihood of what they will draw next since there
is only one remaining draw. The third draw focuses on the outcome with the first player predicting
whether they have a good chance of winning and the second player estimating by how much they won or
lost. These observations are an important part of the lesson as they allow you to do formative
assessments while circulating the room. When students justify their placement choices you gain a deep
understanding of their number sense.
The cards are then placed so the larger number is on top of the smaller number. The math problem is recorded
on the Place Your Values sheet, and the difference is calculated. The answers are compared to make sure both
answers are the same. The player who made the largest number earns that number of points on their score
sheet.
Place Your Value Lesson Plan
5
Play continues in this manner for three more rounds. Then the points are calculated for each player to determine
the overall winner. The differences are calculated to determine by how many points the winner defeated their
opponent. It is important to model how to calculate my points, my opponent’s points and total difference at the
bottom of the sheet so students understand how to complete this section.
Students Play the Game (15 minutes): Tell students they are going to do the following:
1)
2)
3)
4)
Turn over a card to determine who will go first (high card goes first).
Take turns placing a card on their place values game board.
Make an observation at the end of each turn.
Record the math problems on their Place Your Values recording sheet.
Circulate: During the game look for situations and discussions that would be examples to share during
Closure. For example, a game where a student lost in 3 of the 4 rounds but still managed to be the overall
winner, or a student who has an interesting way of justifying their card placements. Look for scenarios that
will allow you to focus the closure on the standards you are teaching while engaging the students in a
meaningful dialogue because you are using the games they just played.
Closure/Eliciting Student Thinking (10 minutes):
Ask students to:




share something that surprised them about the game (for example someone may have lost in 3 of the 4
rounds but still been the overall winner)
tell you why someone might have written the number 132 instead of 321 (the one was probably the last
number drawn but they thought they would get a number higher than 2 or 3 on their last draw).
tell you why someone might have written 793 instead of 973 (the 9 was probably the last number drawn
and they did not think they would get a number higher than 7 on their last draw)
share a strategy they think worked well and that they would use again the next time they play this game
(have them justify why they chose think this is a winning strategy)
Extension:


Extend the game to include numbers of larger magnitudes (five and six digit numbers).
Have students compete to create the lowest number possible. Lowest overall score wins the game.
Place Your Value Lesson Plan
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Place Your Values
Three-Digit Numbers
Round
Round One
Round Two
Difference
Your Name
Opponent’s Name
Points
Points
-
-
Round Three
-
Round Four
-
My Total Points
Place Your Values Student Recording Sheet
My Opponent’s Points
Total Difference
7
Place Your Values
Four-Digit Numbers
Round
Difference
Round
One
-
,
Round
Two
-
,
-
,
-
,
Round
Three
Round
Four
Your Name
Opponent’s Name
Points
Points
,
,
,
,
My Total Points
Place Your Values Student Recording Sheet
My Opponent’s Points
Total Difference
8
Place Your Values
Decimals Game One
Round
Difference
Round One
-
Round Two
-
Round Three
-
Round Four
-
My Total Points
Place Your Values Student Recording Sheet
Your Name
Opponent’s Name
Points
Points
My Opponent’s Points
Total Difference
9
Place Your Values
Decimals Game Two
Round
Difference
Round
One
-
Round
Two
-
Round
Three
-
Round
Four
-
My Total Points
Place Your Values Student Recording Sheet
My Opponent’s Points
Your Name
Opponent’s Name
Points
Points
Total Difference
10
Place Your Values
Multiplication
Round
Multiplication
Problem
Round
One
Difference
Your Name
Opponent’s
Name
Points
Points
-
Round
Two
-
Round
Three
-
Round
Four
My Total Points
My Opponent’s Points
Place Your Values Student Recording Sheet
Total Difference
11
HUNDREDS
Place Your Values Student Template for Placing Cards
TENS
ONES
12
HUNDREDS
THOUSANDS
TENS
ONES
,
Place Your Values Student Template for Placing Cards
13
ONES
TENTHS
HUNDREDTHS
.
Place Your Values Student Template for Placing Cards
14
TENS
ONES
TENTHS
HUNDREDTHS
.
Place Your Values Student Template for Placing Cards
15
TENS
ONES
x
Place Your Values Student Template for Placing Cards
16
TENS
ONES
x
Place Your Values Student Template for Placing Cards
17
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2
3
4
5
6
7
8
9
Place Your Values Digit Cards
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