Current California Math Standards
Integer Addition War
Grade Five Number Sense
1.0 Students compute with very large and very small numbers, positive integers, decimals, and fractions and
understand the relationship between decimals, fractions, and percents. They understand the relative magnitudes of
numbers:
1.5 Identify and represent on a number line decimals, fractions, mixed numbers, and positive and negative
integers.
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
2.0 Students calculate and solve problems involving addition, subtraction, multiplication, and division:
2.3 Solve addition, subtraction, multiplication, and division problems, including those arising in concrete
situations, that use positive and negative integers and combinations of these operations.
Integer Addition War
Integer Addition War
Materials:
One deck of digit cards for every two players (see note below)
One deck of digit cards for demonstrating the game
4 magnets to use during the demonstration
One number line for each player (see page 6)
Note: Using the master on page 5 you can make decks of digit cards. A deck consists of 4 sets of 1-9. You would need
to make 2 sets of 1-9 in Color One (we are using pink) and 2 sets of 1-9 in Color Two (we are using blue) for every pair of
players. Each deck of digit cards needs to be well mixed before distributing to students.
Mathematical Practice Standards:
3. Construct viable arguments and critique the reasoning of others.
7. Look for and make use of structure.
Standards:
Grade 5 – NS 1.5 and NS 2.1
Grade 6 – NS 2.3
Background Information:
This game gives students an opportunity to add positive and negative numbers using a number line. Students gain
experience justifying which sum is greater by referring to the number line. Playing this game encourages students to
focus on whether the integer is positive or negative. It also provides a great foundation for helping students understand
“the rules” for adding integers (positive plus positive is a positive; negative plus negative is a negative; positive plus
negative is situational).
Introduction (5 minutes):
Share with children that they will be adding positive and negative integers. They will be using the number line as a tool
to help them in this game. Explain to students that whenever you add integers you are just moving forward or backward
on the number line.
Draw a number line and label the zero. Show students that 2 + 3 are both forward moves on the number line with an
ending location of 5. Demonstrate how -2 + -3 are both backward moves on the number line with an ending location of
-5. Now demonstrate -2 + 3 and ask students to pair share about where the ending location is. Ask students whether
they think the answer is positive or negative and to tell why they have this opinion. They should say something like “you
moved backwards two spaces and forward three spaces, so it’s positive”). Do 3 + (-2) and ask where the ending location
is. Ask students why it’s the same ending location (we are still moving backward two and forward three; we are just
doing it in a different order).
Tell students they are going to play a game where they are going to add positive and negative integers. Explain that they
will be given a deck of digit cards. Half of the cards are pink and represent negative integers; half of the cards are blue
and represent positive integers. Share with students that you are going to model how to play the game by competing
against one student in the class. (Make sure this is a verbal student who will be a good role model for classmates).
Integer Addition War Lesson Plan
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Demonstration of how to play the game (10 minutes):
Draw two digit cards from the deck and place them on the board using magnets. Use the number line to verbally
demonstrate your math problem. For example, if you drew a pink 4 and a blue 7 you would say “negative four (and use
your finger to point to negative four on the number line) plus positive 7 (move your finger forward 7 spaces, stopping on
each space as you go) equals positive 3. My sum is positive three.” (You are not writing on the number line. You are
just using it to illustrate the problem).
Now the student you are competing against draws two digit cards. You place them on the board using magnets. They
use the number line to verbally answer their math problem. Let’s say they drew a pink 3 and a pink 5. They would say
“negative three (and use their finger to point to negative three on the number line) plus negative 5 (they move their
finger backward five more spaces, stopping on each number as they go) equals negative 8. My sum is -8.”
NOTE: Having students point to the first number and then move along the number line with their finger allows students
to activate another learning modality and will “unlock” the learning for many students.
Whoever has the largest sum justifies that they have the largest sum. You would say “I have a sum of positive three and
you have a sum of negative 8. My sum is further to the right on the number line which means it is a larger number. I
win all four digit cards.” You then take the cards off the board and put them in your pile.
Continue to model the game for three more turns to make sure students see a few different scenarios (positive plus
positive; negative plus negative; positive plus negative; negative plus positive). Stress to the students that they must use
their finger to show their math problem on the number line, and they must verbally answer their math problems.
Eliciting Student Thinking:
During your demonstration you can ask your opponent to think out loud by having them turn over one card at a
time. For example if they turn over a pink 3, they would point to negative 3. Let’s say the next card is blue.
Before they turn over the card, you can ask the student, “What can you say about your sum?” The student
should say something like “it will be larger than -3 because I am going to move to the right on the number line”.
Let’s say they turned over a blue 6. Their sum is positive 3. Now it’s your turn to think aloud by turning over
one card at a time. Let’s say you turn over a blue 9, you would point to the positive 9. Let’s say your next card is
a pink card. Before turning it over you might say, “Well, I know my sum is going to be less than 9 because I will
be moving left on the number line. I think I have a good chance of winning because if I flip over a 5 or less then I
will have a sum higher than 3”. Let’s say you flip over a two. You move two spaces to the left and then justify
why your sum is larger. “Seven is further to the right on the number line than three is so my sum is larger.”
Some questions you may want to ask before a card is flipped over:
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There are two pink cards to turn over. What can you tell me about the sum? (It’s negative.)
There are two blue cards to turn over. What can you tell me about the sum? (It’s positive.)
A pink card is turned over first, and there is a blue card to turn over. What can you tell me about the
sum? (My sum will be larger than the first card I turned over.)
A blue card is turned over first, and there is a pink card to turn over. What can you tell me about the
sum? (My sum will be smaller than the first card I turned over.)
Before they turn over any cards, have the student look at their opponent’s sum and make predictions
about their chances of having a higher sum based only on the color of the cards they get to turn over.
Integer Addition War Lesson Plan
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Students Play the Game (15 minutes): Tell students they are going to do the following:
1)
2)
3)
4)
5)
Remove the digit cards from the baggie and place them in a neat stack on the desk.
Determine who is going to go first by turning over a card (highest digit goes first).
Take turns drawing two cards from the stack and verbally solving their math problem using the number line.
Continue play until the timer goes off or one player has all the digit cards.
Tell them the winner is the player with the most cards when time is up.
Note: When the game first begins make sure you do not “get stuck” helping one or two pairs. You need to first circulate
throughout the entire class to make sure everyone is playing the game correctly. Students may be resistant to using the
number line. Once everyone is on track, circulate and begin asking students questions like those listed above.
Closure (15 minutes):
Closure should tie together the game and the standard you have chosen to focus on. Be sure to highlight the selected
standard in your closure. See below for ideas.
Ask students if they noticed any patterns with their math problems. You want them to notice the structure present (the
rules we usually teach without students having an opportunity to explore them) when adding integers so if the
conversation is not heading that direction ask specific questions such as:
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What happens when we add two positive integers? (You want them to include the number line in their answer
to help them to see that adding two positive integers is two moves forward on the number line which means
the answer will always be positive).
What happens when we add two negative integers? (You want them to include the number line in their answer
to help them to see that adding two negative integers will be two moves backward on the number line which
means the answer will always be negative).
What happens when we add a positive integer and a negative integer? (You want students to include the
number line in their answer to help them to see that the answer is negative or positive based on whether you
moved forward more spaces or backward more spaces. Model an example using the number line).
Will the answer be different if we add a negative to a positive versus a positive to a negative? For example is -5
+ 3 the same or different than 3 + (-5)? Have them talk to their neighbor and then be ready to justify their
response. (This concept was presented in the introduction but many children need to play the game to truly
understand what you were presenting in the introduction. Consider calling on one of your more fragile learners
to see what learning they are taking away from this activity).
Extensions:
1. Have students turn over three cards and use the number line to determine the sum. The player with the largest
sum wins all six cards.
2. Have students ask each other questions based on the color of the cards they are going to draw (just like you did
in the introduction and while you were circulating).
3. Try playing Integer War with playing cards instead of digit cards. Give the jack a value of 11, a queen a value of
12, and a king a value of 13. The red cards would be negative integers and the black cards would be positive
integers.
Integer Addition War Lesson Plan
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Integer Addition War Digit Cards
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Integer Addition War
Pink Cards are Negative Numbers
Blue Cards are Positive Numbers
Integer Addition War
Pink Cards are Negative Numbers
Integer Addition War Number Lines (Copy and cut in half)
Blue Cards are Positive Numbers
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