Common Core Math 7
Unit 1, Days 5-6
Topic: Modeling Addition of Integers
Common Core State Standard(s):
7.NS.1a Describe situations in which opposite
quantities combine to make 0. For example, a
hydrogen atom has 0 charge because its two
constituents are oppositely charged.
7.NS.1b Understand p + q as the number located a
distance |q| from p, in the positive or negative
direction depending on whether q is positive or
negative. Show that a number and its opposite have a
sum of 0 (are additive inverses). Interpret sums of
rational numbers by describing real-world contexts.
7.NS.1d Apply properties of operations as strategies
to add and subtract rational numbers.
Mathematical Practice Standard(s):
MP.4 Model with mathematics and Alice software.
Learner Objective:
As a result in learning, students will be able to…
model addition of integers.
Instructional Resources:
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Modeling Integer Addition Handout
Modeling Integer Addition Notes- Teacher
Copy
Integer Chips
Heaps and Holes
Inner Circle-Outer Circle Activity
Inner Circle-Outer Circle Activity Teacher
Notes
Integer Addition Algorithm Handout
KutaSoftware Integers
Alice software
Warm-up:
Day 5:
 Find the value of each situation:
a)
b)
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What is the additive inverse to 3?
Model -4 two ways.
Day 6:
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Write an equivalent expression for 3(x + 5) – 2
Suzanne says the two expressions 2(3a – 2) + 4a
and 10a – 2 are equivalent? Is she correct? Explain
why or why not?
Day 5:
Instruction:
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The focus of today is to model adding integers. There are three methods that will be addressed- the
number line, integer chips, and heaps and holes.
Distribute the Modeling Integer Addition Handout to each student. Use the Modeling Integer
Addition Notes- Teacher Copy to walk the students through each problem. If you have integer chips,
allow students to use those as you work through the problems. If you do not have any, you may print
the Integer Chips and use these. Be sure to emphasize when there are additive inverses/zero pairs
formed.
For more explanation on Heaps and Holes, read page 9-12 Part E from DPI.
After going through the first four examples as a class, have students do the next one on their own. Go
over as a class and continue through the other examples.
March 2013
Common Core Math 7
Unit 1, Days 5-6
Topic: Modeling Addition of Integers
Guided Practice:
 Make sure students understand how to add integers using a number line. You might need to give
them several example problems to ensure understanding.
 For example, use a number line to add -5 + 7.
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For example
3 + -3
1. Start on 3 on the number line.
2. Be positive! Face toward the positive numbers.
3. The addition sign says to stay facing the same direction, but the negative sign (-3) says to turn the
opposite direction.
4. Walk 3 steps in the direction you are facing, because the absolute value of -3 is 3.
5. You should land on 0; 3 + -3 = 0
 Give students four or five problems to model on the number line. Have groups put their answers on
chart paper and explain how they used the number line.
Independent Practice:
 Give students 10 problems where they add integers. You could use more than two numbers for more
of a challenge. Have students show the number line for at least five of them.
Day 6:
Instruction:
 Complete the Inner Circle-Outer Circle Activity. Use the Teacher Notes for directions.
 Students may have discovered a pattern/algorithm to get their answer. Talk to students about this
and see if they can come up with a rule for adding integers that will always work. \
 Complete the Integer Addition Algorithm Handout.
Independent Practice:
 Have students’ complete #1-10 on the KutaSoftware Integers – www.kutasoftware.com sheet.
Comments / Notes:
Additional Resources Integer Race - Materials Needed: Pawns for the players, 2 dice of different colors, playing mat (Integer
Race Game Board)
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How to play: Before starting the game, decide which color die will represent positives and which will
represent negatives. On a turn, each player rolls the two dice and determines the sum of the roll. The
player with the largest distance from 0 (i.e. larger absolute value) moves forward one. If a winning
player rolls a sum of 5 or -5, he/she will move ahead two instead of one. If the players tie, they each roll
again. The first player to reach the finish is the winner.
March 2013