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. / Instructional Resources:
  • Modeling Integer Addition Handout
  • Modeling Integer Addition Notes- TeacherCopy
  • 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

Mathematical Practice Standard(s):
MP.4 Model with mathematics and Alice software. / Warm-up:
Day 5:
  • Find the value of each situation:
a)
b)
  • What is the additive inverse to 3?
  • Model -4 two ways.
Day 6:
  • 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?

Learner Objective:
As a result in learning, students will be able to… model addition of integers.
Day 5:
Instruction:
  • 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- TeacherCopy 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.
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.
  • 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 – sheet.

Comments / Notes:
Additional Resources-
  • Integer Race - Materials Needed: Pawns for the players, 2 dice of different colors, playing mat (Integer Race Game Board)
  • 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