Objective for Today
1. Review the process for adding integers and the various ways to do so.
2. Find your most effective method for addition of integers
Lesson 2 Addition of Integers
There are many schools of thought when it comes to adding and subtracting integers. Some strategies include...
1) Imagine the number line...adding moves to the right and subtracting moves to the left.
2) "zip zap" ...subtract means add the opposite.
e.g. 7 9 = 7 + (9)
3) Money...you have "x" dollars to start and spend "y" dollars, how much money do you have?
e.g. You have a $20 bill and buy a shirt for $12. How much change will you have
4) Temperature...The current temperature is "n" and the temperature increases "p" degrees, what is the new temperature?
e.g. It is 25oC and it warms up by 3oC. What is the temperature
5)Tokens...Positive and negative tokens are put in a bucket, then remove the "zero pairs".
6) Others?
10 2 3 4 5 6 7 8 9 1012345678910
+ _
We're going to start by looking at some general principles...
Guidelines for Addition of 2 Integers
In real life we deal with paychecks and bills regularly. paychecks positive/negative bills positive/negative
Using the idea of bills/paychecks:1. If I have two bills I owe/gain money which can be represented by ______ numbers. If I add the two bills together what kind of number will I get?
e.g. Ms. Brzak gets a Direct Energy bill for $80.43 and an Enmax bill for $65.32. Does she gain or lose money? How much does she gain or lose? How do you know?
General rule:If we add two negative numbers we get a bigger negative
Guidelines for Addition of 2 Integers
2. If I have two paychecks I owe/gain money which can be represented by ______ numbers. If I add the two paychecks together what kind of number will I get?
e.g. George started his new job at Famoso and gets paid every two weeks. In his first month he gets a paycheck on the 15th for $324.69 and the 30th for $357.28. Does he gain or lose money? How much does he gain or lose? How do you know?
General rule:If we add two positive numbers we end up with a bigger positive number
Guidelines for Addition of 2 IntegersNow it gets a bit trickier...
3. If I have one paycheck and one bill, the paycheck is an own/gain and the bill is an owe/gain.
e.g. #1 Patrick gets paid $1350 and his bills are:* Mortgage $724* Cell Phone $68.50* Electricity $71.32* Heat $80.91* Water $50.37* Garbage/Recycling $35
add all of his bills together = __________ Does he have enough to pay his bills? How do you know?
General rule:If our positive number is bigger we will end up with a positive answer
Guidelines for Addition of 2 IntegersWe will use a similar example to #3
4. If I have one paycheck and one bill, the paycheck is an own/gain and the bill is an owe/gain.
e.g. #1 Patrick gets paid $1350 and his bills are:* Mortgage $724* Cell Phone $68.50* Electricity $71.32* Heat $80.91* Water $50.37* Garbage/Recycling $35* Loans and Interest $600
add all of his bills together = __________ Does he have enough to pay his bills? How do you know?
General rule:If our negative number is bigger we will get a negative answer
Now that we know some general information lets look at strategies, keep in mind you are choosing the strategy that you like BEST
1. Number Lines this strategy will work best if you like to be able to see what's happening and are hands on
* Important info for number line: moving right is adding, moving left is subtracting, you are "jumping" from one number to the next
a) 3 + 5
b) 2 + (+7)
c) 10 + (4)
10 2 3 4 5 6 7 8 9 1012345678910
10 2 3 4 5 6 7 8 9 1012345678910
10 2 3 4 5 6 7 8 9 1012345678910
A.Your first number is where you place your first marker/dot B.The second number indicates which direction and how many stepsC. Where you end is the solution to your problem
2. "Zip Zap" or add the opposite we will do in subtraction
3. Money a very practical method since we use money in daily life, this method can help you keep track of your overall bank balance. use this method if you are strong with numbers and find application to a situation helpful
A. Your first number is how much money you currently have B. The second number tells you have much you are getting (+ like a paycheck) or
spending ( like a bill or a shopping trip)C. How much you have left is your answer
E.g. 75 + (20)Situation: You saved $75 from babysitting and go to a movie with friends and spend $20. How much will you have left?
4. Temperature Similar to a number line but with a practical application
A. The first number is your starting pointB. The second number tells you direction and "jumps" (+ is up, is down)C. Where you end is your solution
E.g. 5 + 13Situation: It is 5oC at night and climbs 13oC to reach the daytime high. What was the temperature
start
_+
5. Tokens/Zero Pairs This is the best hands on strategy
A. Collect the correct amount of + tokens and tokensB. Line all the positives in a row and all the negatives in a row directly under the positivesC. 1 positive and 1 negative make a "zero pair" which cancel each other outD. Whatever cannot be combined to make a zero pair is your solution
a) 5 + 6
b) 3 + (6)
c) 4 + (3)
d) 6 + (+4)
_ _ _ _ _
+ + + + + +
+ + +_ _ _ _ _ _
_ _ _ _ _ _ _
+ + ++ ++ + + + +
6. Other strategies?
Of course if you are proficient with numbers and can just do the addition that is okay as well
*The key is to find the method that works best for you it does not matter which strategy you use. Try them all and figure out which one you like best.
Lesson 2 Hand Out No calculators allowed!Fill out your "what I learned today" page
MiniQuiz Tomorrow!!
Attachments
M9 U1 L2 add intg KEY.pdf
SMART Notebook
Page 1Page 2Page 3Page 4Page 5Page 6Page 7Page 8Page 9Page 10Page 11Attachments Page 1
Top Related