As a parent or teacher, have you ever had to explain and re-explain Adding and Subtracting Integers?
Why do two negatives make a positive…..here are two methods that are clear for the students to understand. Let’s consider the following two examples.
Example 1: 5 – 4
Example 2: 5 – (-4)
Conceptualizing Example 1 is fairly straight forward… we can think of 5 as let’s say, we have 5 dollars, and then -4 represents losing 4 dollars, so all in all we have 1 dollar left, hence the answer of 1. Many students find it useful to use a number line to visualize this as well. When negative we go left on the number line. So staring at 5 on the number line, we then go LEFT another 4 units and end up at 1.
However, Example 2 looks similar BUT is totally different!
There are two methods that I have found to be useful to explain the meaning behind the deep understanding of 5-(-4). The first method is to create a logical chain of mathematical processes.
If we start with 5 and subtract 3, this is represented as 5-3, on the number line we can see the answer is 2
Then we subtract 2, so 5-2 = 3
Next we subtract 1, so 5-1 = 4
Next we subtract 0, so 5-0 = 5
When we look at the PATTERN, we can see that for the final answer we are increasing by ONE unit... so following the pattern
5-(-1) the result would be one more than 5,
so the solution would be 5-(-1)=6
Then we ask, what prcess is happening to arrive at 5-(-1) = 6? The simplified form would be 5+1=6
So it follows that:
5-(-2) = 7
5-(-3) = 8
5-(-4) = 9
The process of following the pattern leads us to conclude that:
a -(-b)= a+b.
This method was explained to me by Dr. Barrie Bennett, my M.Ed. professor at the University of Toronto, Canada. He explained it this way….
If a postitive represents you liking something and a negative represents you hating something….
+(+4) represents you like to like so like overall you LIKE so, +4
+(-4) represents you like to hate so you overall you hate so, -4
-(-4) represents you hate to hate so overall you LIKE so, +4
This was a great way to relate the integers to a personal method the students could use! Thank you Dr. Barrie Bennett!
After the child understands the concept, it’s time to practice. There are many practice sheets online, the fact is that students need to reinforce ideas once they are learned. If you are looking for a fun game that the whole family or class can play, here is a FREE game on Integers.
55,046 downloads … a VERY popular resource
HASSLE FREE MATH GAME – Classroom Ready – Differentiated – Teachers/Student Tested – Answers included
STUDENTS SELF CHECK THEIR WORK……….60 MINUTE ACTIVITY
JUST PRINT AND GO !
“My students really enjoyed this game! Who would have thought that using playing cards would be a great way to randomize problems that students would actually enjoy. Thank you!”
“Your resources are amazing! So clear, concise and hassle-free! ”
“Loved that the game was constantly changing and not just repetition.”
This activity covers:
* adding integers
* subtracting integers
* multiplying integers
* dividing integers
* combination questions with PEDMAS (BEDMAS for Canadians 🙂
* Rationale: how to use the product in the classroom
* Student Instruction handout
* Practical Tips for Teachers
* Game Booklet that includes:
♥ 12 questions: Adding Integers
♦ 12 questions: Subtracting Integers
♠ 12 questions: Multiplying Integers
♣ 12 combination more challenging questions
* Answer key for all 48 questions
* 2 blank student response sheets
A great game for learning integers. Can be used as:
* Game for 1, 2, 3 or 4 players
* Peer Tutoring Game
* Early Finishers
* Milestones Review
* Math Intervention
* Student Activity when you are away from the Classroom!
* SEE THUMBNAILS FOR SAMPLE QUESTIONS
This is a Teams-Games-Tournament in which one pair of students competes against another. The first team selects a card from a deck of cards and answers the matching question on the activity sheet(example 4 of hearts). The 2 students work cooperatively to obtain an answer. If correct they get a point, if not the other team can get the rebound point. Then team 2 selects a card, discusses the answer and so on. It is cooperative because the 2 students work together, yet competitive because it pits one team against another. The students have fun and get the math work done.
Do you have other ways to teach why a subtracting a negative is a positive? We’d love for you to share!
Thanks for visiting our Math blog!
<a href=”https://www.teacherspayteachers.com/Store/Mathematters-By-Jacquie”><img src=”https://www.teacherspayteachers.com/img/settings/silver.large.badge.png”alt=”Fourth, Fifth, Sixth, Seventh, Eighth, Ninth, Tenth, Eleventh, Homeschooler, Staff, Not Grade Specific – TeachersPayTeachers.com” align=”absmiddle” height=”44px” width=”172px” /></a>