Integers

I teach my 6th graders this way:

First you have to make the problem an addition problem by changing the minus to a plus and changing the sign of the last number. For example, 5-6 now becomes 5+ -6. THEN,

If the signs are Different, find the DIFFERENCE between the two numbers.
If the signs are the Same, find the SUM of the two numbers.
Pick the sign of the larger number for your answer.

Hope that helps!

I recently talked to a math specialist and she explained it like this.

On the overhead draw a number line with positive and negative numbers. Then make a character (I liked to cut out a person I printed off the computer and put on an oiverhead so the students can see which way he is facing).

So, take the problem given 7 - (-10)

Have the character start at 7. Since, the next number is a negative number, have your character facing the negative side of the line (to the left)

Okay... so explain to the students that every time you add a number, your character takes a step forward and everytime you subtract, he steps backward. Therefore, since it is subtraction, the character then steps 10 steps backwards landing on #17.


Let me try another problem. -4 -(-6)

The character starts on -4; then, since the next number is a negative, the character faces to the left. Finally, since you are subtracting, the character takes 6 steps backwards landing on 2.

I did this with a fifth grade class and the students really understood. I also had the children act this procedure out and they really got it. I hope this helps and doesn;t confuse you. Let me know if you have any questions.

I am attaching a worksheet I use to help explain subtracting integers.

This is a booklet I give to my students about integers - if you have any questions feel free to contact me

I teach 8th grade and they still don't get integers. I found TeacherTube.com. Go to teachertube.com and search Integer Cheer...this teacher does this really annoying cheer...but it sticks. My kids griped about having to watch it. I would make them watch it over and over and over--but they left my room chanting the cheer. Now when someone makes a mistake with integers, someone always starts chanting the cheer. I use a ladder metaphor for adding and subtracting. I tried the number line but they would be confused about going left or right, they "get" going up(+) and down(-). I have previously told them that they are on a construction site and the foreman made them dig this really deep hole and then put this really tall ladder in this hole. I always make them start at zero (ground level). Positives they climb up and negatives they climb down.

Anyone have anything else? This makes sense to me, different than how I learned but I think the kids will understand this way better than the way the TE says to teach them.

ADDITION:

If the signs are the same then you add the two numbers and keep the
sign.

Ex. 6 + 2 = 8 or -6 + -2 = -8

If the signs are different, subtract the two numbers and take the sign
of the larger number.

Ex. -6 + 2 = -4 or 6 + -2 = 4

SUBTRACTION:

Change the sign of the second number, then add the two numbers using the
rules for addition, above.

Ex. 6 - 2 = 6 + (-2) = 4
Ex. -6 - -2 = -6 + (+2) = -4
Ex. -6 - 2 = -6 + (-2) = -8
Ex. 6 - -2 = 6 + (+2) = 8



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THey see who has the highest hand...or finish the deck to see who has the highest score...red can be negative numbers and black positive...deal out "X" amount of cards have them add them up..then partner or group checks each other

I had a session with him yesterday before getting these ideas, so I invented a game for us. We used 2 different colored dice and a number line. We put the dice in a cup and flipped it over, covering the dice. Without looking, he drew one and moved along the number line forward or backward according to the color. After a few rounds, I had him predict where he'd end up before counting it out. After a couple rounds of that, I changed it again. We rolled both dice and combined the roll. Without any instruction, he discovered the concept of zero pairs, and with further prompting began to understand how to use them to predict where he'd land next. It was fun to see that! Next week, I'll try out the card games you've suggested. Thanks!

We used this one in class this year. It is similar to war and can be done with a regular deck of cards (take out face cards), except the red cards are negative and the black cards are positive. You can do comparing integers by just flipping over one at a time, or you can add/subtract/multiply integers by having each person flip over two cards and find the sum/difference/product. I hope this makes sense. Also, if you do a web search for card games, you will find others. You could also do a variation with dice or dominoes if you feel like being creative.

Good luck!

I just finished using this graphic I created to help my fourth graders understand the concept of negative numbers. As compared to previous years, this visual seemed to help them get a better understanding of the concept.

Maybe someone else will find it helpful...(Hopefully it's not too late!)

I've taped two yardsticks on the board going vertically. The top one has numbers getting bigger in value going up. The bottom one has numbers getting bigger in value going down. I then use the analogy of going under water for the negative numbers.

When comparing negative numbers, I have them think "How far under sea level am I?" The number deeper is farther away from the surface- 0.

Use poker chips as counters, maybe the reds could be - and the blue or white +. Buy them from a dollar store and actually write the symbols on them. Start small with numbers less than 10. After they can master those, build up to numbers less than 20. Let them work in pairs so they can share chips. After students can do problems with numbers up to 20, ask them if they can discover patterns or rules. Also, you could have them draw the - and + "chips" and cross out.

Example: -5 + -3=?

Draw: - - - - - and - - -= -8

or -9 + 5=

Draw: - - - - - - - - - and + + + + +

teach them it's like a balance scale: cross out 5 - and 5 +...
Whatever is left is the "balance"


I also use word problems like "How owe me $6, you go shopping and borrow $6 more to spend, how much do you owe?" "If you owe is it positive or negative?"

Hope this helps!

I also use a number line--a large one either on the wall or projected on wall.

I call each student up and have them use a pointer. The child stands directly in front of and points to zero. If the operation sign is "+", the child does a 90 degree turn so he or she is facing RIGHT. If the second number is a positive number, he/she walks forward, counting and pointing to #'s on the line as he she counts. If the second # is a "-", the child walks backward. (For 2 + 3)--face zero, turn right, put pointer on 2, walk FORWARD-moving the pointer and counting, landing on 5. For 2 + (-3). Face zero, turn right, put pointer on 2, walk BACKWARDS-moving the pointer and counting, landing on (-1).

If the operation sign is (-), the child does a 90 degree turn so that he/she is facing LEFT. The other steps are the same. For 2-3, point to zero, turn left, put pointer on 2, walk forward, landing on -1. For
2-(-3), face zero, turn left, put pointer on 2, walk BACKWARD and count, landing on 5. After several students have walked the line, I give everyone a number line to have, and they walk at the same time another is at the board.

This is much easier to comprehend than "the rules". The steps are the same if the first number is a negative.