I posted this on the Math board, also. I need help with a good activity to teach subtraction and addition of integers (positive and negative numbers). My students can not understand it, and I am getting them more confused.
You could also go about having them use a number line. But make it physical. Write numbers on index cards and have one card with zero on it. Call students up to hold the cards and stand on the correct side of the number line at the front of the classroom. Then, have another student come up and represent what you are adding or taking away. Something along those lines, so the students can see where the positive and negative integers lie on the numberline and what the number becomes when it is used in an algorithm.
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?"
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.
I just posted this to someone else so I cut and pasted it for you. It is really similar to the previous poster. I hope this 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.
Yes.. I do all those things too. I do teach the rules also. I stick to addition of pos and neg numbers until they have it mastered. (make sure to differentiate between the pos and neg signs and the plus and minus operation symbols.. I have them read the examples to me before even solving them.
When I get to subtraction .. I drill this .. KEEP CHANGE CHANGE
This means the first number you keep whatever it is.. Keep
Then Change the operation sign to a plus
Then change the integer sign to opposite of what it is
Then add the way they learned