Need a good trick to teach kids about adding negatives and positives.

[Toddy]

Tutoring kids in Math is so much fun. I really enjoy doing it. Its interesting noticing almost every one of my students has the same problem. They can do all the work, but when it comes to adding/multiplying/dividing negatives and positives they ALMOST all have a problem with it. Each session the kids learn alot the way I teach it but I find the next time I go back they are making the same mistakes and it is with adding these. I'll make up problems and one of example would be -19 + 7 and sometimes the kids will say +12 or -26 etc.

What I've been teaching is "If you have the same sign, add them and keep the sign" and "If you have different signs subtract them and keep the higher sign". When that doesn't work I draw the absolute value line graph and try to show them.

I wondering if anyone has any good little tricks so I can make this clearer to the kids. Thanks.

[FortunaMaximus]

Integer line, boardgame approach, in the case of -19 + 7, try to make clear they start at -19 and have to move 7 spots to the right, in this instance -12. With enough time and patience, the approach will become faster and initutive for those students. if the + value is bigger, say -21 + 32, they'll learn to take away 21 spots and add 11 in the positive end.

[Toddy]

[ QUOTE ]
Integer line, boardgame approach, in the case of -19 + 7, try to make clear they start at -19 and have to move 7 spots to the right, in this instance -12. With enough time and patience, the approach will become faster and initutive for those students. if the + value is bigger, say -21 + 32, they'll learn to take away 21 spots and add 11 in the positive end.

[/ QUOTE ]

Ya I've been doing the integer line (i called a line graph for some reason).. I feel like when I do that its making it so much more confusing for the kids. I was naive going into this. When I left the first student I figured it was just him. Now as I go house to house each kid has the exact same problem. Kinda weird.

[FortunaMaximus]

It isn't natural to think of numbers as having negatives and positives. When you find yourself counting things and have to correct a count because one item's missing, if you sense a slowdown and a gap in logic when you adjust, that's a natural effect. Man isn't supposed to be able to think in these terms, and that has to be learned. Yeah, it's weird. Don't worry, someone'll come along and discredit negative numbers. That's SMP for ya. /images/graemlins/tongue.gif

[BruceZ]

If they can do 19 + 7, and they can do 19 - 7, then when they see 7 - 19, and the second number is bigger, tell them to flip it around to 19 - 7 which they know how to do, and then make it negative at the end. There's no need to tell them to "keep the higher sign", because they aren't having trouble with 19 - 7, and you don't want to confuse them about something they already know how to do.

Then when they see -19 - 7, they can also flip that around and do 7 - -19, and if they know that the 2 minus signs makes a plus sign, this is 7 + 19, and make it negative at the end.

So in both cases, when they see a subtraction problem they don't know, they can flip it around, and make it negative at the end.

This is for subtraction. For addition, when we flip it around we don't make it negative at the end. So -19 + 7 is the same as 7 + -19. Then if you tell them that adding a negative (+ -) is the same as subtract (-), they should be able to do any addition or subtraction with positive or negative numbers. So 7 + -19 becomes 7 - 19, which they handle as above.

[Al6Jets18]

MONEY MONEY MONEY!!!

Kids understand real-life situations much easier. Negatives and positives seem foreign, but the idea of owing money or receiving money is relatable.

Simple pos-pos and neg-neg should be easy with this method, and pos-neg is much easier.

Say, "You owe $10 to Jim, but Bob decides to give you $4. How much do you owe or have?" This will usually work.

[Toddy]

Ok. I have 2 sessions tomorrow. These tips should work. Bruce I did try what you said about flipping it around. I thought that would be the easiest way. What I have to do is find 1 way that works for everyone and stick to it.

[prosellis]

I'm with Fortuna. I've been teaching a basic math course for the past few years and have the same problem that you are. The integer line ("number line" for younger students) has been the most successful tool. I don't even use the board game setting, though that seems perfectly valid. I give each student a small dry erase board (finally graduated from pencil and paper), we draw the line and numbers as a group, and then practice problems by erasing or adding to the line as needed. Hope this helps.

[FortunaMaximus]

The boardgame principle seems to add entertainment value, and makes it fun.

And you should never underestimate that factor, although there is diminishing returns from that approach the older a kid gets.

Bruce, your post confused me initially, how would you simplify it for a primary school student's capability to understand these concepts?

[AWoodside]

God I hate kids.

[DougShrapnel]

The integer line is good for visual learners. I believe that changing the probelm can also give insight. For instant -19 + 7 is really 7 - 19 or 0 - 19 + 7. Rules such as "If you have differnt sight subtract and keep the higher sign" seems rather arbitrary when you can explain why it works that way by having them reformulate the question in a more palpitable form. -26 + -13 = 0 - 26 - 13 or -1(26 + 13).

[Jasper109]

[ QUOTE ]
by having them refomrulate the question in a more palpitable form. -26 + -13 = 0 - 26 - 13 or -1(26 + 13).

[/ QUOTE ]

Trust me, factoring -1 out is not going to be very palatable for a 12 or 13 year old kid.

I haven't taught kids that young for a number of years, but using a number line and/or money always works well.

For places that actually experience winter you can also use temperatures.

[BiPolar_Nut]

not sure if this has been mentioned, but I'd just simply teach them there is no such thing as subtraction. Only addition of negative numbers....and since addition is commutative, it doesn't matter if the negative number comes first or second.

Ignore subtraction all together...just teach to add negative numbers and problem solved.

[Jasper109]

[ QUOTE ]
not sure if this has been mentioned, but I'd just simply teach them there is no such thing as subtraction. Only addition of negative numbers....and since addition is commutative, it doesn't matter if the negative number comes first or second.

Ignore subtraction all together...just teach to add negative numbers and problem solved.

[/ QUOTE ]

Until they get to high school where you don't add negatives any more when you start doing algebra.

[Mickey Brausch]

In various table games, eg Monopoly, you get dealt cards at certain moments of play. These cards are like the numbers in your example.

Some of those cards give you money from the bank; other cards demand that you give away money (to pay fines, etc).

You could draw up a bunch of positive and negative numbers in separate pieces of paper - and then have the kids choose cards randomly and add them.

Mickey Brausch

[garion888]

The way I learned this was with the number line, but We used a car. Example: 9-17.

Always place the car at the first number facing the + direction...After that any time you see a minus sign, turn the car around. After you've finished with any minus signs, go in the direction the car is facing for the second number spaces on the number line...

[BiPolar_Nut]

[ QUOTE ]
[ QUOTE ]
not sure if this has been mentioned, but I'd just simply teach them there is no such thing as subtraction. Only addition of negative numbers....and since addition is commutative, it doesn't matter if the negative number comes first or second.

Ignore subtraction all together...just teach to add negative numbers and problem solved.

[/ QUOTE ]

Until they get to high school where you don't add negatives any more when you start doing algebra.

[/ QUOTE ]

Hrmmmm...school must be different now then. When I learned algebra, that was the first place I learned there was no such thing as subtraction nor division....just adding negatives and multiplying reciprocals.

I guess my nothing town of 3,000 peeps and class of 238 students in 1985 had amazing teachers. *shrug*

[wmspringer]

I agree with you; the only reason I stopped being a math tutor was I couldn't live on what I made :-). Anyway, as to your question, I had the most luck with number lines and money. So 14 + -7 would be, if you have $14 and spend $7, how much do you have?

[Toddy]

These are all very good tools i am looking forward to my lessons tonight thanks

[CityFan]

[ QUOTE ]
[ QUOTE ]
Integer line, boardgame approach, in the case of -19 + 7, try to make clear they start at -19 and have to move 7 spots to the right, in this instance -12. With enough time and patience, the approach will become faster and initutive for those students. if the + value is bigger,
say -21 + 32, they'll learn to take away 21 spots and add 11 in the positive end.

[/ QUOTE ]

Ya I've been doing the integer line (i called a line graph for some reason).. I feel like when I do that its making it so much more confusing for the kids. I was naive going into this. When I left the first student I figured it was just him. Now as I go house to house each kid has the exact same problem. Kinda weird.

[/ QUOTE ]

Do you feel like the line makes things more confusing because you see the kids get confused? Or just because you're worried about making things complicated?

It SHOULDN'T be confusing for the kids, because the line actually captures the structure that is there in the numbers.

Working with minus numbers without the mental image of the line is always going to be hard work: the kids need to have an understanding of what these things represent, and the line should give them that.

[Girchuck]

Dominoes, or any card game with penalties to losers.
Say, jin rummy, where the losers have penalties for each card left in their hand, and a bonus for jin rummy.
Get the kids to keep score. Penalties are negative numbers.
Once they learn to add penalties with positive scores, explaining negative numbers is much easier.

[metsandfinsfan]

Ok....Heres a math teachers tips

Multiplying and Dividing integers can be done with three faces

+ + - - + -
_
\_/ \_/ / \

Face#1 when your awake your happy
Face#2 when your asleep your happy
Face#3 when you get punched in the eye, your not happy

Adding RUles

Draw a scale like so

__________
- /_\ +

Have student place the numbers on the correct side, and ask them which side is heavier, and always to subtract the two sides

[metsandfinsfan]

The faces didnt come out right
/images/graemlins/smirk.gif /images/graemlins/smirk.gif /images/graemlins/confused.gif

1st one has 2 plusses for eyes and a smiley face
2nd one has two minuses for eyes and a smile
3rd one has 1 pos, and 1 neg and a frown