teaching subtracting with negative numbers

[barbseeds]

I have been working with a student who is struggling with subtracting when there are negative numbers involved, either as something like( -3-5) or (-3- -5).  I generally go to the number line but that's only working occasionally.    Does anyone have methods that work for them?
Thanks!

[ChrisR]

barbseeds wrote

I have been working with a student who is struggling with subtracting when there are negative numbers involved, either as something like( -3-5) or (-3- -5).  I generally go to the number line but that's only working occasionally.    Does anyone have methods that work for them?
Thanks!

I generally encourage student to follow the 3-rule method.  These three rules define addition and subtraction, and if you follow them correctly, will yield the right answer every time!  Here, a number's "sign" is whether it is positive or negative.

Addition
1)  If the two numbers have the same sign, combine them and keep the sign the same.
2) If the two numbers have different signs, subtract them and keep the sign of the larger number.
Subtraction
3) Change the sign of the number being subtracted (the right-hand number) to the opposite sign, then change the problem into an addition problem.  From here, follow the two addition rules.

(image below for a clearer walkthrough)
With your examples, -3-5 would be written as (-3) - (+5).  We change the sign of the right-hand number, which becomes (-3) - (-5).  Then, we change the problem into an addition problem: (-3) + (-5).  Here, the two numbers have the same sign, so we add them and keep the sign --> (3+5=8) and since the sign is negative, the answer is (-8).
Likewise, with (-3) - (-5), we change the sign of the right-hand number, to it becomes (+5).  Then, we change the problem to be an addition problem.  Now we have (-3) + (+5).  Since we have different signs, we follow addition rule #2, subtracting the numbers and keeping the sign of the larger number: 5-3=2 and 5 is more than 3, so we keep 5's sign.  The answer is +2.

This process will work every time, but some people find numberlines more intuitive.  However, following these steps correctly will always get you to the right answer.

Does anyone else have another way?

[Michael Ference]

I simply stress that for addition or multiplication that a double negative is a positive.  Same for division with the division written as a fraction where two negatives are a positive.

[Rob.Pyle]

ChrisR wrote

barbseeds wrote

I have been working with a student who is struggling with subtracting when there are negative numbers involved, either as something like( -3-5) or (-3- -5).  I generally go to the number line but that's only working occasionally.    Does anyone have methods that work for them?
Thanks!

I generally encourage student to follow the 3-rule method.  These three rules define addition and subtraction, and if you follow them correctly, will yield the right answer every time!  Here, a number's "sign" is whether it is positive or negative.

Addition
1)  If the two numbers have the same sign, combine them and keep the sign the same.
2) If the two numbers have different signs, subtract them and keep the sign of the larger number.
Subtraction
3) Change the sign of the number being subtracted (the right-hand number) to the opposite sign, then change the problem into an addition problem.  From here, follow the two addition rules.

...

Does anyone else have another way?

I was always a number line guy until I saw this method  While I still "think" in number lines, if I have the problem written in front of me, I use this method.   I learned it from another tutor, and he explains it using terms that I have shamelessly stolen:

1) When you have a subtraction problem, "Add the opposite"
This is a tactile thng that I find gets the students to make two moves with their pencil:  first, you turn the subtraction sign into an addition sign (with a vertical stroke), and then you change the sign of the second number, either by a vertical stroke to change the negative into a positive, or a horizontal stroke to add the negative sign to a positive number.

2)  When adding two numbers of different signs:  "Who is winning, and by how much?"
Using a sports analogy, there are two teams (Positive and Negative).  The winner gets the sign of the answer, and the answer is the difference in the scores (by how much did they win?).  I have found this works very well with kids who play sports, and adults who follow sports (even if their playing days are past!).

Rob

[ChrisR]

Rob.Pyle wrote

ChrisR wrote

barbseeds wrote

I have been working with a student who is struggling with subtracting when there are negative numbers involved, either as something like( -3-5) or (-3- -5).  I generally go to the number line but that's only working occasionally.    Does anyone have methods that work for them?
Thanks!

I generally encourage student to follow the 3-rule method.  These three rules define addition and subtraction, and if you follow them correctly, will yield the right answer every time!  Here, a number's "sign" is whether it is positive or negative.

Addition
1)  If the two numbers have the same sign, combine them and keep the sign the same.
2) If the two numbers have different signs, subtract them and keep the sign of the larger number.
Subtraction
3) Change the sign of the number being subtracted (the right-hand number) to the opposite sign, then change the problem into an addition problem.  From here, follow the two addition rules.

...

Does anyone else have another way?

I was always a number line guy until I saw this method  While I still "think" in number lines, if I have the problem written in front of me, I use this method.   I learned it from another tutor, and he explains it using terms that I have shamelessly stolen:

1) When you have a subtraction problem, "Add the opposite"
This is a tactile thng that I find gets the students to make two moves with their pencil:  first, you turn the subtraction sign into an addition sign (with a vertical stroke), and then you change the sign of the second number, either by a vertical stroke to change the negative into a positive, or a horizontal stroke to add the negative sign to a positive number.

2)  When adding two numbers of different signs:  "Who is winning, and by how much?"
Using a sports analogy, there are two teams (Positive and Negative).  The winner gets the sign of the answer, and the answer is the difference in the scores (by how much did they win?).  I have found this works very well with kids who play sports, and adults who follow sports (even if their playing days are past!).

Rob

Rob, I really like these ways to frame it!