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Rules for Adding and Subtracting Positive and Negative Numbers
Students come into sixth grade knowing what numbers are and many way to work with them. Now they are asked to recognize a letter as a number and a number with a negative sign in front of it. They will work extensively with positive and negative numbers during their sixth grade year and the better they feel about them going into 7th grade they better they will do. There are specific rules for each operation with these numbers. How can math teachers help students conceptualize the rules of positive and negative numbers so that they can be successful as they move on in math?
Word Wall
Integers: The set of whole numbers. They can be positive, negative and zero. No fractions.
Rational Numbers: A set of numbers that can be written as a fraction or a whole number. The quotient of the fraction either ends or repeats in a pattern.
Negative Number: A number less than zero
Positive Number: A number greater then zero
Zero: The number between the set of negative numbers and the set of positive numbers. Zero is neither positive or negative.
Absolute Value: The distance from zero on the number line. The absolute value is always positive.
Absolute Value: The distance from zero on the number line. The absolute value is always positive.
Positive and Negative Number Rules
There are 3 rules for addition:
1) Adding two positive numbers, add and keep the sign.
6 + 3 = 9
2) Adding two negative numbers, add and keep the sign.
6 + 3 = 9
2) Adding two negative numbers, add and keep the sign.
-6 + -3 = -9
3) When adding a positive number and a negative number, subtract the numbers and keep the sign of number with the largest absolute value. -6 + 3 = -3
3) When adding a positive number and a negative number, subtract the numbers and keep the sign of number with the largest absolute value. -6 + 3 = -3
Subtraction:
1) Subtracting two positive numbers is simple subtraction.
7 - 4 = 3
2) Subtracting a positive number from a negative number, change the subtraction to addition and change the number from positive to negative and add. -7 - 4
-7 + (-4) = -11
3) Subtracting a negative number: 7 - (-4)
Two negatives make a positive: 7 + 4 = 11
The following video explains how to subtract integers using positive and negative chips. I love this idea and would use it in the classroom. It really helps to see the idea of zeroing out
Subtracting Integers Using a Chip Model (5:55)
1) Subtracting two positive numbers is simple subtraction.
7 - 4 = 3
2) Subtracting a positive number from a negative number, change the subtraction to addition and change the number from positive to negative and add. -7 - 4
-7 + (-4) = -11
3) Subtracting a negative number: 7 - (-4)
Two negatives make a positive: 7 + 4 = 11
Poster and Chip Models
²
The following video explains how to subtract integers using positive and negative chips. I love this idea and would use it in the classroom. It really helps to see the idea of zeroing out Subtracting Integers Using a Chip Model (5:55)
Chip Models are great manipulatives to use in a classroom to help solidify this idea. They provide a practical way to see what is happening with the positive and negative numbers.
³Common Core Standards⁴
CCSS.MATH.CONTENT.6.NS.C.6
Understand a rational number as a point on the number line. Extend number line diagrams and coordinate axes familiar from previous grades to represent points on the line and in the plane with negative number coordinates.
Understand a rational number as a point on the number line. Extend number line diagrams and coordinate axes familiar from previous grades to represent points on the line and in the plane with negative number coordinates.
CCSS.MATH.CONTENT.6.NS.C.6.A
Recognize opposite signs of numbers as indicating locations on opposite sides of 0 on the number line; recognize that the opposite of the opposite of a number is the number itself, e.g., -(-3) = 3, and that 0 is its own opposite.
Recognize opposite signs of numbers as indicating locations on opposite sides of 0 on the number line; recognize that the opposite of the opposite of a number is the number itself, e.g., -(-3) = 3, and that 0 is its own opposite.
Conclusion
These rules are so specific to mathematical operations, that students must know them if they are going to be successful in the classroom. I think it is important for teachers to slow down at this point in their curriculum and pull out all the manipulatives and support they can find to help students get these rules down. From what I've seen in middle school, 7th grade math teachers expect the students to already know the rules and spend very little time, if any, reviewing them. I'd recommend displaying posters, have students make note cards, watch different video's and use the chip model. Looking at the rules from different perspectives and practicing them will help students understand how they work.
Sources:
1 - https://i.pinimg.com/originals/1d/0e/95/1d0e953c1db6411ac3d1a18e1d82f789.jpg
2 - https://www.pinterest.com/pin/418201515371741167/?lp=true
3 - https://www.slideshare.net/aeherzog/adding-integers-ppt-3331211
4 - http://www.corestandards.org/Math/Content/6/NS/
Jill,
ReplyDeleteThank you for posting the chip model video! I was still struggling a bit to conceptualize adding and subtracting with negative numbers using that model, but your explanation and video made it quite clear.
It's so interesting to me that the way I learned how to do these problems was actually never explained thoroughly to me. The rules were explained and that was it. So when the chip model was introduced in class, it seemed very confusing and it was easy to just rely on what I knew to be true about these problems. But, you're totally right when you say that kids need to know the ins and outs of this concept before they get into algebra and higher level thinking math.
Thanks for your post!
Lauren