How To Teach Adding Signed Numbers

Key concepts On Adding Signed Numbers

Students learn about signed numbers, opposites, and absolute value in 6th grade. We can build on that knowledge to teach students how to add signed numbers. Once they are sure about adding integers, we can move them on to adding rational numbers. 

Different forms of Adding Signed Numbers:

There are a couple of different types of adding signed number problems. One form has the student adding two numbers with the same sign, and another form has the student adding two numbers with different signs. Here are some examples:

• Same sign
  • -15 + -20 = ?
  • 23 + 14 = ?
• Different signs
  • -82 + 45 = ?
  • 6 + (-4) = ?

How do you teach students to add signed numbers?

First talk about what opposite numbers are and how they cancel each other. You can use red and black counters to introduce adding of signed numbers. This model will help students understand why the rules for adding integers make sense.   

Using counters, number lines, and absolute value are all great ways to teach students how to add signed numbers. Here, we will focus on finding the absolute value of both numbers and then determining whether to add or subtract them based on having the same or different signs.

Also read: How To Teach Subtracting Signed Numbers

Step 1: Determine if the signs are the same or different. 

Have students look at the signs of the two numbers and determine if they have the same sign or different signs. 

-18 + 45

Different signs (-18 is negative and 45 is positive)

Step 2: Determine whether to add or subtract.

Refer back to the red and black counters. Will they cancel each other or will you have more of them? If both are the same color counters (same sign), we will just have more of the same counters. If they are different color counters (different sign), they will cancel each other and the more powerful number will be left over.

Same sign: Add the absolute value.  Example: -20 + (-25)

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Different sign: Subtract the absolute value. Example: -18 + 45

Step 3: Add or subtract the absolute values.

Once students have decided whether they are adding or subtracting the absolute values, have them solve the problem. You can call them absolute values – students will most likely call them the “regular” number. 

Same sign: -20 + (-25)

|-20| = 20 and |-25| = 25

20 + 25 = 45

Different sign: -18 + 45

|-18| = 18 and |45| = 45

45 – 18 = 27

Step 4: Determine the sign of the answer.

Now that students have solved the problem, they must decide what the sign will be. 

• If signs are same: Sign stays the same
• If signs are different: The number that is more powerful wins!! Mathematical translation → use the sign of the number with the larger absolute value. 

You can ask questions like “Is there more negative or positive?”.

Examples

Example 1: Adding two negative numbers

Example 2: Adding numbers with different signs 

Example 3: Adding different signed fractions

Why teach adding signed numbers this way?

Introducing adding signed numbers with counters helps to build an intuitive understanding of the operation. It also builds on their understanding of opposites and what opposite numbers do to each other. This visual mode helps them remember the rules.

Using playful language with visual imagery also helps them remember the rules. A question like “Will join forces or cancel each other?” helps students think about whether to add or subtract the absolute values. 

“Is there more negative or positive?” helps them think about what kind of numbers are left after the adding. 

Vocabulary for teaching adding signed numbers

Absolute Value: The distance a number is away from zero on a number line. Absolute value is always positive.

Negative: Any number to the left of zero (0) on the number line. 

Positive: Any number to the right of zero (0) on the number line. 

Misconceptions and Errors

• Students may choose the wrong operation once they find the absolute values of both numbers.
  • You can remind students that if the original problem has different signs, then you subtract the absolute values. If the original problem has the same signs, then you add the absolute values. You could ask “Do they belong to the same team or are they from different teams?”
• Students may choose the wrong sign for the final answer.
  • You can remind students that numbers have the same sign, they belong to the same team, and will carry the same sign. When they belong to different teams, the more powerful team wins – you keep the sign of the number with the higher absolute value. 

Resources

• Downloadable worksheet for practicing adding signed numbers
• Quiz for assessing adding signed numbers

Frequently asked questions on how to teach  adding signed numbers