Subtracting integers

1.

Remind students about what occurs when integers are added. You might use a number line and/or integer cards as a prompt. 

2.

Have students act out additions with a sequence, such as:

• Start on zero and add positive four. Where are you?
• Now add negative five. Where are you?
• Now add negative six. Where are you?
• Now add positive eight. Where are you? (Students should finish on positive one).

3.

Discuss:

• What happens when we add zero?
• If this is what happens when positive and negative numbers are added, what do you think happens when positive and negative numbers are subtracted?

4.

Let students discuss their ideas. Look for a sense of anticipation.

Capture their ideas as a diagram. Many students are likely to be correct in anticipating that negative integers behave in an opposite way to positive integers.

5.

• When you subtract a positive number, which way do you face? (to the left)
• To the left is the subtraction direction with positives. Then you walk forward.

Act that out with 2 – 5 = -3 on a number line.

6.

• When you subtract a negative number, you still face the left. Do you walk forward or backward? (backward)

Act that out with -6 – -4 = -2 on a number line.

7.

Let’s start with a balance. What amount is shown here?

Students should recognise that this is one way to make zero since there are the same numbers of positives and negatives.

8.

• Now I am going to subtract +3. What will the result be? (A balance of -3)

Record the operation as 0 – +3 = -3.

9.

Return to the previous zero balance (positive 5 and negative 5). Act out other subtractions as "takeaways". Good examples might be:

• 0 – -5 = +5
• 0 – +1 = -1
• 0 – -2 = +2.

10. 

Make a model with a balance of negative three, such as:

• Make up different subtraction equations, beginning with the number -3 (negative three).
• Record your equations and check the answers you get on the calculator.

11.

Roam as the students work. Look for:

• Do they connect the subtraction with the correct physical action? For example, is -3 shown as removing three negatives?
• Do they correctly write the equation?
• Do they get the correct answer and confirm the result on their calculator?
• Do they anticipate the direction of the change as more or less than the starting number?

12.

Conclude by combining equations and number lines to represent subtractions. For example:

• 3 - -4 = 7 might be shown as:

• -4 - -7 = 3 might be shown as:

1.

Provide subtraction problems where the starting number (minuend) and the answer are known but the number subtracted is not. For example:

• -5 - □ = -3  What number is □? (□ = -2)
• 4 - □ = -1  What number is □? (□ = 5)

2.

Extend the interpretation of subtraction to the difference. Begin with positive numbers using a number line. 

• What is the difference between 2 and 9? The problem can be written as 2 + □ = 9 or 9 – 2 = □. In both cases, the box number is 7.

• What is the difference between 8 and -3? The problem can be written as -3 + □ = 8 or 8 – -3 = □. In both cases, the box number is 11.