Add and subtract integers using counters

key notes:

Understanding Integers

  • Integers: Integers are whole numbers that can be positive, negative, or zero.
  • Positive Integers: Integers greater than zero, represented by numbers without a minus sign (e.g., 1, 2, 3).
  • Negative Integers: Integers less than zero, represented by numbers with a minus sign (e.g., -1, -2, -3).
  • Zero: The integer that is neither positive nor negative.

Using Counters

  • Red Counters: Represent negative integers.
  • Yellow Counters: Represent positive integers.

Addition

  • Combining Counters: To add integers, combine the red and yellow counters.
  • Same Signs: If the counters have the same sign, add their absolute values and keep the sign.
    • Example: 3 + 4 = 7 (3 yellow counters + 4 yellow counters = 7 yellow counters)
    • Example: -3 + (-4) = -7 (3 red counters + 4 red counters = 7 red counters)
  • Different Signs: If the counters have different signs, subtract the smaller absolute value from the larger absolute value and keep the sign of the larger absolute value.
    • Example: 5 + (-2) = 3 (5 yellow counters – 2 red counters = 3 yellow counters)  

Subtraction

  • Adding the Opposite: To subtract an integer, add its opposite.
    • Example: 5 – 3 = 5 + (-3) = 2 (5 yellow counters + 3 red counters = 2 yellow counters)
    • Example: -2 – 4 = -2 + (-4) = -6 (2 red counters + 4 red counters = 6 red counters)

Learn with an example

➡️ Use counters to subtract 3 -(- 1).

You start with:


You subtract:

Which picture shows the difference?

You are trying to calculate 3 − (-1).

Start out with 3 positive counters, which represent 3:

You would like to take away 1 negative counter. However, it’s not possible to take away 1 negative counter, because there aren’t any negative counters in the first group. You can fix this problem by adding 1 pair of positive and negative counters to the first group, so that you have the 1 negative counter that is needed:

Now take away 1 negative counters:

4 positive counters remain. So 3 − (–1) = 4.

➡️ Use counters to add -7 + 6.

You start with:


Which picture shows the sum?

You are trying to calculate -7 + 6.

Start out with 7 negative counters, which represent -7:

Since pairs made up of a positive counter and a negative counter have a value of zero, cross them out.

So –7 + 6 = –1.

Use counters to add 7 + -5.

You start with:

You add:

Which picture shows the sum?

You are trying to calculate 7 + -5.

Start out with 7 positive counters, which represent 7:

Now add 5 negative counters:

Since pairs made up of a positive counter and a negative counter have a value of zero, cross them out.

2 positive counters remain:

So 7 + –5 = 2.

Let’s practice!🖊️