Integer Addition and Subtraction

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In this lesson, counting pieces are used to model sums and differences by referring back to the meanings of the basic operations explored in previous lessons. For example, if we use the idea of addition to mean combining or joining, we can use collections of counting pieces and the concept of net value to model sums.

Here is an example:

Here are some more examples to think about. Can you imagine or sketch how the combining of collections would look? What is the sum (net value) in each example?

• ⁺7 + ^-7
• ^-6 + ^-3
• ⁺2 + ⁺8
• ^-5 + ^-1

We can imagine the collection-combining idea to think about larger numbers, like in the problem ^-47 + ⁺79...

Here are some more examples to think about. Imagine the net value of the combined collections to get the sum...

• ^-24 + ^-40
• ^-35 + ⁺50
• ^-60 + ⁺52
• ^-27 + ⁺100

What about a problem like ⁺4 - ^-3? What subtraction models can you use to determine the answer to this problem? See if this helps:

Here's another model we can use, also from the subtraction lesson:

When we changed the ⁺4, we changed it by adding 'zero' to it, so we could compare the two quantities.

These integer operation models are important because we will use them extensively in our study of algebra topics. Discuss them with your children, and encourage them to think about them and ask questions in class if they need to.