Teaching Addition and Subtraction, Part One

Teaching Addition and Subtraction, Part One

After writing my last blog post, What’s the Difference?, I thought it would be helpful if I blogged about all the different addition and subtraction situations.

This post will talk about one of three addition and subtraction situations: the Change Plus/Change Minus situation. What I find fascinating is how researchers have found that Pre-K children can understand the concept of adding to and taking away from at the age of 3 or 4 (Clements and Sarama, 2004). But, when I think about it, my kids learned the sign language for and concept of “more” at 18 months when they were eating. And when I “took something away,” they knew that item wasn’t there any more.

What are the concepts kids need to understand? Kids need to understand three things: that a quantity can be represented by a number, the action of addition or subtraction, and the symbols “+” and “-.” Notice: I am not using the equal sign. THERE IS A REASON!! Too many students have the misconception that the equal sign means “the answer.” I would not show students an equal sign until they can understand quantitative sameness.

Let’s talk about a Change Plus/Change Minus situation. Here is a video explaining how to explore it using a number machine.

Seeing the pattern of Start, Change, and Result would represent the Mathematical Practice Standard 7 which is look for and make use of structure. When kids create fact families, they think it is magic that all the numbers can build different equations. BUT, it is the relationship of addition and subtraction that allows fact families to work. Understanding these situations will allow students to understand fact families and not just memorize them.

So as you explain it to your students, emphasize that whether we add or subtract, we always have a start, a change and a result. As your students see this, they will build a folder in their brain called addition and subtraction. Intuitively they will know there is a relationship. You can download the PDF worksheet below to help show your students what happens in the number machine.

Change Plus- Change Minus

Please leave a comment below letting me know how this worked in your classroom.

Click here to read about part two.


Click here to ready about part three.

15 Responses to Teaching Addition and Subtraction, Part One

  1. […] I’m going to use the concept of decomposing and composing as we journey from the concrete to the abstract. Decomposing and composing is new language in the common core, but the idea has been around in mathematics for a long time. In fact in Table 1 of the Common Core Standards they use the language of put together and take apart as one of three addition and subtraction situations. (If you want more info on those situations, check out my blog series on Teaching Addition and Subtraction.) […]

  2. With Common Core, I feel it is important that we understand what the standards truly mean and this blog as helped me see the importance!

  3. I agree… It amazes me to observe students as young as K look for ” the right answer” without trying to grasp the true manipulation of numbers. I have never thought of or heard of leaving out the equal sign…. Cannot wait to use this strategy! Thank you for this thoughtful, researched based idea. AIMS participants will benefit from this discussion and activity as well.

  4. Love this model that ignores the equal sign! Places student focus on what is happening with the numbers and away from the “correct answer” to the problem.

  5. I think the idea of not including the equal sign is powerful. As soon as the equal sign is included, teachers are quickly moving to algorithims for addition and subtraction, taking away to opportunity for young students to really conceptually understand what adding and subtracting is.

  6. What a wonderful concrete model for fact families. When my kids were younger, I watched them mindlessly fill in the blanks on fact family worksheets (they’d fill in all the 3’s, then the 4’s, etc.). The number machine makes this concept both tangible and fun; it also promotes algebraic thinking at an early age. Thanks for the idea!