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