Tag Archives: Kindergarten
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.
I was helping my daughter, who is in kindergarten, with her homework. She claimed the homework was too hard. She was working on subtraction in her class and the instructions for her homework were: FIND THE DIFFERENCE. I thought to myself, does she even understand subtraction as a comparison situation? Was that the thinking her… Continue Reading
In my last post, I talked about the connection between decomposing numbers and place value. Understanding how numbers can be decomposed into parts lays the foundation for breaking apart numbers into specific groups. These specific groups could be anything, but for our numeration system they will be ten. You may want to check out the… Continue Reading
As I talked about in my earlier posts, I am really interested in learning about the Japanese methods of teaching math concepts. As I was exploring a 1st grade Japanese textbook that Phil Daro recommended, I noticed something I wanted to field test. The textbook had the students placing counters on top of the pictures… Continue Reading
This post is a continuation of the story of Froebel’s geometric gifts that was introduced in my previous post. I ended with a promise to tell a story about the famous architect, Frank Lloyd Wright. In 1876, when Wright was eight or nine years old, his mother attended the Philadelphia Centennial Exposition. Wright describes in… Continue Reading
I’ve spent forty years teaching mathematics to undergraduate and graduate students in mathematics education. Through all these years, it was geometry that I most enjoyed teaching. I still have a passion for geometry, and it is this passion and some of the things I’ve learned and continue to learn that I hope to share in… Continue Reading