Teaching Addition and Subtraction, Part Three

This blog post will be the final in a three-part series on teaching addition and subtraction. Part One talks about the Change Plus/Change Minus, and Part Two talks about Composing/Decomposing. Our last situation is Comparison.

After reading Mathematics Learning in Early Childhood, I realized how foundational comparing relations (talking about two sets being more than, less than, or equal to) is to this addition and subtraction situation. Now don’t let the kids fool you, they are perfectly good at comparing. My youngest, Lilly, (2 years old) made it clear that her sister, Bethany (5 years old) had more gummies than she did, and Bethany and Josiah (7 years old) can easily figure out how many more toys they needed to have the same amount. Kids like things fair.

If you have a set of numbers, 5 and 2, you can say a couple of things about the numbers. They are: 5 is more than 2, and 2 is less than 5. Students will slowly see the number 3, which is how many more 5 is than 2. This number is the difference. In my previous blog post, The Difference, I talk about a simple way for students to solve difference problems. Today I am going to give you three ideas that will help students make a connection between comparing numbers and this situation that requires them to see a third quantity: the difference. Seeing the third quantity won’t happen right away, but with thoughtful practice the students will see it.

Comparing Numbers Phase 1

1. Students build two sets and place them in the ten frame.

2. Student use a dry erase marker to fill in the sentence frames.

Comparing Numbers Phase 2

1. Students build two sets and place them in the ten frame.

2. Students fill in how the two sets are the same and how they are different.

Students could count on (addition) to find how many more spaces(?) they would need to have the largest set or take away cubes from the largest set (subtraction) until they had the same amount. I bet most kids will count on. Addition and multiplication seem to be much easier to learn than subtraction and division. (I wonder why?)

Comparing Numbers Phase 3

1. Students build two sets and place them in the ten frame.

2. Students fill in how the two sets are the same and how they are different.

Students will fill in an equation. In subtraction we wonder “How many more is 7 than 5? What makes those two numbers different?” Start with the largest number and take away what is the same. You are left with the difference!

In addition we wonder, “How many more do I need to add to 5 to make 7? How are those two numbers different?” Start with the smallest number, leave the second addend blank and write the largest number on the other side of the equal sign.

I hope this series has been helpful. Facilitating a complete understanding of addition and subtraction is not a small task, but it can be done in engaging and thoughtful ways that will allow the connections to be apparent and the math to make sense!

What do you do to give kids a complete understanding of addition and subtraction? Where do your kids struggle with these concepts? What do you wish you had time to research?