Addition and Subtraction

As we teach addition and subtraction, we need to continue to develop students' understanding of place value. We can do this by using concrete models or place value drawings, making sure we model the relationship between addition and subtraction. We must also relate the visual/manipulative strategy to a written method.

When we use concrete materials when teaching addition and subtraction and relate it to the written form, it allows students to think flexibly about numbers. Decomposing and composing numbers is an essential skill as they grow mathematically. This conceptual understanding and flexibility gives students strategies to solve more complicated concepts later. So not only are we helping them learn the math facts, but those very same strategies can be applied to adding and subtracting larger numbers and even fractions, decimals, algebra, and geometry down the road.

Below is a comprehensive video by Graham Fletcher. He explains the progression of addition and subtraction in a way that is super easy to understand. Please take time to watch the video.

Original Problem was 72+42

"Don't Rush the Development of Child"

The Misconception We See in Addition and Subtraction

Students usually struggle in math because they have underlying issues with place value and have been taught algorithms instead of understanding. As students continue their development in mathematics, it is critical to understand that they are still developing place-value as they learn how to add and subtract.

Graham Fletcher urges us not to rush students through conceptual stages of understanding in his addition and subtraction and multiplication progression videos. When looking at the mistakes in these addition problems, we see that the child may have been rushed in their place value development and must continue developing place value while learning addition and subtraction. The moral of the story is, "Don't Rush the Development of Child."

Modeling Addition and Subtraction with Manipulatives

To help further students' understanding of place value and develop their addition and subtraction skills it is imperative that students continue to use manipulatives and other visual models to develop their conceptual understanding. There are many different models that are used to help children understand the relationship between addition and subtraction (see manipulatives section). Remember what the hands do, the eyes see, the brain remembers. It is equally important to think of these two operations as being connected and should be taught together. I rarely teach one of these concepts without the other, so as students are learning to add, they should also be learning to subtract. Win-WIn! See below for manipulatives and models.

Addition Problem Structure

Subtraction Problem Structure

Unkown Addend Problem

Communitive Property

Combining Using 10 Frame

Ten Frame and Number Bonds

Part-Whole-Model

Bar Model

Using Base-Ten Blocks to Add

Using Base-Ten to Subtract

curriculum_corner-_composing__decomposing_numbers_13-14.docx

The Importance of Composing and Decomposing Numbers

Often, this is a difficult subject for teachers and parents alike. Most of us were taught the traditional way of adding and subtracting. Watch the kids in the video below and you will be shocked! My Abuelo was super fast at math. I was shocked that he could add big numbers so quickly. I finally asked him how he was computing so quickly and basically, he said he was composing and decomposing numbers, which means breaking them apart and putting them back together again. It works and the concept of composing and decomposing numbers develops amazing mathematicians. The video below is a great demonstration of this.

In the early years please help students become fluent at:

Good Questions

Contrary to what people think, decomposing and composing or breaking numbers apart and then putting them back together is not a "Common Core" thing...It's actually a math thing; decomposing and composing numbers helps develop place value and is an essential skill for future math such as algebra. A big part of developing foundational math skills is asking great questions. If you are a parent or teacher teaching math, I highly recommend you print the questions from the link.

Do you think the solution will be more or less ________?
What is your estimate?
What strategy did you use?
How did you begin to think about this problem?
What is another way you could solve this problem?
How could you prove that?
Which words were most important? Why?
How would you draw a diagram or make a sketch to solve the problem?
Is there another way to (draw, explain, say) that?

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