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Math Models from Kindergarten to Fifth Grade

Math Models from Kindergarten to Fifth Grade

Kids can use manipulatives and number bonds together.

Kids can use manipulatives and number bonds together.

I love math models. I haven't always felt this way, but the more I get to know them, the more I just can't get enough of them. 

A number bond can be used to solve addition problems with multiple addends.

A number bond can be used to solve addition problems with multiple addends.

What I like about math models is that they always follow the same rules. This is huge for me because, for most of my education, math was super confusing. I felt like every day we were learning something totally new. I didn't see the connections at all. 

In reality, math concepts are all highly related. I believe that math models are a tool for showing students this interrelatedness. 

For example, number bonds can be used in kindergarten to show addition and subtraction of one-digit numbers. Kids can even start with manipulatives in the number bond and count to complete addition and subtraction equations.

Once kids have a firm understanding of using number bonds to add and subtract, they can use the number bonds to work with bigger numbers as well. Kids can also use the number bonds to model story problems which may help with story problem comprehension. If they have a framework for how to work with numbers in a story problem, they may have an easier time organizing the information in their heads. 

Now that kids have a firm grasp of using number bonds with addition and subtraction, they can be introduced to repeated addition and repeated subtraction using number bonds. The problem with repeated addition and subtraction is that they both take a long time. Guess what will save us some time? Multiplication and division! Same model, just a faster equation. 

Then, when kids start working with fractions (a totally new concept), the number bond can be used to show that unit fractions are just parts of a bigger whole. This idea can be expanded as students work with adding and subtracting fractions or multiply fractions by whole numbers.

Tape diagrams can help kids understand the connection between addition, subtraction, multiplication, and division.

Tape diagrams can help kids understand the connection between addition, subtraction, multiplication, and division.

One model has taken our students through their entire elementary math experiences! 

Number lines can be used to show multiplication and division.

Number lines can be used to show multiplication and division.

The other two models I like for this same purpose are tape diagrams and number lines. In fact, my absolute favorite model is the tape diagram. The number one reason I like the tape diagram is It is super fast to draw. I also like it because it looks like a fraction strip which is helpful as students are learning fractions as well.

I love these three models. I think that every teacher should have an understanding of the progression of how these models can be used from kindergarten to fifth grade. It would give kids a common "box" for their new math learnings. 

If you are comfortable with these three models - that is wonderful! Keep using them to enhance your teaching. 

Tape diagrams can be used to show addition, subtraction, multiplication, and division.

Tape diagrams can be used to show addition, subtraction, multiplication, and division.

If you are not comfortable with these models, or you are looking for something to put in your students' hands, then I have a freebie for you. You can get my Guide to Math Models just by signing up for my newsletter. Everything is automated, so you don't have to wait for me to respond to your request (which is good because I am not always sitting right at my computer - most of the time, but not always). You can sign up for the newsletter by filling in the box at the bottom of this page. It is full of teaching ideas and resources that you can put in your students' hands to make learning more powerful and engaging.

Thanks for reading! Now, please tell me about your favorite math model.

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