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Algebra Fractions Models

There are three algebra fractions models: area, linear and set models.


The AREA model


Learning Fractions - Area Model Learning Fractions - area model

It is a model where you manipulate circles , rectangles or other shapes divided in equal parts.

Obviously, you can also use cut-out shapes at home.The important things is to cut same shapes into many equal parts.

By the way, cutting a circle in equal parts can be a first exercise already...Do you how to cut a circle in thirds using just a compass?


In case, here you can download some PDF files with circles divided in fractions:




This is a part-whole exercise.

Take the the model 1/2 and 1/4 fractions. Take half of the circle. How many smaller 1/4 parts stay in half a circle? and in the whole circle?

Now do the same for 1/3 and 1/6 fractions and 1/5 and 1/10 fractions.





The LINEAR model

Learning Fractions The Linear ModelIt is a model which uses a rod or narrow piece of paper divided in equal parts (e.g. you can fold a strip of paper by succesively folding it in half)



coming soon





The SET model

learning Fractions Set Model  

This model uses sets of objects formed by groups of subsets. It's more difficult to understand but it's worth the effort.

In the picture above are some base-10 blocks which can be used also for teaching algebra. It's not necessary to have them for learning fractions, though. You can have anything you already have at home, for instance a set 6 nuts and another set of 3 apples or just 6 circles and 3 rectangles. And have them grouped together to form fractions of 2/3 or 6/9.

fractions as sets





coming soon


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Source: Elementary and Middle School Mathematics: Teaching Developmentally (7th Edition)




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