# Fraction notation activities and cards: 3 activities to illustrate fraction notation and concepts

Why are fractions difficult?

There are several reasons fractions are extremely difficult for students with dyscalculia. Both the notation, using two numbers close to each other, and the different ways we show fractions can cause confusion.

• When using the fraction notation, students need to work with two numbers at the same time and think of them in relation to each other. Not only is seeing the two numbers so close to each other confusing, the words used to ‘read out’ a fraction leave the impression it is ‘one entity’, ‘one number’ and does not bring in mind the ‘whole’ that is being divided.
• Not only is a fraction is written with two numbers, the numerator and the denominator, those two numbers actually have an opposite working on the size of the fraction:           A larger numerator, the number written above the division line, makes the quantity of the fraction larger, which is in sync with children’s experience with positive numbers. In contrast to that, a larger denominator, the number written below the division line, makes the quantity of the fraction smaller. This is counter-intuitive to students who have learned that bigger numbers mean larger quantities! Students with dyscalculia usually do not understand and remember that these numbers have a totally different meaning depending on the place they are written.
• Another reason students with dyscalculia often get confused with fractions is because they do not automatically see the similarity between different models (such as folded squares, fraction strips, fraction circles, or pizza pies) that are used to illustrate fractions in their textbook or are used in class presentations.
• Last but not least, most students with dyscalculia are slower in copying from the board and prone to making reversals in the numbers as well as in the numerator and denominator of the fractions making for very confusing written notes.

The fraction notation cards and the symbol and number tiles in this activity are designed to show the different meanings of the top and bottom number, focusing on one number at a time, instead of both. The words numerator and denominator are unfamiliar vocabulary and do not add to understanding, so they are not used in this lesson, we call it top and bottom number. The top number shows how many equal parts you count. A larger top number makes the amount of the fraction larger. The bottom number shows what type of parts you count. A larger bottom number makes the amount of the fraction smaller.

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