By: David A. Bernasconi

As a middle grades math teacher, instructional coach, and tutor who works with students across all grades, I witness the struggle with fractions at every level. There are two primary sources of difficulty with fraction operations: The first is recognizing factors hidden in numerators and denominators; the second is choosing the correct rule and applying it properly.

"Fractions with Prime Factor Tiles" is a revolutionary tool for teaching fraction operations that corrects both of these deficiencies through hands-on activities. Numerators and denominators are expressed as products of prime factors with color-coded tiles that make the common and non-common factors of numbers visually obvious. Rules for operations are taught and reinforced through physical manipulation of the tiles in a manner that is logical and intuitive.

## Identify Common Factors to Simplify, Multiply or Divide

When simplifying, multiplying, or dividing fractions, any factors common to the numerator and denominator are cancelled out. In the first video, Prime Factor Tiles are used to simplify and to lowest terms. In the second video, Prime Factor Tiles are used to divide by . These beginning examples identify the greatest common factor and reinforce that factors common to the numerator and denominator cancel out to equal one.

Simplifying Fractions with Prime Factor Tiles

Dividing Fractions with Prime Factor Tiles

## Identify Non-Common Factors to Compare, Add or Subtract

When comparing, adding or subtracting fractions, factors non-common to the denominators are used to make equivalent fractions with like denominators. In the first video, Prime Factor Tiles are used to compare and . In the second video, Prime Factor Tiles are used to add and . In the addition video you will note that Prime Factor Tiles are used to represent and solve problems but are not intended to display all possible solutions.

Comparing Fractions with Prime Factor Tiles

Adding Fractions with Prime Factor Tiles

## Help for Recognizing Factors

When it comes to identifying the factors of composite numbers, recall of times table facts and familiarity with divisibility tests are critical. The "Factor Finder" is included with "Fractions with Prime Factor Tiles". It is a temporary aid that enables students to learn fraction operations while they are still mastering their times table facts.

## Help for Learning Rules

The best way to insure your students genuinely understand the rules for fraction operations is to teach each rule through very simple examples that involve compatible numbers and are based on familiar situations that can be acted-out or physically modeled for confirmation.

In the first video, an activity for adding fractions using coins is modeled. In attempting to add a group of nickels to a group of dimes, students learn *why* like denominators are needed and *how* to generate them both physically and mathematically. In the second video, multiplying fractions is demonstrated using slices of pizza. Setting up and solving the problem mathematically *follows* acting out what it means to take a fraction of a fraction.

Model Addition of Fractions Using Coins

Model Multiplication of Fractions Using Pizza

## Success in Algebra and Beyond

Research indicates that the problem with fractions isn't limited to just fractions: A 2012 analysis of long-term longitudinal studies from the US and UK concluded that knowledge of fractions and division in elementary school uniquely predicts knowledge of algebra and overall math achievement five or six years later.

Prime Factor Tiles allow students to focus on the role of factors in arithmetic operations with fractions, helping students develop a strong foundation for future operations with factors in algebra.