My students used manipulatives and pictures to explore fractions in third grade. As a bridge to numeric representation, I began my lesson by displaying and discussing a sheet entitled Equivalent Fractions With Numberlines.

This established the fact that any given fraction goes by many names. I listed equivalent fractions for one-half and two-thirds and discussed how their favored name is always the first on the list (which can be called

*simplest form*,*lowest terms*, or a*reduced fraction*). We discussed the "counting by" patterns of the numerators and denominators, as well as the relative sizes (or ratios) of the numerators and denominators.
The time had come to jump into numeric computation of equivalent fractions. We reviewed the Identity Property of Multiplication (any number times one equals that number). This, I explained, was how we would generate equivalent fractions.

Using a little trick I learned from Saxon Math years ago, I showed the students how to use a fraction with the same numerator and denominator, which is equal to one, to find equivalent fractions. With pictures, we also explored how this expresses cutting the fraction into smaller pieces. (For the fraction in the picture, for example, we would be cutting each of the thirds into three pieces to get ninths.)

Since my students are relatively good at math, I felt confident that giving them four different ways to practice equivalent fractions would not overload them. I chose these sheets from the Fraction Worksheets page of Common Core Sheets: Finding Equivalent Fractions - Visual, Filling in a Pattern, Missing Number, and Finding Equivalent Fractions (Multiple Choice).

The multiple choice problems were by far the most difficult. To help students limit their choices (and as a springboard to comparing fractions, which we will attempt in a few days), I taught them how to use one-half as a benchmark fraction. If the numerator was less than half of the denominator, the students could see that the fraction itself was less than one-half, and vice-versa.

Moving away from my textbook has allowed me to show my students multiple ways to approach a mathematical concept. Rather than overwhelming them, exploring equivalent fractions in a variety of ways has strengthened their understanding and prepared them for a wider range of problems.