Fractions often pose a significant challenge for elementary school students. Understanding the concept of fractions, especially when it comes to finding equivalent fractions, can be a daunting task. However, there's a powerful tool at your disposal that can make this process much more manageable: the multiplication chart. It's rows and columns of multiples help students to truly understand how equivalent fractions can be found by multiplying or dividing by a factor of 1 while providing continued practice of basic math facts. (This post does contain affiliate links of which I receive a small commission with purchase.)
Using Multiplication Charts to Find Equivalent Fractions
Multiplication charts are typically grids that display the products of multiplying numbers from 1 to 10 (or higher) together. I personally like to use a color coded one with factors to 12 along the sides. I place it in a page protector or Smart Pal (see affiliate link by clicking on the image below) and encourage students to use dry erase markers when working with it. This allows students to write on it and see the patterns that exist.
Understanding the Basics: Factors and Multiples
Before delving into how multiplication charts can aid in finding equivalent fractions, it's crucial to ensure that your students have a solid grasp of factors and multiples. Factors are numbers that divide evenly into another number. These are the numbers that are listed along the top and side of the chart. Students use these factors to place their fingers on a row and column to see the product, or where they intersect.
Multiples are the result of skip counting or repeated addition. When students drag their finger along a row or column, they are seeing the multiples of that number. Where the student stops will be based on the number of times or number of equal groups they are making. This will lead them to the product.
Students in Grades 3-4 may not need to use the specific language of factors and multiples, but they should be able to see how the multiplication chart shows equal groups and repeated addition. Before jumping to use the multiplication chart, it may help students to first use number lines and counters to show what's happening each time you multiply or make another group.
Understanding Equivalent Fractions
Just as students should have an understanding of how a multiplication chart works, they should first have a strong foundation in what equivalent fractions are before using computation to find equivalent fractions. Use paper strips and fraction tiles to help students see how fractions can be divided into different sized pieces of the same whole.
This component is pivotal before moving to the computation method, because it helps students to assess whether their answer makes sense. Students can make 1/2 with a paper strip and fold it again to make fourths. They are really multiplying that by 2 to double the actual groups. Students can try this with other fractions too and paper strips are a great way to see that!
Using the Multiplication Chart to Simplify Your Instruction
Take a look at the chart to the right. If you had a fraction of 1/3, you can use the rows to find all the equivalent fractions for 1/3. Some examples include 2/6, 3/9, 4/12 and so on. Each time I multiply 1/3 by a number, I get an equivalent fraction.
It works to find simplest form too! Simply find your fraction on the multiplication chart such as 9/27 and slide along to the left until hitting the original factors on the chart. Now, I have my simplest form.
You can watch this in action with this quick YouTube video:
Stop slowing down your instruction by wasting time with multiplication facts. This isn't the focus during these lessons. Use a multiplication chart to simplify your life and help students work on visualization strategies.
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