Fractions as Division Lesson-Introduction to Different Representations of Division

How to teach Fractions as Division?

One of the first lessons that I taught in six grade math was fractions as division. Getting students to understand that a fraction is also a division problem is a year-long struggle so introducing an early is necessary so that we can keep practicing it over and over and over again. 

I will admit that at the beginning of my career for teaching math, I was not too big on emphasizing math vocabulary. It’s one of those things that I will regret not doing well with my first class. For this lesson, emphasizing the vocabulary for division problems is super important to help students keep what number is what in a division problem. 

I start the lesson with this PowerPoint presentation. 

Remember from this post, that the best math lessons have students connect with the new learning with something that they already learned in the past. So we discuss vocabulary and look at the division representations that they already know using the division sign and the “house”. I have my students repeat over and over again which number in the problem is the dividend and which number in the problem is the divisor. Then we look at a fraction and students learn how the numerator is the dividend and the denominator is the divisor.

As we are setting up 3 representations of division, we repeat the vocabulary again. By the end of the lesson they are sick of saying the words dividend and divisor but repetition is key here.

   
This presentation is a jumping off point for a fraction as division lesson. From here I would continue to give students real world examples of division and have them write a division representations for those examples.

What are some common misconceptions with fractions as division?

One common misconception that students have is that the bigger number must always be the dividend. This is something that an elementary school teacher probably told them as an easy way to get them to remember to put the bigger number inside the house. This is a habit that middle school teachers have to help students break.

What is next with teaching fractions as division?

I have some other fractions as division resources available in my store. 

• Here is a free puzzle where students need to match a real-world situation with the 3 division representations. 

• Notebook pages with extra practice

• Fractions as Division Math Color by Answer and Riddle