4 Ways to Help Students Master Equivalent Fractions

Error analysis for the win!

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One of my favorite parts of math instruction is teaching fractions. I know several people who when they hear the word fractions shrivel up like a grape left in the hot Sahara sun. Not me though! Fractions are so intuitive and can be taught in a way that really helps students grasp and understand the concepts. Here are 3 things that I used to help my students solidify their understanding of equivalent fractions.

1. Ditch the Pictures!

It may seem counterintuitive to begin teaching about equivalent fractions by not showing students a picture of 1/2 and 2/4. Instead, to introduce fractions, I begin with equal-sharing word problems. I do this because students are so familiar with this example in their real life. 

These problems often involve splitting up some type of food item between a certain number of people. You can use these to help students understand equivalent fractions. Here is a question that I like to use to see if my students can make the connection of equivalent fractions on their own.

"There are two groups of kids sharing pizza. In one group, three children share one pizza equally. In another group, six children share two pizzas equally. Who will get more pizza? A child in the first group or the second group?"

After examining the problem, we can see that each child is going to get 1/3 of a pizza regardless of which group they are in. We can talk about how in one group the students might just get 1/3. In the other group, the students can get 2/6 a pizza. Having these discussions with your students can really help them conceptualize the same amount, just different sizes of pieces.

(And, just because you don't provide students with a picture doesn't mean students can't draw a picture. In fact, it's preferred! That way, students are sharing their model, instead of just doing what the teacher tells them.)

2. Use Manipulatives to Find Equivalent Fractions

Okay, I know I just told you to ditch pictures, but once students have worked through a significant number of equal sharing problems, then I will introduce manipulatives. I don’t like to use manipulatives to start with because I really think that fractions can be intuitive if presented correctly. Manipulatives, however, are a great way to show equivalent fractions after students have 1) already identified what they are, and 2) are familiar with various ways to find them. 

I will do something similar to what I did in the pizza problem. I will have the students pull out 1/2 and 2/4. They will then determine if they are equivalent or if one is greater than the other. The danger with this is that some fractions can look really close to being equivalent well just being slightly off. Take a look at this example.

Here you can see that 3/5 and 7/12 look really close. They are *almost* equivalent. And to students who are still trying to figure out how to be precise, this can be an issue if this is the only way that students are taught to find equivalent fractions.

3. Use Multiplication & Division to Find Equivalent Fractions

After using manipulatives, we talk about how we can find equivalent fractions without using fraction bars. This is when teaching students about multiplying and dividing comes in. It is not enough however to just teach the students how to find the equivalent fraction. It must be accompanied by an understanding in order for students to really internalize it. 

I like to draw models with my students that then show why I multiply by two over two or three over three. We discuss why I can divide a fraction by two or by three in order to find an equivalent fraction.

4. Practice Finding Equivalent Fractions

After students know how and why finding equivalent fractions works, they are ready to practice. My favorite way I have to practice is by using games and other activities in the classroom. Some of my favorite activities to do with my students are games like bingo or a board game set up similar to Candyland. I’ve also used coloring pages to help my students find equivalent fractions as well. Want to check out some of my equivalent fraction activities? Click here to see some of the activities you can use with your students in your classroom.

Teaching equivalent fractions doesn’t have to be the bane of your existence. By introducing equivalent fractions through word problems, manipulatives, having students discover how to find equivalent fractions, and fun and engaging repeated practice, your students are sure to become masters of fractions.

Want a free fraction activity to do with your students? Check out this FREE set of addition and subtraction fraction task cards that focus on error analysis! These are perfect for helping your students find and fix mistakes in their work too!

6 Ways to Help Your Students to Celebrate Mistakes in Math

Error analysis for the win!

I'll send you a free set of error analysis task cards that focus on adding and subtracting fractions.

​

Simply print it off and use it with your class today!

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I always loved Ms. Frizzle’s motto of “Get messy, make mistakes!” As educators, we want our students to be successful, which somehow translates to “don’t make mistakes.” I know that I’ve been guilty of thinking “Man! I’ve taught this concept over and over again! You would think they would have it down perfectly by now.” This is especially true when it comes to my students making mistakes in math.

As I’ve shifted away from this mindset, I’ve come up with 6 ways that I’ve been able to help my students not only identify and fix mistakes in their own work but celebrate them and recognize that they are learning.

Here are 6 ways to help your students identify and fix their mistakes in math:

1. Make Mistakes On Purpose

Each day, my students complete a spiral review with 4 questions. As they are working, I walk around, observing their work. Oftentimes, I will notice that some students are making the same mistake. When we go over the spiral review as a class, I will make the same mistake they have made on purpose. When I get the incorrect answer, I will often have a student say "That's not right!" They then get to explain where my mistake was.

One word of caution with this method: Once you are finished making the incorrect mistake, you want to make it very clear where the mistake was, and how to fix it. With the attention span of a goldfish, some students might just catch the "mistake" part, and not the "how-to-fix-the-mistake" part, and continue to solve it incorrectly. 

Sometimes, I will tell my students before I solve it that I am going to make a mistake and that they need to find what I did incorrectly. This helps my students focus on the work I am doing because they are hunting for the mistake.

2. Have Students Share Out Their Mistakes

After we do our spiral review, I give the students a chance to explain mistakes that they made in their work. They get to come up to the front of the room and tell us what mistake they made and how they fixed it. My students love doing this. If I ever forget to ask "Did anyone make any mistakes they want to share?" one of my students will remind me.

I love this because it allows other students to hear where common mistakes are. They also learn that their peers make mistakes, just like they do. It really helps to build a culture of making mistakes in our classroom (which I talk more about below).

3. Use Error Analysis Activities

I love giving my students the opportunity to find mistakes. It helps them to develop critical thinking skills that they can use to solve their own math work. One of my favorite ways to do this is to grab a set of error analysis task cards that focuses on the math skill that we are working on. 

There is a math problem that needs to be solved on each card. Then, someone has gone through and solved the entire problem. However, there is always some simple mistake in the work that has been done. When we do these task cards, I give my students the chance to go through the work and find the mistake. When they find the mistake, they write down what the mistake was, and then they solve it correctly.

Making error analysis task cards can be a little time-consuming though, so I’ve got a free set for you if you want to check them out. CLICK HERE to grab a FREE set of error analysis task cards for adding and subtracting fractions with like denominators. 

4. Create a List of Common Mistakes Students Make

Another thing I like to do to help my students identify mistakes is to create a list together of common mistakes that students make. For example, when we are talking about multi-digit subtraction, one common mistake is that students forget to ungroup when it is necessary. We give specific examples, like trying to subtract from 0.  Another mistake is that students will make is adding instead of subtracting. We create this list and post it in the classroom, so my students have something to refer back to when they are doing their math work in the future.

5. Create a Culture of Making Mistakes

I believe the most important thing that you can do to help your students find and fix their mistakes is to build a culture of having a growth mindset in your classroom. I love it when my students make mistakes because that is how they learn and grow. I tell them that each day. I praise them for making mistakes. I want them to feel like making mistakes is okay. I want them to feel like when they make mistakes they are learning. 

Making mistakes easier for some students than others. I have had my fair share of students who are such perfectionists that they do not even want to try for fear of being wrong. As we build a culture of making mistakes in our classrooms, our students will feel safer in trying new things, and their confidence in their math skills will grow.

6. Change the Problem to Make the Mistake Correct

Let’s say you are reviewing multiplication facts with your class, and you come to 7 x 8 (a trickier math fact for some kids). One student says the answer is 54. Rather than stating that the answer is 56 and moving on, ask the student if they can come up with a problem where 54 would be the correct answer. This could be a good practice to do with the whole class, or in a small group. By coaching students to see that there is a context in which their answer could be correct, we are empowering them to become more flexible mathematicians in the future. 

Having your students find and fix their mistakes in math can be a challenge. It takes time to build up that culture, but it is well worth it as your students can really find and identify mistakes in their work.