Fraction Vocabulary: It's Critical!

Naming fractions comes so naturally to some of our learners but to others, especially our kids with speech and language needs, naming fractions can be really difficult! One reason why this is such a difficult skill to teach or to learn for some of our kids is because not only are they learning new content, there is also a whole slew of new vocabulary that comes with it!
Much of learning to name fractions in third grade is an exercise in understanding and applying new vocabulary terms. In second grade when students were laying the foundation for fraction work students used words such as half, quarter and whole. Teachers may have talked about parts or pieces but they most likely weren't using words such as numerator and denominator at that point in time.
It can be so helpful at the beginning of a new unit on fractions to be sure to teach and practice vocabulary in a systematic way to help prevent misconceptions and misunderstandings! Let's look at the word denominator as an example. Understanding the denominator of a fraction is not difficult. If you look at a whole broken into 6 pieces you know you are working with sixths and the denominator of the fraction is 6. This is really just an exercise in counting! There is no earth-shattering, difficult to learn math here. But, the word denominator is definitely new to our students and so they need time and room to practice the new concept of identifying and understanding the denominator while applying the vocabulary of denominator.
When our students are really very comfortable with these new fraction vocabulary words they will be able to free up the mental space to think about the new understandings that come along with fractions. Hands on experiences will be more rich when our students are ready to explore and apply their understandings around these new vocabulary words. Am I saying that you need to teach the vocabulary before you can allow your students to explore with fractions? ABSOLUTELY NOT!! What I am advocating for is that once students have had instruction around vocabulary you are sure to give students opportunities to use their new vocabulary to describe what is happening with fractions even if the concepts themselves seem simple.

So how might this play out in the classroom?

  • Day 1: Your students do an activity where they are looking at pizzas that have been cut into equal pieces. You have each pizza labeled with a unit fraction describing one piece of pizza. Students are doing a notice and wonder activity around what they see in the pizzas and what they see in the labels on the pieces of pizza.
  • Day 2: Yesterday, your students noticed that the bottom number of the fractions match the number of pieces of pizza. You tell your students that their observation was spot on and that we have a math word for this- denominator! Next, give some explicit practice of this concept! Look at these different pictures, what would the denominator be on each of these fractions? Practicing math concepts is not a bad thing. Every single math lesson you teach does not need to be a hands on discovery lesson- sometimes, after building an initial understanding you just need to practice!
  • Day 3: Your students have been working with the word denominator so you want to give them a new experience that will allow them to apply their new vocabulary word. Maybe you do an activity with a pan of brownies. You tell an elaborate story about how at first you baked these brownies to share with just 4 friends but, as more friends showed up to your party, you had to cut them into more and more equal pieces. As you work through the story, ask your students what is happening to the denominator of the fraction. Ask if they could write fractions recording the denominator as more and more friends show up. Expect your students to use this word, a lot!

Related Resources: 
This resource is perfect for allowing your students to learn and practice new vocabulary associated with naming fractions. Included you will find: 

  • I can statements
  • Notes reference pages
  • Cloze notes reference pages
  • A worksheet practice page
  • A foldable practice page
  • A homework page

Research Based Strategies 

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Multiplying Fractions by a Whole Number

Fraction concepts are taken up a level in 5th grade and many of the topics are very abstract and difficult for students to understand. Multiplying fractions by a whole number doesn't need to be one of these difficult concepts! By using the CRA (Concrete-Representative-Abstract) framework your students will link what they already know about multiplication to the multiplication of fractions and will be successful in no time at all!

Concrete Multiplying Fractions by a Whole Number

Before you begin with fractions, anchor your students back into what it means to multiply. Give them a pile of blocks and ask them to model something super simple such as "4x3" your 5th graders should quickly and easily be able to model this problem. Ask your students about what they built and how they know it represents the equation. 

Go ahead and get out your pattern blocks. They are the PERFECT fraction representation. Let the hexagon represent a whole and allow your students to figure out which blocks represent 1/3 (rhombus), 1/2 (trapezoid) and 1/6 (triangles). Once your students are all set with their blocks, they are ready to begin! Don't have fraction blocks handy? Fraction circles would work just as well! 

Ask your students "If 4 groups of 3 blocks represented 4x3, how could we represent 4 x 1/3?" Allow students to use the rhombus pattern blocks to represent 4 groups of 1/3. The beauty of using blocks is that students can put these blocks back together to see both the improper fraction and mixed number that is created when fractions are multiplied together.

**This PICTURE is not a concrete model, but if you are creating this model out of fraction tiles, your students are working at the concrete level! **

Representative Multiplying Fractions by a Whole Number

Once your students are able to model 4 x 1/3 you want them to link this understanding to a representative model such as repeated addition. You may begin by asking your students to write a repeated addition equation to represent 4 x 3. This is easy for your students! Now, ask them to  use what they know about multiplication to write a repeated addition equation that represents 4 x 1/3. 

Abstract Multiplying Fractions by a Whole Number 

The concrete and representative steps of this activity allow your students to clearly understand what is going on when multiplying a fraction by a whole number. After your students have had a good deal of exposure at the concrete and representative level, give them a new equation such as 4 x 2/8 and ask your students what they *think* the product will be. You are looking for your students to make generalizations about their multiplication and fraction understandings and to be able to explain their thinking. After a student shares their thinking, ask all students to model with concrete materials or a repeated addition equation to confirm the product!

I have created a set of playing cards that includes multiplication equations, visual models, repeated addition and the resulting products. Your students can play so many traditional card games with this deck of cards - and I have included the instructions for 5 games to get you started! This resource is PERFECT for exploring the link between repeated addition and fraction multiplication. Click HERE to check it out! 

Research Based Strategies 

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