# Teach Think Elementary

## Content, not just cute.

Nothing strikes fear into the heart of third grade teachers like being the first to introduce these adorable, innocent children to the world of fractions. Teaching third grade fractions can be intimidating, especially if you’re a grade-change and come from lower elementary. Fortunately, it seems more difficult than it actually is, and hopefully, by breaking the standards down, we can make it feel more managable.

Usually, third grade is the first time kids officially encounter fractions. Luckily for all of us third grade teachers out there, though, this isn’t really their first experience with fractions. Most students will come in with some prior knowledge of fractions that they have picked up just by existing in the world. Kids tend to be very familiar with the concept of half and making sure the pieces are equal (especially when it comes to sharing snacks!). By third grade, kids have definitely seen a pizza divided up into fractional pieces, and they usually understand that those pieces are meant to be equal.

## Fractions Concepts in Prior Standards

If your school is using the Common Core or other similar standards, they will have been exposed to some basic fraction concepts through those as well. True, there are no explicit fractions standards in the second grade math Common Core, but there are fraction concepts in there.

#### Second grade standards that include fraction concepts:

2.MD.6: Number lines

2.G.2: Partitioning Rectangles

2.G.3: Halves, Thirds, and Fourths- This is the main standard in second grade for fraction concepts.

Even if your students didn’t pick up everything they could have from the second grade standards for whatever reason (global pandemic, I’m looking at you), there are other fraction concepts baked into the third grade standards as well. Most teachers don’t start out the year by teaching fractions (I actually recommend starting with geometry). So you can do your future teacher self a favor and build up those concepts as you go. That way, when you do get to the dreaded fraction unit, your students will already have a strong foundation and you can just glide right on through.

You can also use those additional standards to circle back and review or practice fraction concepts, which takes some of the pressure off trying to make sure every student fully understands everything within the time limit of your specific fraction unit.

#### Other third grade standards that include fraction concepts:

3.MD.4: Measuring to Halves & Quarters of an Inch

This was always a tough one for my kids, and it’s because it relies so heavily on fraction concepts. I would definitely recommend tackling this standard after teaching your fraction unit, if you can. Also, coloring in printable rulers is my one weird trick for this concept.

3.G.2: Partitioning Shapes

I have a whole blog post on teaching fraction of an area within your geometry unit. If you teach geometry at the beginning of the year, your students will already have a solid foundation for this concept by the time you get to fractions. If you teach it later on, it’s a great opportunity to review and build on those fraction concepts.

## Breaking Down the Third Grade Fractions Standards

Ready to get started? If you feel overwhelmed, just stop and focus on one concept – pick fraction of an area, fraction of a set, or fractions on a number line. Or, if you’re looking for someone to just please do it for you, you’re in luck, because I did just that!! You can find my complete, detailed Third Grade Fractions math unit here.

Suggested vocabulary for third grade fractions: fraction, numerator, denominator, whole, half, fourth, quarter, third, sixth, eighth, unit fraction, compare, label, explain, justify, addend, sum, greater than >, less than <, number line, equivalent, double, triple, quadruple.

## Teaching Basic Fraction Concepts (3.NF.1)

3.NF.1: This is a lot of words to say that kids need to understand that if you cut something into 8 parts, that each one is 1/8. And if you color in 4 of them, it’s 4/8. No need to bring algebra and letters into it, imo!

No pressure, but this standard can seem deceptively simple. It can be really easy (and tempting!) to do some cutesy craftivities and have kids getting the right answers without developing the full concepts. I definitely spent more time on these concepts than other teachers, but it always paid off when we got to the more difficult stuff. In my experience, I’d rather put in the time and work up front and build a solid foundation for my students and make the rest of the concepts a little easier on them (and me!).

PRO TIP: Make sure you include fractions like 0/8 and 8/8 in this section and that kids understand that 0/8 and 0 are equal and that 8/8 and 1 are equal (because you have 1 whole pizza, of course!). Trust me on this, it will make everyone’s lives easier in the very near future (as in, when you get to standard 3.NF.3d).

## Teaching Fractions on a Number Line (3.NF.2)

3.NF.2: It’s broken down into two letters, but the main idea is that kids will make fraction number lines between 0 and 1 and be able to label all the fractions between. So, for example, students will be able to make a number line from 0 to 1 and mark off all of the fourths in between.

Hopefully, your kids learned how to make just basic number lines in second grade. But, if they didn’t, or if they are at all shaky on that concept, definitely start there. The keys here are that they understand labeling the beginning and end of the number line and that they can make the correct number of equally spaced marks in between. It’s definitely trickier than it looks!

These concepts are the secret key to getting your kids to understand measuring to the nearest half or quarter inch, so make sure to spend enough time here for them to build that foundation. A ruler is really just a number line that’s already been marked off to the halves and fourths, so once they make that connection, everything will start to fall into place.

Once your kids have the concepts down here, you can challenge them with this FREE Fraction on a Number Line Teamwork Challenge. It’s a group activity, so you’ll be able to see overall how well your students mastered the concepts and if you there are any major gaps in their understanding. It also makes a great review for in the late spring when you want to be outside but need to be doing something educational. Plus, it has over NINETY THOUSAND downloads, so you know it works!

## Teaching Equivalent Fractions & Comparing Fractions

This is definitely a case where you’ll want to teach the standards in order, because 3.NF.3 builds on the concepts from 3.NF.1 and 3.NF.2. The first one was about the basics of fractions of an area (1/8 of this pizza), and the second had the basics of fractions on a number line. In 3.NF.3, students will extend both of those concepts as they work with equivalence, wholes, and comparing fractions.

You could absolutely pull out those concepts and do them together with either 3.NF.1 or 3.NF.2, if that works better for you and your students. Some students or classes might benefit from only working on fractions of an area first, then moving on to only working on fractions on a number line. In my experience, students more strongly ‘get’ one concept or the other, so I always liked to go back and forth between the two. That way, students can use the understanding from their stronger concept to make connections to the weaker one. Plus, it’s more review and reinforcement going back and forth between the two. But I’ve also definitely had classes where that was not the reality, and we had to focus only on fractions of an area for a very, very long time before switching over to fractions on a number line.

## Teaching Finding Equivalent Fractions (3.NF.3a)

3.NF.3a: The basic concept of equivalent fractions. This includes that fractions are equivalent if they are the same size or if they are the same point on a number line.

If you were able to spend plenty of time on the previous two standards, this one should be the next logical step for your students. Visual models are the key here, and more is more on that front, in my opinion. This is a great opportunity to differentiate by learning style or interest. Kids who are more hands on can use paper plates to color & cut out and find equivalent fractions. Meanwhile, those who are more into digital learning can use online manipulatives like these to build their understanding.

## Teaching Generating Equivalent Fractions (3.NF.3b)

3.NF.3b: Make equivalent fractions and explain why. In other words, when given 1/2, students will be able to come up with 3/6, 4/8, etc. and explain why those are equal.

Some kids will just intuitively pick this concept up, especially if you spend a lot of time on 3.NF.3a and they start to become very familiar with the fraction visuals. For those who don’t make that jump naturally, I have a separate blog post on how to use folding to help students understand how equivalent fractions are related.

##### Quick game/ center: Equivalent Fraction Memory/ Matching

Make simple cards with equivalent fractions on them (index cards cut in half or quarters work great, plus… more fractions!). Turn them all face down. Kids turn over two at a time and try to match up the ones that are equivalent. It can get extra tricky if some fractions have more than one match (1/2 can match with 3/6 or 4/8, for example). For stronger students, have them make their own set of cards and test them out. For students who need support, have them draw a picture of each fraction on each card before playing (have them trace a consistent shape to start their drawings!). You can also limit the fractions they can use to support students, or give stronger students more difficult fractions. For accountability/ assessment, have the students record their pairs.

## Teaching Fractions and Whole Numbers (3.NF.3c)

3.NF.3c: Whole number <-> Fraction Equivalence. Understanding that 4/4 is equal to 1 and that 3 is equal to 3/1.

This one is deceptively simple, and uber important. If you headed my pro tip above in 3.NF.1, then your students will already be familiar with the 4/4 = 1 concept. Whenever we made number lines in my class, I made sure they were labeled with both 0/4 and 0 on one end and then 4/4 and 1 on the other end. This helps a lot with kids getting the number of spaces right, but it also sets them up for success on this standard, because they have seen it before.

The trick for the second part of the standard, that 3 = 3/1, is to remember that the fraction bar or slash can also mean ‘divide.’ So then, it makes more sense because 3 divided by 1 = 3. In my experience, kids don’t question or get stuck on this one a whole lot, and it’s just a matter of using it often enough that it doesn’t throw them off.

## Teaching Comparing Fractions (3.NF.3d)

3.NF.3d: Compare two fractions with EITHER the same denominator OR the same numerator. And the second, key part – understand that you can only compare fractions of things that are the same size! (1/2 of the classroom and 1/2 of the school are not the same thing!)

Good news: In third grade, students only need to compare the numerator OR the denominator, not both at the same time. So, they need to be able to compare 1/2 and 1/3, which requires understanding that dividing something in 2 pieces makes bigger pieces than dividing something in 3 pieces. AND they need to be able to compare 1/3 and 2/3, which is somewhat simpler and just requires them to be able to understand that one of something is smaller than 2 of something.

Bad news: That’s actually two very different concepts, and students rightly get confused between the two. It can be really enticing to teach little tricks for remembering the difference between the two, but it’s better to avoid that unless you have specific students who truly need that intervention. Instead, teach your kids to build up those basic fraction concepts, really think about each problem, and to draw pictures or use manipulatives when they aren’t sure or want to check. It’s slower, for sure, but will lead to deeper understanding and way, way fewer mistakes. Plus, you’ll be doing their future teachers a solid.

##### PRO TIPS for teaching comparing fractions:

-Lots of time working with fraction bars and discussing which pieces are the biggest/ smallest and why. (Tenths are smaller than halves, but why?)

-In third grade, kids don’t need to order fractions, only to compare them directly. However, if you need a quick 5 minute activity, you can give the kids cards with fractions on them (either all the same denominator or all the same numerator) and have them line up in order. Makes a super simple transition activity, plus kids get to practice/ review. Just make sure to emphasize which end is the biggest fraction and which is the smallest, or the main point of the exercise might not stick.

-For comparing different numerators, think of sharing a birthday cake. If you have 100 people at your party, you’re going to get a much smaller piece of cake than if you have 4 people. (Of course, the cakes have to be the same size!)

-For comparing different denominators, read the fractions out loud. Then you can hear that one third is going to be less than two thirds, the same way that one apple is less than two apples.

-For comparing different denominators: (This works great for students who need support.) Give the students a printable fraction bar page. Have them color in 1 of each fraction, then discuss which is the biggest, smallest, and why. Color in a second one of each fraction. Now you have 2/2, 2/3, 2/4, etc. Again, discuss which is the biggest, smallest, and why. Just keep going with this pattern until the kids get it. If you don’t have time for all the coloring, you can use plastic fraction pieces, as well. I used the coloring time to do the discussions, but not everyone can multitask!

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Still feeling overwhelmed?? I got you! I’ve spent hundreds of hours designing and creating an entire math unit to specificall cover these fraction concepts. It’s fully aligned to the Common Core standards, and every lesson is differentiated. My third grade fractions unit meets kids where they’re at and breaks down the concepts so kids will truly ‘get it.’ It’s full of detailed lesson plans, engaging activities, clear visuals, great discussion questions, printables, assessments, vocab cards, everything you need to help all your students master the third grade fraction standards. Get it here.

Teacher-Author Note: This post is a work in progress and I’m continually adding ideas & images to provide more content.