Ready for some engaging fraction games and activities to help upper elementary and middle school math students master those fraction concepts?

In my last fraction post, I summed up the different fraction content posts I’ve written over the years. These included a series about fraction basics, as well as a few posts about fraction operations.
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Today’s post is a collection of the fraction games and activities posts, to again give you a type of index of the fraction activities here on the blog.
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Just select the links to head to the posts you’re interested in!

Fraction Games with Card Activities

Fraction Krypto

If you’re looking for an easy, low-prep game, then Fraction Kryptoa is the perfect choice. Just put 5 fraction cards up (or even write 5 fractions on the board) and students use the fraction operations to hit the target number of 1. Examples and detailed explanations are in the post.

Playing Fraction ‘War’

Fraction War is a great game to practice comparing and ordering fractions, as well as identifying equivalent fractions. Students can play in groups of 2 or 3.

Playing Go Fish with Fraction Cards

Just like the traditional Go Fish card game, students play this fraction version by asking other players for fractions equivalent to their own. Then they ‘go fish’ if they don’t get the card they ask for. This is fantastic equivalent fraction practice! Directions and examples are in the post.

Quick and Easy Game for Adding Fractions: Make One

Make One is another fraction card game where students must ask players for certain fraction cards (or cards equivalent to the fraction card). In this game, they’re asking for cards that will help them to ‘make one’ when added to a card(s) in their hand. You can access these cards through the post.

Fraction Games Using Dice

Playing ‘Decimal Dice”~ Converting Fractions to Decimals

Decimal Dice is such a popular and challenging game! This fraction game is kind of like Yahtzee. It requires students to convert fractions to decimals in order to get their scores. It’s full of examples, and students need several, but it provides EXCELLENT practice. Students can play with a partner or with a larger group.

Fraction Games with Partnering Cards

Reviewing Fractions Throughout the School Year: A Quick Way to Practice Fraction Concepts Any Time of Year

This fraction post explains how to use fraction partnering cards or grouping cards when you want to randomly group students. This fraction activity can be used ANY time of year, especially when you’re NOT teaching fractions, as a way to bring fractions into math class in a different way. Using fraction cards that focus on different concepts helps students keep fractions fresh all year:-)

A few of the posts described here include a free fraction game or activity download (or two), which can be accessed by registering for the free Fraction Review Toolkit.

Want even more fraction and fraction operation content and materials all in one place?
Check out the program, Fractions: From Foundations to Operations.

The post Engaging Fraction Games and Activities Your Students Will Love appeared first on Cognitive Cardio Math.

Are you teaching fraction operations in middle school (or reteaching fraction concepts when they pop up in middle school?)

Are you always looking for fraction content or fraction teaching tips?
I’m here to help! I’ve decided to do something I’ve never done on my blog:

• Since I have so many fraction-related posts for upper elementary and middle school math, I’ve added a couple of new ‘summary’ posts as a kind of index.
• One post (this one) will include posts about teaching fraction concepts, and the other will summarize the posts about fraction games and activities. 

​So, let’s get to the fraction content posts.

The first and newest is the series of foundational fraction posts.

• Many of these posts include a free download or two. You can access the downloads by registering for the free Fraction Review Toolkit.

The posts in the fraction operations series include: 

1) Teaching Fractions in Middle School: Reviewing the Basics

• In this post, we talk about the need that always seems to pop up – the need to review certain fraction concepts before moving on to your specific fraction curriculum.
• We review the meanings of fraction terms, how to represent fractions, and a few ways to weave fractions into class even when you aren’t teaching fraction concepts.

2) Teaching Fractions in Middle School: Using Models

• This post addresses the progression of fraction skills through the elementary grades up to 5th grade (and beyond).
• I share a few examples of using fraction models when adding and subtracting fractions and explore a combination of number lines & fraction strips.

3) Teaching Fractions: Benchmarking and Estimation

• As the title indicates, this post focuses on using benchmarks, explores the 4th grade benchmark standard, and includes examples of how to use estimation when adding fractions.

4) Teaching Fraction Operations in Middle School: Finding Equivalent Fractions

• Equivalent fractions are in many situations, and we look at several of these in this post.
• We look at three ways to find common denominators in order to create equivalent fractions, and we explore representations of equivalent fractions.

Fraction Operations in Middle School Content

In addition to the fraction series, I’ve written a few other fraction-related posts over the past several years.

Using the Ladder Method to Find LCD

This method of finding the least common denominator is a favorite of mine because it includes the ladder method. It outlines the steps for finding the least common denominator and explains how this method has been helpful to students.

Fraction Division…Another Way

This post focuses on teaching fraction division using the common denominator method, explaining why this method works, and explaining how my 6th grade students respond to the method.

Teaching Multiplication of Fractions and Mixed Numbers

• Multiplying mixed numbers can be tricky! Breaking it down with students can be so much fun.
• This post shares a common mistake students make, explains the numerical ‘breakdown’ of a problem, and shows the breakdown using different representations.

Why NOT use the butterfly method when adding and subtracting fractions?

• I’ve had some pretty interesting experiences with the butterfly method in 6th grade math. This post shares how I learned about this method and how my students used it.

Want even more (there’s so much more!) fraction and fraction operation content and materials all in one place?
Check out the program Fractions: From Foundations to Operations.

The post Fractions and Fraction Operations in Middle School Math appeared first on Cognitive Cardio Math.

Students often need extra practice with adding fractions, especially when they aren’t technically learning about it anymore. Those fractions pop up in so many situations! A card game for adding fractions can help.’Teaching 6th grade math always seems to come with the need to review much of what students learned about in previous years. This includes:

• identifying fractions
• equivalent fraction
• improper fractions and mixed numbers
• adding fractions
• subtracting fractions
• multiplying fractions

Have you found this as well? Do students need to review these things at the grade level you teach?

Quick Teacher Survey About Fractions

Just to be sure I wasn’t the only one thinking students always need some fraction review, I put a quick poll on Instagram:

• “Math teachers, do you feel like your students always need SOME kind of review?”
• 100% of responders chose “Yes, always.”

So, with the idea of review and practice in mind, I have a quick, easy-prep card game for adding fractions for you! You can use this during your fraction addition unit. OR you can use it as a center activity to keep reviewing fraction addition any time during the school year.

What is This Card Game for Adding Fractions?

This card game for adding fractions is “Make One.” 

Students use fraction cards, which you can access for free below, and their goal during the game is to find as many sets of fraction cards that add together to equal one as possible.

Preparing for the Card Game for Adding Fractions

As I said, the prep is quick. The PDF with the cards includes 36 fraction cards, which should be good for one group of 3-4 players.

• For 5 or more players, you may want to make 2 copies of each page to give you a deck of 72 cards.

To prep for the game:

• print 1-2 sets of cards per group
• laminate, if you have time; if you don’t have time, card stock would work well too
• cut the cards out

Playing the Card Game for Adding Fractions

1) Deal 5 cards to each player.
2) Put the remaining cards face down in a pile in the middle of the game area.
3) To begin playing, Player One puts down any combination of cards from their hand that total 1 when added. Players may use as many cards as they’d like to reach 1.

• The cards should be placed face up so other players can see what has been played.

4) Player One may then ask any other player for a specific card to ‘make one’ when added to a card in his/her hand.

• If the player has the requested card or one equivalent to it in their hand, he/she gives it to Player One, and Player One puts down their ‘one’; if not, Player One draws the top card from the pile.
• If the card drawn is the card Player One was asking for, he/she uses it to put down the cards that equal one. Player One can continue asking players for cards/drawing cards until she/he can’t ‘make one.’
• If the card is NOT the one that was being asked for, Player One’s turn is over, and the player to the left takes her/his turn.
• Players will need to think about equivalent fractions when being asked for a card. For example, a player may ask for 4/20. Players need to remember that if they have a fraction equivalent to 4/20 (1/5), they DO give that card to the requesting player.

**Players may want to phrase their question as “Do you have ____, or any fractions equivalent to _____?”

5) The game continues with each player taking their turns until a player ‘goes out’ by playing his/her last card or until the cards in the middle pile are gone.

Additional Example of How Cards Can be Used

Looking at the set of cards in the picture, we can see this player’s hand of cards has 5/10, 1/4, 1/4, 4/8, and 1/20.

• This player could choose to use 5/10, 1/4, and 1/4 to make 1, using up more of the cards in their hand.
• They could also choose 4/8, 1/4, and 1/4, or 5/10 and 4/8.

After playing the ‘1’ of their choice this player can then ask other players for another card to make one, like 1/2 or 19/20.

Keeping Score

Once a player ‘goes out’, players tally their scores:

• Players receive 1 point for each set of cards that equal 1
• The player who ‘goes out’ adds 2 extra points to their score

The player with the most points wins.

Accessing the Make One Game Cards

You can access these Make One cards, as well as other fraction activities, by selecting the button below.
I hope you can use this card game for some fraction addition practice and review!

Interested in more fraction and fraction operation content?
Check out the program, Fractions: From Foundations to Operations

The post Quick and Easy Card Game for Adding Fractions appeared first on Cognitive Cardio Math.

I have a quick way for you for reviewing fractions and related concepts in middle school math throughout the entire school year!

That way is……….use partner cards or grouping cards whenever you’d like to have students work together in random partners or groups.

Before we get into the specifics of the grouping cards, let’s just touch on grouping strategies for a moment and why I’ve created grouping cards for randomized grouping.

Grouping Strategies

In the book Building Thinking Classrooms in Mathematics by Peter Liljedahl, he talks about the types of grouping strategies teachers might use: 

• grouping homogeneously
• grouping stronger students with weaker students
• grouping and giving students particular roles in the group
• allowing students to self-select their groups

Through their studies, he observed that 80% of students entered these types of groups feeling like they were going to be followers rather than thinkers. He asserts that whether students are strategically placed in a group or they self-select, they know why they’re with the other students, and they meet the expectations of that grouping (or as he puts it, they “…live down to these expectations.”).

So, rather than strategic grouping or allowing students to self-select, the author recommends randomized grouping – more specifically, visibly randomized grouping, so students can see that the groups are truly random….not the teacher saying they were random.

If you want to read more about grouping ideas and haven’t already read this one, check it out – Building Thinking Classrooms in Mathematics.

Partner Cards or Grouping Cards to Keep Reviewing Fractions in Middle School

Ok, on to the idea of the actual grouping cards. ​I know there might be some more ‘fun’ ways to group students, but I like to throw some content into the grouping process just to use the grouping time a little more effectively. Why not use it to review concepts?

I did this with equivalent expressions a few years back, and it was quite helpful – using the grouping cards gave students additional practice several times during the year.

​I’ve got three different sets of partner/grouping cards (which you can access below), to help students review fraction concepts.’

​Reviewing Fractions in Middle School: Equivalent Fractions

This set of partner cards has 16 sets of 2 equivalent fractions to randomly pair students. Just cut them, laminate them (or print them on card stock), and then hand them out.

Example:

• ​students who have 4/5 and 16/20 are partners
• students who have 3/10 and 9/30 are partners. 

You can use these any time of year. You might choose to use them when you’re working with similar concepts, like equivalent ratios. One teacher mentioned she was going to use them for equivalent slopes!

Reviewing Fractions in Middle School: Fraction Representations​

To review fraction representations, you can use these grouping cards that have fractions shown in four different ways:

• fraction bar/strip 
• fraction as a number 
• fraction on the number line 
• fraction of a shape

Students find the other students with the same fraction represented, and they have their group.

• These cards can be used to create groups of 2, 3, or 4.

When I made this set of grouping cards, I did repeat numerators. I didn’t want students to just look for a 3 or a 4, etc. In the picture, you can see there are cards with 3/8 and 3/9. Students have to look at their grouping cards carefully.

Reviewing Fractions: Mixed Numbers and Improper Fractions

These grouping cards have one improper fraction, which is a fraction greater than one. There are also three mixed numbers that are equivalent to it. This way, students can review the various ways the numbers can be expressed.

For these, I used the same denominators for different sets. Students can’t just look at the denominator (like 4, in the picture) to find their group.   

Access the Fraction Partner Cards/Grouping Cards

So that’s it!
To sum up – you can use the partner cards/grouping cards ANY time throughout the year to keep reviewing fractions in middle school (fraction vocabulary, basic fraction concepts, fraction operations, etc) throughout the school year.
AND (added bonus)…you can use the cards as a matching activity in centers as well!You can grab these sets of grouping cards for free (along with 5 or 6 other free fraction resources) when you join my email community. Just select the button below!

You can access the grouping cards when you grab the FREE Fraction Review Toolkit!

The post Reviewing Fractions in Middle School Throughout the School Year appeared first on Cognitive Cardio Math.

GCF (greatest common factor) and spending ‘too much time’ on math topics. These are the middle school math ideas I’m thinking about today.

Day 1 of Reviewing How to Find GCF

Day 2 of Reviewing How to Find GCF

GCF Task Cards

The post How to Find GCF and Spending Time in Middle School Math appeared first on Cognitive Cardio Math.

We talked a little bit about equivalent fractions in the Week 2 modeling post, with the idea of using models, or representations, when adding or subtracting fractions, but we didn’t talk about the how of finding equivalent fractions, so we’ll cover that in this quick post.

When to Use Equivalent Fractions

First off, when do we usually use equivalent fractions?

We often use equivalent fractions when:

• comparing fractions
• adding or subtracting fractions
• dividing fractions
• we can even use them when multiplying fractions, though it just creates more work 🙂

​Once we decide we need equivalent fractions, we find a common denominator for the fractions.  There are a few ways to do that:

• Multiply the denominators together (not a personal favorite)
• List the multiples of the denominators to find the least common multiple/least common denominator
• Use prime factorization
• Use the ladder method

Let’s look at each one, using the same fractions each time, just for comparison’s sake. We could be adding these, comparing these, or dividing these…..it doesn’t really matter; but we’ll choose adding for these examples.

Finding Equivalent Fractions Method 1:

Let’s start with multiplying the denominators together, 12 x 8. This gives us a common denominator of 96.

Then students must multiply 5/12 by 8/8 to get 40/96 and 7/8 by 12/12 to get 84/96.

The addition and simplifying are shown in the image below.

Using this method does seem pretty easy for students who have trouble finding the LCM, but it ends up giving them larger numbers (124/96) to simplify.

There’s a good chance that those same students having trouble finding LCM would have difficulty simplifying the larger numbers in their answers.

Method 2: Find LCM/LCD by listing the multiples

One benefit of using this method is that it helps students practice their multiplication facts. But, if students don’t know the multiplication facts, it might take a while to create the lists (they could use a multiplication chart to help them).

​The multiple lists of 8 and 12 are below.

In the lists, we can see that 24 is the LCM/LCD. To help students remember what to multiply each fraction by to get their equivalent fractions, I’ve found it can help to count which multiple the LCM is in each list.

• For example, in the list of 8’s multiples, 24 is the 3rd multiple (8 x 3 is 24), so we’d multiply 7/8 by 3/3.
• 24 is the 2nd multiple in the 12’s list (12 x 2 = 24), so we’d multiply 5/12 by 2/2.

Using the LCM keeps the numbers in the fractions smaller, and in this case, gives us an answer that’s easier to simplify – students just need to convert from an improper fraction (fraction greater than one) to a mixed number.

Method 3: Find LCM/LCD using prime factorization

Students can use a factor tree or the ladder method to find the prime factorizations.

Benefits of this method:

• Students can see which prime factors the numbers have in common.
• Students can see how both the common and ‘uncommon’ factors contribute to the LCM.

The prime factorizations for 12 and 8 are:
     12: 2 • 2 • 3
      8: 2 • 2 • 2

To find the LCD/LCM:
​   1) Identify the factors that 12 and 8 have in common (two 2s).

2) Identify the factors they DON’T have in common (another 2 and a 3).

3) Multiply the common factors by the ‘uncommon’ factors (three 2s and a 3). 
​
LCD/LCM: 2 • 2 • 2 • 3 = 24

4) To help students decide what to multiply each fraction by to get their equivalent fractions (other than asking, “What do you multiply 12 by to get 24?”), students identify which factor ISN’T in each number’s prime factor list. In this case, 3 isn’t in the list of factors for 8, so 7/8 is multiplied by 3/3. 

The third 2 isn’t in the factor list of 12, so 5/12 is multiplied by 2/2.
And we end up with the same equivalent fractions as above (10/24 and 21/24).

Method 4: Find the LCM/LCD using the ladder method

To use the ladder method for LCD, we put both denominators into the ladder, side-by side, as shown in the diagram below.

• We identify a prime factor and then divide by that factor
• We identify a 2nd prime factor in the resulting quotients and divide again
• We continue identify and dividing by prime factors, until there are no common factors other than 1

(For a more detailed explanation about how the ladder method works, check out the posts listed below.)

Once we’ve removed all the common factors, we get the LCM/LCD by multiplying all the numbers on the outside of the ladder.

• LCM/LCD: 2 • 2 • 2 • 3 = 24

To find the equivalent fractions, students use the factor at the bottom of the ladder that’s under the opposite number

• In this case, 3 is under 12 and isn’t a factor of 8, so 7/8 is multiplied by 3/3. 
• 2 is under 8 and is an ‘extra’ 2 that’s not included in the factors of 12; so 5/12 is multiplied by 2/2.

Ladder Method Resources

If you want more info about the ladder method, I have a couple of posts about it:

• Help Your Middle School Math Students Find LCD When Adding and Subtracting Fractions
• Using the Ladder Method in Middle School Math, for GCF, LCM, Factoring

Using Representations for Help in Finding Equivalent Fractions

Whatever method you use, incorporating models will help students understand that the equivalent fractions represent the same amount. (This is a bit easier when the fractions use smaller numbers.)

In the image, for example, we might be adding 1/2 and 5/6.

• When we convert 1/2 to 3/6, the representation using the fraction strips helps students see that these fractions represent the same amount.

Or, if we were comparing 5/6 and 11/12, we could use the fraction strips to verify that 5/6 is equivalent to 10/12.

Which method do you prefer for finding LCD and equivalent fractions?

Do you use fraction strips or another method to model the equivalences?

Interested in more fraction and fraction operation content? Check out the program, Fractions: From Foundations to Operations.

The post 4 Easy Methods to Teach Finding Equivalent Fractions in the Middle School Math Classroom appeared first on Cognitive Cardio Math.

Teaching Fractions, Week 3: Fraction Benchmarks and Estimation

Using Fraction Benchmarks

Fraction Benchmarks to Estimate Fraction Addition

Include Models for Fraction Estimation

Include Models for Fraction Estimation: Example 2

How will you use Fraction Benchmarks?

Do you need a few tools, like the fraction strips, to help your students master the fraction basics? I’ve got a ‘Fraction Toolkit’ for you!

You can grab the Fraction Toolkit here and learn how to use it in this post!

The post Teaching Fractions Using Fraction Benchmarks and Estimation appeared first on Cognitive Cardio Math.

Welcome to Week 2 of the teaching fractions series. Last week, we talked about basic meanings, and a little bit about fraction models. I suggested a couple ways to work fraction basics into everyday instruction. This week, we’ll take a look at the progression of fraction skills through the grades before our students reach us in upper elementary and middle school math classes. Then, we’ll look at how to include fraction models in our teaching. 

Fractions in Grades 1-4

As upper elementary and middle school math teachers, we know our students have had fraction instruction. They know what fractions are, identify fractions of shapes, find equivalent fractions, compare fractions, and perform some fraction operations. We may not know exactly what students did in which grades. 

1st Grade Math:

• halves, fourths, quarters, half of, fourth of, and quarter of

2nd Grade Math:

• Students partition rectangles into rows and columns of ‘same-size square’ and count to find the total number
• Students again partition circles and rectangles into 2 and 4 parts, but add on partitioning into 3 parts. They continue to use halves, half of, etc. and add on thirds and a third of.
• Students should be looking at wholes and identifying those as two halves, three thirds, and four-fourths.

In 3rd grade math, there’s a lot more going on!

• Students partition shapes into parts with equal areas and identify each part as a unit fraction (1/3,1/4,1/2, etc.)
• Students begin to develop an understanding of fractions as numbers, representing fractions on a number line, and “understanding two fractions as equivalent if they’re the same size or the same point on a number line.”
• Students recognize and generate simple equivalent fractions and should also explain why the fractions are equivalent.
• Students express whole numbers as fractions, like 5/1 = 5
• Students compare two fractions with the same numerator or the same denominator ‘by reasoning about their size.

In 4th grade math:

Students should be doing SO many of the fraction things. I’m not going to list out each skill, but the general goals of fractions in 4th grade Common Core are:

• extend understanding of fraction equivalence and ordering
• comparing fractions with different numerators and denominators by using common denominators or benchmarks
• build fractions from unit fractions (includes understanding addition and subtraction as joining and separating parts, as well as decomposing fractions into sums of fractions)
• add and subtract mixed #s with like denominators (replacing each mixed number with an equivalent fraction)
• solve word problems with addition and subtraction
• multiply fraction by a whole number and understand that a/b (like 5/4) is a multiple of 1/b (¼)
• solve word problems involving the multiplication of a fraction by a whole number
• understand decimal notation for fractions, and compare decimal fractions​​

I think it’s important to note that ‘using visual models’ is included in numerous places in these standards.

Fractions in 5th Grade Math (and beyond)

By the time students get to us in 5th or 6th grade, students should understand all of the 1st-4th grade fraction concepts. Unfortunately, it often isn’t the case……for so many reasons.

• Some students aren’t developmentally ready for all the fraction concepts 
• Some classes may not have gotten as far in the curriculum as they needed to and may never have discussed certain fraction topics
• OR they did discuss the fraction topics, but very quickly or maybe with shortcuts, because there just wasn’t enough time

So that’s all well and good….students are supposed to have done all of this, should be proficient at these fraction skills, and should be ready to apply them and go deeper at the next grade level.

But what are math teachers at 5th, 6th, or higher grade levels supposed to do when this isn’t the case, and their math curriculum builds on that prior fraction knowledge? The ‘time’ issue continues to be an issue. Where does reteaching fit into the curriculum? (A question for many math concepts, but we’ll stick to fractions here!)

Teaching Fraction Models in Middle School

I don’t have all the answers, but I have a few ideas. Let’s look at how using models might be able to help. Based on the standards, students should have been using various models before hitting 5th grade – area models, length models, set models, and number lines. Continuing to use these fraction models will only help students connect the concepts with the processes.
​
One way to help students bridge some of the fraction gaps (or just refresh their memories) is to incorporate these visual models as much as possible.

When teaching a new fraction concept (or briefly reviewing concepts from previous years), bring in the fraction models.

For example, when teaching adding or subtracting fractions with unlike denominators (2/3 + 1/6 or 2/3 – 1/6), include a model next to the problem or have students draw models.

On their models, students can add partitions to show both fractions as sixths, encouraging the continued development of equivalent fractions.

The addition and subtraction of fractional parts is visual for middle school students when they use fraction models.

This combination of process and modeling helps students connect the process with the meaning of the operations or simply finding equivalent fractions.

Other Fraction Models

As students get into higher grade levels, the length model is extremely helpful since it’s easy to transfer to a number line.

While you probably don’t want to redraw the lengths and the number line for every new problem, you can create and post some length/number line models around the classroom and provide models students can refer to on a regular basis. This can again reinforce the concept of equivalent fractions, help students with comparing fractions, and transfer to fraction and decimal equivalences.

Length models, aligned with a number line, can also be helpful to reinforce the idea that students can count by unit fractions the same way they can count by whole numbers.

Fraction Toolkit

Do you need a few tools, like the fraction strips, to help your students master the fraction basics? I’ve got a ‘Fraction Toolkit’ for you!

You can grab the Fraction Toolkit and learn how to use it for your classroom needs. 

The post Using Fraction Models to Help Students Understand Fractions appeared first on Cognitive Cardio Math.

End of School Year Activity #1 

​End of School Year Activity #2

​End of School Year Activity #3

​End of School Year Activity #4

​​End of School Year Activity #5

Not ready to use these ideas yet? Pin it to your end of year activities Pinterest board!

The post End of the School Year Activities appeared first on Cognitive Cardio Math.

Welcome to this blog series about teaching fractions in middle school! For the next several weeks, we’ll be looking at various aspects of teaching fractions: basic meanings, fraction models, finding equivalent fractions, comparing fractions, benchmarks, and estimation.

As an upper elementary or middle school math teacher, you may find yourself needing to review some of these fraction concepts before you can move on to the fraction curriculum for your grade level. When this is the case (needing to review fraction concepts that aren’t part of your curriculum), there usually isn’t much time to squeeze in extra instruction…it can be tough!

We realize that some of our middle school kids just don’t ‘get’ fractions, but our time is limited. I’ve got a couple of ideas at the end of the post for how to weave in some of the ‘fraction basics’ in middle school. But first, for this week, we’ll start with some of the foundational fraction vocabulary terms.

Teaching Fractions: Fraction Terms

First up ~ fraction, numerator and denominator. These are the easy ones, right? We might think so, but sometimes students have misunderstandings around these terms. When I looked for definitions of these terms, I found the following:

• Fraction: “a number, written in the form a/b” and “a part of a whole, less than one”
• Numerator: “the top number in a fraction that tells how many parts are being considered” or “the number above the line in a common fraction, showing how many of the parts indicated by the denominator are taken”
• Denominator: “the bottom number that tells how many equal parts in a whole,” “the number below the line in a common fraction,” and “a divisor”

Teaching Fractions to Younger Students

When students learn about fractions in the earlier grades, images like the ones below represent fractions. The numerator is the colored part (or white part), and the denominator is the total number of pieces.

In 3rd grade, if the class follows common core standards, you should also be teaching fractions as numbers on the number line.

Using the number line and the definition of “a number written in the form a/b” helps reinforce the idea that a fraction is a number that represents an amount, just as the number 2 represents two whole things.

Teaching Fractions to Middle School

By middle school, it often seems that the picture with colored/not colored sections is what students remember best. Not the number line. Do you find this too? The number line model is so important when students start learning about decimals on the number line (and it can help them understand equivalent fractions), so if your middle schoolers aren’t familiar with fractions on the number line, I’d recommend making this a big focus.

When students understand that both fractions and decimals can be represented in the same way on the number line, it helps their understanding of the equivalence of decimals and fractions (and later percents). Fractions, decimals, and percents all represent parts of a whole…they’re just written differently.

​We’ll look at fraction models more in depth in a future post.

A few other important terms we’ll explore in the coming weeks:

Equivalent fractions:

• Fractions that have the same value, or represent the same amounts.
• This can be modeled as 2 shapes of the same size, cut into different numbers of pieces.
• This can be modeled as two fractions marked by the same place on a number line (or ruler) that show the same number.

Improper fractions: 

Fractions that represent an amount greater than 1, so the numerator is larger than the denominator (I know improper fractions are now often referred to as ‘fractions greater than one,’ but I think it’s important for students to know and understand this term…..it’s still used in standardized tests at different levels)

Mixed numbers: 

Mixed numbers also represent amounts greater than 1, and are the combination of a whole number and a proper fraction

Unit fractions: 

Unit fractions are fractions with a numerator of one.

Daily Fraction Reinforcement

Middle students often come to us with varied fraction backgrounds. Some students don’t seem to understand what fractions even are. I’ve found that weaving fractions into parts of our math routine helps keep fraction basics fresh. It also helps students be more prepared for when they must use fractions and fraction operations in other math contexts.

A few ideas include:

1) Review fraction vocabulary at the beginning of the year and provide students with a type of reference sheet.
(The fraction doodle page shown here is part of the Fraction Review Toolkit!)
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2) Keep visual representations around the room. For years, I kept a fraction/decimal/percent number line up above my whiteboard. This kept some of the common fractions and their decimal/percent equivalences visible at all times for quick reference. Students definitely used this.
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Visuals of fraction sets, number lines, and partitioned shapes are all helpful.

3) Include fraction basics in spiral review. If the concepts keep popping up when you aren’t ‘teaching’ fractions, students will become more accustomed to seeing them and working with them.

4) If you do Number Talks, include fraction number talks as often as you’re able. These will give students a chance to explore fraction concepts a bit. If you don’t do Number Talks, consider checking them out!

• Quick example: you can do a Number Talk where you ask students to consider whether 3/8 is more or less than ½.

What other suggestions do you have to help middle school math students with the fraction basics?

Fraction Toolkit

Do you need a few tools to help your students master the fraction basics? I’ve got a ‘Fraction Toolkit’ for you!

You can grab the Fraction Toolkit and learn how to use it in this post!

The post Teaching Fractions in Middle School: Reviewing the Basics appeared first on Cognitive Cardio Math.

Using Mini Whiteboards

Cleaning the Mini Whiteboards

The post Using Mini Whiteboards in the Classroom appeared first on Cognitive Cardio Math.

Translating Words to Expressions – Tricky Phrases

Graphic Organizer for Translating Between Words and Math

Translating from Words to Algebraic Expressions

Resources to practice translating words and algebraic expressions:

The post Translating Words into Algebraic Expressions appeared first on Cognitive Cardio Math.