What Do You Already Know About Fractions
What is it about fractions? It seems like every math teacher wants to know how to teach fractions more finer. And few topics create more than anxiety and frustration for teachers, students, and even parents.
Most standards and textbooks introduce fractions in tertiary grade. Simply many students nonetheless struggle with them throughout middle and high school.
What can y'all practice when younger students become confused? And how can you help older students learn the basics, without falling behind on grade level content?
The good news is that anyone can learn how to teach fractions. All it takes is identifying the nearly common misconceptions. And using a few simple strategies that tin can give your students a solid foundation in fraction concepts.
Learning How to Teach Fractions is Challenging, but Essential
Fractions are confusing considering they don't expect or act like nearly of the numbers nosotros're used to.
The idea that at that place are numbers betwixt 0 and 1 is tough for students. It challenges their understanding of what a number is.
They start define numbers as counting numbers. They can indicate to a group of objects and count upwards one-by-one. Next, they acquire base-10, which allows them to organize numbers into tens, so they can count large quantities.
Then fractions come up along and throw a wrench into the works. It's no longer most counting, or making tens. Suddenly, a whole tin be split up into halves, fifths, or even thirty-sevenths.
On meridian of the conceptual challenges, fractions look and act a bit odd. Are they i number, or two? Why does a bigger denominator make a fraction smaller? Why practise I flip the second fraction to divide?
Given these challenges, information technology can be tempting to avoid fractions completely. Merely it's important that teachers at all class levels understand how to teach fractions. Especially when students arrive in their grade without the foundations.
Students who don't larn the fundamentals continue to struggle throughout their math educational activity. Whenever they come up across topics like ratios, gradient, and algebraic expressions, the old problems resurface.
Fractions in the Real Earth
Besides their abundance in schools, fractions environment us in the real world.
When nosotros're trying to swallow good for you, nosotros may only get for half of a cookie. Our almost popular coin (in the Usa) is worth ane/four of a dollar.
US customary units are designed for fractions. Gallons are divided into iv "quarts," and feet are made upwards of 12 inches.
While many people prefer the simplicity of the metric organization'south adherence to groups of x, there are benefits to standard units. Groups of ten can only exist divided by 2 or 5. But 12 can be split evenly into groups of two, 3, 4, or six. This flexibility comes in handy in carpentry, cooking, and many other areas.
Their unique ability to split up a whole into any number of pieces you wish is what makes fractions so special. But it'southward also what tin can make them challenging. Those who sympathise fractions may not fifty-fifty discover them. Just to the fractionally-impaired, they can be a constant nuisance.
At one point, the A&Due west fast food chain introduced a ⅓ pound burger to compete with the quarter pounder. But they discontinued it when they realized customers thought ⅓ pound was less than ¼ pound.
Fractions Provide a Foundation for Avant-garde Math
Many students are eager to put fractions in the rear view mirror after form school. And nigh heart and loftier school teachers are just every bit happy to avert the topic. Only understanding fractions is essential to success in college math.
I in one case tutored an 8th grade student who was having trouble in Algebra I. Nosotros reviewed the tests she had failed, and I noticed that all her mistakes had ane thing in mutual: fractions.
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I asked a few questions, and realized she had no idea what the numerator and denominator meant. She had learned tricks to add, subtract, multiply, and divide fractions. Just she had never learned (or had forgotten) the underlying concepts. In her mind, information technology was all well-nigh randomly moving numbers around the page.
This meant she didn't understand what it meant for a line to have a slope of ¾. She couldn't simplify rational expressions with inverse operations — because she didn't connect fractions to division. And she didn't empathize how ratios, rates, and percentages worked.
She could utilise algorithms if the problem was straightforward. Simply she was lost when attempting word problems or any problem with multiple steps.
How to Teach Fractions: Three Critical Concepts
It might seem that knowing how to teach fractions requires years of experience pedagogy math. Or that you demand fancy software and expensive curriculum.
The truth is that understanding fractions is pretty simple. It all comes down to three concepts: numerators, denominators, and fraction notation.
Of course, in that location is more to know about fractions than this. But these concepts provide the foundation. Once students have mastered these nuts, they realize that fractions aren't magic. They're just numbers.
And so, they tin apply everything they already know near numbers and operations to working with fractions.
Bottoms Up: Starting time with the Denominator
Knowing how to teach fractions ways targeting the first place students get stuck: the denominator.
Put yourself in their place. When they first come across fractions, our students already use numbers to count, measure, and compare. So information technology simply doesn't make sense that 37/100 could be smaller than ⅔. Or that ⅓ is bigger than one/10.
A denominator is unlike any number they've learned before. A denominator isn't for counting "what we have," but for telling united states of america "what we're counting."
Imagine a colleague tells you lot, "I left iii in your room." That doesn't mean much unless they respond the question, "three of what?" Iii candy bars in your room is great. Iii lions – oh no!
That's the importance of the denominator. The numerator tells us how many pieces we accept. Simply it doesn't hateful much until we know how large each piece is.
1st and 2nd class geometry standards introduce students to the concept of cutting a whole into equal parts. Standard ane.G.A.iii has students "Partition circles and rectangles into two and four equal shares" and depict the parts as halves, fourths, and quarters. In 2nd grade, 2.1000.A.2-iii extend this understanding to include thirds and rectangles.
Neither of these are focus standards —common core describes them every bit "additional standards," meaning they are less of import at that grade level. As a result, many 3rd graders are introduced to fraction notation without the right foundations.
Next Upward: The Numerator
In one case students empathise denominators, understanding the numerator is a breeze. Numerators work just like any other counting numbers.
In 3rd form, the domain, Number as Fractions (NF) appears in the standards. And it'due south assumed that students already sympathize the essence of fractions – cutting a whole into equal parts.
The first standard in this domain, 3.NF.A.ane, starts with "unit fractions." Unit of measurement fractions are those with a numerator of one, such as ½, ⅓, ¼. It then goes on to address fractions with numerators other than 1, such equally ⅔, ⅗ and so on.
Putting it Together: Fraction Notation
The concluding step in how to teach fractions is the annotation. This is the idea that a fraction is a single number, made upwardly of a numerator, a denominator, and a line in-betwixt them.
When students get to third class, they are introduced to fraction notation, often without the foundational concepts. The standards and textbooks assume they've already mastered sectionalization in 1st and 2d grades.
And past 3rd grade, fractions are a focus standard. Simply third grade teachers don't ordinarily accept the 1st and second grade teaching materials. And since the foundations for fractions come from theGeometry domain, many teachers don't realize that fractions are continued to the geometry standards.
(That's why the coherence map from Achieve the Core is such a useful tool. When you map a standard, it shows y'all how each standard relates to prior and following grade levels).
This disconnect explains why and so many students struggle to empathize fractions twelvemonth after yr, to understand fractions.
Aye, they may forget the terms numeratoranddenominator. But the vocabulary isn't the real problem. When students keep making the aforementioned mistakes comparing fractions, simplifying them, or performing operations, check for concepts.You'd be amazed to larn how many middle school students will incorrectly cut a circle into three equal parts.
So make sure your students empathise the denominator cuts a whole into equal parts. And a numerator counts those parts.
So, it'due south simply a thing of writing one on top of the other, with a line in the heart.
How to Teach Fractions: Four Classroom-Tested Strategies
I pretty much relied on trial and mistake equally I learned how to teach fractions. Eventually, I figured out what works. And more than chiefly, what doesn't work.
Similar almost teachers, I started by teaching the style I was taught: by focusing on algorithms and "tricks." Observe a mutual denominator. Multiply across. Go along change flip.
Only at the stop of the day, I was just teaching students to get answers. Answer-getting is what non-mathematicians retrieve math is for. Mathematicians know that math is a language. A thing of beauty. A lens that gives u.s. a deeper agreement of the globe effectually united states of america.
And keep-change-flip….that'due south not whatsoever of those things.
Sure, tricks take their place. Once students understand the concepts, they tin can understand how the tricks work. That allows them to use the tricks appropriately.
But when we skip the conceptual agreement, tricks become counterproductive. Students acquire that math is an arbitrary set up of rules. Something that only "math people" empathise.
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Students who only know the tricks don't cheque their answers. They don't prove their piece of work. They make random guesses. And they utilize the wrong play a trick on at the wrong time. And when they could really use the tricks to solve a word problem or simplify an expression…they don't even realize information technology.
And so if you lot but want your students to become answers. And to forget nigh of what they learn a calendar week later, then stick to tricks.
Just if yous want to know how to teach fractions the right fashion, endeavour these classroom-tested strategies.
Strategy #1: Appraise the Foundations
Like any math standard, fractions don't exist in isolation. Understanding fractions helps with whatever number of advanced math concepts. But it requires certain foundations in numbers and operations. Before introducing fractions, bear formative assessments of these ii concepts.
Offset is the meaning of division. And since sectionalisation is the undoing of multiplication, they should sympathise the meanings of multiplication equally well.
They should be able to show y'all how half dozen divided by 3 can be represented two means. Every bit 6 objects split up into iii groups, with two objects in each. Or dividing six objects into groups of iii.
Once they sympathize how to split groups of objects into equal-sized groups, the next step is to split a whole into equal parts. If students sympathize the meaning of sectionalization, and can employ it to cutting shapes into equal parts, they should be ready for numerators and denominators.
Strategy #2: Concepts Earlier Tricks
Zip will curt-circuit conceptual learning faster than teaching algorithms too early on.
Sometimes, we don't have any option nigh how to teach fractions. You can ship students dwelling with a great conceptual activity for dividing fractions, but to have a parent teach them to proceed-change-flip.
But too often, students are learning these tricks at school. And before they develop conceptual foundations.
I heard a corking saying recently: "Shortcuts save locals time, and go out-of-towners lost."
Nowhere is this truer than in math grade. Once students have the concepts, they can learn how algorithms work and apply tricks effectively.
But teach them too soon, and students get lost. And in one case they're fixated on respond-getting, it's hard to convince them to take the "scenic road."
Strategy #iii: Apply Visual Models and Manipulatives
Visual models and manipulatives are one of the most effective ways to teach whatever math concept.
And they act equally great assessments too. Inquire your students to draw visual models. Y'all'll see why one of my favorite maxims of math class is, "If yous tin't draw it, you don't get information technology."
Visual models are especially effective for teaching fractions. Since fractions piece of work differently from more than familiar numbers, visual and physical models clear upward many misconceptions.
I use google slides with digital manipulatives to introduce fraction basics, multiplying fractions, and any number of fraction concepts.
I besides cover fraction visual models in-depth in both my elementary visual models workshop, and my middle school visual models workshops.
Strategy #4: Expressions and Equations
Visual models and manipulatives are probably the near effective way to introduce fraction concepts.
But one time they are strong in the foundations, students should likewise larn how to use fractions in expressions and equations. This helps students think more flexibly about fractions and deepen their abstract thinking.
A fun way to innovate students to expressions and equations is through number sentence proofs. In this action, students don't just find answers. They determine whether an equation is true or false, and and then prove information technology. Use this downloadable Google Slides action to innovate fraction number proofs to your students.
Y'all can also participate in an online workshop on designing and teaching number proofs, expressions and equations: Cull Expressions and Equations in Elementary or Expressions and Equations in Middle School.
What's Next in Learning How to Teach Fractions?
I promise this post has given you some fresh ideas for how to teach fractions. And for agreement why students struggle with fractions.
At that place is a lot to consider, and it'due south important non to get overwhelmed. Your students may be on the verge of mastering fractions. Or you may first need to dorsum and review concepts from several grade levels.
Your job isn't to ensure that all your students chief fractions right away. If one idea from this article changes how you lot teach fractions, yous've achieved something.
If you'd like to take your math teaching to the adjacent level, I'd love to come across you at ane of my upcoming online workshops for educators. These are not video recordings – each session is conducted in real fourth dimension, with a live facilitator. And they include a wealth of classroom resource that will help yous put your learning into practice.
For even more support, connect one-on-1 with one of our experienced instructional coaches. We'll help yous identify your strengths and areas for growth. And assist yous plan lessons that keep your students actively engaged and moving forward. Whether you're teaching in-person or online.
Finally, you can sign up for our free Facebook group, the Reflective Teachers Community. There, you can enquire questions and share ideas with fellow innovative and enthusiastic educators.
If yous'd like to bring interactive fractions lessons to your students right away, bank check out our Fraction Essentials Parcel. It includes everything you need (eBook, printable classroom activities, and interactive Google Slides) to make fractions make sense.
Get Your Re-create of FRACTION ESSENTIALS
Nigh the Author
Jeff Lisciandrello is the founder of Room to Find and an educational activity consultant specializing in student-centered learning. His 3-Bridges Design for Learning helps schools explore innovative practices within traditional settings. He enjoys helping educators embrace inquiry-based and personalized approaches to educational activity. You tin connect with him via Twitter @EdTechJeff
Source: https://roomtodiscover.com/how-to-teach-fractions-concepts-not-tricks/
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