Thoughts On Instruction Fractions

Fraction misconceptions - MathsPad

Yuvraj (@YuviLite) asked me to write a post nearly teaching fraction addition. I similar a challenge! Fractions are notoriously hard to teach, riddled amongst misconceptions together with crucial to acquire right. If I were to endure thorough on this topic, I’d demand to create a hell of a lot of research together with write a dissertation length weblog post.

I for certain haven't been that rigorous, but I convey establish a few ideas. First read what Yuvraj has written nearly difficulties inwards teaching fractions, thence convey a expect at my ideas at the end.


When I listen students utter the phrase, ‘uh no non fractions’ a minor vocalization buried deep inwards my subconscious feels the same thing. Fractions is 1 of those topics which seems to endure on the system of function for EVERY twelvemonth together with yet in that place are nevertheless thence many students who are befuddled past times them together with this is 1 of the reasons I convey been thinking nearly how I learn the topic.

I am a instructor who believes inwards developing agreement together with non exactly only reducing mathematics to a serial of procedures. I convey ever thought this together with it was drummed into me on my PGCE together with Masters. Yet fractions has brought me to a crossroads. Before I tell you lot why, allow us expect at dissimilar strategies of teaching the add-on together with subtraction of fractions. 

The Cross Multiplying (Butterfly Method). This is the 1 I was taught at school. I had no agreement of why it worked but it got me the correct respond together with at that historic current that is all I cared about. To add together 2 thirds together with 3 quarters nosotros would multiply the denominators together thence cross multiply the numerators and denominators as shown below.

The Grid Method. I of late discovered this choice procedural method. Draw a grid equally shown below. The kickoff fraction is written on the overstep together with the minute along the side. A plus sign is set inwards the kickoff box equally this is the functioning nosotros desire to behave out. We set the products of the other numbers into the grid. We thence depict around the highlighted boxes together with this would give us our numerator, inwards this instance 8 + ix = 17. The white box would endure our denominator.

Fraction Strips. In NixTheTricks, the purpose of fractions strips is advocated to learn the add-on together with subtraction of fractions. For illustration to add together a one-half together with a quarter we would start amongst visual representations equally shown below.

When nosotros set the one-half together with quarter together nosotros can't limited this equally a unmarried fraction without cutting the pieces into equal parts (quarters inwards this case). The thought hither is that the agreement of a mutual denominator is built upward together with linked to the method for adding fractions.

Paper Folding. This method is from Mike Ollerton’s first-class ‘Getting The Buggers To Add Up’ - read the explanation here (or purchase the book!). 

Fraction Wall. I convey also seen teachers purpose fraction walls to aid students equally a method of identifying equivalent fractions. Some people purpose this or shapes to acquire the thought of equivalent fractions across.

My Dilemma
I convey ever gone downwards the conceptual route. I convey championed the conceptual route, until I got to algebraic fractions. The conceptual route ever seems to Pb dorsum to the to a greater extent than procedural route, especially for fractions where the denominators are 2 dissimilar prime numbers, together with for algebraic fractions. If students are to a greater extent than used to the procedural route, they should inwards theory endure able to able this physical care for for algebraic fractions.

Which has led me to question: is it worth the hurting of rewiring students who ever seemed to convey heard of the cross multiplication method fifty-fifty earlier they convey reached me (even the Year 7s)? I convey spent many hours struggling amongst folding bits of newspaper together with sharing cakes to embed the thought of equivalent fractions. 

Is it plenty exactly to explicate why the cross multiplication or grid method plant together with thence ensure fluency inwards the skill?


Thanks Yuvraj. I wonder the same thing. In many topics nosotros combat to notice the correct residuum of conceptual agreement vs procedural methods. Us pitiful maths teachers are forever fretting nearly it.

My preferred procedural method, for both numerical together with algebraic fractions, is the no-frills version (find the lowest mutual multiple of the 2 denominators, thence convert both fractions to equivalent fractions amongst that denominator, thence add together the numerators). It plant for me, but I learn high powerfulness pupils thence I convey a relatively slow life.

Now for a few teaching ideas. I’m non trying to solve the world’s fraction problems, but I promise you lot may notice some interesting activities hither for your fractions lessons.

Don Steward is a Genius
subtracting fractions activity inwards which students expect at the diagram below together with figure out what's going on. As Mr Steward says, this gives the instructor fourth dimension to drinkable their tea! It's a genuinely clear means to explicate fraction subtraction using mutual denominators.

Misconceptions together with Assessment
This blog has some bright ideas for identifying fraction misconceptions which powerfulness endure especially helpful when you lot start tackling fractions amongst a Year vii class. For example, the author asked his students to explicate what's incorrect inwards each of the 3 pictures below together with got some interesting responses.

You could thence inquire students to purpose the same shapes together with notice an accurate means to correspond the fractions indicated. Other ideas inwards this weblog include bespeak the students to consummate the sentences 'Fractions are...', 'When you lot add together 2 fractions you lot convey to...' together with 'You purpose fractions when you...'. Or fifty-fifty inquire pupils to write downwards 'Everything I Know nearly Fractions' together with write a listing of what they'd similar to learn. These activities volition aid you lot create upward one's heed your starting dot inwards Year 7. The blog is good worth a read.

Manipulatives together with Visual Aids
Yuvraj already touched on visual aids. I recollect beingness told during my PGCE that I only must purpose Cuisenaire Rods, but non genuinely having a clue what to create amongst them. There's whole books written nearly this! I establish explanations here together with here - the method seems rather overcomplicated. But if they appeal to you, thence Nrich provides this online tool for demonstrating Cuisenaire Rods on the Interactive Whiteboard.

This website has a lot of proficient materials on fractions together with visual aids, including downloadable fraction circles.

‘Number 1 inwards disguise’
Look at the 'NOID' poster below. Yes, it is quite ridiculous. But it’s really slow to follow the thinking hither together with I wonder if this explanation (or similar) would aid prepare students' understanding. If you’re looking something a trivial less NOIDy for teaching improper fractions thence this weblog post has some first-class ideas using manipulatives.

From cindywhitebcms.blogspot.com

Division
'Ours is non to argue why, ours is but to inverse together with multiply'. This made me express joy because I've never attempted to explicate fraction sectionalization to my pupils beyond the 'KFC' dominion (keep, flip, change). Don Steward has written an first-class post nearly ways to explicate why it plant - this one from moveitmaththesource.com especially appealed to me. I'll leave of absence along this inwards my dorsum steal inwards instance ever asked the question.

Final thoughts
I'm afraid I don't convey the respond to how best to prepare conceptual understanding, but in that place may endure some ideas hither that you lot haven't seen before. In price of resources, there's tonnes of worksheets, games together with activities online - run into my resources library for some recommendations. For to a greater extent than teaching ideas, here's some farther reading:

• The Guardian's 'How to learn fractions' 
• Bruno Reddy's 'With Fractions, Common-Core Training Goes Beyond 'Invert together with Multiply''
• James Tanton's 'Troublesome Fractions'.

Thank you lot thence much to Yuvraj for his helpful input to this post. Comments together with tweets would endure much appreciated - we'd beloved to listen your ideas.

Fraction hopscotch inwards the maths corridor - from cisdmathmusings.blogspot.com