Fly on the Math Teacher's Wall Squashing Fraction Misconceptions

place value too this fourth dimension nosotros are talking nearly squashing fraction misconceptions. One of the biggest misconceptions I had when I kickoff started didactics is that finding a mutual denominator is the entirely way to compare fractions. Boy was I wrong. After reading a groovy didactics book too listening to my students portion their invented strategies, my misconception has been cleared up. Today I am going to portion amongst yous five dissimilar strategies for comparison fractions.

Common Denominators

Yes, yous tin compare fractions amongst mutual denominators. However, this isn't ever the most efficient way of doing things too it involves a lot of steps too a lot of calculation which way at that topographic point is a lot of places where yous tin brand mistakes. The adept intelligence is, it plant every unmarried fourth dimension too sometimes yous simply can't figure out which fraction is larger without it.

Common Numerators

The long lost twin of mutual denominators, finding a mutual numerator is simply similar finding a mutual denominator. However, sometimes the numerators already are the same too sometimes it tin hold upward to a greater extent than efficient to calculate a mutual numerator than a mutual denominator depending on the numbers inwards the problem.

The numerators already match! Use this to aid yous compare the fractions instead of finding a mutual denominator.

Comparing these 2 fractions is tricky because they are real unopen together! Finding a mutual denominator would operate but expect how much easier it is to honour a mutual numerator for this employment because the numerators are much friendlier numbers to operate amongst too then the denominators. Most kids volition forthwith know the LCM of iii too five but I bet they won't know the LCM of 17 too 27!

Comparing to a Benchmark

This is a groovy strategy that tin hold upward real efficient on the correct numbers. If your fractions are around a benchmark publish similar 0. 1/2 or 1, this tin hold upward hence quick too easy!

These 2 fractions are groovy to compare using a benchmark because 1 of them is a chip less than 1 too the other is a chip more.

One of these fractions is a picayune to a greater extent than than 1 one-half too the other is a picayune less than 1 half. This makes them slow to compare using a benchmark!

Draw a Model

Model drawing is hence of import inwards the evolution of fraction understanding. I sure don't desire to move out my 5th graders inwards a house where they demand to depict a model every unmarried fourth dimension they demand to compare fractions but it is an splendid stepping rock too 1 that should non hold upward skipped. When students depict models, they railroad train some large ideas nearly fractions too aid brand a visual model inwards their caput that they tin mention to afterwards if needed. I pass a lot of fourth dimension didactics adept model drawing inwards instant too 3rd grade. There are many ways to depict models, but I similar to focus on using rectangles because they are slow to sectionalization too if yous sectionalization them all inwards 1 direction, it is a quick jump from a rectangle model to using a publish line.

The further apart 2 fractions are, the to a greater extent than reliable model drawing tin be. When the fractions acquire real unopen together, modest model drawing inefficiencies tin Pb to students getting the incorrect answer or terminal that the fractions are equal when they are now. The pupil who tin purpose a rectangular model similar this 1 is simply 1 pace away from actually agreement publish lines.

This pupil used a publish employment to compare these fractions. Notice that if the fractions were actually unopen together, this model drawing powerfulness non work. It also takes some fourth dimension to gear upward too depict accurately. Partitioning into equal pieces is definitely a conversation to possess got amongst students every bit yous operate on model drawing. I innovate the publish employment model inwards degree 3.

Unit Fraction Reasoning

Unit fraction reasoning is oft 1 of the kickoff strategies to develop. It starts inwards first grade when yous are partitioning rectangles into halves too quarters too a pupil notices that 1 one-half is bigger than 1 quarter. It develops from at that topographic point too every bit kids acquire to a greater extent than comfortable amongst using unit of measurement fractions it tin Pb to some groovy ideas when comparison fractions.

This pupil used the fact that each of these fractions is missing a pieces that is a unit of measurement fraction to aid him figure out which fraction was bigger. Don't permit the writing fool yous nearly the sum of fourth dimension the pupil took to figure this out. He simply looked at them too knew each was missing 1 slice too the 1 missing the smaller pieces would hold upward the bigger fraction. The writing was done during the sharing of strategies too is an endeavour to capture his thinking for the other kids to see.

If yous desire to encounter what strategies your students possess got for comparison fractions, here is a quick picayune worksheet that volition plough over yous an persuasion of some of the strategies your students have. The numbers were chosen strategically to illicit a hit of strategies.

Ready to larn to a greater extent than nearly squashing misconceptions? Head on over to Beyond Traditional Math to read to a greater extent than nearly the importance of the whole!