If your child is struggling with fractions, they are not alone. Far from it, in fact. Studies have shown that about 1/3 of the students in the United States don't make much progress on fractions between 4th grade, when they are really introduced, and 6th grade, when students are expected to master fraction operations. In my personal experience, 5th and 6th graders will often tell you that fractions are by far the most difficult part of the math curriculum.
So, what makes fractions so difficult?
Fractions work very differently than whole numbers and decimals. This is because our entire number system is built around tens. All of the processes for adding, subtracting, multiplying, and dividing are consistent between whole numbers and decimals, because they all use the same number system. This system is called base 10, because each digit has ten times more value than the digit to the right. Many students never really think about this system, because it is just how numbers work.
Fractions don't work this way. 2/3 works like a number in base 3. 1/8 works like base 8. 2/7 works like base 7. We can't just add these numbers together because they have different bases. They don't play by the same rules. This is totally different than anything students have experienced with other numbers.
This means that the standard processes, called algorithms, for fraction operations seem really random. Why do you multiply the numerators and denominators to multiply two fractions, but for addition and subtraction you have to find common denominators? Why on earth do you invert the divisor when dividing fractions? These algorithms are all completely different than they are for whole numbers. It takes a lot of work to understand where these algorithms come from, and why they do make sense. This leads teachers to a lot of short cuts "Don't ask questions, don't ask why, just invert and multiply" might help students survive a math test, but it isn't likely to give them much understanding.
Curriculum writers also seem to consistently underestimate these challenges. In particular, they tend to underestimate the huge conceptual leaps between the fourth grade and fifth grade fractions standards. Let's look at addition. Fourth graders are expected to add fractions with like denominators. Here's an example, 1/5 + 3/5 = 4/5. All students need to do is add the numerators. It is one simple step. In fifth grade, students need to add fractions with unlike denominators. Here's an example, 1/3 + 3/5 = 14/15. This is a five-step problem.
Figure out that 15 is a possible common denominator.
Convert 1/3 to 5/15 by multiplying both the numerator and denominator by 5.
Convert 3/5 to 9/15 by multiplying both the numerator and denominator by 3.
Adding 5/15 and 9/15 by adding the numerators to get 14/15.
Determine whether or not 14/15 can be further reduced.
Of these 5 steps, all but step 4 are brand-new skills. Unfortunately, some math programs devote the same number of lessons to adding fractions with like denominators and adding fractions with unlike denominators. This simply does not give students the time and exposure they need to truly understand.
So, what can we do?
Many students need additional support to master fractions. First of all, an experienced tutor can assess students and identify which specific skills students need practice with. Sometimes a student struggling with fractions may even be missing a prerequisite skill, like factors and multiples. Once the skill gap is accurately identified, students need opportunities to practice each skill in isolation. Only then can these skills be combined to successfully complete fraction operations. A skilled tutor can go beyond the textbook to make fractions click for your child.
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