Arrange the numbers in order from smallest to largest:

0, 1, ½, 17/18. 5/9, 6/17

Many kids, even high school students, would say that the fractions come before zero. These kids would not be prepared for success at the algebra level, where they are expected to know multiplication facts and fractions. This should concern parents who want their kids to excel and achieve success academically, because algebra is the bridge to higher level math. Students who complete high school algebra are twice as likely to graduate from college, and significantly have more chances to earn higher earnings from employment. (What to Do about Canada’s Declining Math Scores – Anna Stokke).

**Number Sense**

Kids who answer that all the fractions above are below zero are lacking the ability to appreciate the **size** and **scale** of numbers. Size establishes magnitude, and scale establishes relationship. Number sense doesn’t happen overnight, it requires encounter and interaction with math concepts and skills learned in a way that make sense to them.

Compare these two explanations about proper fractions (such as ¼, 3/7).

- Proper fractions are fractions between 0 and 1.
- Proper fractions are fractions in which the numerators are less than the denominators.

Which one do you think is a better way to grow a child’s number sense i.e., the ability to appreciate the size and the scale of numbers? If you pick #1, that’s a better way in the long run. Ironically, explanation #2 circulates widely in the internet, even by merriam-webster and math tutor programs; it is not an incorrect statement, but it should follow as an additional explanation to #1, not a definition on its own.

Before mastering division, multiplication and other more complex fractional operations and algorithms, a student should have a sense of the magnitude of a fractional number and the relations between fractions. Ordering fractions is one way to learn about this.

**Comparing to One-Half ( ½ )**

Back to our math problem above, how do we solve this? First step is to identify which one is the smallest and the largest.

Since the numbers are 0 and 1 and the fractions are in between, we know that the smallest is 0, the largest is 1, and ½ is exactly in the middle.

Now let’s make ½ as the benchmark number, and compare the rest of the fractions to ½ .

Not only is 17/18 way larger than half, but its missing part is only 1/18 - or it’s almost 18/18 (one).

Based on this, now we can order from smallest to largest:

If the numbers are so close in value, that’s when we need to rename them using common denominators.

**Don’t underestimate the importance of Fractions**

Fractions are foundational to many advanced areas of math and science like chemistry and physics. Fifth graders’ fraction knowledge predicts high school students’ algebra learning and overall math achievement. Most white collar, blue collar and service workers also use fractions in their work. (Fractions: Where It All Goes Wrong – Robert S. Siegler).

So, let’s prepare our child to be successful in algebra and beyond – by mastering multiplications and fractions!

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