Same Math › Grades 4–5 › Benchmark fractions
What are benchmark fractions?
Benchmark fractions are easy reference points, mainly 0, ½ and 1. Kids compare a fraction to them instead of calculating: 3/8 is a little less than ½, so it's smaller than 5/6.
- 3/8 is just under ½, because half of 8 is 4.
- 7/8 is close to 1, only one eighth away.
- 3/8 < ½ < 7/8
Why schools teach it
Kids compare fractions without common denominators
In 4th grade, kids compare fractions with different denominators, and the standard names two ways: make common denominators, or compare to a benchmark like ½ (4.NF.A.2). Benchmarks are often much faster.
In 5th grade, benchmarks become an estimation check (5.NF.A.2). If 2/5 + 1/2 comes out as 3/7, a child who knows 3/7 is less than ½ can see the answer is wrong.
At the kitchen table
What to say, and what to skip
Say this
Is it more or less than half? How do you know?
What's half of the bottom number?
For 3/8, half of 8 is 4. 3 is less, so 3/8 is less than ½.How far is it from 1?
7/8 is one eighth away from 1.Which is closer to 1: 7/8 or 5/6?
A harder question: one eighth is smaller than one sixth, so 7/8 is closer.
Skip this
- Comparing only the top numbers.3/8 vs 2/3 can't be judged by 3 vs 2. That's the mistake benchmarks prevent.
The bigger the bottom number, the bigger the fraction.
It's the opposite: eighths are smaller pieces than thirds.Just convert them to decimals.
That comes later. Benchmarks build the sense of size first.
See it in action
Comparing 4/9 and 5/8
Compare 4/9 to ½
Half of 9 is 4.5, and 4 is less, so 4/9 < ½Compare 5/8 to ½
Half of 8 is 4, and 5 is more, so 5/8 > ½Put them together
4/9 < 5/8
No common denominators, no calculator. One look at ½ settles it.
Free practice sheet
Make a benchmark fractions sheet
Loading practice sheet…
Fridge cheat sheets
Math Fridge Cheat Sheets
Every K–8 math method in one printable book (159 pages): a cheat sheet page like this guide, plus a practice sheet and its answer key for each, in Classic and handwritten Notebook styles. $9 one time, or all 7 subjects for $29.99. See all prices.
Teacher? This method has a classroom pack on TeachersPayTeachers: an anchor chart, a parent letter and practice sheets with answer keys, $4. See the pack
Parents: tell your child's teacher about this guide
Parents also ask
Which benchmarks do kids use?
Mostly 0, ½ and 1. Some classes add ¼ and ¾ in 5th grade.
What if both fractions are less than ½?
Then the ½ benchmark doesn't decide it. Kids use common denominators or compare distances instead.
Is this the same as rounding?
Similar idea. It's like rounding a fraction to the nearest easy value.
When is this taught?
4th grade for comparing (4.NF.A.2), and 5th grade for estimating answers (5.NF.A.2).