Estimating fractions can be a challenge for many students, especially those who don’t have a good grasp of number sense. Before you teach students how to estimate fractions, there are some essential skills that need to be taught systematically. Here are the lessons in order that you will need to teach.
Identify what fraction the number line shows
It boggles my mind when students in my 5th-grade classroom can’t identify fractions on a number line. This is a 4th-grade skill that students should know, but of course, as a teacher, I know that students come to me not knowing a lot of what they “should” have learned in 4th.
Many times students just aren’t developmentally ready so they need to be explicitly taught how to identify a fraction on a number line. Ask your students to count the number of tick marks so they know what the denominator of the fraction will be.
Address Fractions on a Number Line Misconceptions
A common misconception is that students will count the first line as 1, when it is actually zero. Explicitly teach this to your students.
This is also a good time to teach them what a unit fraction is. A unit fraction is any fraction that has 1 as the numerator. If you use the correct vocabulary, they will too!
Label a number line with mixed numbers to estimate
Before your students label mixed numbers, they need to know that there are numbers between whole numbers which are called mixed fractions. Just like identifying a fraction on a number line, they must count the number of tick marks on the number line.
Students should do this using their pencil or finger. This is really helpful for your students who need tactile support. Stick with mixed numbers between 1-9 when first teaching students how to label with mixed numbers. No need to overload the brain with large numbers.
Practice Labeling a Number Line
Your students should first practice labeling a number line already drawn out before they create their own number lines from scratch. Using a small ruler or protractor helps draw out straight lines.
I don’t recommend graph paper because they will want to use the blue lines already on the paper. Odds are, the graph paper will not correspond to the fraction they have to create.
Create a Number Line
Knowing how to draw a fraction number line is a skill that can’t be skipped. If your students are drawing 3 1/4, they need to know that they only draw 3 tick marks in between the 3 and 4 to make fourths. Then they put a large dot on 3 1/4. Again, teach this explicitly.
Once your students have practiced the above skills, they are ready to estimate mixed numbers. I simply ask “What whole number is the dot closest to?” (I eventually move on to more sophisticated questioning using the words “estimate” and “round”. )
Explicitly teach your students that anything above 1/2 rounds up, and anything below 1/2, rounds down.
Estimate using benchmark fractions 0, 1/2, 1
Once your students are able to estimate mixed numbers, they need to learn how to use benchmark fractions for estimating. First, teach your students what a benchmark fraction is. It’s 0, 1/2, and 1. How is zero a benchmark fraction? It is because it is 0/0.
Benchmark fractions are something we do naturally in our heads. If you are at the grocery store and you buy 2 and 3/4 of a pound of peaches, that’s about 3 pounds. That word “about” is something we use often when we are discussing estimation.
Estimate Sums and differences
For your striving students, estimating sums or differences requires a few steps. First, they will need to estimate each fraction that is being added or subtracted. Then they need to add or subtract them.
Doesn’t sound too hard, right? Well, for some of your students, it will be. If your striving kiddos are having a hard time, ask them to imagine the number line.
Or you can draw out the fractions or mixed numbers by labeling them with a dot and ask, “What mixed number or fraction is the dot closest to?”
If your students are struggling with this concept, either have them work with a partner or limit the number of problems you give them. This is the finish line of the Estimating Fractions marathon and is usually the last skill that is taught in the adding and subtracting fractions unit. If you need an engaging digital resource to teach and practice estimating benchmark fractions, check out my resource HERE.
Final Thoughts
My hope is that I have helped you with the pedagogy of teaching estimating fractions. With practice, your students will be able to do this skill quickly and efficiently.
Remember that all kids are developmentally different, so don’t sweat it if they aren’t getting it. Keep trying and revisit the skill later in the year. You got this! Giselle