comparing fractions benchmarks worksheet

$comparing fractions benchmarks worksheet$

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Comparing Fractions Worksheets

Our printable comparing fractions worksheets for grade 3 and grade 4 help children compare like fractions, unlike fractions, and mixed numbers with nuance and range. Shepherd kids through a plethora of number line diagrams, bar models, pie models, shapes, and reams of practice exercises. Let them refresh their knowledge of fraction equivalence and benchmark fractions so they never feel out of it comparing fractions with same and different numerators. Keep your eyes open for our free fraction comparison worksheets!

$comparing fractions benchmarks worksheet$

Comparing Fractions Using Number Lines

If it's fraction comparison, think of number line models! For few other tools are more effective. Locate the given pairs of fractions and mixed numbers on the model and compare their values based on the position.

$comparing fractions benchmarks worksheet$

Comparing Fractions - Pie Models

Use this set of pdf comparing fractions worksheets featuring pie models to reason out the size of fractions. Identify the fractions described by the model and compare them using the <, >, and = symbols.

$comparing fractions benchmarks worksheet$

Comparing Fractions - Bar Models

Bar models are partitioned into several equal parts; a few of them are shaded, too. Let 3rd grade and 4th grade children recognize the fractions represented by the model and then compare their values.

$comparing fractions benchmarks worksheet$

Comparing Fractions - Shapes

Split into equal parts, each shape in these printable comparing fractions worksheets represents a fraction. Figure out the two fractions and determine if one is less than, greater than, or equal to the other.

$comparing fractions benchmarks worksheet$

Comparing Proper Fractions with Same Denominator

These comparing like fractions worksheets help grade 3 kids get an excellent grasp of the concept. All they need to do is compare the numerators and plug in the appropriate sign in between.

$comparing fractions benchmarks worksheet$

Comparing Improper Fractions with Same Denominator

Presenting pairs of improper like fractions for comparison, these worksheets require observing the numerators, too. Find out which numerator is greater and fill in the comparison signs accordingly.

$comparing fractions benchmarks worksheet$

Comparing Proper Fractions with Different Denominator

Our comparing unlike fractions pdf worksheets are a notch above the rest in this series! The fraction comparison is done by generating equivalent like fractions and comparing the resulting numerators.

$comparing fractions benchmarks worksheet$

Comparing Improper Fractions with Different Denominator

Only when two fractions refer to the same whole are comparisons valid. Let children of grade 4 hammer this home to create fractions with common denominators first before moving on to comparing them.

$comparing fractions benchmarks worksheet$

Comparing Fractions - MCQ

Included here are objective type questions on identifying the fraction as (not) less than, (not) greater than, and (not) equal to another fraction. Perform mixed number comparison to answer a few questions!

$comparing fractions benchmarks worksheet$

Comparing Mixed Numbers Worksheets

Delve into our printable comparing mixed numbers worksheets and become well-versed in comparing a pair of mixed numbers using <, >, and = symbols and also, determining the greatest or smallest mixed number from a set.

(12 Worksheets)

Related Worksheets

» Ordering Fractions

» Converting between Improper Fractions and Mixed Numbers

» Estimating Fractions

» Equivalent Fractions

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Alyssa Teaches

an Upper Elementary Blog

Using Benchmark Fractions to Compare Fractions

$These tips and activities make it easy to get started teaching students to use benchmark fractions!$

Ever hear groans when you start a fraction unit? I sure have. And I totally get it. Fractions can be hard! But with the right strategies and resources, they’re much easier for kids to understand. When teaching elementary students to compare fractions, one of my favorite strategies to use is benchmark fractions.

What Are Benchmark Fractions?

So first, what are we talking about? Benchmark fractions are common fractions that we compare other fractions to . They are simple fractions that students are familiar with. They’re helpful to use when comparing and ordering fractions that are harder to visualize, like 8/11, because they can help us estimate. For that reason, they’re also useful when teaching students how to estimate sums and differences of fractions.

Generally speaking, benchmark fractions are 0, 1/2, and 1 . These are the numbers I’ve used with 4th grade students. With 5th graders, I might use 0, 1/4, 1/2, 3/4, and 1.

$An anchor chart like this one is a great way to show students a benchmark fractions definition and examples.$

Why Teach Benchmark Fractions?

Let’s pretend we need to compare 2/12 and 6/7.

It looks tricky at first, right? If we solve this problem the long way, we have to calculate the lowest common denominator, multiply both fractions so they have the same denominator, and then compare them.

It’s much faster and easier if we instead compare these fractions using the benchmarks of 0, 1/2, and 1.

By using these familiar and simpler fractions, students have an easier time doing the computation we’re asking them to do. This strategy helps them develop their fraction number sense and mental math skills.

Benchmark Fractions Activities

A simple way to kick off a lesson on benchmark fractions is to show students a picture like the one below and ask questions like, “Which donut is approximately half-eaten? Which donut is nearly whole, and which one is almost gone?” This example helps students see that we actually use benchmarks in real life!

$I like to start a benchmark fractions lesson with a real-world visual example.$

Start with Visuals and Fraction Manipulatives

To start, I recommend modeling problems using a number line and manipulatives like fraction circles and fraction tiles . These visuals help to make benchmark fractions more concrete as you’re introducing this skill.

I like to begin by comparing fractions to 0 and 1. This is a little easier for students. For example, I might show fractions like 1/9 and 10/12 and ask students whether they’re closer to 0 or to 1.

After some practice, we can tackle comparing fractions to one half, again using number lines and manipulatives.

After students have this down, we can move to comparing fractions to each other by comparing both of them to the benchmarks.

$Students can compare fractions by using benchmark fractions. This strategy is great to develop fraction number sense.$

When comparing 4/10 and 6/7, students can use the benchmarks of 1/2 and 1. Since 1 is larger than 1/2, students can estimate that 6/7 is larger than 4/10.

Benchmark Fractions with Mental Math

The next step is to try this strategy without visual aids. You’ll want to have already taught equivalent fractions before starting this.

It’s fairly easy for students to compare fractions to 0 and 1 by comparing the numerator to the denominator. Comparing fractions to 1/2 requires a little more mental math. I ask students to look at the denominator of the fraction and determine what fraction (using that denominator) would be equivalent to 1/2. A simple way to do this is to just divide the denominator by 2.

For example, let’s use the fraction 4/10. 5/10 is equivalent to 1/2. So if we have a fraction with 10 as the denominator, we know that 5/10 is exactly half. When we compare 4/10 to 5/10, we see it’s only 1/10 away. It’s much closer to 5/10, or 1/2, than it is to 0 or 1.

$comparing fractions benchmarks worksheet$

Students definitely need repeated practice with this! It’s harder with odd-numbered denominators, so I recommend starting with even denominators of 12 or less.

In our earlier example of 3/11 and 6/7, 3/11 is closer to 0 and 6/7 is closer to 1. 0 <1, so we know that 3/11 < 6/7. If you choose to also use 1/4 and 3/4 as benchmarks, that can help students reach a more specific answer.

Benchmark Fraction Resources

A sorting activity is a great way to assess if students are grasping this skill.

$A benchmark fractions sorting activity is a great way to practice these skills with your 4th and 5th graders.$

Be sure to grab these free benchmark fractions worksheets and anchor chart !

$comparing fractions benchmarks worksheet$

I hope this post helps you see why benchmark fractions are a great strategy for comparing and ordering fractions! If you want to save time, you can grab my benchmark fractions bundle . Be sure to let me know what other strategies you use to teach this lesson!

$Teaching students to compare fractions? Get started planning a benchmark fractions lesson with these ideas and free resources from Alyssa Teaches!$

This post includes Amazon Affiliate links. I earn a small commission on items purchased through these links at no extra cost to you.

$comparing fractions benchmarks worksheet$

Compare 5 8 to the benchmark fraction 1 2 using = , , or > : 5 8 1 2 .

Which of the following is less than 1 2 ?

Complete the following using = , > , or : 1 2 2 3 .

Complete the following using > , , or = : 7 1 2 1 2 .

Complete 1 7 9 using .

Which of the following fractions is less than 1?

Which of the following fractions is greater than 1?

Without calculating equivalent fractions, select the fraction that is less than 3 5 .

Hint : How can using a benchmark fraction help you?

Using 1 whole as a benchmark to compare, complete the following using , > , or = : 3 8 6 5 .

Practice Means Progress

$comparing fractions benchmarks worksheet$

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Fractions Worksheets

Welcome to the fractions worksheets page at Math-Drills.com where the cup is half full! This is one of our more popular pages most likely because learning fractions is incredibly important in a person's life and it is a math topic that many approach with trepidation due to its bad rap over the years. Fractions really aren't that difficult to master especially with the support of our wide selection of worksheets.

This page includes Fractions worksheets for understanding fractions including modeling, comparing, ordering, simplifying and converting fractions and operations with fractions. We start you off with the obvious: modeling fractions. It is a great idea if students can actually understand what a fraction is, so please do spend some time with the modeling aspect. Relating modeling to real life helps a great deal too as it is much easier to relate to half a cookie than to half a square. Ask most students what you get if you add half a cookie and another half a cookie, and they'll probably let you know that it makes one delicious snack.

The other fractions worksheets on this page are devoted to helping students understand the concept of fractions. From comparing and ordering to simplifying and converting... by the time students master the material on this page, operations of fractions will be a walk in the park.

Most Popular Fractions Worksheets this Week

$Adding and Subtracting Mixed Fractions$

General Use Fractions Printables

Fraction circles.

$comparing fractions benchmarks worksheet$

Fraction circle manipulatives are mainly used for comparing fractions, but they can be used for a variety of other purposes such as representing and identifying fractions, adding and subtracting fractions, and as probability spinners. There are a variety of options depending on your purpose. Fraction circles come in small and large versions, labeled and unlabeled versions and in three different color schemes: black and white, color, and light gray. The color scheme matches the fraction strips and use colors that are meant to show good contrast among themselves. Do note that there is a significant prevalence of color-blindness in the population, so don't rely on all students being able to differentiate the colors.

Adding fractions with fraction circles will involve two copies on paper. Cut out the fraction circles and segments of one copy and leave the other copy intact. To add 1/3 + 1/2, for example, place a 1/3 segment and a 1/2 segment into a circle and hold it over various fractions on the intact copy to see what 1/2 + 1/3 is equivalent to. 5/6 or 10/12 should work.

Fraction Strips

$comparing fractions benchmarks worksheet$

Fractions strips are often used for comparing fractions. Students are able to see quite easily the relationships and equivalence between fractions with different denominators. It can be quite useful for students to have two copies: one copy cut into strips and the other copy kept intact. They can then use the cut-out strips on the intact page to individually compare fractions. For example, they can use the halves strip to see what other fractions are equivalent to one-half. This can also be accomplished with a straight edge such as a ruler without cutting out any strips. Pairs or groups of strips can also be compared side-by-side if they are cut out. Addition and subtraction (etc.) are also possibilities; for example, adding a one-quarter and one-third can be accomplished by shifting the thirds strip so that it starts at the end of one-quarter then finding a strip that matches the end of the one-third mark (7/12 should do it).

Teachers might consider copying the fraction strips onto overhead projection acetates for whole class or group activities. Acetate versions are also useful as a hands-on manipulative for students in conjunction with an uncut page.

The "Smart" Fraction Strips include strips in a more useful order, eliminate the 7ths and 11ths strips as they don't have any equivalents and include 15ths and 16ths. The colors are consistent with the classic versions, so the two sets can be combined.

Modeling Fractions Worksheets

Besides using the worksheets below, you can also try some more interesting ways of modeling fractions. Healthy snacks can make great models for fractions. Can you cut a cucumber into thirds? A tomato into quarters? Can you make two-thirds of the grapes red and one-third green?

More picture ratios can be found on holiday and seasonal pages. Try searching for picture ratios to find more.

There are many different strategies other than staring at the page that will help in comparing fractions. Try starting with something visual that will depict the fractions in question. We highly recommend our fraction strips (scroll up a bit). Using a straight edge like a ruler or book or folding will help students to easily see which fraction is greater or if they are equal. We should also mention that the things that are compared should be the same. Each fraction strip for example is the same size whereas if you took a third of a watermelon and half of a grape, the watermelon would probably win out.

Comparing Simple and Improper Fractions

$comparing fractions benchmarks worksheet$

Another strategy to use when comparing fractions is to use a number line and to use benchmarks like 0, 1, 1/2 to figure out where each fraction goes then see which one is bigger. Students actually do this one all the time since they can often compare fractions by recognizing that one is less than half and the other is greater than half. They might also see that one fraction is much closer to a whole than another fraction even though they might both be greater than a half.

Comparing Simple, Improper and Mixed Fractions

$comparing fractions benchmarks worksheet$

Another strategy for comparing fractions is to convert each fraction to a decimal and compare the decimals. Decimal conversions can be memorized (especially for the common fractions) calculated with long division or using a calculator or look-up table. We suggest the latter since using a look-up table often leads to mental recall.

Ordering fractions on a Number Line

$comparing fractions benchmarks worksheet$

Many of the same strategies that work for comparing fractions also work for ordering fractions. Using manipulatives such as fraction strips, using number lines, or finding decimal equivalents will all have your student(s) putting fractions in the correct order in no time. We've probably said this before, but make sure that you emphasize that when comparing or ordering fractions, students understand that the whole needs to be the same. Comparing half the population of Canada with a third of the population of the United States won't cut it. Try using some visuals to reinforce this important concept. Even though we've included number lines below, feel free to use your own strategies.

Ordering fractions

$comparing fractions benchmarks worksheet$

The ordering fractions worksheets in this section do not include a number line, to allow for students to use various sorting strategies.

Simplifying & Converting Fractions Worksheets

Rounding fractions.

$comparing fractions benchmarks worksheet$

Rounding fractions helps students to understand fractions a little better and can be applied to estimating answers to fractions questions. For example, if one had to estimate 1 4/7 × 6, they could probably say the answer was about 9 since 1 4/7 is about 1 1/2 and 1 1/2 × 6 is 9.

Simplifying fractions

$comparing fractions benchmarks worksheet$

Learning how to simplify fractions makes a student's life much easier later on when learning operations with fractions. It also helps them to learn that different-looking fractions can be equivalent. One way of demonstrating this is to divide out two equivalent fractions. For example 3/2 and 6/4 both result in a quotient of 1.5 when divided. By practicing simplifying fractions, students will hopefully recognize unsimplified fractions when they start adding, subtracting, multiplying and dividing with fractions.

Multiplying fractions is usually less confusing operationally than any other operation and can be less confusing conceptually if approached in the right way. The algorithm for multiplying is simply multiply the numerators then multiply the denominators. The magic word in understanding the multiplication of fractions is, "of." For example what is two-thirds OF six? What is a third OF a half? When you use the word, "of," it gets much easier to visualize fractions multiplication. Example: cut a loaf of bread in half, then cut the half into thirds. One third OF a half loaf of bread is the same as 1/3 x 1/2 and tastes delicious with butter.

Dividing Fractions

$comparing fractions benchmarks worksheet$

Conceptually, dividing fractions is probably the most difficult of all the operations, but we're going to help you out. The algorithm for dividing fractions is just like multiplying fractions, but you find the inverse of the second fraction or you cross-multiply. This gets you the right answer which is extremely important especially if you're building a bridge. We told you how to conceptualize fraction multiplication, but how does it work with division? Easy! You just need to learn the magic phrase: "How many ____'s are there in ______? For example, in the question 6 ÷ 1/2, you would ask, "How many halves are there in 6?" It becomes a little more difficult when both numbers are fractions, but it isn't a giant leap to figure it out. 1/2 ÷ 1/4 is a fairly easy example, especially if you think in terms of U.S. or Canadian coins. How many quarters are there in a half dollar?

Adding Fractions

$comparing fractions benchmarks worksheet$

Adding fractions requires the annoying common denominator. Make it easy on your students by first teaching the concepts of equivalent fractions and least common multiples. Once students are familiar with those two concepts, the idea of finding fractions with common denominators for adding becomes that much easier. Spending time on modeling fractions will also help students to understand fractions addition. Relating fractions to familiar examples will certainly help. For example, if you add a 1/2 banana and a 1/2 banana, you get a whole banana. What happens if you add a 1/2 banana and 3/4 of another banana?

Adding Mixed Fractions Worksheets

$comparing fractions benchmarks worksheet$

A common strategy to use when adding mixed fractions is to convert the mixed fractions to improper fractions, complete the addition, then switch back. Another strategy which requires a little less brainpower is to look at the whole numbers and fractions separately. Add the whole numbers first. Add the fractions second. If the resulting fraction is improper, then it needs to be converted to a mixed number. The whole number portion can be added to the original whole number portion.

Subtracting Fractions

$comparing fractions benchmarks worksheet$

There isn't a lot of difference between adding and subtracting fractions. Both require a common denominator which requires some prerequisite knowledge. The only difference is the second and subsequent numerators are subtracted from the first one. There is a danger that you might end up with a negative number when subtracting fractions, so students might need to learn what is means in that case. When it comes to any concept in fractions, it is always a good idea to relate it to a familiar or easy-to-understand situation. For example, 7/8 - 3/4 = 1/8 could be given meaning in the context of a race. The first runner was 7/8 around the track when the second runner was 3/4 around the track. How far ahead was the first runner? (1/8 of the track).

Although some of these worksheets are single operations, it should be helpful to have all of these in the same location. There are some special considerations when completing operations with negative fractions. It is usually very helpful to change any mixed numbers to an improper fraction before proceeding. It is important to pay attention to the signs and know the rules for multiplying positives and negatives (++ = +, +- = -, -+ = - and -- = +).

Order of Operations with Fractions Worksheets

Order of operations with fractions.

$comparing fractions benchmarks worksheet$

The order of operations worksheets in this section actually reside on the Order of Operations page, but they are included here for your convenience..

$Go Math Practice - 4th Grade Chapter 6 - Fraction Equivalence and Comparison$

Go Math Practice - 4th Grade Chapter 6 - Fraction Equivalence and Comparison

$comparing fractions benchmarks worksheet$

Easel Activity

Also included in: Go Math Practice - 4th Grade Worksheets For Entire Year Bundle

$Comparing Fractions with Benchmarks Worksheets CCSS Math 3.NF.A.3.D$

$comparing fractions benchmarks worksheet$

Internet Activities

Also included in: Benchmark Fractions Bundle

$Comparing Fractions Using Benchmarks Math Video and Worksheet$

Comparing Fractions Using Benchmarks Math Video and Worksheet

$comparing fractions benchmarks worksheet$

Also included in: Equivalent Fractions Math Video and Worksheet Bundle / Distance Learning

$comparing fractions benchmarks worksheet$

Comparing Fractions and Ordering Fractions Differentiated Assessments Practice

$comparing fractions benchmarks worksheet$

Also included in: 4th Grade Fractions 4.NF Adding Subtracting - Comparing - Multiplying - Decimal

$NEW: RIT Band 161-230 Worksheets NWEA MAP Prep Math Practice #testscores$

Interactive Unit Fractions Drag unit fraction pieces (1/2, 1/3, 1/4, 1/5, 1/6, 1/8, 1/9, 1,10, 1/12, 1,16, and 1/20) onto a square that represents one whole. You can see that, for example, 6 pieces of 1/6 fit into one whole, or that 3 pieces of 1/9 are equal to 1/3, and many other similar relationships. /interactives/unit_fractions.php

You can also include visual models (fraction pies), which will make comparing easy and works well for making fraction comparison worksheets for grades 3-4.

To create problems where it is necessary to find a common denominator, choose "random fractions".

$comparing fractions benchmarks worksheet$

Math Made Easy, Grade 4 Math Workbook

This workbook has been compiled and tested by a team of math experts to increase your child's confidence, enjoyment, and success at school. Fourth Grade: Provides practice at all the major topics for Grade 4 with emphasis on multiplication and division of larger numbers. Includes a review of Grade 3 topics and a preview of topics in Grade 5. Includes Times Tables practice.

See more Math Made Easy books at Amazon

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Unit 7: Lesson 4

Compare fractions using benchmarks

$comparing fractions benchmarks worksheet$

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Comparing and Ordering Fractions

Compare and order fractions and mixed numbers. Includes "greater than," "less than," and "equal to" symbols. This page has printable task cards, learning center games, and worksheets.