Fun with Fractions!

In this course, you will learn all about fractions and what they mean on a number line!  You will learn how to place them correctly across a number line as well as how to compare different fractions, and find some that are equivalent all using that number line!  Get ready to have fun and learn!  This course is designed mainly for third grade students, but it never hurts as a review, or a way for younger students to challenge themselves. 

Fractions Review

Introduction

I hope you are ready to learn!!!

This course will take you through different ways to use fractions with a number line.  We will begin with a small review on what a fraction is as well a number line separately before putting them to work together.  Navigate through this course in the order provided, and be sure to complete each section 100% before moving on.  Each section will give an explanation on what you will be learning as well as examples.  You will then get a chance to try it all out on your own before moving onto the Checkpoint, or short quiz.  Once passing, you may then move onto the next section.  At any time, feel free to use the menu bar on the left hand side of the screen to go back to any part where you feel you need more review.  Take your time through the course, but have fun as well! 

What is a Fraction?

To start, we are going to review what a fraction means, and the different parts of one!

Terms to know

The top of a fraction is called the numerator (nuum-er-a-ter).  This shows the amount of parts the fraction has.  The example above shows there are 3 parts. 

The bottom of a fraction is the denominator (dee-nom-in-a-ter).  This shows the whole, or how many equal parts a shape has.  The picture above shows a denominator of 4.

How Fractions are Written

You will see this all throughout the course.  In order to say the name of the fraction, we use what is on the denominator.  The first fraction shown above is one half.  The second is one third, and the final is one fourth.  

Example of a Fraction

The shaded picture above is an example of a shaded fraction.  The circle is partitioned (split up into its equal groups) into six equal parts, or sixths.  Out of the six, four pieces are shaded in, or four parts.  Our parts over our whole makes this fraction four-sixths, written as 4/6. 

Fraction Review!

Use your previous knowledge and what was reviewed to match the following words with their definitions or correct fractions. 
  • The numerator shows how many _______
    Parts
  • The denominator in a fraction shows the _______
    Whole
  • The proper term for splitting a shape into equal parts is ____
    Partition
  • 1/2
    Halves
  • 1/3
    Thirds
  • 1/4
    Fourths
  • 1/6
    Sixths
  • 1/8
    Eighths

Number Line Review

Number Line Review

Now we are going to briefly review how to label a simple number line.  Below you will see a number line.  Your next task is to drag the numbers to the correct spaces to label the number line from 0 to 10 in increasing order. The ends of 0 and 10 have already been labeled for you. 

  • 1
  • 2
  • 3
  • 4
  • 5
  • 6
  • 7
  • 8
  • 9

Ready To Go On?!

Did you notice how the numbers on your number line increased from the smallest number to the largest?  The same is true when labeling fractions!  They increase from the smallest fraction to the largest fraction!  You may now move onto the first real learning section, how to label fractions across a number line! 

Labeling Fractions on a Number Line

How to Label

Tips for labeling fractions on a number line: 

1. Since fractions are less than 1, our number line will always range from 0 to 1.

2. Always place ½ in the middle of the line since ½ is halfway in between 0 and 1.

3. Your 0 is always 0 over your denominator (example 0/3 or 0/4), where your 1 is considered a whole, so your numerator and denominator are the same (example 3/3 or 4/4).

4. When labeling, start with 1 as your numerator, and end with your denominator.  For example, labeling 4ths would be ¼, 2/4, ¾, and end with 4/4 on the 1 whole.

5. Be sure to space them out evenly along the line. 

Here is the completed number line labeled from 0/4 to 4/4. 

Spacing The Fractions Apart

It is extremely important the fractions are evenly spaced out on the number line between the 0 and the 1, especially the further along in the course we move.

You can see how evenly spread out my fractions are across the number line!  Just as partitioning fractions creates equal parts, it is the same when partitioning them onto the number line.

Hmmm...What if They Aren't Spaced Out?

Hmmmm...what if my fractions are not spaced out evenly?!

In this example, the fractions are not evenly spaced! This makes a big difference in how my fractions look.  See that huge gap between 4/5 and 1 whole?  That makes a fifth look huge, yet at the same time it doesn’t look that big of a space from 0 to 1/5. This number line also makes 3/5 look smaller than ½.  Yet, when you look at the correct number line on the previous slide, it is clear 3/5 is actually greater than ½ because it is closer to 1 whole.  This is why it is very important they look evenly spaced.

How Can I Make Sure My Fractions are Evenly Spaced Out?

We can use fraction tiles! As you can see below, the tiles above the number line really help to space out those fractions evenly!  See if you can match up each fraction to its correct spot on the correct number line. I have already put the tiles on for you.

  • 1/2
  • 1/3
  • 2/3
  • 1/5
  • 2/5
  • 3/5
  • 4/5
  • 1/8
  • 2/8
  • 3/8
  • 4/8
  • 5/8
  • 6/8
  • 7/8

Try It Out!

Now its your turn to try! Take your time and go through this page and the next as many times as you need to.  Your first checkpoint quiz is coming up soon! 

On the next page are a couple practice problems before taking the real quiz.  It is up to you how much you want to practice.  

You may also use the website linked below as extra practice.  It is a great site to practice correctly labeling fractions across a number line!

http://mrnussbaum.com/grade_3_standardsfracline/ 

Review Labeling the Number Line

Wendy is getting ready to bake a cake for her school bake sale.  She has a lot of measuring cups all mixed up in her cupboard! Help her find the right order for all of her thirds, fifths, eighths, and tenths. 

For each number line you are going to click on the spot where the correct answer would be.  The first two have fraction bars on top to help you, the second two do not. 

#1- Find where 2/3 would be on the number line.

#2 - Find where 2/5 and 4/5 would be on the number line.

#3 - Find where 4/8 would be on the number line.

#4 - Find where 1/10, 2/10, 6/10, and 9/10 would be on the number line.

Checkpoint #1

Here is your first quiz!  Be sure to read through each problem carefully and take your time.  In order to move on, you must get at least 80% of the questions correct (4 out of 5). You will have two true/false questions, two multiple choice, and one you must label the number line. Good luck!

Checkpoint #1

  • All fractions are greater than 1. True or False?
  • It doesn’t matter where I put my fractions on a number line as long as they are in between 0 and 1. True or False?

Checkpoint #1

  • A
  • B
  • C
  • D
Choose the correctly labeled number line 

Checkpoint #1

  • A
  • B
  • C
  • D
Choose the correctly labeled number line.

Checkpoint #1

Place all of the 6ths in order along the number line

  • 1/6
  • 2/6
  • 3/6
  • 4/6
  • 5/6

Comparing Fractions

Compare the Numbers

We are going to begin this section with a short review on how to compare using greater than, less than, and equal to signs.  Remember to think of them like an alligator or crocodile if that helps you to remember which way the signs go.  The next slide will contain a short review using whole numbers before we use these signs with fractions.    

Compare the Numbers Try It!

5 is 3

6 is 6

10 is 2

7 is 8

Comparing Like Denominators

Steps to comparing fractions with like denominators on a number line: 

1.Label your number line 

2.Circle the two fractions you are comparing 

3.The fraction that is closer to 0 is the smaller fraction, and the fraction closer to 1 is the larger fraction

Here is a picture of what it looks like to compare fractions on a number line with like denominators. 

What About Different Denominators?

Oh no! 

I need to now compare the two fractions ½ and ¾!  But, they have different denominators!!  Is this possible?!

The answer is YES! 

Let me show you how!

The denominators are different. 

How to Label With Two Number Lines

Now that you’ve learned how to label number lines, I want to teach you to label and use two that are right on top of one another in order to compare those fractions with different denominators. 

For all of the following activities, we are going to use two number lines.

Don’t forget!! The number lines should be evenly spaced!  Which also means they should be matched up one right on top of the other in order to get accurate results!

Here you can see I have labeled my halves as well as fourths across two different number lines with one right on top of the other, and are both still very evenly spaced out. 

Comparing Different Denominators

Here is again what it looks like to label two number lines. 

Steps to comparing fractions with different denominators:

 1.Label two number lines, one on top of the other. 

2.Circle the two fractions you are comparing. 

3.The fraction on one number line that is closer to 0 is the smaller fraction, and the one that is closer to 1 is the larger fraction.

The biggest difference between comparing with different denominators is the use of two number lines!

The reason this is done is because, for example, labeling thirds on a number line and fifths on the same line tends to look messy!

This video explains all the steps on comparing two fractions with different denominators.  Follow along to see how it is done when I try to compare 3/4 to 6/8.  

Try It Out!

Now its your turn to try again! Take your time and go through this page as many times as you need to.  Your second checkpoint quiz is coming up soon! 

On the next page are a few practice problems before taking the real quiz.  It is up to you how much you want to practice.  

You may also use the website linked below as extra practice.  It is a great site to practice comparing fractions.

http://www.shodor.org/interactivate/activities/FractionQuiz/

Review Comparing Fractions

Wendy’s friend Sophie wants to help her make the best cake for the bake sale.  However, the recipe is not very exact.  It tells Wendy and Sophie they need to compare two fractions in order to find out which one to use.  Can you help them so the cake comes out great?

Use the number line below to help you compare the following fractions to review:

2/3  4/6

7/8  2/8

5/10  3/5

1/4  4/5

Checkpoint #2

Here is your second checkpoint!  Be sure to read through each problem carefully and take your time.  In order to move on, you must get at least 80% of the questions correct (4 out of 5). You will have two true/false questions, two multiple choice, and one you must click on the right answer on a number line. Good luck!

Checkpoint #2

  • You can compare fractions with different denominators. True or False?
  • 3/4 is less than 1/2. True or False?

Checkpoint #2

  • A
  • B
  • C
  • D

1.Which is correct?

Checkpoint #2

.

  • A
  • B
  • C
  • D

Checkpoint #2

Click on all of the fractions greater than 3/5 on the number line.

Equivalent Fractions

Do You Notice Anything the Same?

Is there anything you notice between these two number lines?!

Look at the fractions that are highlighted in blue. 

These fractions are in the same spots!  This means they are equivalent fractions!

We can even use number lines to find fractions that are equivalent to one another!

Once again, this is why it is so important they are evenly spaced apart.  If they weren’t, these fractions wouldn’t look the same. 

Finding Equivalent Fractions Using 2 Number Lines

Just as with comparing, the easiest way to find two equivalent fractions is by using those two number lines one on top of the other again.

Steps to finding equivalent fractions on the number line:

 1.Label the number line using the appropriate denominators. 

2.Circle the two fractions you are trying to find if they are equivalent or not.

3. Are the fractions in the same spot? Yes, then they are equivalent.  No, then they are not equivalent. 

OR

4. If you are trying to find fractions that are equivalent, look to see which fractions line up in the same spots.

Try It Out!

Now its your turn to try again! Take your time and go through this page as many times as you need to.  Your third and last checkpoint is coming up fast! 

On the next page are a few practice problems before taking the real quiz.  It is up to you how much you want to practice.  

You may also use the websites linked below as extra practice.  They are great practice for equivalent fractions. The first one is pretty simple.  Once that one seems easy, move onto trying the second, and finally the third is the hardest, but still great practice. 

1. https://www.ixl.com/math/grade-3/find-equivalent-fractions-using-number-lines

2. https://www.ixl.com/math/grade-3/graph-equivalent-fractions-on-number-lines

3. https://www.ixl.com/math/grade-4/equivalent-fractions

Review Equivalent Fractions

Wendy and Sophie are ready to bake that cake!  They’ve just ran into one little problem.  Through all the rushing, Wendy lost some of her measuring cups.  Can you help her find which other measuring cups she could use that would be about the same as her missing ones?  Click on the correct equivalent fraction in each pair.

Checkpoint #3

Here is your third and final checkpoint!  Be sure to read through each problem carefully and take your time.  In order to move on, you must get at least 80% of the questions correct (4 out of 5). You will have two true/false questions, two multiple choice, and one matching. Good luck!

Checkpoint #3

  • There are not any fractions equivalent to ½. True or False?
  • The numerators and denominators must both be equal in order for a fraction to be equivalent. True or False?

Checkpoint #3

  • A
  • B
  • C
  • D

1.Which are equivalent?

Checkpoint #3

  • A
  • B
  • C
  • D

Which are equivalent? 

Checkpoint #3

Use the number line below to match the equivalent fractions.
  • 0/6
    0/12
  • 1/6
    2/12
  • 2/6
    4/12
  • 3/6
    6/12
  • 4/6
    8/12
  • 5/6
    10/12
  • 6/6
    12/12

Review!

Review It All

I hope you’ve learned a lot about fractions and number lines!  I’ve really enjoyed making this course for you to learn.

Now is your chance to go back and review everything you have learned before moving onto your final assessment which will incorporate all three skills.

Look back at all of the individual reviews for each section as well as the websites, and look over all of those again. Here is where you should click back to in order to review:

1. Labeling Fraction on a Number Line - "Reviewing Labeling the Number Line"

2. Comparing Fractions - "Review Comparing"

3. Equivalent Fractions - "Review Equivalent"

Websites to help review:

Final Assessment

Final Test

You made it!!! On the following page is your final assessment.  I will remind you again, but read through it very carefully, and take as much time as you need to.  Good luck and have fun with it!  

Final Assessment

Welcome to your final test!  Below are a series of questions that relate to one another as you move through.  Read through them very carefully and take your time!  Grab a scrap piece of paper, and use number lines in any way you need to!  You cannot move onto a next question until you have answered the previous one correctly.

Your scenario is all about Sophie.  She is trying to bake cookies for a bake sale, but is having many complications with her measuring cups and the recipe.  It is your job to help her make her cookies correctly in time for the sale! Good luck!

Conclusion

It Is Complete!

Congratulations!!!! I hope you had a great time taking this course!  I tried to make it as fun as possible for you, even being math. Now that you have completed the course, you are an expert on fractions!  You have learned how to label fractions on a number line, compare fractions using the number line, and even how to find equivalent fractions.  You can take this new knowledge into your real life when baking, and many other scenarios as well!  Great work!!