problem solving find equivalent fractions lesson 6 5

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1. Connect the pictures that show equivalent fractions. Write the name of each fraction beside its picture.

2. Make a chain of equivalent fractions.

3. Split the pieces by drawing the new pieces in the right-hand picture. Write the equivalent     fractions.

b.   Split each piece into three .

c.   Split each piece in two .

d.   Split each piece in two .

e.   Split each piece into three .

f.   Split each piece in two .

g.   Split each piece in two .

h.   Split each piece in two .

i.   Split each piece into five .

4. Write the equivalent fraction. Imagine or draw the helping arrows.

b. Split each piece in two .

c.  Split each piece into six .

d. Split each piece into four .

e. Split each piece into five .

f. Split each piece into three .

g. Split each piece into ten .

h. Split each piece into eight .

i. Split each piece into seven .

j. Split each piece into eight .

5. Figure out how many ways the pieces were split and write the missing numerator or denominator.

b.  Pieces were     split into ____ .

c.  Pieces were     split into ____ .

d.  Pieces were     split into ____ .

e.  Pieces were     split into ____ .

6. Mark the equivalent fractions on the number lines.

    c. Find and mark two fractions on the 12th parts number line that do not         have an equivalent fraction on the 3rd parts number line. Write them here →

    d. Find and mark two fractions on the 24th parts number line that do not         have an equivalent fraction on the 12th parts number line. Write them here →

Math Mammoth Fractions 1

A self-teaching worktext for 5th grade that teaches fractions and their operations with visual models. The book covers fractions, mixed numbers, adding and subtracting like fractions, adding and subtracting mixed numbers, adding and subtracting unlike fractions, and comparing fractions.

Download ($3.50) . Also available as a printed copy.

Learn more and see the free samples!

See more topical Math Mammoth books

Trending Post : Teaching Fractions with Food

10 Fun and Exciting Ways to Teach Equivalent Fractions | Activities and PDFs | Answer Key

Teaching equivalent fractions.

Fractions! For some of our kiddos, the term ‘equivalent fractions’ makes them quiver in their sneakers and want to barf all over the desk. It doesn’t have to be that way though. There are many interactive, fun ways to learn and then practice fractions. I just had to put a list together just for equivalent fractions, including a hands on equivalent fractions activity.

There are many fun ways to teach equivalent fractions. This is a nice assortment of multisensory learning–including visual, verbal, tactile…and most of all, fun!

For each of the activities listed, I have started the description with a hyperlink so you can go learn more about that specific equivalent fraction activity. You can download all of the printables that are mine (the ones that have pictures) in one place with my Equivalent Fraction Activities Bundle.

This activity comes with an answer key. I kept them as separate PDFs.

And here is that answer key for the How to Teach Equivalent Fractions activity set.

Equivalent Fractions Activities

We all know that hands-on instruction is the way to go for teaching math concepts. Teaching the way to solve the problem has its place, but understanding why those steps works are just important. And these equivalent fraction activities will help you teach this concept.

Teaching Fractions with Food -Kids love food, and they understand food. When beginning your fraction unit why not pull out a Hershey bar or an orange? It is a great way to not only teach what a fraction is, but also to introduce an equivalent fraction by having them share the food. Start your equivalent fractions lesson with some fun and colorful food, and you’ll have their attention!

Interactive notebook for teaching equivalent fractions with models   -A simple way to have students use fractional models to figure out equivalent fractions. Students take a model given and divide it up into equal parts. By the time they have worked through the first model they have found four equivalent fractions.

Interactive notebook for teaching equivalent fractions with number lines. -This is very similar to the first interactive notebook, but this time instead of fractional models you get number lines. I love giving children as many ways to see a concept as I can. You never know which way will make the lightbulb go on or prompt that “a-ha!” moment that is so fun to witness as a teacher.

Learning Resources Magnetic Rainbow Fraction Tiles -Many students need to see many different representations of fractions and how they are equivalent. I love this activity and it makes a great Amazon Wish List item if you do that and share with parents. Using Fraction Tiles the students work to figure out which fractions are equivalent. This “lesson” does not involve a ton of direct instruction, but the children are learning through exploring with manipulatives and making observations. That is the best type of learning.

• These magnetic fraction strips make learning fractions is easier with visual, hands-on magnetic aids
• This magnetic fraction set will Introduce fraction concepts, parts to whole, equivalents, and comparisons
• Magnetic fraction bars can be used at home or in the classroom and are easy to wipe clean
• 51-piece set includes color-coded, soft foam, magnetic tiles to depict wholes, halves, thirds, fourths, fifths, sixths, eighths, tenths, and twelfths
• Ideal for ages 6+

Fractions on a Number Line -Number lines are a great way to build fraction sense, and they are also a fun way to teach equivalent fraction. While they are creating their number lines they are working on what numerators are, what denominators are, finding the LCM, and so much more.

Pattern Blocks Task Cards -Pattern blocks are another great way to explore and learn about equivalent fractions. These task cards are a great place to go after children have a basic understanding of equivalent fractions. They will definitely get your kiddos thinking and problem-solving, and quickly reveal any misconceptions.

Using visual models is a great way to build fraction sense, and helps children understand equivalent fractions better. This is a series that Math Geek Mama and I did together. It walks you through numerous ideas on helping children visualize fractions …not just memorize how to solve a problem.

Practicing Equivalent Fractions

After you have spent some time teaching, now students are ready to play or practice their new found knowledge. To reinforce what they have learned, try out some of these activities.

Fraction Dominoes -These fraction dominoes have fractions, models, and number lines. Children can play a card by matching up two equivalent fractions, a fraction and model, a model and number line, etc. You can even get some fraction adding by having the children add up all the fractions left in their hand when another player goes out. The person with the highest sum loses.

Oh No, Fraction Man -This game is similar to Old Maid, but instead of an Old Maid you have a fraction man. All the children have to do is pull cards from another player’s hand. If they have a match to the card they pulled they may lay it down in front of them. The game ends when all matches have been made and one person is left with the fraction man. The cards have fractions, fractional models, and number lines on them.

Clip Cards – Instead of pulling out a worksheet to assess students knowledge, gather them around you and have them solve the problems by placing clips on the equivalent fraction. Many of the clip cards have two or three correct answers. This forces the children to really analyze the card before saying they have completed it.

Tic-Tac-Toe with Fractions -This game is very similar to Tic-Tac-Toe, just with a twist. The children must find the equivalent fraction to whatever space they want to cover up. If they choose the wrong fraction, they have to cover up the space that equals that fraction. Since the game of Tic-Tac-Toe leaves little room for mistakes, a wrong move can end the game. You can play with models, number lines, or both.

Fishing For Equivalent Fractions -This game is similar to Go Fish – and children will love their quest to find pairs that are equivalent.

Simplifying Fractions – This is a BINGO game that focuses on simplifying fractions, and we know how much our kiddos enjoy doing that. Simplifying Fractions is a wonderful way to practice equivalent fractions, and who doesn’t love a simple BINGO game.

Digital Equivalent Fractions -These digital equivalent fraction activities are a great way to get some practice in, especially if you are virtual.

Ooops! What kind of math teacher am I? I said 10 activities, but this is more than 10. I assure you that I can count. But when it comes to fun activities, sometimes I get carried away.

I hope you enjoy these equivalent fraction activities . There are so many fun ways to teach equivalent fractions and get your children engaged as they dive into this concept.

You’ve Got This!

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Teaching Equivalent Fractions

Equivalent Fractions is a concept that is generally introduced in the 3rd grade. In the US 3rd grade Common Core (CCSS.Math.3.NF.3):

Explain equivalence of fractions in special cases, and compare fractions by reasoning about their size. a. Understand two fractions as equivalent (equal) if they are the same size, or the same point on a number line. b. Recognize and generate simple equivalent fractions, e.g., 1/2 = 2/4, 4/6 = 2/3. Explain why the fractions are equivalent, e.g., by using a visual fraction model. c. Express whole numbers as fractions, and recognize fractions that are equivalent to whole numbers. Examples: Express 3 in the form 3 = 3/1; recognize that 6/1 = 6; locate 4/4 and 1 at the same point of a number line diagram. d. Compare two fractions with the same numerator or the same denominator by reasoning about their size. Recognize that comparisons are valid only when the two fractions refer to the same whole. Record the results of comparisons with the symbols >, =, or <, and justify the conclusions, e.g., by using a visual fraction model.

This is further extended in the 4th grade (CCSS.Math.4.NF):

Extend understanding of fraction equivalence and ordering. 1. Explain why a fraction a/b is equivalent to a fraction (n x a)/(n x b) by using visual fraction models, with attention to how the number and size of the parts differ even though the two fractions themselves are the same size. Use this principle to recognize and generate equivalent fractions. 2. Compare two fractions with different numerators and different denominators, e.g., by creating common denominators or numerators, or by comparing to a benchmark fraction such as 1/2. Recognize that comparisons are valid only when the two fractions refer to the same whole. Record the results of comparisons with symbols >, =, or <, and justify the conclusions, e.g., by using a visual fraction model.

The concept of equivalent fractions seems simple – just multiply the numerator and denominator by the same factor to get another fraction that is equivalent to the origin. However it is not trivial at all, and with intentional design in the instruction delivery, the topic can be introduced in a way that strengthens the students’ reasoning and inductive skills and at the same time, lay a stronger foundation for the future, especially in fraction arithmetic and algebraic manipulations.

Logic Reasoning and Induction

When teaching equivalence of fractions, teachers often start by stating the procedural rules. “Whatever you do to the numerator, you’d do for the denominator”. So,

Not only is this not helping in the conceptual understanding of equivalent fractions, but introducing the topic in this way wastes a perfectly good opportunity for the students to exercise their logic reasoning and induction muscles and discover for themselves what equivalence means, which fractions are equivalent and how to find them.

Another better way is to use bar models or fraction strips. The fraction strip  paper folding exercise  which we first wrote about after a lesson study at a local school, is what we generally use to introduce the topic of equivalent fractions.

First, have the students fold a paper strip in half and note that there are two equal parts. Then fold it again and note that now we have 4 equal parts.

• Without folding it again, ask the students how many equal parts do they think they will have if we were to fold the paper strip a third time. Some might guess 6, a natural progression from 2 and 4, while others might reason that the pattern is multiplying by two, not adding.
• Next, have the students shade the fraction 1/2, 2/4, 4/8 etc on different strips of paper and paste them on the same blank paper, on top of each other. An example is shown below.
• What do you notice?
• Is there a pattern?
• Is there a rule?
• Extend the exercise to other fractions pictorially, using different shapes.

Let the students have fun exploring equivalent fractions by deriving their own “rules” through induction. To read more about our experience using the fraction strip exercise, see our previous post here .

Equivalent Fractions

Equivalent Fractions on the Number Line

Generally, students first learn about equivalent fraction using an area model, e.g.

Through area models, student observed “how the number and size of the parts differ even though the two fractions themselves are the same size” (CCSS.Math.4.NF.1).

The next step is to transfer their knowledge to the number line (see our previous post on the importance of understanding fractions on the number line ). However, many students have problem visualizing equivalent fractions on the number line. For example, it is not intuitive to see that 2/3 and 4/6 are the same point on the number line.

Here again, the bar model or fraction strips will come in very handy. To make it easier to visualize, teachers/parents can present the fraction strips along with the number lines.

In this way, it is very intuitive to see how the concepts of equivalent fractions can be transferred to the number line.

The case of 1

The case of 1 is often overlooked by teachers, but the concept is so important. This simply refers to the fact that the whole number 1 is also made up of equivalent fractions, e.g.

This is extended to other whole numbers, e.g.

and even further to

The concept is important when the students start to apply their knowledge of fractions in addition and subtraction and other fraction manipulations. For example, in fraction subtraction, many students resort to converting the mixed fraction to an improper fraction before proceeding to subtract, and finally convert the resulting improper fraction back to mixed.

5 1/3 – 2/3 = 16/3 – 2/3 = 14/3 = 4 2/3

If the students understood the concept that whole numbers also have equivalent fractions, they can do a “re-grouping” as follows

5 1/3 – 2/3 = 4 4/3 – 2/3 = 4 2/3

Special Notes

Lastly, some special notes to be mindful about when teaching equivalent fractions.

Fraction Simplification

Equivalent fractions is not always about multiply up. It is also important to learn that simplifying fractions to lower terms is also finding equivalent fractions. Fraction simplification is very important when it comes to fraction arithmetic (add, subtract), algebra and general word problems.

Don’t say ‘cancel’ or ‘reduce’

Terms like ‘cancel’ or ‘reduce’ give the impression that the “size” is somehow reduced and can be confusing to young students who have not fully understood equivalence yet. Instead, use the universal term ‘simplify’.

TeachableApp

Want to see a fun way to teach Equivalent Fractions using an interactive manipulative? Check out the Fraction Wheel App here .

Equivalent fractions is such an important concept for students to understand, however under the pressure of time, it is sometimes tempting for teachers and parents to skip to procedural methods and not emphasize on conceptual understanding. However with some thoughts and design, the topic can be a fun way for students to discover more facts about fractions that they have not realized before and at the same time strengthen their confidence in fraction manipulations for the future.

This article is part of a series of blog posts on Fractions:

• >> Read the next post on Fractions:  On Comparing Fractions
• << Read the previous post on Fractions:  Fractions on the Number Line
• Or start from the beginning: Understanding Fractions as Equal Parts

More Fraction Resources

For more fraction resources, refer to our main fractions page .

1 thought on “Teaching Equivalent Fractions”

This was just what I needed as I move on to fractions for my students!

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Go Math Interactive Mimio Lesson 6.5 Find Equivalent Fractions

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Equivalent Fractions Challenge

Subject: Mathematics

Age range: 7-11

Resource type: Worksheet/Activity

Last updated

21 January 2016

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Thank you for this resource. Great for my Year 6 children!

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Fantastic activity - perfect for my more able Year 6s. Thank you very much!

great break down of concepts and worksheet to reflect the main fraction skils

mary_burgess

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