Saturday, 3 June 2017

Reinforcing Equivalent Fractions via Games

Introduction to Equivalent Fractions: “Show Me″
Materials: 2 sets of fraction strips for each student, numberline for each student, numberline and fraction strips for teacher to display on overhead, document camera, projector, or just hold up.
Format: Students working individually or in pairs
Game Play:
The teacher names a fraction and asks students use specific fraction strips to build that same value on the number line: “Show me ____ made out of ____ strips.” The teacher continually walks around the group and confirms with a nod or verbal yes if the fraction is right. If not the teacher says, “try again.”
Start with making 1/2 out of powers of 2 (4ths, 8ths)
Move to making 1/2 out of other even numbers (6ths, 10ths, 12ths)
Then make other unit fractions out of their multiples (1/3 out of 9ths, 12ths, and 15ths, 1/5 out of 10ths and 15ths, etc.)
Then make other proper fractions out of their multiples (2/5 out of 10ths, 2/3 out of 15ths, etc.)
Then make simpler fractions from reducible fractions (10/12 out of 6ths, 2/4 out of halves, 12/15 out of 5ths, etc.)
Finally, make improper fractions (7/5 out of 15ths, 15/12 out of 4ths, etc)
Extra Support: Encourage students to make the identical fraction to yours first, and then line up the strips you requested below it until the lengths are the same.
Extra Challenges: Ask for impossible equivalences, like 1/2 made out of 3rds, or 10/12 made out of 5ths. Ask students to come up with possible and impossible challenges.



EQUIVALENT FRACTIONS GAME OF 'SPOONS'



This game for practicing equivalent fractions is a variation on the classic card game "Spoons."  If you've ever played "Spoons" before, you know that the game is super fast-paced and lots of fun.  I figured that if I could combine the fun and exciting parts of "Spoons" with some equivalent fractions practice, I'd have a center game that my students would be dying to play.  And let me tell you, this one does not disappoint!
How to play Equivalent Fractions "Spoons":

Number of players: 3-6 players
Preparing the materials:
1. Print out the Equivalent Fraction cards that was created for this game by CLICKING HERECut out each of the cards.
Want a fun, low-prep equivalent fractions game to use in your math centers tomorrow? Read about how we've put an equivalent fractions twist on the classic
2. Grab some plastic spoons (or any other object that can be grabbed by the players).  You need one fewer than the number of players.  For example, if you have 6 players, you'll need 5 spoons.
Object of the game:
To be the last player remaining in the game.  Players get closer to being eliminated each time they are left without a spoon, which earns them the next letter in the word S-P-O-O-N.  Once a player has earned all 5 letters in the word S-P-O-O-N, he or she is out.
Getting ready to play:
1.Arrange the spoons in a small circle in the center of the table.
2.Shuffle the equivalent fraction game cards and deal four cards face down to each player.  The players may look at their own cards, but may not show their cards to anyone else.
3.Choose a dealer for the round.  The remaining cards should be placed in a pile facedown beside the dealer.
Playing the game:
1.The dealer takes a card off the top of the pile so that he or she now has five cards in his or her hand. The dealer removes one of the five cards from his or her hand and passes it facedown to the player on his or her left.  The dealer then continues to pick up cards from the pile and discard one card at a time to the player on his or her left.
2.The player to the left of the dealer picks up the discarded card from the dealer.  Like the dealer, he or she removes one of the five cards from his or her hand and passes it facedown to the person on his or her left.  He or she continues to do this as cards continue getting discarded to him or her.
3.This quick picking up and passing of cards continues around the circle.  The last player in the circle always places his or her discarded card into a trash pile.  These cards are now out of play for the round.
4.Once someone gets four-of-a-kind (four fraction cards that are equivalent makes four-of-a-kind) in his or her hand, he or she grabs a spoon from the center of the table.  Once the player with four-of-a-kind takes a spoon, everyone else tries to immediately grab a spoon (even if they do not yet have four-of-a-kind).
Check out this fun, low-prep equivalent fractions game to use in your math centers!
5.The player left without a spoon earns a letter in the word S-P-O-O-N. 
6.The round is now over and the game begins again.  If any players were eliminated during the last round, a spoon must be removed so that there is always one fewer spoon on the table than players.

Equivalent Fractions Musical Plates

eqiv-fraction-plates
Get children up and moving with this fun, kinesthetic fraction activity. Children are given a fraction and dance around to music, trying to find its equivalent. Written and visual representations of fractions are used to assess children’s understanding!
What you need:
  • sticky notes
  • paper plates
  • permanent marker to write fractions
  • visual representations of fractions to glue on the plate
  • music
What to do:
Give each student a fraction written on a sticky note. Students remember their fraction and stick it on their shirt. Next, lay out the paper plates with fractions written or pasted on them. You should make a variety of equivalent fraction plates for each student and spread them far apart. Then each student will have to really look to find a plate that is equivalent.
Start the music. Students dance and hunt for a fraction that is equivalent to their own. When they find it, they stand on the paper plate. If they don’t find an equivalent fraction before the music stops, they’re out! For each round, students keep hunting for fractions. Once there are no more fractions that are equivalent to their own, they sit out. They found all of their fractions!
This fraction game for kids can be played as a whole group or with small groups to assess learning.

Interactive Online Games





Reinforcing Equivalent Fractions with Videos

Video Tutorials:
  • Using Area Models
https://learnzillion.com/lesson_plans/9049-recognize-equivalent-fractions-using-area-models

  • Using Number Lines
https://learnzillion.com/lesson_plans/4739-recognize-equivalent-fractions-using-number-lines


  • Generating Equivalent Fractions using Area Models

Tuesday, 30 May 2017

Introducing the concept of Equivalent Fractions

How to introduce the concept of Equivalent Fractions

Conceptual Understanding:

  • Equivalent Fractions via Paper Folding

The fraction strip paper folding exercise is generally used to introduce the topic of equivalent fractions.

Another better way is to use bar models or fraction strips.










Equivalent Fractions Singapore Math


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.
  • Ask the following questions, and have a discussion with the class:
    1. What do you notice?
    2. Is there a pattern?
    3. Is there a rule?
  • Extend the exercise to other fractions pictorially, using different shapes.












exploring equivalent fractions
Exploring Equivalent Fractions


  • Equivalent Fractions using Area Models
After students have grasp the concept of paper folding to derive various equivalent fractions, you can now transfer that knowledge to the use of area models:











Equivalent Fractions Singapore Math
Let the students have fun exploring equivalent fractions by deriving their own “rules” through induction. 

Equivalent Fractions Singapore Math


Through area models, students will observe “how the number and size of the parts differ even though the two fractions themselves are the same size” .

Example 1

Each fraction in example 1 represents the same number. These fractions are equivalent.

Let's look at some more examples of equivalent fractions.
Example 2
Two-thirds is equivalent to four-sixths.

Example 3
The fractions three-fourths, six-eighths, and nine-twelfths are equivalent.

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

  • Equivalent Fractions using the Number Line

The next step is to transfer their knowledge to 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.

Equivalent Fractions Singapore Math

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


Procedural Understanding of Equivalent Fractions

 Multiply the numerator and denominator by the same factor to get another fraction that is equivalent to the origin. 

“Whatever you do to the numerator, you’d do for the denominator”. So,



Equivalent Fractions Singapore Math

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.
1 = 3/3
This is extended to other whole numbers, e.g.
3 = 3/1
and even further to
3 = 9/3
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

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

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.

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’.

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

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.



Defining Equivalent Fractions

What are equivalent fractions?

In this post, we are going to understand what equivalent fractions are and how you can find out what fractions are equivalent.
Equivalent fractions are fractions that represent the same quantity. For example, which of the following do you believe will be the biggest?
equivalent fractions
What have you figured out? We are going to see it with an example, sharing this pizza in as many slices as the fraction indicates.
equivalent fractions 2
In order to represent 1/2, we will divide the pizza in 2 slices and keep 1 slice for ourselves:
equivalent fractions 3
In order to represent 3/6, we will divide the pizza into 6 slices and keep 3 slices for ourselves:
equivalent fractions 4
In order to represent 4/8, we will divide the pizza into 8 slices and keep 4 slices for ourselves:
equivalent fractions 5
Is there a piece of pizza that is bigger? No! Notice, the three fractions represent the same quantity of pizza, one half; therefore those are equivalent fractions:
equivalent fractions 6

How do we know if two fractions are equivalent?

Two fractions are equivalent if they represent the same decimal number.
For example, the three previous fractions represent the same decimal: 0.5.
Equivalent Fractions
1/2 is 1 divided by 2, which is 0.5
3/6 is 3 divided by 6, which is 0.5
4/8 is 4 divided by 8, which is 0.5

Mistakes in Teaching Equivalent Fractions

Common mistakes made in introducing the concept of equivalent fractions


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”. 

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.


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.