Compare Fractions GAME

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SWBAT compare fractions with different denominators by using various comparison strategies.

Big Idea

This lesson builds towards students ability to compare fractions by creating common denominators or numerators - 4.NF.2

Number Hook

7 minutes

For this number hook, I give students a riddle rather than a magic trick. I roll five dice and show the dice under the document camera.  Then I tell students, "The name of the game is Polar Bears Around the Ice Hole. The name of the game is important! How many polar bears are there?"

The following is an example of how this looked during this riddle:

 The first roll produced 4, 6, 1, 3, 2. "Six," said Billy. "No, two," Johnny replied. The next roll was 5, 1, 5, 2, 4. "Four?" said Billy. "No, eight," Johnny said. The next rolls were 3, 5, 3, 1, 2. There were 8 polar bears. The next rolls were 6, 2, 1, 2, 4. There were no polar bears. How does Johnny figure out the number of polar bears?

The answer to this riddle is quite simple, but one that my students have not figured out yet. My students LOVE this riddle and based on previous experience, I predict I will get many requests to play this again, often.

Dice all look the same. On a die, the 1, 3, and 5 all have a dot in the center. The 3 has 2 dots on either side of the center dot, and the 5 has 4 dots around the center dot. Johnny simply counted the number of dots around the outside. A "3" has 2 "petals around the rose, or polar bears around an ice hole." The "5" has 4 "petals" or "polar bears." Roll some dice and it will become clear!!

Warm Up

10 minutes

Students will start today's lesson with a fluency assessment.  This assessment is from Monitoring Basic Skills Progress Second Edition: Basic Math Computation by Lynn S. Fuchs, Carol L. Hamlett, and Douglas Fuchs.

This is an assessment I have my students do each week and then graph their results.  It allows them to reflect on their learning of basic math facts, as well as using all four operations with whole numbers, and adding and subtracting unit fractions.  (It also happens to be the quietest time in my math classroom all week!!) 

This is what my classroom looks like as students work on this assessment.


This is sample of a student's graph. You can also click here to hear my thoughts about this graph below. 


 Click hereto see an example of a typical fourth grade fluency decrease since students are completing the fourth grade fluency set that incorporates division, multiplication, addition, subtraction, and adding and subtracting fractions with like denominators. (At this point, students have not had many fraction lessons, thus very very students are able to complete the fraction problems) 

I do not start my students with the fourth grade skills, but at this point in the year, all students are using the fourth grade set.. I chose to start them with the end of the third grade skills which covers addition, subtraction and multiplication and division of basic facts. I strongly believe in a balanced math approach, which is one reason why I also believe in common core standards.  By having a balance of building conceptual understanding, application of problems, and computational fluency, students can experience rigorous mathematics.  I want to make clear that this assessment ONLY measures basic math computation.  It is only one piece of students' knowledge. The assessments in this book, for each grade level, do not change in difficulty over the course of the year.  Therefore, a student's increase in score over the school year truly reflects improvement in the student's ability to work the math problems at that grade level.

Concept Development

40 minutes

I begin this lesson by playing this learn zillion video as a review.

This is the fourth lesson related to comparing fractions my students have had. Their skills are growing and this is getting much easier for them. In the previous lessons, students compared fractions using a number line and the benchmark fraction 1/2.  Today, students will practice using an area model to compare fractions in order to play a card game.  Since students are building up skills in order to compare fractions by creating common denominators or numerators, this lesson helps add to their conceptual understanding about the relative size of fractions using an area model.  4.NF.A.2 states that students will compare fractions by creating same numerator or denominator as well as by using benchmark fractions and justify their conclusions, e.g., by using a visual fraction model. This lesson allows students to refine their ability to use visual fraction model and extend their understanding. I also like for students to be familiar with area models to represent fractions since area models are very helpful when multiplying fractions later in fifth grade. 

Students will play a game called Order the Fractions.  Students will play this game with a partner. The material needed for this game are:  24 (3” x 5”) cards marked as follows: 1/1, 1/2, 2/2, 1/3, 2/3, 3/3, 1/4, 2/4, 3/4, 4/4, 1/6, 2/6, 3/6, 4/6, 5/6, 6/6, 1/8, 2/8, 3/8, 4/8, 5/8, 6/8, 7/8, 8/8 (I write these on index cards for students to play with and then laminate them)

To play the game,

1. Shuffle the cards.

2. Deal three cards in a row, face up, to both players. (One extension could be to deal players 4 or more cards.)

3. Put remaining cards in a pile between the two players. Turn the top card over.

4. In turn, players replace one of their cards with the card that is face up or with the top card from the pile in order to try and make all three of their cards greater than the card to it's left.

5. On a players turn, they may pick the top card showing, or they may pick a card from the draw pile.  After a turn, a student places discard on the discard pile. 

The first player to arrange their cards so that each card is greater or equal to the one on the left is the winner and play can then continue for a new round. 

To play this game, I also require my students to show their final three cards on the Order the Fractions Worksheet. This allows me to use this as a formative assessment of how my students are doing using an area model to model comparing fractions. 


 This is an example of a student's work and their final three cards.  This shows a very common error students make when using an area model when comparing fractions. Click here to hear my thoughts about this error and my teacher moves to help this student.


This student is showing her final three cards on a separate piece of paper. She wanted to be able to draw larger fraction bars for her area model which is one strategy we discussed as a way to model more accurately. 


You can hear in this video the student says, "That's a knock" when he thinks his fractions are in order. This is a management technique I use when students play games. A student can knock on his or her turn and then the partner gets one more turn to try and get his/her cards in order from least to greatest. I have found that it cuts down on arguments about whether or not a partner "cheated" or is "playing fair."