Which Fraction is Greater?

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Objective

SWBAT: • Compare fractions • Develop strategies for comparing fractions

Big Idea

Which fraction is greater: 9/8 or 4/3? Students play the comparing game in order to develop strategies for comparing fractions.

Do Now

10 minutes

See my Do Now in my Strategy folder that explains my beginning of class routines.

Often, I create do nows that have problems that connect to the task that students will be working on that day.  Today I want students practicing different ways to represent a fraction.  Drawing thirds on a circle can still cause some students trouble.  If this is the case I remind students that they can draw a Y inside the circle for thirds.  For the group of circles, a common mistake is that a student will shade 2/3 of one of the circles, rather than 2/3 of the group of circles.  If this occurs I have the students reread the directions out loud.  Some students may struggle with problem 4 because it presents the rectangle as two-thirds of the wall.  The students must figure out that if they split the “wall” into two equal pieces, each piece will represent 1/3 of the entire wall.  They will need to add another third to create the entire wall.    

Students participate in a Think Pair Share.  I call on students to share out their thinking. If I notice any of the common mistakes mentioned above I present them and have students share their thinking.  Students are engaging in MP3: Construct viable arguments and critique the reasoning of others.

Which fraction is greater?

10 minutes

Notes:

  • I use the data from the Fractions Pretest to Create Homogeneous Groups
  • Each group will need a 1-10 spinner and a paper clip, or a 1-10 die.
  • Another possible scaffold is for students to use 6-sided dice instead of 1-10 spinner.

I have students move into their groups.  I ask for a volunteer to come up and play the game with me so everyone can learn the rules.  The game has 4 versions, but everyone will start with version 1 where the larger fraction wins a point.   I explain that each player will take turns rolling the die until they have rolled 4 numbers.  Each time you roll, you write the number in one of the boxes.  Once you write a number in a box, you can’t move it.  When you’re done you’ll have a fraction and two extra or “reject” numbers.  A common misunderstanding is that students have to use the same numbers.  Each player rolls and writes his/her own numbers.

The volunteer and I take turns rolling and recording our numbers.  Once we finish we need to create models of each fraction.  We decide on which shape should represent one whole (circle, rectangle, etc.) and we each create a model of our own fraction.  I ask the class, which fraction is greater?  With some rounds it will be clear just looking at the models.  With other rounds students may need to create equivalent fractions.

Once we have determined the winner we write an inequality.  For example, the number sentence might be 3/2 < 5/2.  Then I’ll ask students how we could rewrite the inequality using mixed numbers instead of improper fractions.  If students struggle with this, I return to the model to count the wholes and the parts of a whole.

I tell students that once they finish their Version 1 game board (worksheet) they need to check in with me before moving on to the next version.

The Comparing Game

25 minutes

As students work, I walk around and monitor student progress and behavior.  I make sure that groups check in with me when they complete the version 1 game board, before moving on to the other version.  Students are engaging in MP1: Make sense of problems and persevere in solving them and MP4: Model with mathematics

If students are struggling I have them explain their models.  I ask them which fraction they think is greater and why.  I make sure that students’ model matches the fraction and they are able to explain why their model is correct.  Who won?  I ensure that students can clearly explain who is the winner and why.  If I feel that a group is not ready to move on to the next version, I will give them a new game board of the same version so that they can continue to practice.

Closure and Ticket to Go

15 minutes

For Closure I ask students to look at the pairs of fractions on the Closure sheet and to think about which fraction is greater.  I challenge students to not pick up their pencils, but to just look at the fractions and see which pairs they can determine are greater.  I want students to apply what they were practicing in the game and notice patterns.  Students participate in a Think Pair Share. 

I ask students to share out a pair of fractions where they can easily see which one is bigger.  Some students may share that when the numerators are the same, the fraction with the smaller denominator is bigger.  I ask if this is always the case and I have students come up with more examples that support this idea.  Other students may share that if the denominators are the same, then the fraction with the larger numerator is bigger.  I ask, “Why does that happen?”  I want students to explain that if the two wholes are cut into equal pieces, the fraction with more pieces selected (higher numerator) is greater.  Other students may share a strategy of using benchmark numbers (0, ½, and 1) to help them visualize and compare.  Students are engaging in MP7: Look for and make use of structure.

I specifically ask students about “g” and “i”.  For “g” I want students to realize that 4/3 is the same as 1 1/3 and that 9/8 is the same as 1 1/8.   One-third is much larger than 1/8, so I know that 4/3 is greater.  I emphasize how using the strategies that students have shared is usually much more efficient than creating common denominators.  Yes, there will be times when you need to create common denominators, but a lot of the times you can use your fraction number sense to help you!

I pass out the Ticket to Go and I collect students’ game boards to look at.  Then I pass out the HW Which fraction is greater.