Benchmark Fractions and more

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SWBAT use benchmark fractions to compare and order fractions.

Big Idea

When students understand how to use their benchmark fractions they can work more fluently to compute, compare, and order them.


15 minutes

Students will be sorting fractions into sections labeled 0, ½, 1, 1 1/2.  The object of this activity is to get the students more familiar with location of the fractions along with being able to use their benchmarks when estimating sums and differences.  As students complete their sort, I’m going to have them do a HUSUPU to share and explore their solutions.  Students should speak about the reason they decided to place a certain fraction.  They can use their fraction strips or a number line to help support their answer.  As students return to their seats, ask them the following questions:

  1.  What strategy did you use to determine where to place your fraction?  Choose several students to share their strategy.  You can have them model their thinking on the board too.
  2. How can you use benchmark fractions when computing?  This is a stretch question, but I’m hoping to hear that benchmark fractions will help you with estimating.


Comparing and Ordering using benchmark fractions

20 minutes

Begin using the slide for comparing because there are only two fractions to work with.  Have the students use their benchmark fractions to decide whether the fractions are greater than, less than or equal to each other.  As students work through these problems, make sure they discuss their strategy.  So, if they choose to use a number line to visualize the benchmarks then that would be a strategy.  If they use fractions strips or fraction circles, that is fine too.  When using a visual be sure to watch for the equal parts.

As students work through the comparing, have them share their strategy with partner. (SMP 3)

Next, have the students use their benchmark fractions (0, 1/2, 1, 1 ½ ) to put the fractions in order from least to greatest. 

I’m not showing the students how to make equivalent fractions to compare and order when using benchmark fractions allows them to do this more fluently.

Fractions greater than 1

15 minutes

Students will be using their benchmark fractions again to develop an understanding of improper and mixed numbers.   Students will be asked to recognize the marks in between the whole numbers and identify the mixed number.  Then they will be asked to write the mixed number as a fraction.  At this point it might be a good idea to remind students that fractions have numerators and denominators.  Also, if students are having difficulty finding the improper fraction, you can ask them how many halves do you count to get to 2 1/2?   If students still do not understand, have them draw fraction bars so they can see the 5/2 better.

Recognizing that a fraction is improper is difficult for students.  They see a numerator and a denomintor without recognizing that the numerator is greater than the denominator.  Using the numberline will help students pay attention to the numbers they are working with. 

Performance Task

25 minutes

Students will be working on a performance task and applying their knowledge of benchmark fractions, equivalent fractions, comparing fractions and mixed and improper numbers to answer questions based upon real world problems.   For each problem, I’m going to have the student read the problem, use a strategy, then find the solution. (SMP 1,2, 5).  The strategies I’m expecting to see are using the number line or fraction bars.  Remind students that it is important to represent the fraction using equal parts (SMP 6).

I liked this problem because the students need to apply their learning and each problem is connected to the other which is very real life learning. 


15 minutes

I want to give the students time to reflect upon their learning over the past few days.  I want them to answer 4 questions that I will be collecting as evidence of student learning. Students should work independently, at first, then they can share and explore with a partner or tablemates.

On a piece of paper have the student write their name.

  1.  Describe your strategy for finding equivalent fractions.
  2. Explain how you know one fraction is greater than another fraction.
  3. When working with fractions greater than 1, describe how you write a mixed number.
  4. Describe how you write a mixed number as a fraction