6th Grade Math : Unit #4 - Number Sense : Lesson #10

Benchmark Fractions and more

Objective: SWBAT use benchmark fractions to compare and order fractions.
Standards: 6.NS.C.6 MP1 MP2 MP3 MP5
Subject(s): Math
60 minutes
1 DO NOW - 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.


The most valuable part of this lesson
Student Ownership

This was truly the most valuable part of the lesson.  I allowed the students time to work on this part on their own.  They had to decide where to place the fractions.  I called this their struggle time.  Some student got started right away, while others had a difficult time because of their lack of understanding of fractions.  After a few moments, I allowed them to work with their tablemates. During their conversation, I overheard them talking in terms of if the numerator and denominator being close together or farther apart would determine whether they were closer to zero or one.  Then I heard them talking about half and how they would figure out if the fraction was closer to 0, 1/2 or the whole.  One student said, you have to look at the denominator to figure out if it's half.

As students finished sorting their fractions, I went through each one and placed in on the board in the column the appropriate column as students advised me to.  If there were questions on any or if students disagreed, I placed a circle around it so we could discuss it as a group.

This part of the lesson formed the ground work for the remainder of class.  Unfortunately, this lesson took 2 days instead of one, but I wouldn't change it as the students had a great, conceptual understanding of fractions. 

Because the students had a good idea of how to use benchmark fractions they were able to compare and order with ease. 

I finished the day with comparing and ordering.  Day 2:  we worked with mixed and improper fractions and the performance task. 

 For students that struggled, I gave them a fraction sort to do at home.  They need to cut out the fractions on the first two pages.  Then fill in the numerators for the fractions on page 3 and 4.  The numerators should match the column heading of 0 1/2, 1, 1 1/2.

Fraction sort supplement

For examples:  0/3, 1.5/3, 3/3, 4.5/3.


Video example of a fraction in question.

2 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.

3 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. 

A great connection
Student Led Inquiry

As we were working with mixed numbers and improper fractions, I posed this question to the students

2 1/2 = 5/2  how can we prove this is true?  I was expecting the students to show me on the number line.  I was hoping for them to figure out the the algorithm for converting mixed numbers in to improper fractions. 

Making connections to mixed numbers

4 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. 

5 Closure - 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