More Back to Basics!

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SWBAT compare fractions using a variety of strategies.

Big Idea

Students learn that there are multiple strategies for comparing fractions (number lines, common denominators, and using benchmark fractions to estimate). Different fraction combinations can determine the best strategy.


5 minutes

The majority of the fraction work we have been focusing on this year has been fractions as part of a whole.  One basic skill I need to revisit with the majority of the class is fractions as part of a set.  To start today, students work for 5 minutes in their math journals in response to a prompt.

Show an example of a fraction representing a part of a set.  You may choose to write or draw out your example. 

Students share their examples.


10 minutes

For this lesson, I use the launch as a means to transition student thinking from fractions as part of set, to fractions as part of a whole.  To do this, I ask the students for help in recapping the lesson from yesterday.

To prompt students thinking, I draw a number line on the board and write the fraction 3/5 and write the word focus. 

What the the focus of yesterday's back to basics' lesson?

Students turn and talk with their group members about the lesson from yesterday.  Then groups share out their thinking. As they share their thoughts, I make notes on the board and use the notes to wrap up the launch.

The focus of yesterday's class was to make us more precise in our speaking and thinking about fractions.  Before, we would say something like 3/5 is two away from 1.  But this doesn't make sense because it is not 2 wholes away.  We have to use the denominator too.  3/5 is 2/5 from 1 whole. The denominator tells the size of the pieces!  The numerator and denominator have to work together.

Guided Practice/Group Activity

10 minutes

To build the focus on the whole fraction, I ask the students to work in their group and use any strategy they can to determine which fraction is larger -- 2/7 or 3/6.

I choose these fractions because 3/6 is equivalent to 1/2, so once that is established all students can access this problem and participate in the discussion.  I choose 2/7 because it has an odd denominator and it is close to 6.  

As I circulate the room, I see the students applying a variety of strategies to determine the answer.  Groups who use one strategy were encouraged to try more.  

After all groups come to a decision, I ask students to share their approach.  Three strategies are used.

  1. Equivalent fractions (MP7 - Look for and make use of structure. Students are considering the structure of the fraction to determine equivalent fractions).
  2. Number line (MP4 - Model with mathematics.)
  3. Benchmark fractions (MP2 - Reason abstractly and quantitatively).

Independent Practice

20 minutes

For independent practice, students are asked to choose 1/3 of the problems from the set of 12.

These problems came from a page in a 4th grade math workbook.  The directions require students to place 3 fractions (with unlike denominators) in order from least to greatest.  

I also add the expectation that they prove their answers as correct by solving with two of the strategies we discuss today.

This lesson continues tomorrow, student work is not collected and there is no exit ticket work today.