Susan C. Anthony

Fractions 7: Comparing Fractions


  • A fraction kit for each student.
  • Fractional manipulatives for the teacher or a method of projecting so as to model what to do.
  • Student worksheets.

Note:  Words in green are words the teacher actually says.


  • Yesterday, you learned how many fractional parts are in a whole.
  • How many sixths are in a whole? (Six) Write 1 = 6/6 on the board.
  • How many eighths? hundredths? 364ths?
  • How do you know? (If you cut something into 6 equal pieces and still have all six of them, you have the whole thing.)

Anticipatory Set:

Learning: Today you will learn how to tell which of two fractional pieces are larger. What will you learn today?

Purpose: Determining which of two fractional pieces is larger is much different than determining which of two whole pieces is larger. This is an important concept of fractions. Not understanding it will cause you a lot of confusion.

Transfer: You'll be using the kits and pieces just like we did yesterday. Who remembers the rules for using the kits?

Motivation: Tomorrow there will be a quiz on everything we've learned so far: how to identify fractions, name fractions, shade in fractions, find the numerator and denominator, find how many parts are in a whole and determine which fractional piece is larger, which is what you'll learn today.


  • You will use the symbols < and >. Which side will go toward the larger fractional piece? (The big side.) Which will go toward the smaller fractional piece? (The small side, or point.)
  • You will lay out your pieces like you did yesterday. Then pick up the two pieces in the problem to see which which is larger, like this: Pick up 1/2 and 1/3. Write on the board 1/2 1/3. Write the appropriate symbol between them.
  • Be sure to use the pieces for all of the problems above the dotted line, even though you may see the pattern and be tempted to rush ahead. Find the rule for telling which piece is larger and use that rule to do the problems below the dotted line. If you have trouble seeing the pattern, raise your hand and I'll help you.
  • What are you to do above the dotted line? below the dotted line? if you can't see the pattern?

Guided Practice

Pass out the kits. As soon as a student has his/her pieces organized, give him/her the worksheet. Circulate to reinforce correct use of pieces and correct answers. Give assistance as needed.


Check worksheets together.

  • What is the rule? (A larger number on the bottom means it is a smaller piece.)
  • Does anyone know why 1/3 is smaller than 1/2 when 3 is larger than 2? (Because the denominator stands for how many pieces you cut something into. If I have a candy bar and share it with one other friend, we each get 1/2. That's MORE than I get if I share it with two other people. Then we would each get 1/3. 1/2 is more than 1/3.)

Collect the fraction kits and store in a box in the classroom.

You now have a very good grasp of the concept of fractions. Tomorrow we will have a quiz on what we've learned so far: How to identify fractions, name fractions, shade in fractions, tell the numerator and denominator, find how many parts are in a whole and determine which fractional part is larger.

Source:, ┬ęSusan C. Anthony