Susan C. Anthony

Fractions 2: Concept of Fractions, Naming Fractions


  • Teacher needs: 3-4 candy bars, same size but different kinds, knife
  • Student worksheets
  • Students need: scissors, crayons, glue

Depending on how students do on the diagnostic test, the teacher may opt to combine some of these early lessons. It is much better to go step by step, however, even with the most advanced students.

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

Anticipatory Set

Learning:  Today you will learn what a fraction is and how to name fractions. You will also learn the meaning of "numerator" and "denominator." Write those terms on the board, with numerator on top.

Purpose: Who remembers some of the reasons people use fractions? Did anyone find any more?

Transfer: You probably already use fractions more than you realize. Name some ways you personally have used fractions.

Motivation: A suggestion: after students have completed the lesson successfully, offer to break the candy into fractional parts and share it.

Check for Understanding: Some sample questions are below. It is important to check for understanding frequently throughout every lesson. I will indicate good places to check for understanding with a pound sign: #.

  1. What will you learn today?
  2. Why are fractions important?
  3. What will you get if you do a good job today?


  • A fraction is an equal part of a whole. # (The asterisk means to ask: What is a fraction? In a classroom situation, all students may answer at once. This kind of back and forth communication keeps students engaged and on task.)
  • For example, if I have one whole candy bar and I want to share it with a friend, what can I do? (Divide it in half.)
    Right. I'll do that. (Cut.)
  • Now can I share it with a friend? (Yes.)
  • The part I give to my friend is written like this: Write 1/2 on the board, with a horizontal rather than a diagonal line.
  • The top number in a fraction is called the numerator. Point to the "1" on the board. # What is the top number called?
  • The bottom number in a fraction is called the denominator. Point to the "2" on the board. # What is the bottom number called?
  • Write some fractions on the board and point to numerators and denominators at random, having children name them.
  • Then erase the words and have the children continue to name them.
  • The denominator stands for the number of equal pieces I cut the whole into. How many pieces are there? (2) What does the denominator stand for? (number of equal pieces the whole is cut into)
  • Another way to look at it is the denominator stands for how many people I have to share the whole candy bar with. In this case, I'm sharing it with two people, so 2 is the denominator.
  • The numerator stands for the number of pieces I gave my friend. How many pieces did I give my friend? (1) What does the numerator stand for? (The number of pieces I gave my friend.)
  • Now, what if I have two friends and myself and only one candy bar? (Divide it in three pieces.)
  • How much of the candy bar do I get to eat? (1/3, review "numerator" and "denominator")
  • How much do I give away? (2/3)
  • What if I have three other friends? Continue with examples until kids have the idea.
  • Non-example: The parts you divide a whole into must be equal. Say I have one friend to share this candy bar with. Divide the candy into unequal pieces. This wouldn't be fair, would it? Pieces are not halves unless the whole candy bar is divided into two equal pieces.
  • What is important to remember when dividing a whole into fractions? (They must be equal.)

Guided Practice

Now, you'll divide circles into fractional parts. # What will you do now? Pass out the papers.
Let's read the directions together. List materials and steps. Get out the materials.


Remember to cut neatly and only use a spot of glue. Be very careful not to get glue on the desk.

During guided practice, circulate among the students, giving assistance and reinforcement as needed.


Let's go over what we learned today.  What is a fraction? (An equal part of a whole.)
What part of the candy bar am I holding up? (1/2, 2/3, etc.)
In the fraction 3/4, which is the numerator? Which is the denominator?

Go on to read Fractions 3: Identifying Fractions
Source:, ┬ęSusan C. Anthony