Susan C. Anthony

Fractions 6: Parts to Wholes


  • A fraction kit for each student. You can buy these or make your own. For these worksheets, each kit should have at least 3 wholes, 4 halves, 6 thirds, 8 fourths, 12 sixths, 18 ninths, and 16 twelfths.
  • 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.


  • By now, you know how to name and identify fractions of all kinds and shapes.
  • What are some examples of fractions? (1/2, 3/4, etc.) Write these on the board.
  • Which is the numerator? What does it stand for?
  • Which is the denominator? What does it stand for?
  • What are some examples of shapes that can be divided into fractional parts? (circles, squares, etc.)
  • Put up some shaded examples and have students name the fraction.

Anticipatory Set:

Learning: Today you will use individual fraction kits to learn how many of each kind of fraction is in a whole. What will you do today? You'll also learn how to organize and use the kits, which we'll need for the rest of the lessons on fractions.

Purpose: Although the concept of parts to wholes will seem very simple, It is extremely important. Kids who don't understand this completely and thoroughly often get very confused when they get to more complicated work with fractions, like reducing improper fractions and subtraction with regrouping. Why is this important to know?

Transfer: You really already know this because you know how fractions are made. This is another way of looking at what you already know.

Standards for Fraction Kits: The reason we are using actual fractional pieces to learn concepts is because actually seeing them and using them will help you get the ideas set in your mind. They will help you remember what you know. Later, if you forget exactly how to do a certain kind of problem, you can imagine the pieces in your mind and figure out how to solve the problem.

Here are the rules for the kits:

  • Have your pencil on your desk before you open the envelope.
  • Take out the fraction pieces carefully.
  • Separate them into piles of halves, thirds, etc. On the first day of use, if the kits have been used before by someone else, have students count to ensure they have all the pieces. Collect any extras and supply any pieces missing from individual kits.
  • Lay out the pieces along the top of your desk. Put the background circles in front of you. Be careful not to fold, play with, or lose pieces.
  • When we are finished with the lesson, put the pieces back in the envelopes. Check around your desk to see if any have dropped on the floor and pick them up.

Pass out the kits and have kids organize them.


  • You will be getting a worksheet that will ask you to use the pieces to find answers. Please use the actual pieces to do all the problems up to the dotted line. You may see the pattern before then, and be tempted to rush along without using the pieces. Please don't, as the pieces will help you get a picture in your mind so you will be much less likely to forget when you are in the middle of a long complicated fraction problem with many steps.
  • The first problem is: How many halves are in a whole? Write 1 = __/2 on the board. Use a horizontal rather than a vertical line.
  • Do it like this. Demonstrate by putting two halves on the background circle, then writing 2 in the answer space on the board. Read: 1 equals two halves.
  • Be careful that the pieces don't overlap or have spaces between them. Demonstrate mistakes, especially 3/8 ≠ 1/3.
  • Below the dotted line on your worksheet, you will have to use the pattern you learn so you can answer questions for which there are no pieces? What happens when you get below the dotted line?

Guided Practice

Pass out the worksheets. Students work quietly. Circulate and reinforce students for correct use of pieces, and for finding and applying the pattern.


Correct worksheets together.

  • Who can tell me the rule for knowing how many parts are in a whole? (When the numerator is the same number as the denominator, it is a whole)
  • Right. If I have a whole candy bar, cut it into four equal pieces and keep all the pieces for myself, I have the whole thing.
  • Let's look at it the opposite way. If I have 5/5, what does that equal? (1) Give more examples until students clearly understand the concept.
  • Tomorrow, we'll use the fraction kits to compare fractions.

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

Go on to Fractions 7:  Comparing Fractions
Source:, ©Susan C. Anthony