Description
Students “count up” using unit fractions (for example,
1
/
4
,
1
/
3
,
1
/
2
,
1
/
8
, etc.). The students or teacher can choose any unit fractions, and the teacher or students can set game rules such as: "When you get to one whole, stand up and state the quantity as both a fraction and as a whole". Note: this game is similar to a wellknown number game called BUZZ.

Mathematics
A unit fraction is the base unit of any fraction and always has a numerator of 1. For example onefourth is 1 onefourth of the fourths. 2 onefourths are 2 onefourth units. When we count these fourths, we use the language "1 onefourth", "2 onefourths", "3 onefourths", "4 onefourths", "5 onefourths" and so on. This helps students understand that we are counting units that are fourths and this allows us to count beyond one whole, such as 5 onefourths.

Curriculum Connections
Students will:
 learn how to count fractions in various ways, developing a sense of magnitude;
 count using unit fractions to go beyond one whole (e.g., 15 onefourths);
 develop the ability to calculate halves and wholes mentally based on unit fractions counting.

Instructional sequence
 Start in a circle, and have students count the unit fraction of your (or a student’s) choice. If the fraction selected is
1
/
4
, for example, the first person in the circle would say “1 onefourth”; the second person would say “2 onefourths”; the third person would say “3 onefourths”, and so on. When a student arrives at a whole number (such as 4 onefourths), they need to stand up and say the whole number equivalent.(This continues for each whole number, for example, the student that gets 8 onefourths needs to say “two”.)
 Be sure students count well beyond one (such as counting to 28 onefourths).
 When all students have counted ask students key questions.
Variations on the game
 Use concrete materials to help count by unit fractions (e.g., lay down a corresponding fraction strip piece for each count).
 One person states a unit fraction (such as onefifth). Students move around to join with enough people to represent 1 or 2 or 3 wholes (e.g., to make two wholes counting onefifths, 10 people, each representing onefifth, would join together).
 Add a second action/word whenever you get to the equivalent of the halfway mark between each whole.
 Have students represent the fraction using a model of choice when a random buzzer sounds.

Highlights of student thinking
Students may:
 connect counting unit fractions to counting other units, such as units of measure or items in whole number units;
 find the concept of the unit fraction challenging at first;
 get ‘stuck’ when counting beyond the whole;
 come up with a wide range of variations to the game when invited to do so.
Note: Field testing of this game demonstrated that it aided students in distinguishing between unit fractions (e.g., 5 onefourths) and mixed fractions (e.g., 1 and onefourth). Further, it supported student understanding of what made up a whole (in both area and set models).

Key questions
 If each person counted onefourth in our count, how many onefourths would we have counted in total? (e.g., if there are 27 students, they will have counted 27 onefourths, or 6 wholes and threefourths).
 How many wholes did we count? Did we end on a whole?
 How many onefourth units did it take to make one? How do you know?

Materials
 Optional materials include number lines, and/or concrete materials, such as Cuisinaire rods or fraction tiles.
