Unit D

# Unit Fractions Counting Game #### Description

Students “count up” using unit fractions (for example, 14, 13, 12, 18, 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 well-known number game called BUZZ.

#### Mathematics

A unit fraction is the base unit of any fraction and always has a numerator of 1. For example, one fourth is a single one-fourth unit. Two fourths are two one-fourth units. When we count these fourths, we use the language "1 one-fourth", "2 one-fourths", "3 one-fourths", "4 one-fourths", "5 one-fourths" 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 one-fourths.

#### 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 one-fourths)
• develop the ability to calculate halves and wholes mentally based on unit fractions counting

#### Instructional Sequence

1. Start in a circle, and have students count the unit fraction of your (or a student’s) choice. If the fraction selected is 14 , for example, the first person in the circle would say “1 one-fourth”; the second person would say “2 one-fourths”; the third person would say “3 one-fourths”, and so on. When a student arrives at a whole number (such as 4 one-fourths), they need to stand up and say the whole number equivalent.(This continues for each whole number, for example, the student that gets 8 one-fourths needs to say “two”.)
2. Be sure students count well beyond one (such as counting to 28 one-fourths).
3. When all students have counted ask students key questions.

#### Variations on the game

1. Use concrete materials to help count by unit fractions (e.g., lay down a corresponding fraction strip piece for each count).
2. One person states a unit fraction (such as one-fifth). Students move around to join with enough people to represent 1 or 2 or 3 wholes (e.g. , to make two wholes counting one-fifths, 10 people, each representing one-fifth, would join together).
3. Add a second action/word whenever you get to the equivalent of the half-way mark between each whole.
4. 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 one-fourths) and mixed fractions (e.g., 1 and one-fourth). Further, it supported student understanding of what made up a whole (in both area and set models).

#### Key questions

1. If each person counted one-fourth in our count, how many one-fourths would we have counted in total? (e.g. , if there are 27 students, they will have counted 27 one-fourths, or 6 wholes and three-fourths).
2. How many wholes did we count? Did we end on a whole?
3. How many one-fourth 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.