Preparing for the Lesson
Several practice fractions have been provided on the second page of the Fractional Clothesline Activity Sheet. Create a class set of the fractions by gluing each
fraction to an index card. You may want to adapt and use different
fractions that your class has been struggling with or that you wish to
add to extend your number line.
Fractional Clothesline Activity Sheet
Additionally, create index cards for the number 0, 1, 2, 3, and
4, and stretch a string across the length of your classroom, attaching
the ends to opposite walls with tape.
Student Number Line
Students should work in pairs or groups to allow for
discussions. Pass out the 0, 1, 2, 3, and 4 index cards to any
5 students in your class. Have those students place their cards on the
clothesline. Each of these whole numbers should be spaced an equal
distance apart. As students place them, one or more of the cards may
need to be adjusted to appear equally spaced. As a class, discuss
whether the cards were spaced evenly and are agreed upon. The string
and number line will cover the length of your classroom and should have
several feet between the whole numbers. This will allow for other
cards, representing fractions, to be placed on the number line.
Distribute the prepared fraction cards (one per student/pair/group). Once all the students
have a card, tell them to arrange themselves in number line order,
similar to the string. They will need to be in order from least to
greatest, according to the value on their card. During this part,
students will have to apply various strategies to compare and order
themselves. You may remind students of strategies you’ve used to
compare fractions. Several of the cards do not have common denominators
and students will have to decide which is larger through common
numerators, or based on decimal equivalents. Some students may organize
themselves realizing that 3/4 is actually three 1/4's
and figure out where to be. You may also have students use a calculator
to verify their answers. Question students to help them explore their
thinking. This portion of the lesson can be done quickly or, if you
wish, extended to incorporate maximum comparison strategies, depending
on students' experience with multiple fractions with different
In their groups, have students discuss briefly where the cards
should be pinned on the clothesline. Once the groups have come to some
conclusions, have the members of one group come up to the clothesline
and pin up their index cards with paper clips or clothespins. For
students who have equivalent numbers (e.g., an improper fraction that
is equal to a mixed number), clip the cards together in a column so
they are both in the same spot and still visible. Once all cards have
been placed, have a whole-class discussion to decide as a group if any
cards need to be moved, changed, or adjusted. Ask the class, “Do these
cards look like they are in the proper spot? Are there any cards that
need to be moved?”
As students are placing the cards, there are several ways to
compare fractions. You can point out that fourths are dividing the
distance from 0 to 1 into 4 equal lengths. This can also be done for
thirds, fifths, etc. Then discuss how 2/3 compares to 3/4 or other fractions by using lengths of wholes instead of the usual circles and squares.
Ask students, "What strategies did you use to decide if a fractional card is closer to 0, 1/2, or a whole number?"
[Each multiple of the denominator is a whole number. If
the numerator is close to the next multiple, it’s close to another
Repeat this process for each group until all the index cards are
placed. It is important to note that as more students begin to place
cards, it will be come more obvious when previously placed cards are
not in the correct spot. This is where discussion through the process
can be invaluable. Lead your students in identifying whether some cards
should be moved slightly so that the card currently being added will be
placed accurately. Have students continue to adjust the cards on the
clothesline until they are reasonable estimates.
Ask students, "What type of fractions are on the number line that are greater than 1 whole?"
[Mixed numbers are greater than 1 whole and are a way of writing numbers so the whole and the part are seen separately.]
They may also notice that several mixed numbers and improper fractions overlap. It is important to have students use the words equivalent or equal when discussing this.
The Clothesline Addition Game is a way for students to combine
different amounts that are represented on the clothesline using
estimation. To play the game, distribute the Fractional Clothesline Activity Sheet, and allow time for students to cut out the fraction
cards on the page 2. Students should start the game by flipping over
2 cards from a face-down pile of fraction cards, and then estimating
what they think the sum of the 2 cards will be. They should place a
marker or penny on their sheet that shows where they think the sum is.
For example, if they add 1/2 and 13/4, they will place their marker close to 21/4.
Remind students to look at the lengths each fraction is represented by
on the clothesline and to picture those lengths being placed end to end
to create the sum. Once they agree on the answers, they repeat the
process. If any students struggle, have them use calculators to double
check their estimations. You may have students perform the operations
according to a time limit or until the deck runs out of cards. As you
move through the classroom, help students find exact answers for
themselves if there are any disagreements.
Concluding the Lesson
After students have played several rounds of the Clothesline
Addition Game, ask them to summarize the lesson and lead them in a
discussion about their strategies for the game. Ask probing questions
to find out how they thought of adding the fractions together.
Some key questions may include:
- How are you combining fractions with other fractions?
[Some students may see the fractions as lengths on the
number line; some may see decimals; some may create equivalent
- What strategy are you using when you have to add a mixed number with a proper fraction?
[Some may create improper fractions; some may estimate the fractions and whole numbers separately.]
- How can you tell if a proper fraction is closer to 1 whole or closer to 0?
[The closer the numerator value is to the denominator, the closer to 1 it becomes.]
- In an improper fraction, how can you tell which whole number it is closer to?
[Each multiple of the denominator is a whole number. If the
numerator is closer to the next multiple, then it is closer to the next
whole value. For example, in 5/4, the numerator
is between 4 and 8, two multiples of the denominator. Since it is
closer to 4 than to 8, it is closer to the whole number 1 than the
whole number 2.]
- Are there any patterns you see in the placement of fractions on the number line?
[All proper fractions are greater than 0 and less than 1.
Fractions beyond 1 involve a whole number and are actually mixed
numbers or are improper fractions.]
Some students may think of using equivalent fractions while others
may think of using lengths on the clothesline. Allow students to
express their strategies and the patterns they noticed. It might also
prove a useful tool to leave the clothesline up for a while following
the lesson as a visible tool in the room.
Shodor, Connected Mathematics Grade Six, Bits & Pieces II, Investigation 3: Estimating with Fractions and Decimals.