Summary
Students will use sticky notes to learn about fractions.
Materials
- 3" x 3" Post-it® notes
- 1 1/2" x 2" Post-it®
notes
- Various sizes of
rectangular-shaped
paper
- Rulers and yardsticks
- Scissors
Background for Teachers
This activity works best when students have a familiarity with
division, even if only with whole numbers. Students should know such
terms as divisor, the number by which another number is divided;
dividend, a number that is divided by another number (divisor); and
quotient, the answer to a division problem.
Having already learned operations with fractions, such as addition,
subtraction, and multiplication, students should also understand the
difference between the numerator (top number) and the denominator (bottom number). The line between the two means divided by.
Therefore, the numerator represents the dividend, and the denominator
represents the divisor, or the bottom number divides the top number.
Finally, a concept used in fractional division is multiplicative inverse,
or the reciprocal. The product of a fraction and its multiplicative inverse
equals one (e.g., 3/4 x 4/3 = 1).
Intended Learning Outcomes
2. Become mathematical problem solvers.
4. Communicate mathematically.
Instructional Procedures
Invitation to Learn
Give each pair of students a Post-it® note. Ask the class a series of
questions, such as:
- What, if anything, do Post-it® notes have to do with math?
- How might a Post-it® note be used to demonstrate a
mathematical idea?
- In what way(s) can Post-it® notes be used to represent operations
of fractions?
Notice the questions get more specific.
List responses on the board. Explain and discuss how math is "all
around us," even in the form of Post-it® notes.
Instructional Procedures
- Show students a piece of 8 1/2" x 11" piece of paper. Ask, "How
many 3" x 3" Post-it® notes would be needed to fit the width of
the piece of paper?" Elicit responses from someone who has
solved the problem. (2 5/6)
- Model the process by taking the 3" x 3" Post-it® notes and
carefully placing them along the 8 1/2" edge of the paper.
Carefully cut the overlapping part of the Post-it® note. Measure
the remaining part, which should be close to 5/6 of 3" or 2 1/2".
Measure the cut segment, which should be 1/2".
Note: To understand the concept of 5/6 of 3, ask the students to
take the 1/2" amount they cut off and, using their ruler,
determine how many 1/2" segments would be in 3". There
should be 6. Since they have cut off one of those 6 segments,
there are only 5 left, or 5/6 of the original 3". That means
there are 2 full Post-it® notes and 5/6 of a third one that fit
within the 8 1/2" side of the paper.
- Perform the same procedure with the 11" side of the piece of
paper by dividing 11 by 3. Then place the 3" x 3" Post-it® notes
along the 11" edge, again trimming and measuring as above. Add
the fractions together to get the total number of Post-it® notes to
measure the length and width.
- Do the same procedure with the 1 1/2" x 2" Post-it® notes for
both dimensions. Make sure students select either the 1 1/2" side
or the 2" side to measure with.
- Explain the process mathematically, using traditional division,
show how many 3" x 3" Post-it® notes would fit by dividing
8 1/2" by 3, like this: 8 1/2 ÷ 3, which is the same as
- After modeling the above, pass out two different sizes of
rectangular paper to groups of students, depending on class size.
- Have students determine mathematically how many of each kind
of sticky notes it would take to cover both dimensions (length and
width). After doing the math, students request the number of
Post-it® notes they need and cover their paper. Cut the fractional
part of the Post-it® by measuring it first.
- Display the students' work and discuss strategies and steps for
finding the answer.
Extensions
- Students can use what they've learned about fractions, division,
multiplication, and measurement to apply this process to a real
world situation, such as hanging wallpaper. Give students the
height and width measurements of a wall to determine how much
wallpaper is needed. Using the concept of area, students
determine how much wallpaper is needed to cover the wall.
- Have students write, using sequencing, the steps of the process for
this activity. They can write the steps on sticky notes and place
them on the board or a wall.
- Ensure that tactile and kinesthetic learners have the opportunity to
place the Post-it® notes and cut the overlapping parts.
Family Connections
- Encourage students to try this activity at home with family
members, making sure they use the mathematical operations
learned for division and multiplication of fractions.
- Instruct students to find three items at home, square or rectangular
in nature, to measure with Post-it® notes. Share the results with
the class.
Assessment Plan
Observation of students at they complete the Post-it® note
activity. Do they understand how to divide and multiply fractions
both mathematically and graphically?
Bibliography
Research Basis
Weisenberg, R.C. (1997). Appropriate technology for the classroom--using "Post-it® Notes"
as an active learning tool. Journal of College Science Teaching. 26(5), 339-44.
This article addresses the use of Post-it® notes as effective teaching
tools. It lists activities using Post-it® notes, such as modeling, concept mapping,
and constructivist group activities.
Widmer, C. & Sheffield, L. (1998). Modeling mathematics concepts: using physical,
calculator, and computer models to teach area and perimeter. Learning and Leading with Technology. 25(5) 32-35.
This article examines ways middle school students use simple
problems to gain a deeper understanding of mathematical concepts. It
demonstrates the use of sample area and perimeter problems.