Lesson Title: Making Fraction Sets
Creator: Kimberly R. Perkins
Grade Level: Third
Big Idea: Equivalency
Essential Question: How could you make equal or fair shares? What strategies could
you use to order and compare parts of a whole?
CSOs, LS, TT:
Content Standards and Objectives:
M.O.3.1.5
Students will demonstrate an understanding of fractions as part of a
whole/one and as part of a set/group using models and pictorial representations
M.O.3.1.6
Students will create concrete models and pictorial representations to
compare and order fractions with like and unlike denominators, add and subtract
fractions with like denominators, and verify results.
M.O.3.1.14 create grade-appropriate real-world problems involving any of four
operations using strategies, explain the reasoning used, and justify the procedures
selected when presenting solutions.
Learning Skills:
21C.O.3-4.1.LS3 Student, cognizant of audience and purpose, articulates thoughts and
ideas accurately and effectively through oral, written or multimedia communications.
21C.O.3-4.2.LS1 Student engages, with teacher assistance, in a critical thinking
process that synthesizes knowledge and ideas.
21C.O.3-4.2.LS3 Student engages in a problem solving process that promotes
questioning, planning investigations and finding answers and solutions.
Launch/Introduction (suggested time 15-25 minutes)
Activating Prior Knowledge- To activate student’s prior knowledge about fair shares, fold
a piece of red construction paper in half, mark the fold with a dark marker, unfold it and
show it to the class. Ask the students:
How many equal pieces did I make?
What fraction is each part?
How could you write that?
Write ½ on each section in dark marker and write ½ on the board. Tell the students that
each pair has received five sheets of colored paper (the five colors are: red, yellow,
orange, green and blue). Then tell each pair that they will now fold and cut one red
sheet into two equal pieces, one yellow sheet into four equal pieces, one orange sheet
into eight equal pieces, one green sheet into three equal pieces, and one blue sheet
into six equal pieces.
Then you will label each piece with its fraction name, as I did on my halves. I wrote ½
on each piece.
Specialized Vocabulary Development –The vocabulary will be introduced during
discussion in the investigation/explore:
numerator
denominator
whole
equivalent
Investigate/Explore: Give each pair of students five sheets of the 8 ½” x 11” paper.
Explain that they will be using these sheets to make Fraction Sets. Post the directions
that you prepared on chart paper. Now direct the pairs to fold and label, in pencil, their
½ fraction set. As students label each piece, ask them:
How would you compare a piece with another piece?
Do you agree that you have equal pieces and that your fraction names are correct?
When students think they are ready, ask them to hold up their sheet halves. Tell the
students that you are going to double-check your set. Think aloud accepting student
responses:
How do I know that I made equal pieces?
How do I write that they are equal?
Through this discussion, use the vocabulary words: whole and equivalent. Emphasize
that students are expected to use these terms to refer to fractions in our class
discussions. Then cut your halves apart for the students to observe what you expect.
Students work in pairs to do the same. The pairs will continue working until their entire
set is complete. When most students have finished making their Fraction Sets, bring
the class back together briefly.
Have each pair of students bring up one of their pieces from their Fraction Sets. You
may need to encourage a pair to bring up a particular fraction piece, in order to, make
sure all of the fractions are on display. Walk around and check for pairs that folded and
cut a piece differently for a fraction and display those as well. For example, some
students may have cut “thin” sixths, and some may have cut “chunky” sixths. These are
equal, but they are different. Tape the fraction pieces to the board in no particular
order. Below is an example of the fractional parts that may be displayed in two ways:
“Thin” sixths
“Chunk” sixths
Tell the students we want to order these fraction
pieces from smallest to largest with the smallest over here (to the left) and the largest
over here (to the right). Ask them: Which of these would be the smallest?
As the students begin to think and respond, use the vocabulary: numerator and
denominator during the class discussion. Set the expectation for the students to use
their vocabulary to describe the fractional parts. Give the class time to respond to the
questions with you, and then let them know that they will continue this discussion with
their partners to prove their reasoning. Students then order their own Fraction Sets
from smallest to largest. They will discuss their ordering at the end of the session.
Ongoing assessment will take place during this part of the lesson. Walk around and
make observations about the students work. Ask yourself:
Do students judge the size of each fraction by measuring one against the other in some
way?
Do some students use the denominator to determine the size of the fraction?
Do they notice anything about the relationship between the size of the denominator and
the size of the piece?
Summarize/Debrief the Lesson: Bring the class together to look again at the Fraction
Set pieces we taped to the board. Ask the students: What did you and your partner
notice about the order of these fractions as you compared them?
As students share, allow them to come to the board as needed and compare physically
the fractional pieces. Discuss their methods for ordering the fractions and demonstrate
that different-shaped pieces that are the same fraction of the same whole have equal
areas.
As an informal assessment of the lesson, have the students fill out an exit slip using a
post-it slip of paper. Write the essential questions, from the beginning of the lesson, on
a piece of chart paper and have the students write their answers on the post-it papers.
By having some way for the students to label their post-its so that one can identify which
student wrote the answer, one can identify which students may need some assistance
with this concept in further lessons. The following questions are the essential questions
that should be written on the chart paper: How could you make equal or fair shares?
What strategies could you use to order and compare parts of a whole?
Once the discussion is complete, distribute envelopes or plastic bags for the students to
store their Fraction Set for the next lesson.
Materials:
Poster with directions (prepared ahead of time)
Five sheets of 8 ½” x 11” paper per pair (one of each: red, yellow, blue, orange, green)
Scissors for each pair
Envelopes or resealable plastic bags
Rulers (as needed)
Teacher-made fraction set
Post-its
Duration: This is a sixty minute lesson.
Teacher Notes: This lesson comes from the unit entitled, Finding Fair Shares, in the
Investigations series. Prior to this lesson, students divided rectangles into equal pieces.
They also discussed how to prove that each piece is equal and how to label an equal
share as a fraction of a whole.
Identifying the Mathematical Goals- In this lesson students will:
recognize that a fraction is a part of the whole
demonstrate that different-shaped pieces that are the same fraction of the same area
have equal areas
order unit fractions
Anticipate ConfusionStudents may attempt to draw on past experience with numbers, and may think at first
that 1/3 is greater than ½, because 3 is greater than 2. In this case, students may still
conceptualize fractions as two separate numbers.
Students may ignore that all the fractional parts combined will make the whole.
Therefore, they may cut off part of the whole in order to make the pieces equal.
To make it easier to recognize “top” and “bottom” numbers, write all fractions that
students will see with the numerator directly above the denominator and with the divide
line horizontal rather than diagonal.
Students may cut fractions into equal parts in the shape of triangles.