Lesson Title: Making Fraction Sets



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

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“Chunk” sixths

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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 Confusion-

Students 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. [pic]

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