Pose the following question to the whole group and have them discuss in small groups or pairs:

"Would you rather share one pizza between two or one pizza with four people? Show or explain why or why not." [You would get more pizza if you shared one pizza between two people. Make sure you emphasize that the pizzas are the same size.]
(SMP 4 is employed if students generate a model to show how they make sense of the problem.)

Have students share their thinking with the group.

Clearly state the purpose of today's lesson. "We will be investigating denominators as we cut the same size paper strips (unit) into more and more pieces."

Explore

Model:

Pass out six strips of construction paper (one of each color) to each student. Specify one color and hold it up. Explain that this first strip will represent one whole unit. Write "1 Whole" on one side. Have students do the same.

Hold up a second strip and have students hold up the same color. Use the following set of questions for each strip as you move on to cut halves, fourths, and eighths (SMP 7). Use a pre-marked template with thirds rather than trying to get them to fold the strip into thirds. After that the students can fold the thirds in half to make sixths.

Ask:

"What strategy can you use to cut this strip into two (4,8, …) equal pieces?" [When dividing the strip into two equal pieces you could fold the strip in half. Fourths will require the students to fold the strip in half and then fold each half in half.]

"How do we know they are equal? Why is it very important that each fold/cut be exact?" [Check for equality by placing the strips one below the other.]

"What fraction name can we give each piece? Why do we give it that name?" [Example: When we cut the first strip into 2 equal pieces, we name each piece ½. Each piece is one of two equal sized pieces.]

"What fraction name can we give each piece? Why do we give it that name?" [Example: When we cut the first strip into 2 equal pieces, we name each piece ½. Each piece is one of two equal sized pieces.]

"How do we write this?" (put on the board)

"What does the numerator represent in ½, ¼…?" [The numerator tells how many equal sized pieces are named.]

"What does the denominator represent in ½, ¼…?" [Denominator tells how many equal sized parts the whole is divided into.]

Model how to carefully fold and cut the strip to create equal parts. Label each piece with the unit fraction using the same color for each part. Have students do the same. Continue this process for fourths and eighths.

After completing ½, ¼ and 1/8 move on to ⅓ and 1/6.

Once everyone has a complete set of fractions strips; have them organize them on their desks from largest pieces to smallest.

Ask, "As the denominator increases, what happens to the size of the pieces?" [The pieces get smaller as the denominator increases.]

This is an example of student work using 9" x 1 "strips in a math journal.

Discussion / Number Talk:

Ask students to hold up a fraction piece. Chose one student (holding up ½, 1/3, ¼, or 1/6) to stand and write the fraction on the board. Have the other students put down their piece, choose a fraction that is smaller than the fraction recorded on the board, and hold it up. Wait until all students are holding up just one piece.

Ask:

“How did you decide on that piece?”

“What is the numerator? What is the denominator?” “What do those numbers represent?”

“Are there other fractions smaller than the one recorded on the board? If so, what are they?”

Using the Activity Sheet, continue comparing fractions in small groups or individually until all of the fractions have been compared and recorded.

Synthesize

Ask students to think about why comparing fractions can be confusing when thinking about comparing whole numbers.

Share with the class that one of the most common misconceptions is thinking fractions with smaller denominators (1/2) are smaller than fractions with larger denominators (1/8). In this closing discussion the goal is to compare the size of 2 and 8 to the relative sizes of ½ and 1/8. This can be a whole group or small group discussion (SMP 7).

"If 2 is smaller than 8, why is ½ larger than 1/8? How do you know? What did we do in this lesson to help us better understand the difference between whole numbers and fractions?"
[This is discussed above: Ask, "As the denominator increases, what happens to the size of the pieces?" [The pieces get smaller as the denominator increases.]

Choose two fractions from below to compare. Using words, numbers and/or pictures explain which is larger.

1/2 1/4 1/3 1/8 1/6
[This sheet has an answer key.]

Extension

Ask student to think about fraction strips that are cut into more than 8 pieces (12, 16….). How would they compare to the existing strips?

Teacher Reflection

How do you know which students understand that a fraction can be represented as part of a whole?

What information do you get from this exit slip about student learning? How can this information be used to adjust instruction continually in ways that support and extend learning?

How do you know which students can articulate the relationships between fractions? What activities are appropriate for students who have not yet developed this understanding?

“As the denominator increases, what happens to the size of the pieces?”

Standards

CCSS, Content Standards to specific grade/standard

CCSS.Math.Content.3.NF.A.1 Understand a fraction 1/b as the quantity formed by 1 part when a whole is partitioned into b equal parts; understand a fraction a/b as the quantity formed by a parts of size 1/b.

CCSS.Math.Content.3.NF.A.3.d Compare two fractions with the same numerator or the same denominator by reasoning about their size. Recognize that comparisons are valid only when the two fractions refer to the same whole. Record the results of comparisons with the symbols >, =, or <, and justify the conclusions, e.g., by using a visual fraction model.

CCSS, Standards for Mathematical Practices

SMP 4 Model with Mathematics.

SMP 7 Look for and make use of structure.

PtA, highlighted Effective Teaching Practice and/or Guiding Principle CCSS