Use Fraction Strips to Name and Compare Fractions

Lesson 1 of 4

3rd grade

60 minutes

Description

Create and use fraction strips to discover name fractions and compare two unit fractions.

Materials

• 9 x 12 sheets of construction paper in six different colors. Cut into twelve 1 x 9 inch strips; each child will need six strips, one of each color.
• Scissors
• Chart Paper
• Lesson 1 Activity Sheet
• Lesson 1 Activity Sheet Answer Key

Introduce

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.]

Assessment

Exit Ticket
Exit Ticket Answer Key
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?

This week I chose to explore a lesson on fractions for third graders.  I really would like to try this lesson with students.  It is set up well and provides a good visual of the larger number denominator with the same numerator representing less.  For example, it shows 1/8 next to 1/4 and it is clear to see that 1/8 is smaller.  I also like how the introduction of the lesson generates interest by asking a question that the students could immediately relate to.  "Would you rather share one pizza between two or one pizza with four people?

 It would also be interesting to a similar activity on an interactive smart board.

 

 

Closing (3 minutes)

Exit Ticket (4 minutes)

 

Name                                                                                                                                                    Date                                                                                                                                            

Lesson 11: Factoring Expressions

Exit Ticket

Use greatest common factor and the distributive property to write equivalent expressions in factored form. 1. 2𝑥 + 8𝑦

2.     13𝑎𝑏 + 15𝑎𝑏

3.     20𝑔 + 24ℎ

 

Exit Ticket Sample Solutions

Problem Set Sample Solutions

𝒃

𝒂

𝒃

Number Correct:                

Greatest Common Factor—Round 1

Directions: Determine the greatest common factor of each pair of numbers.

1.	GCF of 10 and 50			16.	GCF of 45 and 72
2.	GCF of 5 and 35			17.	GCF of 28 and 48
3.	GCF of 3 and 12			18.	GCF of 44 and 77
4.	GCF of 8 and 20			19.	GCF of 39 and 66
5.	GCF of 15 and 35			20.	GCF of 64 and 88
6.	GCF of 10 and 75			21.	GCF of 42 and 56
7.	GCF of 9 and 30			22.	GCF of 28 and 42
8.	GCF of 15 and 33			23.	GCF of 13 and 91
9.	GCF of 12 and 28			24.	GCF of 16 and 84
10.	GCF of 16 and 40			25.	GCF of 36 and 99
11.	GCF of 24 and 32			26.	GCF of 39 and 65
12.	GCF of 35 and 49			27.	GCF of 27 and 87
13.	GCF of 45 and 60			28.	GCF of 28 and 70
14.	GCF of 48 and 72			29.	GCF of 26 and 91
15.	GCF of 50 and 42			30.	GCF of 34 and 51

 

Greatest Common Factor—Round 1 [KEY]

Directions: Determine the greatest common factor of each pair of numbers.

1.	GCF of 10 and 50	𝟏𝟎		16.	GCF of 45 and 72	𝟗
2.	GCF of 5 and 35	𝟓		17.	GCF of 28 and 48	𝟒
3.	GCF of 3 and 12	𝟑		18.	GCF of 44 and 77	𝟏𝟏
4.	GCF of 8 and 20	𝟒		19.	GCF of 39 and 66	𝟑
5.	GCF of 15 and 35	𝟓		20.	GCF of 64 and 88	𝟖
6.	GCF of 10 and 75	𝟓		21.	GCF of 42 and 56	𝟏𝟒
7.	GCF of 9 and 30	𝟑		22.	GCF of 28 and 42	𝟏𝟒
8.	GCF of 15 and 33	𝟑		23.	GCF of 13 and 91	𝟏𝟑
9.	GCF of 12 and 28	𝟒		24.	GCF of 16 and 84	𝟒
10.	GCF of 16 and 40	𝟖		25.	GCF of 36 and 99	𝟗
11.	GCF of 24 and 32	𝟖		26.	GCF of 39 and 65	𝟏𝟑
12.	GCF of 35 and 49	𝟕		27.	GCF of 27 and 87	𝟑
13.	GCF of 45 and 60	𝟏𝟓		28.	GCF of 28 and 70	𝟏𝟒
14.	GCF of 48 and 72	𝟐𝟒		29.	GCF of 26 and 91	𝟏𝟑
15.	GCF of 50 and 42	𝟐		30.	GCF of 34 and 51	𝟏𝟕

Greatest Common Factor—Round 2

Directions: Determine the greatest common factor of each pair of numbers.

Number Correct:                  Improvement:             

 

1.	GCF of 20 and 80			16.	GCF of 33 and 99
2.	GCF of 10 and 70			17.	GCF of 38 and 76
3.	GCF of 9 and 36			18.	GCF of 26 and 65
4.	GCF of 12 and 24			19.	GCF of 39 and 48
5.	GCF of 15 and 45			20.	GCF of 72 and 88
6.	GCF of 10 and 95			21.	GCF of 21 and 56
7.	GCF of 9 and 45			22.	GCF of 28 and 52
8.	GCF of 18 and 33			23.	GCF of 51 and 68
9.	GCF of 12 and 32			24.	GCF of 48 and 84
10.	GCF of 16 and 56			25.	GCF of 21 and 63
11.	GCF of 40 and 72			26.	GCF of 64 and 80
12.	GCF of 35 and 63			27.	GCF of 36 and 90
13.	GCF of 30 and 75			28.	GCF of 28 and 98
14.	GCF of 42 and 72			29.	GCF of 39 and 91
15.	GCF of 30 and 28			30.	GCF of 38 and 95

 

Greatest Common Factor—Round 2 [KEY]

Directions: Determine the greatest common factor of each pair of numbers.

1.	GCF of 20 and 80	𝟐𝟎		16.	GCF of 33 and 99	𝟑𝟑
2.	GCF of 10 and 70	𝟏𝟎		17.	GCF of 38 and 76	𝟑𝟖
3.	GCF of 9 and 36	𝟗		18.	GCF of 26 and 65	𝟏𝟑
4.	GCF of 12 and 24	𝟏𝟐		19.	GCF of 39 and 48	𝟑
5.	GCF of 15 and 45	𝟏𝟓		20.	GCF of 72 and 88	𝟖
6.	GCF of 10 and 95	𝟓		21.	GCF of 21 and 56	𝟕
7.	GCF of 9 and 45	𝟗		22.	GCF of 28 and 52	𝟒
8.	GCF of 18 and 33	𝟑		23.	GCF of 51 and 68	𝟏𝟕
9.	GCF of 12 and 32	𝟒		24.	GCF of 48 and 84	𝟏𝟐
10.	GCF of 16 and 56	𝟖		25.	GCF of 21 and 63	𝟐𝟏
11.	GCF of 40 and 72	𝟖		26.	GCF of 64 and 80	𝟏𝟔
12.	GCF of 35 and 63	𝟕		27.	GCF of 36 and 90	𝟏𝟖
13.	GCF of 30 and 75	𝟏𝟓		28.	GCF of 28 and 98	𝟏𝟒
14.	GCF of 42 and 72	𝟔		29.	GCF of 39 and 91	𝟏𝟑
15.	GCF of 30 and 28	𝟐		30.	GCF of 38 and 95	𝟏𝟗