Equivalent Fractions Lesson 1
Create and use fraction strips to discover name fractions and compare two unit fractions.
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."
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.
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.
Using the Activity Sheet, continue comparing fractions in small groups or individually until all of the fractions have been compared and recorded.
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.]
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.]
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?
Leave your thoughts in the comments below.
Use Cuisenaire rods to explore fractional relationships. This lays the foundation for work with challenging fraction concepts like equivalence.
Students generate and explore equivalent fractions using Cuisenaire rods.
Reason and develop an understanding of how to place equivalent fractions on a number line.
CCSS, Content Standards to specific grade/standard
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CCSS, Standards for Mathematical Practices
PtA, highlighted Effective Teaching Practice and/or Guiding Principle CCSS