Composing and Decomposing Fractions - Math Interventions

[Pages:4]Composing and Decomposing Fractions

Student Probe

Find the missing number that would make the fractions equivalent: 2 6

3

Answer: 9

Lesson Description

This lesson is intended to help students explore fraction relationships and equivalent fractions through work with fraction strip models to develop a conceptual understanding of fraction equivalence. No algorithm for finding equivalent fractions is taught in this lesson.

Rationale

Conceptual development of fractional equivalences provides students with a firm foundation of fractions and prepares them for the computational skills that are reliant upon these ideas. Students' understanding of a conceptually based algorithm will arise out of a conceptual understanding of fractional equivalences. The linear model for fractions is particularly helpful for students locating fractions on a number line.

At a Glance

What: Use Fraction Strips to compose and decompose fractions Common Core State Standard: CC.4.NF.2. Compare two fractions with different numerators and different denominators. Recognize that comparisons are valid only when the two fractions refer to the same whole. Record the results of

comparisons with symbols >, =, or ,< and justify

the conclusions. Mathematical Practices: Reason abstractly and quantitatively. Use appropriate tools strategically. Attend to precision. Look for and make use of structure. Who: Students who cannot find equivalent fractions Grade Level: 5 Prerequisite Vocabulary: Whole, halves, thirds, fourths, fifths, etc. Prerequisite Skills: division of whole numbers Delivery Format: pairs, small group, whole group Lesson Length: 15-30 minutes Materials, Resources, Technology: Fraction Strips Student Worksheets: Fraction Strips

Preparation

Prepare a copy of Fraction Strips for each student.

Lesson

The teacher says or does...

1. What fraction is shown at the very top of the Fraction Strip worksheet?

Expect students to say or do... One whole

If students do not, then the teacher says or does...

The teacher says or does...

2. Look under the "one strip". What do you see? What fraction do you see under the one half strip? Which strip is 1 of the 4 whole?

3. How many one-fourth strips does it take to make a whole strip? So we can write 4 1 . 4 (Model on the board.) Notice that 4 equals the 4 same length as 1.

4. What else do you see that equals one whole?

5. What fractions have the same value as 1 ? 2

6. What fractions have the same value as 2 ? 3

7. Work with your partner to find another relationship using your fraction strips. (After a few minutes, ask for someone to volunteer a relationship that they found.) Using an example that the students found, write an equivalence statement. For example: 1 1 1 663

Expect students to say or do... One-half strip

One-third strip One-fourth strip 4

4 , 5 , 6 , etc. 456 3 , 4 , etc. 68 4 6 Answers will vary. For example, it takes two 1

6 strips to make 1 .

3

If students do not, then the teacher says or does... It is the same length as the whole, but it is divided into how many pieces?

Look at your strips. Do you see it takes four 1 strips to

4 make one whole? We say 1 1 1 1 4 or one 44444 whole.

Model these examples.

Guide students to notice the relationship between numerator and denominator. Model.

The teacher says or does...

8. 1 1 equals how many 66 sixths? How can we write 2 sixths?

So we can say that 2 1 . 63

9. We call 2 and 1 6 3

equivalent fractions. 10. Use your fraction strips to

find an fraction equivalent to 3 .

4 How do you know? So there are 2 correct answers? 11. Find the missing number that would make the fractions equivalent: 8 12 3 How do you know? 12. Find the missing number that would make the fractions equivalent: 61 12 How do you know? 13. Use your fraction strips to find 1 1 .

43 Explain how you know.

Expect students to say or do... 2 sixths

2 6

6 or 9 , because they are 8 12 the same length.

2

8 is the same length as 2

12

3

2

1 is the same length as 6 .

2

12

13 4 12 14 3 12 11 3 4 7 4 3 12 12 12

If students do not, then the teacher says or does... If you have one apple and one apple, how many apples do you have? It is the same with 1 and 1 .

66 You have 2 sixths.

Show that the fraction strips are the same length.

Look for a strip that is the same length as 3 .

4

Find the length of 8 . 12

Find the thirds strip. How many 1 s does it take to be

3 the same length? Find the length of 6 . What

12 strip will it only take one of to be the same length?

1 4 12 1 3 12

The teacher says or does...

14. Repeat with additional equivalent fractions.

Expect students to say or do... If students do not, then the teacher says or does...

Teacher Notes

1. Cuisinaire rods, another linear model, can be used in place of fraction strips. 2. At this point, look for student understanding that a fraction can be represented as a part of

a linear region. Observe whether students can articulate the relationship between fractions through their written expressions. 3. This lesson extends into comparison of fractions and ordering of fractions.

Variation

None

Formative Assessment

Find the missing number that would make the fractions equivalent: 3 96

Answer: 2

References

Russell Gersten, P. (n.d.). RTI and Mathematics IES Practice Guide - Response to Intervention in Mathematics. Retrieved 2 25, 2011, from rti4sucess. Institute of Educational Sciences (IES). (2010). Developing effective fractions instruction for Kindergarten through 8th grade. Retrieved September 2010. Van de Walle, J. A., & Lovin, L. H. (2006). Teaching Student-Centered Mathematics Grades 5-8 Volume 3. Boston, MA: Pearson Education, Inc.

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