📊 Lesson 6.5 Outline-Equivalent Fractions with Linear Models-(For Teacher- Do Not Publish)

Lesson 6.5-Equivalent Fractions with Linear Models

For full lesson outline please see  Advantage Math Lesson 6.5.

Standards:

4.NF.1: Explain why a fraction a/b is equivalent to a fraction (nxa)(nxb) by using visual fraction models, with attention to how the number and size of the parts differ even though the two fractions themselves are the same size. Use this principle to recognize and generate equivalent fractions.

Objectives:

Math Objective: I can create equivalent fractions with linear models and relate the models of the fractions to mathematical equations.

Language Objective: I can describe how equivalent fractions can be generated with linear models and how equivalent fractions can be represented with multiplication or division equations.

Vertical Alignment:

3.NF.3a: Understand two fractions as equivalent (equal) if they are the same size, or the same point on a number line.

3.NF.3b: Recognize and generate simple equivalent fractions, e.g., 1/2 = 2/4, 4/6 = 2/3. Explain why the fractions are equivalent, e.g., by using a visual fraction model.

4.NF.1: Explain why a fraction a/b is equivalent to a fraction (nxa)(nxb) by using visual fraction models, with attention to how the number and size of the parts differ even though the two fractions themselves are the same size. Use this principle to recognize and generate equivalent fractions.

5.NF.1: Add and subtract fractions with unlike denominators (including mixed numbers) by replacing given fractions with equivalent fractions in such a way as to produce an equivalent sum or difference of fractions with like denominators.

Notes:

When creating equivalent fractions, use caution to keep the denominators within the fourth grade standards of denominators 2, 3, 4, 5, 6, 8, 10, and 12.

Lesson Outline:

🚀Launch A (in class or remote)

• Print the fraction strip sheet or use the following website to complete the task: https://toytheater.com/fraction-strips/ Links to an external site.
• Give students time to experiment with the task of figuring out ways fraction strips relate to a number line.
• Students may discover the following:
  
  • Just like a number line with fractions, the fraction strips are divided into equal pieces. 
  • The number of pieces needed to create a whole is represented in the denominator. 
  • Each piece of the fraction strips represents a unit fraction while on a number line, the markings indicate the distance from zero, and the distance from each marking to the next is the size of that unit fraction.

🤔Explore A (in class or remote)

• Have students use their fraction strip worksheet or the following website to complete tasks: https://toytheater.com/fraction-strips/ Links to an external site.
• Students will use the fraction strips to find fractions equivalent to 1/2.
• Have students try to create equations that change 1/2 to the equivalent fraction using multiplication.
  • Vocabulary: equivalent fraction

💬Discuss A (in class or remote)

• Have students use their fraction strip worksheet or the following website to answer questions: https://toytheater.com/fraction-strips/ Links to an external site.
• Students will submit a screenshot or picture with a text that explains why there are no fractions equivalent to 1/2 that have 3 or 5 in the denominator.
  • Vocabulary: denominator, numerator

🚀Launch B (in class or remote)

• Students will look at the number line below to complete the following task:
• Students will try to find equivalent fractions to 4/6 by partitioning or breaking apart the number line into new fractions. They can use their fraction strip worksheet or the website: https://toytheater.com/fraction-strips/ Links to an external site.

• • Vocabulary: partition

🤔Explore B (in class or remote):

• Students will use the following story problem to complete tasks:

• Students will submit a video, picture, or text entry that explains and shows how Anika's and Leon's distances of walking are equivalent. 

💬Discuss B (in class or remote)

• Students will discuss the following question as a class or by submitting a picture or text entry:
  • When would using equivalent fractions be helpful while trying to solve fraction story problems?

Additional Resources:

Teacher Resource Mathwire Fraction Models: http://www.mathwire.com/fractions/fracmodels.html Links to an external site.

Student Resource Fraction Number Line: https://www.mathsisfun.com/numbers/fraction-number-line.html Links to an external site.

Student Resource Video Fractions on Number Lines: https://learnzillion.com/lesson_plans/4739-recognize-equivalent-fractions-using-number-lines/#fndtn-lesson Links to an external site.

• Differentiation (in class or remote)
  • Challenge:
  • For students who need a challenge, invite them to create a real-world situation in which knowledge of equivalent fractions would be necessary for determining a solution.
    
    • Ways to make remote:
    • Create an assignment or group discussion where students can insert a picture or video showing what they created.
  • Struggling:
  • For students who need help finding equivalent fractions using a number line, make the transition from area models to linear representations by giving students a narrow strip of paper. Students can label the furthest left-hand side as zero and the furthest right-hand side as one. Students can then fold the paper strip to create equal partitions along the long edge of the paper to locate the given fraction. Further folding can be used to find additional equivalent fractions.
    
    • Ways to make remote:
    • Have students join you in an online meeting format (Zoom or Teams) and do the exact same activity. If you don't have enough manipulatives to send home, then do a demo for students.

• Lesson Extension (in class):
  • As an extension, have students respond to the following writing prompt:
    • Describe how division can be used to find equivalent fractions.