📊 Lesson 6.4 Outline-Equivalent Fractions with Area Models-(For Teacher- Do Not Publish)

Lesson 6.4-Equivalent Fractions with Area Models

For full lesson outline please see Advantage Math Lesson 6.4.

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 determine a frac=onal amount in a set model or determine the whole given the fractional parts using money as a context.

Language Objective: I can describe why a quantity can represent both a fractional amount and a whole in diﬀerent situations

Vertical Alignment:

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.

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:

If money manipulatives are available, they work really well for this lesson; if they are not readily available, a page of coins is available in the student pages to copy and cut apart. Additionally, students could draw pictures of coins on their whiteboards to represent the various set models.

Common Misconceptions:

Some students may not recognize the relationship between the whole and the parts; the size of the parts depends on the size of the whole.

Lesson Outline:

🚀Launch A (in class or remote)

Distribute ten 3x3 square piece of paper or sticky notes. Students can do this easily at home with paper.
Students will submit a video or picture that completes the following tasks:
1. Fold a square piece of paper or sticky note in half.
3. Color in 1/2 of the paper.
Questions you could ask:
- - What do you think will happen to our fraction if we fold the paper in half again?

🤔Explore A (in class or remote)

Have students fold the paper in 1/2 again to create 2/4.
Discuss the meaning of an equivalent fraction.
Have students submit a video or text entry that answers the following question:
- Why are 1/2 and 2/4 equivalent?
- Vocabulary words: equivalent

💬Discuss A (in class or remote)

Have students discover other fractions that are equivalent to 1/2 by experimenting with folding.
Students will submit pictures of their work.

🚀Launch B (in class or remote)

Have students use the 1/2 paper or sticky note to complete the following tasks:
1. How could we change 1/2 to 2/4 using math?
2. Try it out by writing an equation that changes 1/2 to 2/4.

🤔Explore B (in class or remote):

Have students use a new piece of paper or sticky note to complete the following tasks:
1. Fold your paper or sticky note into thirds.
2. Shade in 1/3.
3. Experiment with folding to find two equivalent fractions to 1/3.
4. Write an equation that shows how to change 1/3 to your equivalent fractions you found.

💬Discuss B (in class or remote)

Students will submit a picture or text entry answering the following questions for your discussion:
1. What if we folded our paper into 3/4?
2. What are two equivalent fractions to 3/4 we could find by folding?
3. What equations could we create to change 3/4 to our equivalent fractions?

🚀Launch C (in class or remote)

Have students use a new piece of paper or sticky note and submit a video and picture to complete the following tasks:
1. Fold the paper into thirds vertically and in fourths horizontally. You should end up with 12 squares.
2. Shade in 6/12.
3. How can the sections be combined to represent another fraction equivalent to 6/12?

🤔Explore C (in class or remote):

Use the same piece of paper or sticky note from Launch C to answer the following questions:

1. How could we change 6/12 into 3/6?
2. Why do we want to divide instead of multiplying?

Questions to ask:
- What fraction is represented? (6/12)
- How can the sections be combined to represent another fraction equivalent to 6/12?

💬Discuss C (in class or remote)

Students will submit a picture or text entry answering the following task for your discussion:
1. Use multiplication or division to find another fraction that is equivalent to 6/12 and 3/6.
2. When would you want to use multiplication versus division when creating equivalent fractions?

Additional Resources:

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 to determine 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:
- Intervention 1: For students struggling to write multiplication equations to show the relationship between the equivalent fractions, it may be helpful to relate the two fractions using a multiplication chart (e.g., the fractions 4 6 and 8 12). Use a multiplication chart to ﬁnd the row beginning with 4 and the row beginning with 6. What number is at the top of the column where 8 and 12 are seen as the respective multiples of 4 and 6? (2; meaning that 2 times 4 is 8 and 2 times 6 is 12.)
  - 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 multiplication can be used to ﬁnd equivalent fractions