📊Math G4 L6.18 Outline-Mixed Numbers-(For Teacher-Do Not Publish)

📊Math G4 L6.18 Outline-Mixed Numbers

For full lesson outline, please see Advantage Math Lesson 6.18

Standards:

4.NF.2: Compare two fractions with different numerators and different denominators, e.g., by creating common denominators or numerators, or by comparing to a benchmark fraction such as 1/2. 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, e.g., by using a visual fraction model.

Objectives:

Math Objective: I can identify and write fractions as mixed numbers and mixed numbers in fractional form.

Language Objective: I can describe the relationship between a mixed number and a number written in fractional form.

Vertical Alignment:

3rd Grade:

Understand unit fractions (3.NF.1Links to an external site.)
Understand fractions as a number and represent fractions on a number line (3.NF.2Links to an external site.)

5th Grade:

Add/subtract fractions with unlike denominators (5.NF.1Links to an external site.)

Notes:

1. The focus is for students to see the equivalency of a mixed number and a number written in fractional form. This is accomplished initially with the use of manipulatives and models, but gradually, students should be encouraged to think through the relationship using reasoning, drawing on their knowledge of fraction addition and decomposition of fractions.
2. The algorithm for converting the two forms is not taught; however, students should be able to describe the patterns used to convert one form to another and may come up with an algorithm on their own.
3. This lesson may take more than one day.

Common Misconceptions:

Some students may be confused by the term improper fraction as it may lead them to believe that a fraction in this form is unacceptable. This causes confusion when students study algebra where a fraction in this form is often preferred. It may also lead students to believe that an acceptable, “proper” fraction has to be less than 1. Avoid using the term improper fraction; instead, simply refer to them as fractions.

Lesson Outline: As there is not a website with the particular set of pattern blocks used for this lesson, pictures of the blocks have been inserted. Preferably, this lesson would be done in class.

🚀Launch A (in class or remote)

Have students complete the model below. They can use pattern blocks or draw a picture to the best of their ability.

🤔Explore A (in class or remote)

Discuss the following questions as a class about the model above:
a. What unit fraction equation represents the model?

b. What fraction represents the whole?

c. What whole number is equivalent to the fraction 4/4?

💬Discuss A (in class or remote)

Further student thinking by discussing what equation would represent the whole plus one more. How would we model that?

🚀Launch B (in class or remote)

Have students decompose the set of fractions below in as many ways as possible. There are a few examples provided in their canvas assignment.

🤔Explore B (in class or remote)

When fractions and whole numbers are added together, the result is called a mixed number. A mixed number consists of a whole number and a fraction.
Have students try to replace any of the fractions they created with a whole number.

💬Discuss B (in class or remote)

Discuss examples of fractions that are equivalent to whole numbers.

🚀Launch C (in class or remote)

Have students try to write the fractions 9/6, 5/2, and 14/12 as mixed numbers. Remind students to try and create as many wholes as they can when creating a mixed number.

🤔Explore C (in class or remote):

Have students create a model for the equation below. See if students are able to create a whole or not with their fraction pieces.

💬Discuss C (in class or remote)

Have students rewrite the equation from "Explore C" and replace some of the fractions with whole numbers. Discuss why this works when creating a mixed number.

🚀Launch D (in class or remote)

Have students create an addition fraction equation for the model below. Explain that the whole is 6/6. See if they can write the fraction in both fraction form and as a mixed number.

🤔Explore D (in class or remote)

The fraction represented below is . Have students write an addition equation to determine the total number of tenths in the mixed number and write the answer in fraction form as a fraction greater than 1.

💬Discuss D (in class or remote)

Discuss how the process of adding fractions is related to mixed numbers. Why do we want to create wholes out of our fractions in order to create fraction addition equations?

Additional Resources:

Differentiation (in class or remote)
- Challenging:
- As a challenge, ask students to come up with a real-world context for mixed numbers and fractions greater than 1. (i.e. "A mom cut some bananas in half for an after school snack for her children. She had 7/2 pieces of banana. What is this quantity written as a mixed number?")
  - Ways to make remote:
  - Create an assignment or group discussion where students can insert a picture or video of their writing.
- Struggling:
- For students who are struggling with the conversion of fractions greater than 1 and mixed numbers, consider decomposing a fraction using a number bond instead of an equation. Start by decomposing the whole into unit fractions and then have students group unit fractions together that total one whole. The number of circles represents the whole number, and the remaining fraction is the fractional part of the mixed number
- 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, do a demo for students.