### Lesson Plan

# Farming Fractions: Comparing Fractions and Constructing Arguments

In this sixth lesson from Farm to Table, students will explore what makes a mathematical argument valid as well as practice critiquing others' mathematical reasoning.

Grades

3–5

Duration

45 MINUTES

### Quick links to lesson materials:

### Objectives

**Students will:**

- Construct a mathematical argument
- Compare and multiply fractions
- Critique others’ mathematical arguments

### Materials

- Farming Fractions Student Worksheet printable
- Whiteboard and markers
- Computer and projector or chart paper

### Set Up

Make a class set of the Farming Fractions Student Worksheet printable.

### Lesson Directions

**Step 1: **Engage students in the lesson by presenting a faulty argument on the board, such as: “I read that each student should have 15 minutes of homework a night. Since there are 20 students in our class, I should be assigning 5 hours of homework each night.” (You can customize this example to meet your students’ interests.)

**Step 2:
**Ask students to turn and talk with a partner about whether the statement is valid and why. Lead a discussion about which students’ arguments are most convincing.

**Step 3:
**Review with students the guidelines for creating an argument. For example:

- Saying “because I think so” is not enough to construct an argument.
- A strong argument includes an explanation of the correct process.
- Using examples and drawings or models will help support your argument.
- When critiquing an argument, asking questions in your mind about how others reached their conclusions is a good way to start.
- You can look for errors in others’ logic or calculations and contrast it with the correct process to critique their arguments.
- It’s important to be polite when critiquing an argument.

**Step 4:
**Explain that the class will now apply this strategy to a mathematical argument. Share the following example using a projector or chart paper: “Tina and Henry are having a snack. Tina pours 1/8 of a carton of milk into a red cup and 1/6 of a carton of milk into a blue cup. Henry wants the cup with the most milk, so he chooses the blue cup. Did he choose the right cup?” (Answer: Yes; 1/6 > 1/8).

Use the following questions to guide your class’s discussion:

- What is the process for comparing fractions?
- How could a drawing of the situation help us?
- Did Henry make any errors in his calculations?

**Step 5: **
Present another argument to the class: “Hassan needs 1/3 cup of olive oil for a recipe. He has 1/4 cup of olive oil in his kitchen. Does he have enough olive oil to make the recipe?” (Answer: No; 1/4 < 1/3) Ask students to work with a partner to determine whose reasoning is correct.

**Step 6: **Invite pairs to share their reasoning with the class.

**Step 7:
**Have students complete the Farming Fractions Student Worksheet printable to practice constructing and critiquing arguments.

**Answer Key**

**1a.** No, the friend is wrong because 1/2 is actually bigger than 1/4. The denominator tells how many total equal pieces the whole is broken into. A bigger denominator means the whole is broken into more pieces, so each piece is smaller than if the whole were broken into fewer pieces.

**1b.** Grass is the largest part of the cows’ diet because it’s more than 1/2, so any fraction that’s left would have to be less than 1/2 (because if you were to add
1/2 to more than 1/2, you get a total greater than 1, but the cow only has one diet). Therefore,
no other fraction of the diet can be bigger than the grass portion.

**1c.** 1/2 > 1/4

**2a.** Yes.

**2b.** 1/5 is less than 1/4 because 5 is the bigger denominator (see 1a, above), so 1/5 has to be a smaller amount than the 1/4 maximum.

**2c.** 1/5 < 1/4

**3a.** Nevaeh’s estimate of 5 homes is closer.

**3b.** 1/15 of the energy for one home multiplied by 80 cows equals 5.33.