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### Lesson plan

# Equivalent Fractions: Are They Equal?

#### Learning Objectives

Students will be able to determine if two fractions are equivalent using visuals.

#### Introduction

*(5 minutes)*

- Write the following question on the board:
*Are 1/4 and 2/8 equal?* - Ask students to think about how they would explain whether the answer is yes or no.
- Give students time to sketch and work out the problem on their whiteboards, then allow them to share ideas with a partner.
- Call on partners to share their answer and thought process with the class. Encourage students to show their sketches in order to prove their answers.
- Confirm that the two fractions are equal, and share that the lesson will focus on determining if two fractions are equivalent using shapes. Point out how the visuals helped demonstrate that the fractions were equal.

#### Explicit Instruction/Teacher modeling

*(10 minutes)*

- Explain to students that these two fractions, 1/4 and 2/8, are equal, which means they are
**equivalent**. Draw a visual to show a shape divided into four equal parts. Shade one part. Draw another visual to show a shape divided into eight equal parts. Shade two parts. Point out that the two visuals show an equal, or equivalent fraction. The shaded areas are equivalent. - Use fraction tiles to model the above problem.
- Model thinking through the following problem:
*Are 4/6 and 2/3 equivalent?*Draw the visuals of each fraction to confirm that these fractions are equivalent. - Repeat the think-aloud process with the visual drawings and fraction tiles with two more examples:
- Are 3/5 and 2/4 equivalent?
- Are 1/4 and 1/2 equivalent?

- Display a copy of Matching Equivalent Fractions to model finding equivalent fractions by looking at the shapes alone. Write the fraction next to each shape so that students see the connection between the visual and numerical representations of the fractions.

#### Guided Practice

*(10 minutes)*

- Use the Equivalent Fractions 1 Exercise to have students practice determining equivalent fractions.
- Have students take out their whiteboards and whiteboard markers while the exercise is displayed on the projector.
- Instruct students to respond on their whiteboards, writing down the original fraction shown with the example shape, as well as the equivalent fraction they chose. (Note: The answer choices on the exercise are not lettered in a multiple choice fashion, so be sure to guide students to an understanding that the first option would be A, the second option would be B, etc.)
- Take the time after each question to offer praise, correction, and explanation.

#### Independent working time

*(10 minutes)*

- Distribute a copy of the Fraction Practice: Equivalent Fractions worksheet to each student and go over the instructions.
- Give time to complete the worksheet. Circulate and monitor student struggles and successes as they work.

#### Differentiation

**Support:**

- Provide students with a digital fractions tutorial using the Fraction Basics app. (See Technology)
- Use different visual models, such as tiles, circles, and strips, to model creating equivalent fractions.
- Allow students to use manipulatives, such as fraction tiles, circles, and strips.
- Give more practice with the Equivalent Fractions 1 Exercise. (See Suggested Media.)
- Teach a pre-lesson that reviews fraction basics, such as identifying and naming fractions.
- Create a word wall or anchor chart with key terminology to use when talking about fractions, including
**numerator**,**denominator**,**fraction**,**parts**,**whole**,**equivalent**,**equal**. Be sure to include visuals to accompany each of the words.

**Enrichment:**

- Give advanced students the Color by Fraction worksheet for them to determine equivalent fractions with larger numerators and denominators.

#### Technology Integration

- Put two students to one device in order to complete the Equivalent Fractions 1 Exercise in Guided Practice. Give them the opportunity to discuss the answer choices. Circulate and monitor while students work.

#### Assessment

*(3 minutes)*

- Display the question,
*Are 1/4 and 2/6 equivalent?* - Group students into A-B partnerships and instruct them to discuss the answer. Remind them to utilize visual models of fractions as they work to determine equivalency.
- Circulate and observe student conversations, listening for academic language in explanations.
- Call on a non-volunteer to offer an answer to the question. Call on another non-volunteer to either agree or disagree, providing an explanation of the process with visuals.

#### Review and closing

*(2 minutes)*

- Instruct students to turn and talk to a partner about why visual models are helpful in math, and especially with fractions.
- Explain to students that visual models of fractions will always be a foundation to which they can return. There are processes for finding equivalent fractions that they will learn in upcoming lessons that do not involve the visual models, but referencing the visual models is a good strategy to use.