### EL Support Lesson

# Explaining Fraction Addition

This lesson can be used as a pre-lesson for the
Make It Work! Adding Fractions with Unlike Denominators
lesson plan.

#### Objectives

##### Academic

Students will be able to add fractions with unlike denominators.

##### Language

Students will be able to explain how to add fractions with unlike denominators using visual aids.

#### Introduction

*(5 minutes)*

- Display a visual addition problem with fractions that have the same denominator without the fractions listed using a tape diagram or number line (see the top of the Adding Fractions worksheet for reference).
- Ask students to think about what the problem shows for 30 seconds, and then turn and talk to their partner about the problem. Have them use their whiteboards to take notes or solve the problem.
- Choose a student to solve the problem on the board and ask the class how they knew they could add the numerators together. Have volunteers share their ideas.
- Ask students to look at the vocabulary cards for "alike" and "unlike" and ask them to circle the numbers that are alike and box those that are unlike on each of the cards. Have students turn and talk about something in their lives that is unlike someone else's. For example, "Natasha always brings her lunch to school, but I always get my lunch at school."
- Tell students that today they will discuss how to find alike or common denominators in fractions so they can add the fractions together.

#### Explicit Instruction/Teacher modeling

*(8 minutes)*

- Provide an everyday scenario where you would add fractions with unlike denominators. For example, say, "I ran ¾ of a mile yesterday and another ⅔ of a mile today. How many miles did I run in total?" Have students write the fractions on their whiteboards, circle the denominators, and write if they're alike or not alike. (They're not alike.)
- Display the multiplication chart from the Find the Patterns! Multiplication worksheet on the board and highlight the
**multiples**for 4 (i.e., 4, 8, 12, 16, etc.). Explain that they will need to know the multiples of a lot of numbers to then be able to change denonimators so they're alike. Highlight the multiples of 3 (i.e., 3, 6, 9, 12, etc.) and circle the multiples they have in common (i.e., 12, 24, 36). - Circle the smallest common multiple and tell students it's the
**least common denominator**, or LCD, because it's the smallest multiple they have in common. Then, think aloud how to change the denominators to 12. For example, say "I need the denominators to equal 12, so I need to figure outand multiply the numerator and the denominator by that**____**x 4 = 12**factor**. I know**12 ÷ 4 = 3**, so I need to multiply the denominator and the numerator by three." Follow the same thought process for the next fraction (i.e., ⅔) and then model how to add the numbers together () to get the final answer of^{9}⁄_{12}+^{8}⁄_{12}^{17}⁄_{12}(or 1^{5}⁄_{12}).

#### Guided Practice

*(6 minutes)*

- Ask a student to restate how you were able to find the LCD for the fractions. Write some of their common phrases down on the board to convert to sentence frames. Rephrase the students' explanation after the presentation using some of the following transition words to support further explanations:
- "First, I
**____**." - "After I
**____**, I."**____** - "Then, I
**____**." - "My next step was
."**____**

- "First, I
- Model completing another problem using the same running scenario but different unlike denominators, such as
. Find the LCD with the students (without the multiplication chart) by asking for the next steps and making intentional mistakes that they can correct as you complete the addition problem. Again, have another student restate the process, but this time write down the steps the presenter shares for solving the problem on chart paper to serve as an anchor chart. They should include the following:^{3}⁄_{5}+^{7}⁄_{9}- Find the LCD by listing the multiples of the unlike denominators.
- Multiply the numerator and denominator by the factor needed to get the LCD.
- Add the numerators but leave the denominators the same.
- Change the improper fraction to a mixed number.

- Tell students to refer to the anchor chart as they complete their group assignment where they'll create explanations about how they added two fractions with unlike denominators.

#### Group work time

*(10 minutes)*

- Have students work in groups of four where each member is a number from 1–4. Have members work together to find the least common denominator for the addition problem
and change each fraction so they have like denominators. Distribute a chart paper to each group for their notes.^{2}⁄_{3}+^{7}⁄_{9} - Challenge the students to make sure they can all explain their process in finding the LCD and change the fractions so they can be added together. Tell students you will choose a number 1–4 and the student who has that number will explain the process aloud. The student presenters can use any notes the group created to solve the problem in their explanations.
- Choose a student from each group to present. (Tip: select groups with advanced ELs first so they can model the explanation process for the class first and the other students can refine their answers.)

#### Additional EL adaptations

**Beginning**

- Allow students to use their home language (L1) or their new language (L2) in all discussions. Provide bilingual reference materials to assist in their vocabulary word acquisition.
- Encourage them to use the vocabulary cards and terms in their conversations and writing. Allow them to draw pictures to support their understanding of the terms and represent their ideas with bar models or tape diagrams.
- Remind students to refer to the anchor chart or their vocabulary cards when they ask questions or share information. Allow them to point to the vocabulary cards and anchor chart to assist them with their explanation.

**Advanced**

- Pair students with mixed ability groups so they can offer explanations and provide feedback to beginning ELs when appropriate.
- Ask students to restate the explanations and to share sentence frames or stems they can use in their explanation of how to add fractions when they have unlike denominators.

#### Assessment

*(6 minutes)*

- Distribute the Adding Fractions worksheet and ask students to complete two addition problems from the bottom section. Then, distribute lined paper and have them explain the process they followed to complete the problem of their choice.
- Have students refer to the board for sequencing sentence stems and their vocabulary cards for assistance with the key terms.

#### Review and closing

*(5 minutes)*

- Ask students to share their assessments with their elbow partner for one minute. Then, ask for a volunteer to share their assessment with the class.
- Allow students to share a positive statement about the assessment. Correct misconceptions as necessary.
- Tell students that they will see fractions when they go shopping and even while running, and being able to add fractions with unlike denominators is a useful skill for more difficult math and everyday mathematical problems.