EL Support Lesson
Comparing Two Division Methods
Students will be able to solve division problems with up to three-digit dividends and one-digit divisors.
Students will be able to compare two methods for division using peer conversations and sentence stems.
- Distribute one half of the precut vocabulary cards to each student. Have students find their matching pairs, either carrying the definition of the word or the word itself. (Note: make sure each student will have a pair by making extra copies if necessary.)
- Gather information on students' background knowledge based on the questions they ask to find their partners. Monitor students' progress and ask struggling students leading questions to help them find their partner (e.g., "Can you read the word? Does the word remind you of another word?").
- Ask students to guess about today's topic after you've read all the terms and their definitions.
- Tell students that during the lesson they will compare two different division strategies for solving the same expression.
Explicit Instruction/Teacher modeling(5 minutes)
- Show the vocabulary card for the word compare and ask students to share some phrases they use when they compare two things. Write their responses on the board and allow students to correct each other when necessary (e.g., "____ is easier/harder than ____ because ____," or "They are alike/different because ____.").
- Display the digit-by-digit model example in the Two Methods for Solving Division Problems worksheet. Explain it is the standard way that people solve division problems and relies on remembering rules and steps. Ask students to share aloud what the color-coding might represent. Correct misconceptions if necessary after a few students share.
- Write "The Digit-by-Digit Method" on a piece of chart paper and model how to solve the problem from the example using the digit-by-digit method. Maintain the same color-coding used in the worksheet. List multiples on the side for the divisor (4) if students need additional assistance in understanding the steps. Solicit input from other students as well.
- Model how to solve the problem from the example using the rectangle sections method on chart paper labeled "The Rectangle Sections Method." Relate the method to area in that the dividend is the whole area and students must find the missing side (i.e., quotient) to determine the full area equation of length x width = area (e.g.,____ x 4 = 378). Mention that the two left over from the dividend did not spread equally so it is not a part of the area of the rectangle.
- Ask students to turn and talk to their partners about their impressions of the two methods. Ask them questions, such as, "Which seems harder? Which do you think you'll prefer? Why do you think one involves rectangles?" Allow them to ask questions about the two methods as well.
- Write down some of the student conversations you overhear from their partner conversations on chart paper titled "Compare and Contrast Language."
Guided Practice(5 minutes)
- Review some of the students' ideas you captured on the Compare and Contrast Language chart paper and discuss them with the class. Ask for agreements and have students add onto the points if they can ("I want to add... I agree with ____, but I also think...") Model this language with another student if necessary.
- Ask students to look at the two chart papers of the methods again and rethink some of the ways the methods might be different or the same. Continue to add language students can use in the Compare and Contrast Language chart paper. Create separate sentence frames from student discussions onto the chart paper:
- "One difference/similarity is ____."
- "I appreciate the ____ because..."
- "The digit-by-digit method has/shows ____ while the rectangle section method has/shows ____."
Group work time(10 minutes)
- Conduct a jigsaw activity where half the class recreates the rectangle sections method and the other half uses the digit-by-digit method using a different expression (e.g., 692 ÷ 8). Within the two split groups, form sets of four students and give each set a sheet of white construction paper. Have each set solve the problem together with their given method (digit-by-digit or rectangle sections) so they can become experts and share their insight with the class.
- Choose one volunteer from a set of four to share their white construction paper. Tell them to focus on the steps they used to solve the problem. Choose another student from a different set but still a part of the same method group to add more detail to the presentation (e.g., "I want to add... I agree with ____, but I also think...").
- Conduct a whole group discussion about the two methods given the information presented from the groups. Use the comparative language from their previous discussions and the Compare and Contrast Language chart paper to guide the discussion revolving around similarities and differences. Add more language to the chart as students introduce it into the discussion.
Additional EL adaptations
- 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.
- Read to the students the vocabulary terms and preteach the words if necessary.
- Model how to use the sentence stems.
- Pull them into a small, teacher-led group during the first partnership activity and work as a group to compare the two strategies.
- Ask students to share their comparative phrases aloud and add them to the Compare and Contrast Language chart paper.
- Ask them to share their ideas first as an example for students on appropriate language for the assigned task.
- Pair students with mixed ability groups so they can offer explanations and provide feedback to beginning ELs when appropriate.
- Distribute the Two Methods for Solving Division Problems worksheet and read the directions aloud. Make sure students understand what to do in both of the problems.
- Ask students to solve the same division equation using the two different strategies.
- Review the answers to the division equations as a whole group and ask for input on which strategy was more or least helpful ("The ____ is more/least helpful because..." or "I prefer the ____ method because...").
Review and closing(8 minutes)
- Have students think about the two methods and argue for the one they think is the best method.
- Give students five minutes to share with their elbow partner about which is the best method. Give an example opinion of your own and write some sentence frame examples on the board:
- "I think the ____ is better/easier than ____ because..."
- "While ____ is ____ , I think ____ is..."
- "Since ____ is/has ____, it is..."
- Call on volunteers to share their ideas with the whole class.