EL Support Lesson
Dividing with the Divvy Out Method
Students will be able to solve division problems with one-digit divisors and no remainder using the partial quotients strategy.
Students will be able to explain their strategy for solving division problems using the divvy out method.
- Write the following problem on a piece of paper and project it on the document camera: "Kira, Dan, and Esteban washed cars in their neighbourhood and made a total of $54. If they want to share the money equally among the three of them, how much will they each get?"
- Read the problem aloud, circling the numbers "54" and "3" and the word "share."
- Ask students to turn to a partner and discuss what they think this problem is asking and how they think they could solve it.
- Guide students to notice that this is a division problem because it asks them to equally share the money they earned together. Explain to students that division means dividing a number of items into equal groups.
- Record students' ideas and responses on chart paper and provide feedback. Point out and validate the various strategies that students may use to solve this problem (standard algorithm, array, number line, etc.).
- Explain that today students will learn another method for division called Divvy out. Tell them that divvy out is like distributing or handing out a deck of cards; we must give each person or group the same amount of cards until there are no more cards.
Explicit Instruction/Teacher modeling(7 minutes)
- Write 54 ÷ 3At the top of a piece of paper on the document camera and model how you draw three equal sized circles below the problem.
- Tell students that in order to solve the problem, we will divvy out small chunks of the Dividend(the number that is being divided) into the three groups. Label the number 54 as the dividend and 3 as the Divisor(the number of groups you are dividing into), preferably with different colored markers for emphasis.
- Consider out loud what numbers to use as equal chunks in each circle or group. For example, say "It's best to use manageable chunks that are easy to add or multiply mentally. So, I'm going to start by putting 10 in each circle." On the side of the circles, write 54 - 30 = 24. Continue with the process by stating, "Now I have 24 left of dividend which still needs to be divvied out equally into the groups. I know that if I do 10 again, it won't work because I don't have $30. I'm going to try place a smaller amount, such as 4 into each group, which gives me 12 total. 24 - 12 = 12." Complete the process until there is no money left to divvy out. Then tell students that in order to figure out the QuotientOr answer to the division problem, we need to add the amounts we wrote in one of the circles (in this case, we did 10 + 4 + 4 = 18). Note: emphasize the importance of each circle having the same amount, after all, that is the point of division—to distribute equally!
- Write the answer at the bottom of the paper: "Kira, Dan, and Esteban will each get $18."
Guided practise(8 minutes)
- Model to students how you solve another division problem using this method (e.g., 312 ÷ 6). Make sure you verbalize your thinking each step of the way.
- Place students into partnerships and hand each student a whiteboard and marker.
- Write this problem on the board: "Guadalupe made 152 cookies. She wants to give the same amount to each of her 4 friends. How many cookies would each friend receive?"
- Ask students to read the problem aloud to their partner. Instruct students to identify and circle the dividend and divisor in this problem.
- Tell students to work with their partner to solve this problem using the divvy out method. Model to students how you draw 4 circles for this problem because the divisor is 4.
- Write and display the following sentence stems for students to refer to as they solve:
- "The question is asking ____."
- "To solve the problem, first I ____."
- "Then, I ____."
- "Finally, I ____."
- Give students time to solve the problem on their whiteboards with their partner.
- Call on a few pairs of students to explain how they solved for the quotient. Remind students to explain each step they used.
Group work time(12 minutes)
- Hand out a copy of the Divvy Out Method for Division practise worksheet to students and display a teacher copy on the document camera.
- Read aloud the example at the top of the page and walk students through the problem. Point out which numbers represent the dividend and divisor.
- Model how you use the divvy out method on the first problem. Emphasize to students that the divisor represents the number of circles you need to draw.
- Write transition words such as, "First," "Then," and "Finally" on the board and model to students how you explain each step of solving the problem using these words as a guide.
- Place students into effective partnerships and have them work on the second problem together.
- Invite a set of partners to come up to the document camera to share with the class how they solved the second question. Confirm their answer or correct any misconceptions.
- Instruct students to work independently on problem three. Once all students have solved the problem, create groups of 6 and have 3 students stand in an inner circle, while the other 3 stand in the outer circle, each one holding their worksheet. Each student in the inner circle should face a student in the outer circle.
- Tell students that they will engage their classmates in a discussion, explaining how they used the divvy out method to solve this division problem. Inform them that they will explain the problem multiple times so that they get better at talking about maths and sharing their mathematical process and reasoning.
- Remind students to use transition words such as "First," "Then," and "Finally" and explain each step in the process. Mention the importance of actively listening to the partner who is talking as they share their problem. Partners are also encouraged to ask clarifying questions if need be.
- Have students orally share their problem-solving process with their first partner (with the worksheet in their hands), and then rotate the inner circle so that they have a new partner. For the second time, have students place their worksheets on their desks so that they focus solely on the oral explanation. Students will explain and share their method for solving the third problem a total of three times, once with the support of their paper and twice without.
- Observe students' explanations to compare the first and the last explanations to see if they were more detailed, thorough, and smooth.
Additional EL adaptations
- Give students partially solved divvy out problems (e.g., the first number has been placed in the circles).
- Pair students with advanced ELs for partner work.
- Write out the step-by-step instructions for the divvy out method and ensure they are accessible throughout the lesson.
- Provide students with home language resources such as bilingual glossaries and online dictionaries.
- Invite students to practise the divvy out method with greater numbers.
- Ask students to repeat directions and share their ideas first to their classmates.
- Instruct students to compare the divvy out method to another division strategy they know.
- Have students solve this problem on the whiteboards: "The school collected 276 cans of food for the food drive. They want to donate the cans evenly amongst three food banks. How many cans will go to each bank?"
- Tell students to solve the problem using the divvy out method and show their work on the whiteboard.
- Place students into A–B partners and have each partner take turns showing how they solved the problem. Make sure students notice whether they used the same numbers in the circles or whether they used different ones.
- Circulate and listen in on students' sharing to gauge their understanding of the lesson.
- Ask students to complete the following sentence stems orally:
- "Divvy out is..."
- "The divvy out method helps me..."
- "When I had to explain my strategy three times, I..."
Review and closing(3 minutes)
- Call on a few students to share their responses.
- Tell students that soon they will learn how to perform long division using a similar strategy to the divvy out method that is called partial quotients.