Part-Whole Model: Word Problems with Division
Students will be able to solve division word problems using the part-whole model strategy.
- Draw a simple part-whole model on the board with only numbers listed and an equation frame with blanks underneath the drawing.
- Ask students to think for 30 seconds about what the drawing represents and how they might complete the equation. Tell them to use their whiteboards to write or draw some of their ideas. Then, have them share their answers with their elbow partners.
- Call on volunteers to share their ideas aloud and write them on the side of the board to consider later. Gather background knowledge on their knowledge of division within part-whole models through their whiteboard responses and peer conversations.
- Choose a student to read a student-friendly learning objective: "I can solve division word problems using the part-whole model strategy."
Explicit Instruction/Teacher modeling(10 minutes)
- Define the key terms in the learning objective. Tell students the part-whole model is a visual drawing that separates numbers into parts and a whole using rectangles.
- Provide a simple example of a part-whole model that students would understand, such as repeated addition or multiplication where there are four $4 small rectangles and a large $16 rectangle to represent the total allowance a student earned in four weeks.
- Define division as the action of separating a whole into parts. Remind students that the quotient is the answer to a division problem, while the divisor is the number of parts the whole is separated into. The dividend is the whole in a part-whole model.
- Provide an example of a part-whole model with division by writing down the following word problem on the board: "Nine classes resolved to raise $549 for the food pantry. If they split their goal between all the classes, what is the minimum amount each class needs to raise?" Draw a part-whole model for the division problem and model your thinking as you solve for the problem.
- Ask students to turn to their elbow partners and redo the division word problem together using their whiteboards.
- Distribute the worksheet Part-Whole Models with Division Word Problems and display the top teaching component. Read through the description. Ask students to turn and talk with their partners about their observations and how it relates to the model you drew on the board.
Guided Practice(12 minutes)
- Separate students into mixed-ability partnerships and ask them to complete problem #1 from the worksheet Part-Whole Models with Division Word Problems.
- Remind partnerships to draw their own part-whole model and do the division calculation on their own papers and then explain their answer to each other after they've solved it.
- Choose volunteers to share their partner's answers aloud.
- Tell students to put a thumbs up or a thumbs down if they agree or disagree with the answer. Allow students to raise their hands and give more information if they would like to expand on the presenter's explanation.
Independent working time(15 minutes)
- Assign problems #2 and #3 to students to work on independently.
- Ask them to share their answers with partners when they are done to confirm or challenge their ideas.
- Have student volunteers share disagreements they had with their partner regarding the answers or ideas, and then ask for students to help settle the disputes.
- Ask students to think about how they have used the part-whole model in the past and share their ideas aloud.
- Provide visuals and definitions for difficult vocabulary and sentence stems for ELs and students with disabilities.
- Allow students to use cut paper or transparency sheets as manipulatives to visualize their part-whole model. They should write the known information from the word problems on the sheets of paper for each problem.
- Read the word problems aloud to each student before asking them to reread the question aloud to themselves if they struggle with reading comprehension.
- Have students explain to you the process for solving part-whole model division problems before asking them to complete their independent assignment.
- Have students model their thinking aloud by allowing them to share their explanations. Use some of their language and write it on the board for other students to consider or use in their own explanations.
- Challenge them to try other strategies from their toolbox for solving division word problems (e.g., standard algorithm, area models, repeated subtraction).
- Ask students to consider how they can convert the division word problem into a multiplication problem and think about what words and numbers would change in the word problem. Allow them to share their answers aloud to the class during the Review and Closing section of the lesson.
- Conduct a Connect, Extend, and Challenge exercise in pairs where students answer the following three questions:
- How do the ideas about the part-whole model with division connect to what you already knew? ("These ideas are similar to the way I solve word problems for addition, subtraction, and multiplication, except I have the total, or whole, and I need to find either the divisor or quotient.")
- What new ideas did you get that extend or push your thinking in new ideas? ("I understand even more about the connection between all the operations because I can use the same part-whole model for various words problems, even if it's an addition word problem.")
- What is still challenging for you to understand? ("I still don't understand... Nothing was challenging, but...")
- Write the questions on the board and read them aloud to the students.
- Give each partner their own sheet of lined paper so they can write down some ideas or draw pictures to emphasize their point. Ask students to label their answers 1–3 on their papers.
Review and closing(5 minutes)
- Ask volunteers to share one of their answers to the assessment. Have another student add onto the presenter's response with their own answer. Make sure to choose volunteers so that at least one student answers questions 1–3 at least once.
- Remind students that not all the division word problems will follow the part-whole model, but that it is a good tool to consider when solving word problems in general.