# Part-Whole Division Sentences

This lesson can be used as a pre-lesson for the Part-Whole Model: Word Problems with DivisionLesson plan.

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This lesson can be used as a pre-lesson for the Part-Whole Model: Word Problems with DivisionLesson plan.

Students will be able to create part-whole division word problems.

##### Language

Students will be able to talk about and create division word problems using a graphic organizer and sentence stems.

(5 minutes)
• Write two sentences on the board that are separate but pieces of a word problem (e.g., "1. The class has a total of \$150 to spend on book bundles," and "2. They buy 6 bundles."). Number them 1–2 and ask students to brainstorm what information the sentences share.
• Gather background information from students by listening to their discussions. They should understand that sentence #1 discusses the total or whole amount (e.g., \$150 to spend on the bundles) and sentence #2 talks about a part or piece of the whole (e.g., 6 book bundles).
• Draw a Part-whole modelOn the board and tell students they will discuss keywords and hints within story problems that show a part-whole relationship.
(8 minutes)
• Review the vocabulary terms and distribute the Vocabulary Cards to each student. Read through the cards and their meanings.
• Assign a group of five, mixed-ability students a new vocabulary word they will use to complete a Frayer Model worksheet. Use the words "part-whole model," "part," "whole," and "dividend" and allow words to repeat if you need more than four groups.
• Model presenting your Frayer Model for the word "quotient." Write the sentences you create on the board and then write the sentence frames that correspond with the descriptions you shared.
• "The meaning of the word ____Is ____."
• "I drew the picture ____Because ____."
• "An example of ____Is ____."
• "A nonexample of ____Is ____."
• Assign the five students in each group a number 1–5 and have them label the boxes in the Frayer Model 1–5 (excluding the word). The student with the corresponding number will present that section of the Frayer Model to the whole class. (Note: choose students who are confident in their understanding of the new term, and allow the listeners to turn and talk to their partner about the new term after the brief presentation.)
• Spend extra time with the sentences students created to represent the whole or part in their Frayer Models. Choose a few sentences students created on their Frayer Model and write them on the board. Circle common language throughout (e.g., "total," "all," "everything," "separated," "divided," "groups," etc.).
• Write sentences that depict wholes or parts on sticky notes throughout the lesson to use in the Review and Closing section activity. Listen to student conversations throughout the lesson to gather this information.
(7 minutes)
• Create a part-whole model with tape on the floor (see the Co-Craft Questions: Division Word Problems graphic organizer for reference). Distribute the sentence strips A and B two at a time so that one student has slip A and another student has slip B. Retain all slip Cs.
1. Assign the first student to read the sentence aloud and display it on the document camera.
2. Have students as a class discuss the placement of the sentence in the part-whole model (i.e., does it mention the part, whole, or both). They will put a sentence that describes a whole in the whole section and a sentence that describes the part in the part section.
3. Repeat the same process with the second student where they read the slip of paper and help determine in which part of the part-whole model it should be.
4. Read the sentence strip labeled "C," that shows the question and place it in the remaining part section of the graphic organizer.
5. Ask students to create an expression for the sentences on their whiteboard after they've determined the part and whole from the sentences.
• Continue steps 1–5 until you've separated all the sentences and created expressions for them. Throughout the activity, prompt students to identify keywords that hint towards a sentence mentioning a whole (i.e., dividend) or part (i.e., divisor). Also, have them state the noun that corresponds with the number when they read their expression. For instance, "The expression is 75 cupcakes divided by 5 classes."
• Make sure to discuss how the question leads them to believe they need to divide to find the missing answer (e.g., keywords such as "each ____").
(7 minutes)
• Assign mixed-ability partnerships and tell students they will now create their own sentences that have the language to tell about the whole or a part (e.g., the number of groups or the number in each group).
• Distribute the Co-Craft Questions: Division Word Problems worksheet and review the instructions with the whole class. Choose a student to tell what they must do in each section of the graphic organizer.

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 students to use the vocabulary cards and terms in their conversations and writing. Allow them to draw pictures to support their understanding of the terms (e.g., the Frayer Model, vocabulary cards, their written part-whole sentences, etc.).
• Provide them with sentence frames and stems for all their writing. Allow them to dictate their answer and point to the part of the graphic organizer you should write the sentence.

• Pair students with mixed ability groups so they can offer explanations and provide feedback to beginning ELs when appropriate.
• Ask students to create a whole division word problem and then switch their problems with another partner so each partner will have a unique, student-created problem to solve.
• Provide more simplistic sentences from word problems that do not have a significant amount of key terms listed. For example:
• "A 12-pack of lemonade costs \$15. How much does each lemonade bottle cost?"
• "The meal costs \$55 for 5 people. How much did it cost for them to split the bill?"
• Ask students to explain key ideas from the lesson, such as how keywords can help students determine the whole and part in a division problem.
• Have students explain to the class how to solve the division expressions if they understand the mathematical process.
(8 minutes)
• Review the graphic organizer with students once they've completed it. Choose volunteers to share their sentences.
• Listen to student conversations and take note of the sentences they created and the language they use to create the sentences. Transcribe their ideas and language onto the Formative Assessment: Peer Explanations Checklist worksheet to inform you about their language growth and communication ability.
• Write some on sentences for the word problems students create on the sticky notes as you listen to their responses.
(5 minutes)
• Conduct a "snowball" activity with some of the sticky-note, student-created sentences you wrote throughout the lesson.
1. Crumple the sticky notes and place them in front of you.
2. Pick up a random sticky note and read the sentence aloud as you display it on the document camera.
3. Choose the first person that raises their hand to tell you if the sentence talks about a part, a whole, or the quotient.
4. Have students confirm or deny the answer with a thumbs up or down. If a student get the answer wrong, have students correct the answer as a whole group. Then, ask the student who answered incorrectly to restate the correct answer and why.

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