Guided Lessons

# Number Relationships in Division

Help your students use multiplication to support their conceptual understanding of division. Use this lesson alone or as a pre-lesson for *Division: Solving for Unknown Factors*.
This lesson can be used as a pre-lesson for theDivision: Solving for Unknown FactorsLesson plan.

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This lesson can be used as a pre-lesson for theDivision: Solving for Unknown FactorsLesson plan.

Students will be able to solve for unknown factors in division problems.

##### Language

Students will be able to explain their approach for determining number relationships in multiplication and division using sentence supports.

(2 minutes)
• Write the term UnknownOn the board and explain that it means something that is not known. Point out that the prefix at the beginning of the word, "un", means not.
• Ask students to think of times in their life when something is unknown and how they handled the situation. Have them turn and talk to a partner, then share out with the whole group.
• Instruct them to think of times in mathematics when information is unknown and how they handled the situation. Have them turn and talk to a partner before sharing out.
• Explain that sometimes we can solve problems with unknown information by making connections to what we already know. Share a student-friendly language objective with the class and have them repeat it aloud.
(8 minutes)
• Teach the key vocabulary for the lesson by showing each word on the vocabulary cards, one at a time. Read aloud the word and have students repeat it, and then facilitate a discussion about what students know about it. Ask students, "What do you know about the word?" Instruct them to gauge their knowledge by putting up a finger based on the following rating scale:
• 1 - I've never heard the word before.
• 2 - I've heard the word before, but I don't know what it means.
• 3 - I know a little bit about what the word means.
• 4 - I know this word and can explain its meaning.
• Call on students who display three or four fingers and have them share what they know about the word. Invite the rest of the class to describe the images they could put on each of the Vocabulary Cards. Then, reveal the image and definition on each card.
• Ask students, "Is the image on the card close or related to the image you suggested?" Provide a sentence stem to support student answers, such as "The image was/was not close because ____."
• Display a multiplication and division problem on the board and model labeling the parts of the equations using the words on the Vocabulary Cards. For example, write 3 x 4 = 12, and label the 3 and 4 with the word FactorAnd label the 12 with the word Product. Write 12 ÷ 4 = 3, and label the 12 as the Dividend, 4 as the Divisor, and 3 as the Quotient.
• Point out how the problems are related because they can be reversed with the same numbers and use a different operation. Share that multiplication and division are inverse operations, so they can use the same three numbers to create a few mathematical expressions.
• Write new multiplication and division problems on the board and invite students to come up to the board to label the parts using the Vocabulary Cards.
• Give each student a set of their own Vocabulary Cards to use as a word bank for discussion throughout the lesson.
(10 minutes)
• Display the Multiplication and Division: Which One Doesn’t Belong? worksheet on the document camera and tell the class that there are four numbers, but one doesn't belong. Share that it is up to us to figure out which three numbers are associated and how they are associated. Remind them that the focus of today's lesson is multiplication and division, so we can come up with an association for the three numbers based on those mathematical operations.
• Point to the first problem on the worksheet and begin thinking aloud, "I know that I can create a multiplication problem with 3 and 5 as the factors and the product is 15. I also know that I can create a division problem with 15 as the dividend and 3 as the divisor. The quotient is 5. The number 9 does not fit into multiplication and division problems with the rest of the numbers."
• Fill out the sentence stems/frames underneath the numbers with the information from the think aloud.
• Distribute a copy of the Multiplication and Division: Which One Doesn't Belong? worksheet to each student.
• Invite students to do the next two examples together as a class. Ask questions to prompt student conversation, and provide sentence stems/frames to support the discussion:
• What multiplication problems can you create? (The multiplication problems are ____.)
• What are the factors? (The factors are ____.)
• What is the product? How do you know? (The product is ____Because ____.)
• What division problems can you create? (The division problems are ____.)
• What is the dividend/divisor/quotient? (The dividend/divisor/quotient is ____.)
• How are the multiplication and division problems connected? (The problems are connected ____.)
• How did you decide that the other number doesn't belong? (We decided that ____Doesn't belong by ____.)
(10 minutes)
• Pair students in A-B partnerships and instruct Partner A to be the discussion leader for the fourth problem on the Multiplication and Division: Which One Doesn't Belong? worksheet, while Partner B will be the discussion leader for the fifth problem.
• Direct them to complete the next two problems on the worksheet and discuss. Display the questions and sentence stems to support the conversation between the partners:
• What multiplication problems can you create? (The multiplication problems are ____.)
• What are the factors? (The factors are ____.)
• What is the product? How do you know? (The product is ____Because ____.)
• What division problems can you create? (The division problems are ____.)
• What is the dividend/divisor/quotient? (The dividend/divisor/quotient is ____.)
• How are the multiplication and division problems connected? (The problems are connected ____.)
• How did you decide that the other number doesn't belong? (We decided that ____Doesn't belong by ____.)
• Gather the class back together and discuss the two problems that partners worked on. Call on students to explain their thinking. Have students restate a peer's explanation and challenge them to add onto the statement. Provide sentence stems to support the discussion, such as "I agree because ____. I would also say ____."
• Remind students that the multiplication and division problems show the inverse relationship between the two operations. Tell them that they are opposite, and knowing how the three numbers are associated can help us with our maths facts.

BEGINNING

• Have learners repeat instructions and key vocabulary to the teacher.
• Provide a word bank of key terms and phrases for students to use in group and class discussions.
• Group students intentionally based on academic and language needs.
• Read aloud the sentence stems/frames on the worksheet for students.
• Pair students with supportive partners or a peer with the same L1, if possible.

• Allow learners to utilize glossaries and dictionaries for unfamiliar words.
• Encourage students to answer questions and participate in discussions without referring to the sentence stems or frames for support.
• Choose advanced ELs to share their ideas first in group and class discussions.
• Have learners repeat instructions and key vocabulary, summarizing important information for the class.
• Put students in mixed ability partnerships so they can offer explanations and provide feedback to beginning ELs when appropriate.
(7 minutes)
• Instruct students to independently complete the final example on the Multiplication and Division: Which One Doesn't Belong? worksheet.
(3 minutes)
• Call on volunteers to explain their thinking on the final problem on the Multiplication and Division: Which One Doesn't Belong? worksheet. Encourage them to reference their Vocabulary Cards to make sure they use the content-specific vocabulary in their explanations.
• Ask the same prompting questions that were asked earlier during the lesson, and be sure to support students' oral language with sentence stems and frames.
• Remind the class that the problems are related because they can be reversed with the same numbers and use a different operation. Reiterate that multiplication and division are inverse operations, so they can use the same three numbers to create a few mathematical expressions. This helps us know our maths facts better!