Number Relationships in Division

Explicit Instruction/Teacher modeling

• 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 factor and 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.

Guided Practice

• 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 ____.)

Group work time

• 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 math facts.