Guided Lessons

# Multiplication and Division: What's the Connection?

Numbers are connected in many ways! Take students on a journey to uncover multiplication and division fact families and inverse relationships. Teach this lesson on its own or prior to the lesson Division and Multiplication Relationship.
This lesson can be used as a pre-lesson for theDivision and Multiplication RelationshipLesson plan.

No standards associated with this content.

Which set of standards are you looking for?

This lesson can be used as a pre-lesson for theDivision and Multiplication RelationshipLesson plan.

Students will be able to show understanding of the inverse relationship between multiplication and division.

##### Language

Students will be able to identify the number that does not belong in the fact family and explain their reasoning using sentence starters and peer support.

(4 minutes)
• Gather information on students' background knowledge by asking them to define the term "fact family" to a partner. Tell them to talk about what "fact family" means to them and how they have encountered the term before.
• Ask students to share their conversations with the whole class and record students' responses on the board. Some students may mention addition and subtraction fact families while others may relate multiplication and division fact families. Acknowledge all students' background information and make a point of restating their ideas using correct terminology.
• Tell students that today they will delve deeper into the concept of inverse relationships in maths as they relate specifically to multiplication and division.
(8 minutes)
• Tell students that they will first review some key vocabulary that will help them discuss the maths concepts in this lesson.
• Have students conduct a brief self-assessment on their depth of knowledge of each vocabulary term. Read each vocabulary word aloud, one at a time. Have students show you a thumbs-up if they know the word and can explain its meaning to a friend, a thumb to the side if they have heard the term before but cannot explain it to a friend, or a thumbs-down if they have not heard the term before. Based on students' self-assessments, determine how much time to spend on vocabulary development.
• Distribute a copy of the Glossary worksheet to each student. Have them write "Example" in the far right empty column on the Glossary. Model how to come up with an example for each term to add in this column. Have students continue adding examples, either in their home language (L1) or in English (L2) for the rest of the vocabulary terms. Invite a few students to share their examples with the class. Have students paste the Glossary into their maths journals, if applicable, for future reference.
• Introduce the concept of number relationships by showing an example of a simple multiplication equation on the board or document camera such as 7 x 2 = 14. Ask students to think of other number sentences or equations related to it. Remind students of the commutative property of multiplication which states that the order of factors in a multiplication sentence does not matter, therefore we can also write 2 x 7 = 14.
• Show students how you can write two division equations with these three numbers too. Have students work with a partner to orally state the division problems we could write with these numbers (14 divided by 2 = 7 and 14 divided by 7 = 2). Write out the four number sentences one on top of another to show the pattern and relationship. Explain that multiplication and division are inverse operations which means that they are opposite operations.
• Ask a student volunteer to come up and draw a visual representation of one of the multiplication and division sentences from this fact family (e.g., a 7 x 2Array, 7 circles with 2 items in each circle, etc.).
(8 minutes)
• Explain to students that it is useful to know the multiplication facts to be able to accurately and quickly discover multiplication and division fact families. However, tell students that if they need the support of a multiplication chart, they are welcome to use one as a resource.
• Place students into partnerships and hand out a whiteboard and marker to each pair of students.
• State another multiplication fact such as 6 x 7 = 42. Tell kids to work together with their partner to write the other three multiplication and division sentences that go with the fact family.
• Instruct students to compare their whiteboards with another pair of students and notice if there are any differences.
• Repeat this process with 9 x 8 = 72.
• Have students share their strategies of writing out the complete fact family and provide the following sentence starters as a guide:
• "First, I... Then, I... Finally, I..."
• "I know my fact family is complete and correct because..."
• Ask students to share their feedback on ways of knowing the entire fact family. Lead them to the realization that if you know just one multiplication or division fact, you can easily figure out the other three.
(12 minutes)
• Distribute the Multiplication and Division: How Do the Numbers Relate? worksheet and read aloud the directions.
• Go over the sample problem. Ensure that students have access to their Glossary from earlier in case they need help with word definitions or images.
• Tell students to complete all but the last problem on the worksheet independently. Students are to circle the number that does not belong in the fact family, complete the sentence frames that explain the relationship of the numbers, and draw a visual representation of the fact family.
• Gather students together once they have completed the four problems. Have students share their work and read their answers aloud to a partner. Tell students to also describe the visual representation they drew and how it accurately demonstrates the fact family. Listen in on students' conversations as they share.
• Ask students to share if there were any discrepancies or differences in their work and that of their partner's. Ask them to share how they worked through the differences.
• Review any challenging problems as a whole group.

Beginning

• Allow students to do acitivities with a partner.
• Translate key terms into students' home language (L1).
• Have students work in a small, teacher-led group during group work time.
• Create and display a word/phrase bank with helpful terms from the lesson for students to refer to, with images if applicable.

• Tell students to create a story situation or word problem based on a multiplication and division fact family.
• Ask students to rephrase instructions and paraphrase important learning points throughout the lesson.
(5 minutes)
• Instruct students to solve the last problem on the worksheet using their own words to explain the relationship between the numbers. Students are also to draw a visual representation and explain how the drawing matches the fact family.
(3 minutes)
• Invite a few students to share their explanations and drawings on the document camera.
• Reiterate that it is helpful for us to know the relationship between division and multiplication so that we are able to have a strong number sense to manipulate numbers when solving more difficult maths problems.