Guided Lessons

# Multiplication and Division Fact Families

Support your students' maths fluency by teaching them about the relationship between multiplication and division through fact families. This lesson can stand alone or be used as a pre-lesson for the *Do You Know Your maths Facts?* lesson.
This lesson can be used as a pre-lesson for theDo You Know Your maths Facts?Lesson 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 theDo You Know Your maths Facts?Lesson plan.

Students will be able use their knowledge of the relationship between multiplication and division to fluently multiply and divide numbers within 100.

##### Language

Students will be able to explain the relationship between multiplication and division with grade-level vocabulary using visual aids.

(2 minutes)
• Write the word RelationshipOn the board and ask students to talk with a partner about the relationship, or the way the two things are connected, between daytime and nighttime. Listen to students' conversation, specifically listening for the word Opposite.
• Gather students together and explain that the relationship between daytime and nighttime is that they are opposite of each other. They are completely different for many reasons.
• Share the Language Objective for the lesson, and explain that students are going to look at the relationship between multiplication and division today.
(10 minutes)
• Hold up the Vocabulary Card for the term Fact familyAnd read the definition. Give an example of addition and subtraction fact families (1, 9, 10), and explain that addition and subtraction have an opposite, or Inverse, relationship.
• Display the top half of the Icy Fact Families worksheet and model drawing a visual (e.g., small dots) to represent each number in the expression. Explain that addition means you are putting the numbers together, and subtraction means you are finding the difference between two numbers. Label each set of dots in the expression with a number to make the connection between the visual and the expression, and think aloud about how the numbers are the same in the addition and subtraction expressions, but the OperationIs different.
• Share that today they will be looking at the operations of multiplication and division and creating visuals to understand how they are related.
• Tell the class that you are having some people over to your house, and you have four different tables. You have room for three people at each table. You are trying to find out how many people can be at the party.
• Write the following multiplication problem on the board or document camera: 4 x 3 = ?. Explain that since you know multiplication is talking about equal groups, the expression really means "four groups of three". Draw a visual of four groups of three by making four circles with three dots inside of each. Then, count the individual dots out loud to point out that you have twelve dots, which means twelve people.
• Think aloud about another problem, using the same factors in the multiplication expression. Say, "What if I only had three tables and I put four people at each table? How many people could be at the party then?" Draw a visual of three groups of four by making three circles with four dots inside of each. Then, count the individual dots out loud to point out that you have 12 dots, which means 12 people. Explain that 3 x 4 = 12Is in the fact family because it uses the same numbers as 4 x 3 = 12.
• Use the same numbers (3, 4, 12) to show the division expressions in the fact family. (e.g. Say, "There are twelve people coming to the party. If we want to have four people at each table, how many tables do we need?") Write the following division problem on the board or document camera: 12 ÷ 4 = ?. Explain that since you know division is about breaking things into equal groups, the expression means "how many in each group". Draw 12 dots to represent the people, and create groups of four by counting four dots and circling them to represent one group. Count the number of groups that were created, and point out that three is the answer (three tables are needed). Note that these numbers are the same as the previous two examples, so it fits in the fact family.
• Show the final expression in the fact family with a word problem. Say, "I know that there are 12 people coming to the party. If there are only three people at each table, how many tables do we need?" Write the following division problem on the board or document camera: 12 ÷ 3 = ?. Draw twelve dots to represent the people, and create groups of three by counting three dots and circling them to represent one group. Count the number of groups that were created, and point out that four is the answer (four tables are needed). Note that these numbers are in the previous examples, so it also belongs in the fact family.
• Ask students to talk to a shoulder partner about the relationship between the three numbers in the fact family, as well as the relationship between multiplication and division. Allow them to draw visuals and provide a sentence starter, such as "These numbers/operations are related because ____."
(10 minutes)
• Tell students that they are going to play a game called "Which One Doesn't Belong?" Explain that each partnership will get a strip of paper with four numbers on it. They must decide together how to group the numbers so that three of them fit into a fact family and one does not. Each partner must be prepared to explain to other students how they agreed on the fact family and which number did not fit.
• Display a strip of paper with four numbers, three of which belong in the same fact family. Think aloud about the relationship between the numbers, creating multiplication and division expressions and drawing visuals to prove that they fit into the same fact family.
• Engage the class in discussing another example together. Guide them through creating the multiplication and division expressions, and have them draw visuals on their whiteboards. Give students time to talk to a partner or small group about which number they think doesn't belong. Discuss as a class.
(10 minutes)
• Pair students and give each partnership a strip with four numbers on it. Instruct them to use their whiteboards to visually represent each expression in the fact family as they work to determine which number does not belong.
• Scramble the partnerships and have each student explain which number did not belong in their original group of four numbers. Have them orally explain, supporting their points with visual representations of the multiplication and division expressions.

Beginning

• Have learners repeat instructions and key vocabulary to the teacher.
• Provide a sentence frame for discussion during the game. For example, "The number ____Doesn't belong because ____."

• 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.
(6 minutes)
• Give each student an index card and ask them to respond to one of the following questions using words and visual aids:
• What is the relationship between multiplication and division?
• How can you figure out if numbers fit into a fact family?
• Are five, seven, and 35 in a fact family? How do you know?
(2 minutes)
• Ask students to share their index card with a partner, and then call on a nonvolunteer to share their response.
• Remind students that understanding the inverse relationship between multiplication and division will help them as they develop their maths fluency. It will help them be faster and more automatic with their maths facts when multiplying and dividing.