Guided Lessons

# Foundations of the Commutative Property

Let your students explore similarities and differences between arrays, and help them understand the commutative property of multiplication. Use this as a stand alone lesson or as a prelesson for *Parking Lot Multiplication*.
This lesson can be used as a pre-lesson for theParking Lot MultiplicationLesson plan.

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This lesson can be used as a pre-lesson for theParking Lot MultiplicationLesson plan.

Students will be able to make arrays to represent the commutative property of multiplication.

##### Language

Students will be able to explain the similarities and differences between array representations of multiplication problems using sentence starters and peer supports.

(2 minutes)
• Draw an array on the board with two rows of six dots. Facilitate a think-pair-share by instructing students to think about how they would describe the image on the board.
• Have students talk to a partner and describe what they see. Then, call on students to share with the whole group. Listen for the vocabulary students use, and note whether they mention any of the tiered words you'll go over in this lesson.
• Tell the class that you drew an array on the board, which is an arrangement of the dots in columns and rows. Point out the columns and the rows to provide a visual for students. Tell them that this is a visual representation of a multiplication problem (2 x 6).
• Go over the student-friendly Language Objective and share that students will be exploring the similarities and differences between arrays during this lesson.
(10 minutes)
• Display the Vocabulary Cards for the terms previously introduced (array, column, row) and show the image along with the definition. Ask students to compare the images on those cards to the example in the Introduction. Provide a sentence starter to support their comparision. (e.g., The arrays are similar/different because ____.)
• Teach the remainder of the vocabulary words with the cards. Ask students to discuss the image and how it relates to the definition of each word. Provide additional examples or clarification, as needed.
• Give each student a copy of the Glossary and have them label the last column as "Related Word." Have students add a word in this column that will help them remember the definition of the tiered word. This can be a synonym, additional example, or the word in their home language.
• Read aloud the word problem, "Yolanda makes three loaves of bread. Each loaf has five slices in it. How many slices does she have in all?
• Show how to create a multiplication problem based on the word problem (3 x 5) and explain that you know you'll need to create three groups of five based on the order of the factors in the problem. Draw the array on the board and use the vocabulary terms to explain what you drew.
• Read aloud another word problem, using the same factors. Say, "Yolanda makes five loaves of bread. Each loaf has three slices in it. How many slices does she have in all?"
• Show how to create a multiplication problem based on the word problem (5 x 3) and explain that the order of the factors shows five groups of three. Point out that you'll need five rows of three in each. Draw the array on the board and use the vocabulary terms as you explain how the array connects to the word problem and multiplication expression.
• Ask students to consider the similarities and differences in the multiplication problems and the arrays on the board. Provide a sentence starter to support their discussion, such as "They are similar/different because ____."
(12 minutes)
• Distribute a copy of the Comparing Arrays worksheet to each student and tell them that they will play the role of both Partner A and Partner B for the first problem so they can learn the steps of the exercise.
• Guide students to create a multiplication expression for each of the problems on #1 (e.g., 4 x 6And 6 x 4). Engage them in conversation about how to create the arrays so that they are able to show "____Groups of ____" based on the factors listed and the context of the word problem.
• Write the following questions on the board and facilitate a discussion with them to get students comparing the arrays:
• How did you decide the number of dots in the rows? (I decided the number of dots in the rows by ____.)
• How did you decide the number of dots in the columns? (I decided the number of dots in the columns by ____.)
• What does your array show? (My array shows ____.)
• How are the arrays similar/different? (The arrays are similar/different because ____.)
• Do you agree or disagree? Why? (I agree/disagree because ____.)
• Put students into A-B partnerships. Tell the class that Partner A will complete Problem A on #2 on the worksheet, while Partner B completes Problem B. Instruct them to complete the work independently, and then share their arrays with their partner. Each student should record their partner's work on their own worksheet while their partner explains.
• Circulate and note which students clearly communicate about the similarities and differences between the arrays, and listen specifically for conclusions that partnerships draw about the relationship between the multiplication expressions.
(8 minutes)
• Refer to the questions on the board and facilitate a discussion with the class to get students comparing the arrays:
• How did you decide the number of dots in the rows? (I decided the number of dots in the rows by ____.)
• How did you decide the number of dots in the columns? (I decided the number of dots in the columns by ____.)
• What does your array show? (My array shows ____.)
• How are the arrays similar/different? (The arrays are similar/different because ____.)
• Do you agree or disagree? Why? (I agree/disagree because ____.)
• Lead students to the conclusion that the arrays are similar because they include the same total number of dots, which represents the product of the multiplication expression. Add that the dots are arranged in a different way because the order of the factors is different in each expression.

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.
• Give students their own set of Vocabulary Cards to reference throughout the lesson.

• 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 groups so they can offer explanations and provide feedback to beginning ELs when appropriate.
(5 minutes)
• Instruct students to complete both problems on #3 on the Comparing Arrays worksheet. Remind them to use an array to solve each problem. Tell them that when they have finished their work, they should observe the similarities and differences between the arrays and be prepared to verbally complete the sentence stem "The arrays are similar/different because ____."
(3 minutes)
• Go over the problems on #3 on the Comparing Arrays worksheet by having students share their sentence stems with a partner. Then, call on students to share if they had the same answers as their partners.
• Discuss the similarities and differences between the arrays, and come up with a class version of the sentence stems.
• Tell students that they just worked to understand the foundation of an important property of multiplication. Share that the commutative property of multiplication says that the order of the factors does not change the product. Two factors can be multiplied in any order and the answer will remain the same. Remind students about the different examples, and write them on the board again or display them on the document camera to provide a visual.