Guided Lessons
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# Explore the Associative Property of Multiplication

Use this lesson with your students to allow them to explore the associative property of multiplication by having deep discussions in small groups. Use this as a stand alone lesson or alongside *Associative Property of Multiplication*.
This lesson can be used as a pre-lesson for the Associative Property of Multiplication lesson plan.

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This lesson can be used as a pre-lesson for the Associative Property of Multiplication lesson plan.

Students will be able to apply the associative property to multiply single-digit factors.

##### Language

Students will be able to explain the associative property of multiplication with content specific words and phrases using peer supports.

(4 minutes)
• Invite students to observe you solve a multiplication problem on the board.
• Write and solve a multiplication problem using the associative property of multiplication without thinking aloud about your steps. For example, solve the following problem: 2 x (3 x 5) using just numbers, without explaining your steps. Repeat the same process for (2 x 3) x 5.
• Ask the class what they noticed about the process and the answers. Have them share with a partner before sharing with the whole group. Provide a sentence starter to support sharing, such as "I noticed that ____."
• Explain that there are certain properties of multiplication that help us understand multiplication better. Add that each of the mathematical properties works in a specific way and is used in certain situations.
(10 minutes)
• Begin by displaying the Vocabulary Card for the word property. Ask students what they know about the word. Point out that this word has multiple meanings. It can mean a piece of land that someone owns, but it has a different meaning in math. Explain that it is important to know the properties because they help with number sense. Once we have that number sense, we can efficiently solve multiplication problems. It helps us make sense of math.
• Teach the rest of the tiered vocabulary words by displaying the Vocabulary Cards. Have students repeat the word aloud and then orally share the definition in their own words. Ask students to discuss how the image connects to the word, and have them brainstorm whether another image could go on the Vocabulary Card to help them remember the word's definition. Provide sentence starters to support student conversation.
• Go over the student-friendly Language Objective and have students repeat it aloud. Tell them that you are going to teach them about the associative property of multiplication as you solve an equation in two different ways.
• Read aloud a word problem and tell students that you will show them how to solve it using arrays. For example, "There are three dogs in each backyard on my street. There are four houses on my street. How many dog legs are there?"
• Model solving the problem, and think aloud about each step. Follow the steps below as you solve the equation in two ways.
• 1 - Set up the equation with parentheses around two numbers.
• 2 - Build an array of the problem inside the parentheses.
• 3 - Look at the third digit in the equation to see how many times you have to build that array.
• 4 - Solve for the area of each of those arrays and add them up.
• Explain that the problem was (3 x 4) x 4, which means that there are 48 dog legs. Show students how to move the parentheses and follow the same exact steps. Use 3 x (4 x 4) as the equation and emphasize that the answer is the same in both equations. Both equations use the same numbers, and the position of the parentheses is the only thing that changed.
(10 minutes)
• Divide the class into small groups and instruct them to take out their whiteboards and whiteboard markers. Have a representative from each group choose a card from the bag or envelope.
• Instruct groups to solve the equation using the strategy of arrays that was modeled at the beginning of the lesson. Then, have them move the parentheses and solve that equation.
• Direct the groups to discuss how the associative property works and how they know their answer is correct. Write the following questions and sentence starters on the board to guide groups' discussions:
• What do the parentheses mean? (The parentheses mean ____.)
• What do the parentheses do to the answer? (The parentheses ____.)
• How did the problem change from the first to second time you solved it? (The problem changed by ____.)
• How did the problem stay the same from the first to second time you solved it? (The problem stayed the same by ____.)
• Why does this property work? (This property works because ____.)
• How would you explain this property to someone who has never learned about it before? (I would tell them ____ about the associative property of multiplication. I would explain that ____.)
• Circulate and support groups in their conversations. Jot notes about which students show confidence and proficiency in terms of calculation and explanation.
• Call on students in each group to share what they learned about the associative property of multiplication by sharing their equations and how they solved them.
(8 minutes)
• Ask them to think about which words and visuals were really helpful in communicating about the associative property of multiplication. Tell them that they will come up with a step-by-step process for teaching someone how the property works.
• Scramble the groups and have them work together to create a list of four steps. Encourage them to use some of the tiered words taught in this lesson, as well as any other words they deem important from their work with the associative property of multiplication.
• Give each group a sheet of chart paper or construction paper on which to record their step-by-step process.
• Call on each group to share out, and then present your established list of steps:
• 1 - Set up the equation with parentheses around two numbers.
• 2 - Build an array of the problem inside the parentheses.
• 3 - Look at the third digit in the equation to see how many times you have to build that array.
• 4 - Solve for the area of each of those arrays and add them up.

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 a (partially completed) Frayer Model graphic organizer to complete for the Assessment in order to provide structure for them.

• Allow learners to utilize glossaries and dictionaries for unfamiliar words.
• Have students describe their math processes without relying on the sentence stems/frames.
• 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)
• Distribute a blank piece of paper to each individual and have them create an informational poster for the term associative property of multiplication. Instruct them to include the term, a definition in their own words, and images to help explain the property.
(3 minutes)
• Invite students to share their informational posters with a friend. Provide sentence starters to support their sharing, such as "I included ____ on my poster because ____.
• Remind the class that it is important to understand the properties of multiplication because it helps to build our number sense and overall understanding of the math world.