Guided Lessons

# Justifying the Distributive Property

Let's talk about the distributive property! Give students a chance to explain their thinking of how and why this property of multiplication works. This lesson may be taught as a standalone or as support to the lesson Distributive Property.
This lesson can be used as a pre-lesson for theDistributive PropertyLesson plan.

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This lesson can be used as a pre-lesson for theDistributive PropertyLesson plan.

Students will be able to apply the distributive property of multiplication.

##### Language

Students will be able to explain the solution to a multiplication problem using partner support and a graphic organizer.

(3 minutes)
• Tell students that in maths, there are often rules that apply to certain mathematical operations. These rules, or properties, often make it easier for us to solve certain maths problems.
• Inform students that today they will focus on one of these properties called the Distributive propertyFor multiplication. Tell students that the word "distribute" means to deal out or hand out something. Give examples of distributing, such as a teacher distributing pencils to students or a coach distributing soccer balls. Ask students to discuss their connections to the concept of distributing with a partner.
• Read aloud the content and language objectives and have students repeat or rephrase them to a partner.
(10 minutes)
• Tell students that they will first review some key vocabulary related to today's lesson.
• Distribute a copy of the Glossary worksheet to each student and display a teacher copy on the document camera.
• Call on student volunteers to read aloud each vocabulary term and its definition.
• Model to students how to draw a visual to help explain the meaning of the word Addend(e.g., draw 12 + 23 = 35And circle the 12 and 23).
• Have students continue drawing visuals for the remaining vocabulary words. Tell students to share their visuals with a partner, and explain how the drawing gives more meaning to the word. Have a few students share their visuals with the whole class on the document camera. Provide sentence stems/frames to help students share, "I drew ____. This visual helps me to understand the word ____Because..."
• Have them glue the Glossary worksheet into their maths journal for future reference.
• Explain to students that the Distributive propertyIs useful when we want to multiply larger numbers more easily by DecomposingOne of the factors into smaller pieces. Reiterate that the distributive property means that we can distribute the multiplication to each of the factors by breaking up one of the factors into more manageable addends.
• Display the Sweet Distribution worksheet on the document camera. Read the steps to use the distributive property and go over the sample problem. Emphasize the importance of using arrows to demonstrate how you are distributing the factor to each addend.
• Read aloud the first word problem, defining any tricky words in students' home languages (L1s) and in English (L2).
• Model how to solve the problem using the distributive property for multiplication. Say, "I know that I need to multiply 18 by 4 because there are 18 members of the team and they each got a four-scoop ice cream sundae. I will decompose the 18 into 10 and 8 to make the multiplication easier. This gives me 4 x (10 + 8) = Which becomes (4 x 10) + (4 x 8) = . Then I get 40 + 32 = 72. There will be 72 total scoops of ice cream."
(10 minutes)
• Tell students that they will practise multiplying using the distributive property by solving some problems and explaining their reasoning of the process.
• Distribute copies of the Sweet Distribution worksheet to students and have them redo the first problem using your explicit teaching as a guide.
• Hand out the Refine Your Justification worksheet to each student and read aloud the teaching box.
• Place students into strategic A-B partnerships (i.e., those with the same home language could be placed together, or a beginning EL could be placed with a supportive intermediate EL). Tell Partner A that they will solve problem 2 while Partner B will solve problem 3 on the worksheet.
• Tell them to solve their assigned problem on the Sweet Distribution worksheet on their own using the distributive property. Then, write their explanation down in the first section on the graphic organizer. Remind students that for this first explanation they are simply to write down the explanation using whatever terms make sense to them.
• Have them rewrite their first explanation again in the second section of the graphic organizer, this time focusing on adding more details regarding WhatThey know is true and HowThey know it is true. Provide sentence stems to support students:
• "First, I decomposed the ____Into ____And ____."
• "Then, I distributed the factor ____And multiplied it by____And ____."
• "This gave me the partial products of ____And ____."
• "I know this part of my solution is true because..."
• Have students share their first and second explanation to a friend.
(10 minutes)
• Have the students provide feedback to their classmate about their explanations.
• Give them sentence stems/frames to support them:
• "I like how you explained that..."
• "The part where you wrote ____Helps me understand..."
• After both Partner A and B have given their feedback to their classmate, give students time to rewrite their explanation a final time, this time with a focus on the WhyTheir solution is correct.
• Tell students to imagine they are explaining the problem and solution to a person that does not have experience with the distributive property for multiplication. Remind them to use evidence such as drawings, examples, step-by-step maths work, and complete sentences in this last and most thorough explanation.
• Have students read their third explanation to their partner.
• Invite a few students to read aloud their final explanation to the whole group. Celebrate the accuracy and use of evidence in their explanations.

Beginning

• Read aloud the word problems to students during the Guided and Group work time. Define any unclear words from the word problem.
• Allow students to explain the process of solving the problems in their home language (L1) before rephrasing (using sentence stems/frames) in English.
• Have students work in a small, teacher-led group during group work.
• Create and display a word/phrase bank with helpful terms from the lesson for students to refer to, with images if applicable.
• Place students in specific partnerships based on their language needs.

• Encourage students to rephrase the directions throughout the lesson.
• Have students share their answers aloud without referring to the sentence stems/frames for support.
• Allow them to utilize glossaries and dictionaries for challenging words.
• Have learners repeat and explain key vocabulary for the class.
(4 minutes)
• Distribute a half sheet of copy paper to each student and have them write an explanation of the "distributive property of multiplication." Instruct them to include the term, a definition in their own words, an example, and visuals to help explain the property.
(3 minutes)
• Have students share their assessment with a partner.
• Invite a few students to share their sheet with the whole class. Congratulate students on their in-depth work to understand and explain the meaning of the distributive property.