Primary Type: Lesson Plan
Status: Published
This is a resource from CPALMS (www.cpalms.org) where all educators go for bright ideas!
Resource ID#: 28078
The Distributive Property
Introductory lesson on the distributive property using word problems as context for area models.
Subject(s): Mathematics
Grade Level(s): 6
Intended Audience: Educators
Suggested Technology: Document Camera, LCD
Projector
Instructional Time: 45 Minute(s)
Resource supports reading in content area: Yes
Freely Available: Yes
Keywords: distributive property, equivalent expressions
Resource Collection: CPALMS Lesson Plan Development Initiative
ATTACHMENTS
Distributive Property Practice 1.pdf
Distributive Property Practice 1 Answer Key.pdf
LESSON CONTENT
Lesson Plan Template: General Lesson Plan
Learning Objectives: What should students know and be able to do as a result of this lesson?
Students should be able to write two equivalent expressions to represent a situation which proves the validity of the distributive property.
Students should be able to generate an equivalent expression using the distributive property.
Prior Knowledge: What prior knowledge should students have for this lesson?
Students should be familiar with the term "equivalent expression." Students should have practice writing equivalent expressions using the commutative and associative
properties.
From previous grades, students should be familiar with finding the area of a rectangle as well as terms such as "square feet" since this lesson relies on modeling
using area.
Guiding Questions: What are the guiding questions for this lesson?
How can I write equivalent expressions using the distributive property?
Teaching Phase: How will the teacher present the concept or skill to students?
1. See formative assessment.
2. After several students share their methods for solving Cedric's problem, guide students through writing two equivalent expressions to represent the problem
(4*5+4*3, 4(5+3)). The advantage of using an area model problem is it allows students to see the distributive property in a very concrete way. Start by
displaying a visual of the two areas using colored tiles, models on graph paper or a poster you previously constructed. If possible, represent both areas in
different colors which will enhance understanding as you guide students through writing the expressions. Ask students what the problem is asking us to find
(trying to find the total area) and show students that finding the areas separately (4*5+4*3) then pushing the models together and treating it like one big
rectangle (4(5+3)) generates the same answer (thus proving the expressions are equivalent). Drawing the models on graph paper also works.
page 1 of 3 *Using two different colors for the two areas will especially help struggling students because both areas are still distinguishable when they are grouped together as
one area. VisualizationofCedricsProblem.pdf
1. Give students new dimensions such as 2 by 4 and 2 by 6 to go with the same problem. Have students write two equivalent expressions to represent the problem
and prove they are equivalent by evaluating each problem (e.g. 2*4 + 2*6 and 2(4+6)). Allow students to use manipulates or graph paper if they wish. Have
partners compare expressions and then discuss as a class, emphasizing the method of justification that the expressions are equivalent (evaluating both expressions
and arriving at the same answer proves the expressions are equivalent).
2. Introduce the term "distributive property" and how the rule looks expressed as variables (e.g. a(b+c)=ab+ac). Emphasize that this property involves both addition
and multiplication. The idea of "distributing" is foreign to students. To reinforce the concept of "distributing the a," which is a commonly used phrase, use an
example students can relate to in your explanation (e.g. "Let's say I have two pieces of candy to give to each girl in the class and 2 pieces of candy to give to each
boy in the class. I distribute two to Susie, two to Maria (you can hand out manipulates or actual candy, continue until everyone has gotten "candy"). How many
pieces did I hand out to girls and how do you know? How many pieces to boys and how do you know? How many pieces did I handout altogether?" Continue to
solicit answers for each question until students state you multiply two times the number of girls (boys, total number of students). Write out the appropriate
expressions using the distributive property. If you have 12 girls and 7 boys: 2*12+2*7= 2(12+7). "What if I gave out three pieces instead?" Again, looking for
students to associate "3 for each" as multiplying the number for three. Write this expression as well starting with 3(12+7) and show how to "distribute the three" to
form 3*12+3*7). Bring the discussion back around to the rule in variables. Start with a(b+c) and show how to "distribute the a" to get a*b+a*c.
3. Propose the following question to students: "Will the distributive property work with subtraction instead of addition?" Display the rule using variables, a(b-c)=a*b a*c. Encourage students to work in partners and substitute numbers in for a,b and c in order to determine if the expressions are equivalent.
4. Hand out "Distributive Property Practice 1." Allow students to work together in pairs and use whatever tools they wish (graph paper, Legos, etc.) to find the
answers. The teacher should be moving between pairs of students and assisting as needed. Emphasize that clear written work is important since it shows their
mathematical thinking which helps you to informally assess student mastery and target misconceptions.
5. Students determine whether one expression is equivalent to another. See "summative assessment."
Guided Practice: What activities or exercises will the students complete with teacher guidance?
Provide assistance as needed while the students are working on "Distributive Property Practice 1."
Independent Practice: What activities or exercises will students complete to reinforce the concepts and skills developed in the
lesson?
Students will answer a prompt individually as a summative assessment. Assigning more practice for homework would be appropriate.
Suggested homework practice:
DistributivePropertyHomeworkPracticeandAnswerKey.pdf
Closure: How will the teacher assist students in organizing the knowledge gained in the lesson?
The teacher brings the class back together to discuss several main points:
1. Using the distributive property to write equivalent expressions will become very important in subsequent years (Algebra 1 and Algebra 2).
2. We can verify that two expressions are equivalent.
3. Post the rules using variables again (e.g. a(b+c)=ab+ac, a(b-c)=ab-ac) and walk students through the concept of "distributing the a" one more time.
If time allows in the class period, show students how to use the distributive property to do mental multiplication:
ex. 5(49) = 5(50 - 1) = 5(50) - 5(1) = 250 - 5 = 245 *49 is equivalent to 50 minus 1; it is much easier to do 5 times 50 and 5 times 1 (which the distributive property
allow us to do) in your head. Students can verify this by multiplying 49 and 5 the traditional way.
Summative Assessment
Ask students to respond to the following prompt:
Kim was given the expression 8*3+8*4 and asked to write an equivalent expression using the distributive property. She wrote the following: 3(8+4)
Decide whether Kim's expression is equivalent or not. Then explain how you know it is equivalent or not equivalent. If you think it is not equivalent, write an expression
that is equivalent using the distributive property.
Formative Assessment
Place the following word problem under the document camera:
Cedric wants to cover two areas of his wall with 1 foot by 1 foot square cork boards so he can put up pictures of his friends and family. The first area is 4 feet by 5
feet and the second area is 4 feet by 3 feet. How many cork boards does Cedric need to purchase?
Ask students to solve the problem. Have several different supplies available for students to choose from. For example: graph paper, Legos, base ten blocks, square
counters, etc. Let students choose a method to solve. Some students may go for a concrete method (manipulatives), others representational (graph paper) while
others may use an abstract method (4 times 5 plus 4 times 3). While students are working, walk around and observe their comfort level with this type of problem.
Have several students share the method of solving with the class.
Feedback to Students
While students are working on the distributive practice, the teacher should move between pairs of students and ask questions to help clarify students' thinking.
Questions such as: How do you know those expressions are equivalent?
For students who are struggling, encourage them to make area models. Models can be generated even for the problems without context (word problems).
Emphasize that verbal explanations should also be clearly expressed in written form. She the Distributive Property Practice 1 Answer Key for more details.
ACCOMMODATIONS & RECOMMENDATIONS
Accommodations:
Differentiation of Process: students are given the opportunity to choose from a variety of tools to help them solve the problems. Some students will use manipulatives
page 2 of 3 such as square tiles or graph paper to help them visualize and see the connections. Stronger students will be able to solve the problems abstractly.
Extensions:
Students who have a strong grasp on the concept can explore whether or not the distributive property can be applied to multiplication 4(3*7) and division 4(6/3).
Students with a strong grasp on the concept could explore double distribution (2+3)(4+5) using manipulatives.
Students can also explore problems such as (24+18)/6=24/6+18/6. This connects back to multiplication of fractions (dividing by six is the same as multiplying by onesixth which means the distributive property holds true for this pattern (a+b)/c=a/c + b/c).
Suggested Technology: Document Camera, LCD Projector
Special Materials Needed:
manipulatives such as Legos, square counters, etc.
graph paper
SOURCE AND ACCESS INFORMATION
Contributed by: Kathleen E. Brown
Name of Author/Source: Kathleen E. Brown
District/Organization of Contributor(s): Manatee
Is this Resource freely Available? Yes
Access Privileges: Public
License: CPALMS License - no distribution - non commercial
Related Standards
Name
MAFS.6.EE.1.3:
Description
Apply the properties of operations to generate equivalent expressions. For example, apply the distributive property to
the expression 3 (2 + x) to produce the equivalent expression 6 + 3x; apply the distributive property to the expression
24x + 18y to produce the equivalent expression 6 (4x + 3y); apply properties of operations to y + y + y to produce
the equivalent expression 3y.
Remarks/Examples:
Examples of Opportunities for In-Depth Focus
By applying properties of operations to generate equivalent expressions, students use properties of operations that
they are familiar with from previous grades’ work with numbers — generalizing arithmetic in the process.
MAFS.6.EE.1.4:
MAFS.7.EE.1.2:
Identify when two expressions are equivalent (i.e., when the two expressions name the same number regardless of
which value is substituted into them). For example, the expressions y + y + y and 3y are equivalent because they
name the same number regardless of which number y stands for.
Understand that rewriting an expression in different forms in a problem context can shed light on the problem and how
the quantities in it are related. For example, a + 0.05a = 1.05a means that “increase by 5%” is the same as “multiply
by 1.05.”
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