Distributive Property Using the GCF

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SWBAT factor out the GCF

Big Idea

Students will relate area of rectangles to the distributive property.

Do Now

10 minutes

Prior to this lesson, students worked on GCF and LCM Word Problems Lesson.  The Do Now problem is a review of the concept.  Students will have about 7 minutes to work on the problem independently.

I am planting 50 apple trees and 30 peach trees. I want the same number and type of trees per row. What is the maximum number of trees I can plant per row?  Show your work and explain your reasoning.

After students have worked on the problem, we will discuss strategies.  Since we worked on using KWL charts, I will orally ask students for the information that would complete the chart.   My questions will be:

1.  What's the important information in the problem?

2.  What is the problem asking us to find?

3.  Is this a GCF or LCM problem?  How do you know?  What key words, phrases, ideas helped you?

4.  What method did you use to arrive at your answer?

5.  What is your answer?

6.  What did you learn?  What does your answer mean?

7.  Does your answer make sense?

For each question, I will select a few students to share their answers.  For the most part, I will select lower level math students to assess their understanding.  It is important to remember, that these students may struggle through their answers, but that is part of the process.

Mini Lesson

20 minutes

Previously, students learned about the distributive property, with the focus being on multiplying.  This lesson focuses on factoring out the GCF.  We will work through a few different examples together as a class.

Ex. 1  Rewrite 56 + 96 using the distributive property.

Step 1 - Find the GCF = 8

Step 2 - Factor out the GCF 8 x (7 + 12)

Some students may be able to find the GCF using mental math, but other students may need to rely on previous methods (Greatest Common Factor Lesson).  Although students are familiar with factors, they may not be familiar with the phrase "factoring out".  I will ask:  What does factoring out a number mean to you?  How does factoring out the GCF change the expression?  Can you factor out a number that is not the GCF?

Ex. 2  Rewrite 48 + 144 using the distributive property.

Step 1 - GCF= 48

Step 2 - 48 x (1 + 3)

The third example that we will work through together is a visual representation of the distributive property and the GCF.  It also challenges students with the concept of area, which is a 5th grade topic.  For Example 3  I will ask students:  How do you find the area of a rectangle?  How does finding the area relate to the distributive property?

Ex. 3 - Show two different ways to represent the area for the large rectangle.
Students may know from 5th grade that to find the area of a rectangle they need to multiply the length by the width. With this concept and given that there are two rectangles, they can develop the answer of (6 x 15) + (6 x 3).



Independent Practice

15 minutes

Students will practice problems independent of my direction.  (See Independent Practice)Students are grouped heterogeneously, so there may be students in the same group using different strategies to rewrite the expression.  I will encourage discussion (MP3) among students so they have an opportunity to see how another student may be approaching the problem differently, but still have the same answer. (MP3)

After about 10 minutes, I will discuss the problems with students.  I will randomly select students for each question.  If a student has rewritten the expression, but has not found the GCF, this will open the discussion up for how they can repeat their steps.

If a student should finish early, I will challenge him to create a rectangle model for each example.

As students work, I will circulate around the room.  Although I am informally assessing all students for understanding of the distributive property concept, I will focus on those students who I know still need help with finding the GCF.

Exit Slip

5 minutes

Until this point, students have used the distributive property with only two numbers.  I will ask:  Can you create an area model for the distributive property with 3 numbers?  We will discuss it as a class, with students sharing their ideas and examples.