1. Distributive Property

2. Warm Up
Objective: Students will be able to apply the distributive property to write equivalent expressions.
Language Objective: Students will be able explain how to use the distributive property verbally and in writing.
Ronisha and Kalyn are arguing whether the answer to can be found by doing the following work.
Do you think this is correct? Explain.
(4 min) 4 minutes passed
In-Class Notes
Read the slide as it appears.
Give students a few minutes to discuss the problem.
Advance the slide for the explanations to appear.
Preparation Notes
The lesson’s objective is for students to apply the distributive property. This multiplication problem was answered by using the Distributive Property. This is just a way to start kids thinking about this method when multiplying two numbers.
Yes, this method can be used because 27 is still being multiplied by 8.
27 is just split into 20 and 7 first before it is multiplied by 8.
Agenda

3. Launch- High School Vs. College B-ball
A standard size high school basketball court is 84ft long and 50ft wide in the shape of a rectangle.
84 ft
50 ft
To find the area of the court you can use the formula of A=l  w
(3 min) 7 minutes passed
In-Class Notes
Read the slide as it appears.
Remind students how to find area of a rectangle.
Either ask for volunteers to explain how they found the area, or just advance the slide to show students the process.
Preparation Notes
The purpose of The Launch is show students there are two ways to finding area of a ‘divided’ rectangle. This slide’s purpose is to review finding the area of a rectangle. The next slide will extend the basketball question a bit father.
Read the slide as it appears to the class. You may ask for a volunteer to explain how to find the are of the basketball court, but again, this is just a review.
A = 84 ft  50ft
A = 4200
Agenda

4. College Basketball Court
Launch- High School Vs. College B-ball
Did you know that a college basketball court is usually 10ft longer than a high school basketball court?
84 ft
10 ft
50 ft
College Basketball Court
(5 min) 12 minutes passed
In-Class Notes
Read the as it appears.
Pause at the movement when the slide moves the 50 ft asking students if they understood what happened. It would be a nice visual for students to point out the two rectangles that were formed.
Have students copy the basketball court (the divided rectangle) into their notebooks.
Give students time to work with their partner to find the area of the college basketball court.
Preparation Notes
The goal for this slide is for students to find the area of the divided rectangle; most likely students will use two different methods. That is the focus of this slide. If the class uses the same method, students will have to be prompted to try to find another method, depending what method they used. Give students time to work with a partner to find the area. If some groups finish before others, encourage them to find a different method.
Can you think of a method to find the area of the college basketball court?
Agenda

5. Launch- High School Vs. College B-ball
84 ft
50 ft
10 ft
Can you think of a method to find the area of the college basketball court?
Why parenthesis?
Method 1
Method 2
50(84+10)
84+10
84 50  +
10 50  94  50
4200 +
500
(5 min) 17 minutes passed
In-Class Notes
Read the slide as it appears.
Ask students who used the method of finding the sum first, since it appears first.
Continue with the second method, the distributive property, but remember students are not yet aware of this vocabulary.
Advancing the slide again will show both expressions. This is a crucial part in the lesson. Be sure to discuss why the parenthesis are used in the first method and why the 50 is now part of the expression.
Repeat the same questions for the second method, but asking students where is the 50 located in this expression.
Explain that from the first expression, the 50 appeared twice.
The final questions of the slide is to encourage students to make the connection that both expressions (methods) are the same.
Preparation Notes
This slide is an explanation of the two methods. Ask for students to share the method they used. Once students have shared their findings, call on a group who used the method of finding the sum first. The first explanation shows taking the sum first, then multiplying. The way the process appears is based on what students will say. “They added first. The sum is 94. Then multiply 84 by 50.
The second method is the distributive property, but students are not yet aware of this vocabulary. Again, the process will appear based on how students would have answered the problem. Multiply 84 and 50, then multiply 10 and 50. Last, add them together. Students may have said 50 times 84; use this opportunity to quickly review that the commutative property was used.
Advance the slide for both expressions to appear. This is a crucial part of the lesson. Ask student why the parenthesis had to be inserted. Prompt students to think back to what operation was performed first. Also ask “Why the 50 is placed outside of the parenthesis?” Once students have an understanding of this, move to the second method. Again, review what was provided. Show the students the 50 appeared twice, to help later make the connection of the Distributive Property. Once students have an understanding of these two expressions, ask the final question on the slide: “What can we say about these two expressions?” Prompt the students to make the connection that even though the expressions look different, they are equivalent because they equal the same thing, and calculate the same area.
A = 4700
A = 4700
What can we say about these two expressions?
Agenda 5

6. Explore- Splitting Athletic Fields
Ambria lives in a neighborhood with three rectangular fields that all have the same area. The fields are split into different sections for different sports.
20 yds
120 yds
30 yds
50 yds
120 yds
50 yds
80 yds
40 yds
(2 min) 19 minutes passed
In-Class Notes
This slide is an introduction to the Explore Activity.
Explain to the students that they will compute the areas of the same rectangular fields using different expressions.
The main focus is for the students to look for ways to rewrite an expression into an equivalent expression.
Allot enough time to discuss students’ findings. (The next two slides explain the results.)
Preparation Notes
This slide is just an introduction to the Explore Activity the students will be working on. Explain to students that in this activity they will compute areas of the same rectangular fields using different expressions. The purpose is to look for ways to rewrite an expression into an equivalent expression. Say “In this problem, you will compute areas of rectangles using different expressions. Look for ways to rewrite an expression into an equivalent expression that is easier to compute.” Give students about 20 minutes to work on the first four problems. Allot enough time to discuss students’ findings, which are shown in the next two slides. Circulate the room to observe students work. Prompt questions if students are having trouble with some of the questions.
Agenda

7. Explore- Splitting Athletic Fields
1. Find the area of this field near Ambria’s house.
50 yds
120 yds
2. This field is divided into two parts.
20 yds
120 yds
30 yds
a. Find the area of each part and record your steps as you go. Prove the area is the same as in the first field?
(15 minutes for first four problems with discussion) 34 minutes passed
In-Class Notes
This slide is to be used to discuss the class work.
Advance the slide to reveal the answers.
Focus on 2a, emphasizing the fact that 120 was used to multiply BOTH 20 and 30.
Preparation Notes
The next three slides are to be used when discussing the solutions to the class work. Ask students for the answers with an
explanation. Advance the slide to have the answers appear, giving attention to 2a. It is important for students
to make the connection that in problem 1 and 2, both areas were the same. Prompt a discussion on why this is try,
emphasizing on the fact that 120 was used to multiply BOTH 20 and 30.
=240  +
=360 
Agenda

8. Explore- Splitting Athletic Fields
20 yds
120 yds
30 yds 
=240  
=360 
b. Write one numerical expression that will calculate the area based on the work you did in part a.
c. Find a different way to calculate the area of the entire field and write it as one numerical expression.
(15 minutes for first four problems with discussion) 34 minutes passed
In-Class Notes
This slide is to be used to continue to discuss the class work.
Advance the slide to reveal the answers.
2b is just another way to write what students found in part a.
2c, students may need clarification why the expression is written as 120( ). Be sure to focus on where the came from.
Preparation Notes
This part of the class work is to have students connect what they did in part a, to writing their findings as one expression.
If students are having a hard time with this, explain the goal is to take the ‘work’ from part a and make it into one expression.
Part c will be tricky for some students. Some students may write the expression as ( )120, which is a quick discussion
using the Commutative Property on why it is the same as the one provided: 120( ). Have students quickly prove that this
expression still equals 600 square yards as do the others.
20 yds
120 yds
30 yds +
Agenda

9. Explore- Splitting Athletic Fields
3. The field is divided into two parts.
a. Write 2 different numerical expressions that will calculate the area of the entire field.
40 yds
80 yds
50 yds
4. The field below is split into two parts but are missing the dimensions.
a. Fill in the missing dimensions of the rectangular field whose area can be calculated using the expression. 50
______
_________
100 20
(15 minutes for first four problems with discussion) 34 minutes passed
In-Class Notes
This slide is to be used to continue to discuss the class work.
Advance the slide to reveal the answers.
Make the connection of how the second expression in 3a came from the first expression. (A formal explanation is on the next slide.)
Question 4 is a great way to push students thinking to work backwards.
Preparation Notes
This is the last of the questions in the class work. Advance the slide for the answers to appear. In number 3, make the connection that the second expression can be derived from the first expression. A formal explanation is discussed in the next slide, but is a great reinforcement before students are exposed to the definition of the Distributive Property. Question 4 is a way to challenge students for them to think about going backwards. May need to prompt a question asking why the 100 is placed where it is as supposed to the 20. The segment representing the 100 is longer than the segment representing the 20.
b. Write a different numerical expression to calculate the area of the field.
Agenda

10. Summary- The Distributive Property
50 yds
80 yds
40 yds
20 yds
120 yds
30 yds
Let’s look at the two equivalent ways of finding the area and connect it to an important property in math.
The Distributive Property
(1 min) 35 minutes passed
In-Class Notes
This slide is just to introduce the word Distributive Property.
Read the slide as it is advanced.
Preparation Notes
This slide is where students will see the word Distributive Property for the first time. The next slide will explain in more detail what the Distributive Property is.
Agenda

11. 400 600 200 600 The Distributive Property
Summary- The Distributive Property
The Distributive Property 50 80 40
50 yds
80 yds
40 yds
400
600
200 50
120 50 80 40
600 50 80 40 50 80 40 50
(4 min) 39 minutes passed
In-Class Notes
Read the slide as it appears.
As the slide is advanced, make the connection that students already used both methods. The visuals prove how both methods are equal, but also connects how both expressions are equivalent.
Again, may want to point out that the 50 was multiplied to both the 80 and 40.
Preparation Notes
This slide ties together both methods the students have been working on. The units were taken out after the first click so
students can focus on the numbers without being distracted. This is a great visual demonstrating why both methods are
equivalent. Advance the slide, emphasizing to the students that they have been using the Distributive Property all along. May
want to point out again, that the 50 multiplied both numbers in the parentheses, 80 and 40, as this has been mentioned in
previous examples. You may want to prompt students why we call this the Distributive Property to make the connection that
distribute means to pass out, similar to passing out the 50 to the 80 and 40. +
Agenda

12. The Distributive Property
Summary- The Distributive Property
The Distributive Property
The Distributive Property is a property in mathematics which helps to multiply a single term and two or more terms inside parenthesis.
Check it out!
Lets use the distributive property to write an equal expression. 2 2 3 5 +
Examples
(5 min) 44 minutes passed
In-Class Notes
Read the definition to the students.
Advance the slide to give students an example without using a rectangle. One is provided at the right to make the connection, but is not there to be used to find the area. This slide is to show an equivalent expression using the Distributive Property.
Point out the arrows, since this is the first time students are seeing this notation. Also, make the connection to the rectangle off to the right.
Advance the slide for the next two examples.
Preparation Notes
This is the first time students are provided with a formal definition of the Distributive Property. There are two definitions provided. The definition that appears on the slide is age appropriate. A more advanced definition can be shown by clicking at the bottom where it says ‘formal definition’. The slide continues with students seeing the “arrows” for the first time that are used when using the Distributive Property. Read the definition out loud with the students. Give students a few minutes to turn and talk about the expression. Advance the slide. Be sure to point out that the expression is modeled by the rectangle off to the right. As you click the slide, make the connection to the arrows and the shading of the rectangle. Do the same for 2 times 5.
The following two examples are not modeled with a rectangle, but the arrows are shown. Take the time to emphasize that we have to multiply everything in the parentheses. Also, may want to explain that we are ‘distributing’ a number or ‘passing’ it to everything inside the parentheses. The last example is to show the process is the same using variables.
The purpose is not to ask students to evaluate the expressions, just to show equivalence. (If students need reassurance that their work is correct, with the expression that contains all numbers, students can evaluate both expressions to prove they are equal.)
Formal definition
Agenda

13. The Distributive Property
Summary- The Distributive Property
The Distributive Property
The Distributive Property is a property in mathematics which helps to multiply a single term and two or more terms inside parenthesis.
States that the product of a number and a sum is equal to the sum of the individual products of addends and the number.
This is a hidden slide if want to show students a more formal definition of the Distributive Property.
example
Agenda

14. Explore- Splitting Athletic Fields
5. An algebraic expression to represent the area of the rectangle below is 8 x
a. Write two different expressions to represent the area of each rectangle below. 5 x 2 3 x 4
(12 minutes for the remainder of the activity) 56 minutes passed
In-Class Notes
The is the last part of the explore activity.
The next two slides will provide the answers by advancing the slide.
May want to point out why 5x + 2x is best was to write the expression. Also, a great opportunity to reinforce vocabulary.
Preparation Notes
This is the last part of the explore activity. Students can work on this individually or back in their groups. The next two slides go
over question 5 and 6. By advancing the slide, the answers will appear. Be sure to discuss in part a, why 5x + 2x is the best
way to write expression. Again, this is a great opportunity to focus on vocabulary, the Commutative Property.
Agenda

15. Explore- Splitting Athletic Fields
6. Use the distributive property to re-write each expression. You may want to draw a rectangle to represent the area.
a) 10( a + 7) = ___________
b) 7(x + 3)=________________
c) x( )= ___________
d) a(10 + 9)= _______________
e) -2(x + 10)=_______
f) 3x(x + 10)= ______________
(12 minutes for the remainder of the activity) 56 minutes passed
In-Class Notes
Advance the slide for the answers to appear.
Some of the questions may seen difficult for students depending on the prior background, therefore, some guidance may be needed.
Preparation Notes
This is the last question in the activity. Advancing the slide will reveal the answers. Some of the questions may seen difficult for students depending on the prior background, therefore, some guidance may be needed.
There is a Challenge question at the end of the activity. This PowerPoint does not provide answers for the students.
Agenda

16. Provide evidence to support your answer.
Assessment- Exit Slip
Who correctly used the distributive property to write an equivalent expression?
Provide evidence to support your answer.
Riley
Michael
(4 min) 60 minutes passed
In-Class Notes
Hand out the exit slip to each student, giving them a few minutes to answer.
Spend time discussing what Riley did incorrectly.
Preparation Notes
Hand out the exit slip to all students, giving them a few minutes to answer. This problem was chosen because there were not any problems in the lesson or class work where three numbers/variables were in the parenthesis. This pushes students to focus on the process and apply it despite what the problem looks like. It is suggested to spend a few minutes discussing what Riley did incorrectly.
Michael did because he correctly distributed the 7 to all terms inside the parenthesis.
Agenda