1. Expanding and Factoring Algebraic Expressions
Lesson 7.4
Expanding and Factoring Algebraic Expressions

2. d a c b Warm Up-Matching 1) 2) 3) 4) a) 18+9x b) 3x-6 c) 9x-18 d) 3x+6
OBJECTIVE: SWBAT write an algebraic expression from a written expression.
LANGUAGE OBJECTIVE: SWBAT discuss the difference between algebraic and written expressions.
Choose the numerical expression that best matches each written expression.
Algebraic Expression
Expanded Expression d 1) 2) 3) 4)
a) 18+9x
b) 3x-6
c) 9x-18
d) 3x+6 a
(Time on this slide - 5min) Time passed 5 min
In-Class Notes
Read the slide as it appears.
Have students put answers in their notebook.
Give students 3-5 minutes to answer the questions in their notebook.
Do not need to go into great detail about the vocabulary at this point. Will be enforced later in the lesson.
Preparation Notes
This warm up is to get students to start thinking about the words that are associated with operations. Have students answer the questions in their notebook, giving them about 3-5 minutes to complete. Ask students for the correct answers and click the button. This will cross out the written expression that was used. This is a nice segue way into the objective for the lesson. There does not need to be a great deal of discussion pertaining to the vocabulary words, numerical and written expressions. They are further discussed in the lesson. c b
Agenda

3. Agenda: OBJECTIVE: SWBAT expand algebraic expressions. 1) Warm Up
LANGUAGE OBJECTIVE: SWBAT solve problems that involve expanding algebraic expressions
1) Warm Up
Matching-Independent
2) Launch
Operations to Words-Groups
3) Explore
Mini Lesson-Whole Class
4) Practice
Centers
5) Assessment
Exit Slip-Independent and Partners
(Time on this slide – 1 min) Time passed 6 min
In-Class Notes
Quickly go over agenda. Great chance to review objective and language objective with students.
Preparation Notes
Agenda

4. Launch-Operations to Words
Directions: Put each word from the list into the operation’s box that it most likely expresses.
plus
difference
less than
Addition
Subtraction
Multiplication
Division
factors
decreased by
times
ratio
increased by
separate
minus of
sum
product
multiplied
less
more than
in all
(Time on this slide min) Time passed 16 min
In-Class Notes
Pass out the worksheet for this slide.
Read the directions to the class.
Have students work with in groups giving them only 8 minutes. Can use the online timer.
When ready for the discussion, click the PC User link if you have a PC.
Preparation Notes
The goal of this slide is to have students use their prior knowledge in regards to words pertaining to the four operations. This activity is meant to go quickly to see what knowledge students have and what area(s) need to be focused on. Pass out the worksheet to each student. Once the directions have been read and there are not any questions, have students work with in groups of four to complete the worksheet. Set the online timer for 8 minutes; this gives students about two minutes for each operation. The next slide is to be used for the discussion.
NOTE: If using a PC, you can click the PC link at the bottom.
divided
quotient
per
subtract
each
twice
PC Users
Agenda

5. Launch- Mac User more than plus increased by sum in all Addition
Directions: Put each word from the list into the operation’s box that it most likely expresses.
plus
difference
less than
more than
Addition
Subtraction
Multiplication
Division
plus
factors
increased by
decreased by
sum
times
in all
ratio
increased by
minus
difference
separate
decreased by
less than
minus of
subtract
less
sum
product
times
product
factors
multiplied
less
twice of
multiplied
more than
each
in all
(Time on this slide – 3 min) Time passed 19 min
In-Class Notes
Review the slide to make sure students have the correct words in the appropriate boxes.
Be sure to clear up any misconceptions students might have.
Remind students to keep this in a safe place as they will need it for today and future lessons.
Preparation Notes
When the time is up, it is important to review the words and operations. You want students to have the correct words in the appropriate operation box since this is a tool students will use throughout the unit. To reveal the answers, click to see the words appear in the correct operation box. The words will appear in order as listed to the right. Another suggestion would be to have students come to the board and write in their answers.
The words associated with division, might be difficult for some students, therefore more time may be needed for explanation. Again, be sure students have the correct words in the appropriate boxes. Give time for students to make their corrections. This is a great opportunity to connect this part of the lesson to the objective. Teacher may want to explain to the class that we are now putting words with the operations so we can now write expressions. Emphasize that this is a tool that will be used throughout the unit, so keep it in a safe place.
divided
divided
quotient
quotient
per
separate
per
subtract
ratio
each
twice
Next Slide
Agenda

6. Explore-Mini Lesson 3(k + 6). 6(2x+3) Write the following as an
expanded expression.
3(k + 6).
6(2x+3)
(Time on this slide – 4 min) Time passed 23 min
In-Class Notes
Worksheet for this explore, will be on back of the launch worksheet.
After the first question, click on the word, numerical expression, at the bottom to show the definition.
Continue with the questions. Be sure to emphasize that the ‘dot’ is the proper way to express multiplication.
Students may need more prompting for the last question, even after the hint is given.
If needed, ask students if they have seen “letters” in math class to prompt the students towards the word variable.
Click for the word to appear.
The expression for the last problem is discussed on the next slide.
Preparation Notes
The goal of this slide is for students to start writing numerical expressions from written expressions. Read the slide as it appears. After the first question is shown and read, ask students what is a numerical expression (may guide students to think back to the warm up). Click on the word, numerical expression. Continue on with the slide. Students do not need to write the definition down in their notebook at this time. Click to advance the written phrase. Ask students for possible expressions. At this point, the ‘dot’ for multiplication really needs to be emphasized here. Although the ‘x’ is correct, students really should be using the ‘dot’ for multiplication. Continue on with the next problem. The third problem is not a numerical expression, therefore should be pointed out the class why it is not. This is where students will need some prompting. Click for the question, “Think…what can we use to represent a number when we don’t know the actual number?” Depending on what students have been exposed to, answers will vary. If students are stuck, you may have to ask if anyone has seen a letter used in math. Then proceed to ask what is the name for a letter in math. Click for the word variable to appear. (Note: Variable can also be defined as a quantity that changes, which some students may have been exposed to). The expression for this problem is discussed on the next slide.
Click to reveal next part
Agenda

7. Expand: Whatever is inside the ( ) needs to be treated as a "package".
Explore- Mini Lesson
Expand: Whatever is inside the ( ) needs to be treated as a "package".
So when multiplying: multiply by everything inside the "package"
Now, for my next trick, I will expand the algebraic equation!!!!
Expand the algebraic expression.
4(4y-1)
(Time on this slide – 5 min) Time passed 28 min
In-Class Notes
This slide is continued from the previous slide.
Read the definition of variable. Be sure to tell the students that the letter can be any letter in the alphabet, but typically x, n, t are used.
Emphasize again that the ‘dot’ should be used for multiplication.
Have students say out loud that 10n, can be said, “10n or 10 times n”.
Preparation Notes
This slide explains the last problem from the previous slide: The product of ten and a number. The slide starts with the definition of variable, since it was the last discussion from the previous slide. Students do not need to copy the definition at this time; time will be given for students to copy all definitions. Explain a variable can be represented by any letter in alphabet. Most common ones are x, n, t, but you can use any letter you choose.
Click the slide for the phrase, “the product of ten and a number” to appear. Ask students for ways to represent this by writing an expression, but explain you are going to use the variable n, for no particular reason. Click to reveal the first two expressions. Point out that it is the same process as the previous two examples, but now we are using a variable, so really our process has not changed. Again, emphasize that the ‘dot’ should be used for multiplication. Ask students why. Students should come up with the fact that the ‘x’ now may look like a variable and can be too confusing. Click the slide for the magician to appear and read what is written in the box. Click for the 10n to appear and discuss what students notice. Click again to point out that a number next to a variable means to multiply and can be said as, “10n or 10 times n”. Have students repeat out loud, as a whole class, “10n or 10 times n”.
Agenda

8. Vocabulary Explore- Mini Lesson
Factor - are numbers you can multiply together to get another number. Each number can have MULTIPLE factors
(Time on this slide – 5 min) Time passed 33 min
In-Class Notes
Read slide as it appears.
Conduct a very quick turn and talk about algebraic expressions
This worksheet is located on the back of the launch.
Be sure to point out that none of the expressions are using an ‘x’ for multiplication.
Discuss the similarities and difference of the examples given.
Have students read the definitions out loud, and copy onto the worksheet.
Go right into the next slide for more vocabulary.
Preparation Notes
This slide is designed to introduce Algebraic Expressions (the next slide continues with more definitions). Click the slide, reading to the students what 10n is called. Advance the slide again, to have students start thinking why it is called an algebraic expression and not a numerical expression. Conduct a very quick turn and talk. Then take a few answers from students. See what student’s responses are before clicking to show the definition. Advance the slide for examples to appear discussing the similarities and differences of each expression. Also may want to emphasize the variable is any unknown number and what is happening to that particular variable. Again, point out that the ‘x’ is no longer used. Have students read out loud each expression.
Now ask students to copy down the definition on the worksheet. (If there is different way vocabulary is designed in your classroom, students do not need to copy down the definitions at this time, but the next slides are highly encouraged to read through with the class.)
Click to reveal next part
Agenda

9. Practice- Whole Class
See if the expanded expression and the algebraic expression are equivalent.
Important!!!!
Remember
what to do about the package
a) 6(x + 5) and 6x + 30
b) 4(y – 4) and 4y - 4
c) 7(x + 3) and x
Agenda 9

10. Factor each algebraic expression.
Practice- Whole Class
Factor each algebraic expression.
Important!!!!
Remember
what to do about the package
a) 2y + 10
b) 6z -9
Agenda 10