1. 21st Century Lessons
Writing Algebraic Expressions
Primary Lesson Designer(s):
Kristie Conners
Sean Moran
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2. 2
This project is funded by the
American Federation of Teachers.
3. 21st Century Lessons – Teacher Preparation
3
Please do the following as you prepare to deliver this lesson:
• Spend AT LEAST 30 minutes studying the
Lesson Overview, Teacher Notes on each
slide, and accompanying worksheets.
• Set up your projector and test this PowerPoint file to make
sure all animations, media, etc. work properly.
• Feel free to customize this file to match the language and
routines in your classroom.
*1st Time Users of 21st Century Lesson:
Click HERE for a detailed description of our project.
4. Lesson Overview (1 of 3)
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Lesson Objective Lesson Objective:
Students will be able to write and read expressions in which
letters stand for numbers.
Student Friendly Objective:
Students will be able to write an algebraic expression from a
written expression.
Language Objective: Students will be able to discuss the
difference between algebraic and written expressions.
Lesson Description This lesson is the first of two lessons where students will start
writing algebraic expressions. The launch of the lesson is an
important part of lesson. This is the first time students are asked to
associate words to operations. This will be used through out the
lesson and the rest of the unit. The whole class examples are
designed in a manner where students will be following the same
process, so when variable is introduced, some confusion may be
prevented. The class work assignment is a matching activity since it
is the first time with this skill. In the next lesson, more writing will
take place.
5. Lesson Overview (2 of 3)
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Lesson Vocabulary Algebraic Expression: an expression containing at least one variable.
Numerical Expression: an expression containing one or more numbers and
operations.
Written Expression: an expression written with words.
Variable: any letter in the alphabet or symbol that represents a quantity.
Materials Copies of three class work assignments, (tape and scissors, depending), 3-2-1
assessment, and the homework.
Scaffolding The launch worksheet is designed for students to have all at times for the
remaining part of the unit. This will help ELL students and students with
learning disabilities equate the word with the appropriate operation. Also, the
first activity is a matching activity designed specially with the understanding
that this is the first time students are asked to perform this skill. This will
benefit ELL students and students with learning disabilities.
Enrichment The class work assignment can modified by not making the assignment a
matching one. Change the assignment by taking out Column B, making the
students come up with the algebraic expressions on their own.
Online Resources for
Absent Students
Tutorial (this video is long, but covers all important content. The last section will
be coved later in the unit.)
http://www.schooltube.com/video/167d4fecea6d4c11b4f5/
Online Practice
http://www.ixl.com/math/grade-6/write-variable-expressions-to-represent-word-
problems
6. Lesson Overview (3 of 3)
Common Core
State Standard
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6.EE.2 Write , read, and evaluate expressions in which letters stand for
numbers.
6.EE.2a Write expressions that record operations with numbers and with
letters standing for numbers.
6.EE.2.b Identify parts of an expression using mathematical terms (sum,
term, product, factor, quotient, coefficient); view one or more parts of an
expression as a single entity.
Before and After This lesson is the third lesson in the unit. Students will have a strong understanding
of the order of operations. This lesson is designed to develop students’ ability in
writing algebraic expressions and written expressions. The next lesson in this unit
continues writing algebraic expressions, giving students a strong sense of the concept.
Because of the previous lessons, students will have an easier transition into evaluating
algebraic expressions by substitution.
Topic Background The link below gives a small background on the history of Algebra. This is
also a great opportunity to connect topics covered in social studies with
mathematics.
http://www.ehow.com/video_4977241_who-invented-algebra.html
7. Warm Up-Matching
OBJECTIVE: SWBAT write an algebraic expression from a written
expression.
LANGUAGE OBJECTIVE: SWBAT discuss the difference between algebraic and written
expressions.
Agenda
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Choose the numerical expression that best matches each
written expression.
Numerical Expression Written Expression
9 3 a) the product of 9 and 3
b) 9 subtracted by 3
c) 9 divided by 3
d) the sum of 3 and 9
3 9
93
93
1)
2)
3)
4)
8. Agenda:
1) Warm Up
2) Launch
3) Explore
4) Practice
5) Assessment
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OBJECTIVE: SWBAT write an algebraic expression from a written
expression.
LANGUAGE OBJECTIVE: SWBAT discuss the difference between algebraic and written
expressions.
Matching-Independent
Operations to Words-Groups
Mini Lesson-Whole Class
Matching Expression-Whole Class and Partners
Exit Slip-Independent and Partners
Agenda
9. Launch-Operations to Words
9
difference
less than
factors
decreased by
times
ratio
increased by
separate
minus
product
multiplied
less
divided
quotient
Agenda
Directions: Put each word from the list into the operation’s box
that it most likely expresses.
Addition
Subtraction
Multiplication
Division
plus
of
sum
more than
in all
per
subtract
each
twice
PC Users
10. Launch- Mac User
10
difference
less than
factors
decreased by
times
ratio
increased by
separate
minus
product
multiplied
less
divided
quotient
Agenda
Directions: Put each word from the list into the operation’s box
that it most likely expresses.
Addition
Subtraction
Multiplication
Division
plus
sum
more than
increased by
in all
minus
less than
difference
subtract
decreased by
times
of
less
product
factors
each multiplied
divided
per
quotient
twice
separate
ratio
plus
of
sum
more than
in all
per
subtract
each
twice
Next Slide
11. Explore-Mini Lesson
12
Agenda
Write the following as a
numerical expression.
•The product of ten and seven.
7 10 7 10
•The product of ten and five.
5 10 5 10
•The product of ten and a number.
Think…what can we use to represent a number when
we don’t know the number?
VARIABLE
or
or
Click to reveal next part
12. Explore- Mini Lesson
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Variable: a letter or symbol that represents an
unknown quantity.
Agenda
Write as a algebraic expression.
The product of ten and a number.
n 10 n 10 n10
Now, for my next trick, I
will introduce a new way
to write multiplication.
A number written next to a
variable means multiplication.
13. Explore- Mini Lesson
This new expression, 10n, is called an Algebraic Expression.
Why do mathematicians call them Algebraic Expressions?
• Algebraic Expression: an expression containing at least
one variable.
• Numerical Expression: an expression containing one or
more numbers and operations.
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Click to reveal next part
x n 4 8 5 t
47 57 8
Agenda
14. Explore- Mini Lesson
• Written Expression: an expression written with words.
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The sum seventeen and number
Three times the difference of nine and seven
• Variable: any letter in the alphabet or symbol that
represents an unknown quantity.
n p h
Agenda
15. Practice- Whole Class
Write an algebraic expression for the problems
below.
a) The sum of ten and a number.
17
x 10
b) The quotient of a number and twelve.
t 12
t
c) Eleven decreased by five times a number.
115n
Important!!!!
Identify the
operation(s) by
underlining key
words.
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Agenda
16. 18
Name ________________ Date ___________
Agenda
Class Work: Written Expressions vs. Algebraic Expressions
Directions: Match the written expressions in Column A with the
algebraic expressions in Column B.
COLUMN A COLUMN B
The sum of a
number and ten
Ten divided by
a number
The product of
ten and a
number
increased by
eight
Eight less than
twice a number
The quotient of
a number and
eight
Ten decreased
by three times
The product of a number
eight and a
number
10 x 10 x
x 8 x 10
10 3x 10 2x
10x 8 8 x
2x 8
Eight increased x
by a number
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Practice- Partners
17. 19
x
Agenda
Class Work: Written Expressions vs. Algebraic Expressions
Directions: Match the written expressions in Column A with the algebraic expressions
in Column B.
COLUMN A COLUMN B
10 x 10 x
x 8 x 10
x 3 10 x 2 10
10x 8 8 x
2x 8
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Practice- Summary
The product of
ten and a number
increased by
eight
The sum of a
number and ten
The quotient of a
number and eight
Eight less than
twice a number
Ten divided by a
number
Ten decreased
by three times
a number
Eight increased
by a number
The product of
eight and a
number
A number
decreased by ten
Ten more than
twice a number
18. Assessment- Exit Slip
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Directions:
1) Write your own algebraic expression using n, 3, 5.
You must use at least 2 operations.
Agenda
2) Translate your algebraic expression into a
written expression.
3)
Turn and Talk: Read your written expression to
your partner. Have your partner write the algebraic
expression. Switch roles.
19. 21st Century Lessons
The goal…
The goal of 21st Century Lessons is simple: We want to assist teachers, particularly in
urban and turnaround schools, by bringing together teams of exemplary educators
to develop units of high-quality, model lessons. These lessons are intended to:
•Support an increase in student achievement;
•Engage teachers and students;
•Align to the National Common Core Standards and the Massachusetts curriculum
frameworks;
•Embed best teaching practices, such as differentiated instruction;
•Incorporate high-quality multi-media and design (e.g., PowerPoint);
•Be delivered by exemplary teachers for videotaping to be used for professional
development and other teacher training activities;
•Be available, along with videos and supporting materials, to teachers free of charge via the
Internet.
•Serve as the basis of high-quality, teacher-led professional development, including mentoring
between experienced and novice teachers.
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20. 21st Century Lessons
The people…
Directors:
Kathy Aldred - Co-Chair of the Boston Teachers Union Professional Issues Committee
Ted Chambers - Co-director of 21st Century Lessons
Tracy Young - Staffing Director of 21st Century Lessons
Leslie Ryan Miller - Director of the Boston Public Schools Office of
Teacher Development and Advancement
Emily Berman- Curriculum Director (Social Studies) of 21st Century Lessons
Carla Zils – Curriculum Director (Math) of 21st Century Lessons
Brian Connor – Technology Coordinator
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Notes de l'éditeur
(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.
(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
(Time on this slide - 10 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.
(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.
(Time on this slide – 3 min) Time passed 19 min
In-Class Notes
NOTE: THIS SLIDE IS ONLY FOR PC USERS!
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 had.
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 through out the unit. To reveal the answers, you have two options. 1. Click on each word off to the right and it will appear in the correct box. 2. Click the words at the bottom of the slide: addition, subtraction, multiplication, and division, and all the words associated with the operation will appear in the box. 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.
(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.
In-Class Notes
This is a hidden slide.
(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”.
(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.)
(Time on this slide – 4 min) Time passed 37 min
In-Class Notes
This slide is a continuation from the previous slide.
Have students read the definitions out loud.
Give students time to copy the definitions down.
Preparation Notes
This is a continuation from the pervious slide. Advance the slide for the vocabulary word to appear. Have a student read the definition and then have them copy onto the worksheet. Also ask for students to provide examples.
(Time on this slide – 4 min) Time passed 41 min
In-Class Notes
Read the slide as it appears.
Ask for student to point out the key word(s). Encourage students to underline the key words.
Students should have their activity sheet from the launch available for these questions (and the up coming activity).
Point out that different letters were used.
Show the ‘dot’ was used for the last problem to denote multiplication.
Preparation Notes
The goal of this slide is for students to practice three problems as whole group. It is also designed to lead right into the class work assignment. Read the directions to the class. Click for problem a. to appear. Ask the class, what is important in this expression? Once students respond with, sum, have them underline it. By clicking, an underline mark will appear. Be sure to explain to the class that this is a strategy to use at all times…underlining the key words. If students need help with the key words, use the activity sheet from the beginning of the class. Encourage students to have it out and ready to use. When the expression appears, discuss that this time an x was used and it does not mean multiplication.
When problem b. appears, again, ask which word(s) are important and encourage students to underline them. Clicking will show the underlined word. Also, be sure to point out that this time a ‘t’ was used as the variable. The second example with the fraction bar needs to pointed out that this is also a way to represent division. This may be new to some students.
Part c. is the hardest one since there are two operations being used. Following the same process, ask student what are the key word(s). Be sure to point out that the best way to represent multiplication is not using the dot or the ‘x’, but the number and variable right next to each other without any symbol. The dot is acceptable, but the number and variable without any symbol is best.
Students may want to switch the order of the expressions. Some discussion needs to take place whether this s correct or not. However, the third problem where five times a number can be written as x5, but 5x is more appropriate, should be discussed.
(Time on this slide – 13 min) Time passed 54 min
In-Class Notes
Hand out worksheet to each student (unless having partners cut out the pieces, only one sheet per group).
Read the directions to the class. Clear up any misunderstandings.
Circulate the room encouraging students to underline key words and use their worksheet from the beginning of the class.
Give students 15 minutes for the activity.
Preparation Notes
This class work assignment is very similar to the problems discussed in the previous slide. Read the directions to the class. Students should be put into pairs for this activity. There are two options to fort implement this activity:
Have students write the algebraic expressions next to the written expression.
Have students cut the boxes from Column A and Column B out. They can match the written expression with the algebraic expression and tape them together. An option to make this go faster during class time is to have the pieces already cut out, however, is very time consuming for the teacher.
Give students about 15 minutes to complete this activity. Circulate the room encouraging students to underline key words and use their worksheet from the beginning of the class. The answer key is provided and should be quick for students to see how they did. Be sure to clear up any misunderstandings or any questions students may still have.
Note: there is one problem that was purposely used that was not discussed in the lesson; eight less than twice a number. Students should be able to figure it out by process of elimination, but it is a good discussion to have after the activity because it will lead into the next day’s lesson.
Also, should a group finish early, have them create their own algebraic expression and challenge their partner to write the written expression that it matches and vise versa.
(Time on this slide – 2 min) Time passed 56
In-Class Notes
By clicking, each algebraic expression will slide over next to the correct written expression.
Can have the answers already posted, or can go over each problem.
Preparation Notes
When students completed the activity, this slide is to go over their answers. Either have the matches already posted or go over each problem by clicking. Each click will advance the algebraic expression to the correct written expression.
(Time on this slide – 4 min) Time passed 60 min
In-Class Notes
Have students answer 1 and 2 in their notebook on their own.
Direct students to answer part 3 with their partner.
Make sure there is enough time for students to share out their responses.
Preparation Notes
This assessment is meant to be implemented where there is a discussion before the period ends. Give students about 5 minutes to complete the task. Once they are finished, click the slide for question 3 to appear. Have students now turn to their partner and read their written expression out loud to their partner. Have them write the algebraic expression and check to see if they obtained the correct expression. Now switch roles. When the class is finished with this, ask the class if there was any disagreements between partners. Clarify if needed, but also ask a student to share their expressions.
