Subject Area: Mathematics
Lesson Design
Mathematics
Grade Level: 7 & CAHSEE
Benchmark Period 1 & 2
Duration of Lesson: 2 days
Standard(s): 7th grade Algebra & Functions 1.1 - Students express quantitative relationships by using
algebraic terminology, expressions, equations, inequalities, and graphs: 1.1 Use variables and appropriate
operations to write an expression, an equation, an inequality, or a system of equations or inequalities that
represents a verbal description (e.g., three less than a number, half as large as area A). (2 questions on
CAHSEE)
Learning Objective: Students translate math expressions in English into mathematical language.
Big Ideas involved in the lesson: Translating and identifying mathematical expressions, equations and
inequalities
As a result of this lesson students will:
Know:
Vocabulary: Translate, Variable, Coefficient, Equations, Expressions, Inequalities, Order of operations
 Mathematics is a language with its own grammar related to the properties of mathematics.
Understand:
 Translate math expressions in English into mathematical language.
 Translate mathematical language into English
Be Able To Do:
 Model translating mathematical expressions into expressions or equations.
Assessments:
Formative:
CFU Questions:
What will be
 What does a variable represent?
evidence of student  ABWA
 What is an expression?
knowledge,
 Whiteboard
 What operation does this imply?
understanding &
 Matching Activity
 Name at least 3 different ways to imply subtraction.
ability?
 Independent
 Identify the word that means division in the following
practice worksheets
expression: The quotient of six and a number
 x - 5 can be said as:
Summative:
 Translate 6y into a verbal phrase in at least two ways.
Teacher made quiz
 Does it make a difference "t + 5" or "5 + t"?
or test or
 What does it mean "50% of p"? p/2? 0.5p?
RiverDeep quiz:
 Explain how the variable "n" represents the words "a
Quiz Translate
number".
Verbal Expression
 What is the difference between "less than" and "is less
found in shared
than"?
folder
 Identify the inequality in the phrase then translate to an
expression: A number is six more than a number.
 Translate the following sentence into a verbal phrase:
The sum of a number and eight is twenty.
 Translate the following equation into a verbal sentence:
8x = 25. Is there more than one way to say it?
Lesson Plan
Anticipatory Set:
Objective: Today we will be learning how to translate math expressions, equations and
a. T. focuses students
inequalities into mathematical language.
b. T. states objectives
1
7 A&F 1.1 Lesson Plan
c. T. establishes purpose
of the lesson
d. T. activates prior
knowledge
Instruction:
a. Provide information
 Explain concepts
 State definitions
 Provide exs.
 Model
b. Check for
Understanding
 Pose key questions
 Ask students to
explain concepts,
definitions, attributes in
their own words
 Have students
discriminate between
examples & nonexamples
 Encourage
students generate their
own examples
 Use participation
2
Lesson Design
Mathematics
RiverDeep Lesson: Mastering Algebra 1, Course 1, Module 1,Language of Algebra, Unit
1 Variables, Expressions & Equations. Session 1 Translating words in expressions
screen 3.
Ask the following questions for CFU
 What does the variable t represent?
 Why are we subtracting 3 from time?
 Explain
 What operation does this imply?
 What does t represent?
 What’s the time difference between New York and London?
 What would the time difference be from Los Angeles to London?
 What operation does the later imply?
 Does it make a difference “t + 5” or “5+ t?”
 Why is t only the numbers 1-12?
 Could it be 3?
 If it is 3 what does t mean?
 Could t be 2:30pm?
 Could t be 26?
 What does s mean?
 What does p mean?
 Does the “blank” mean: add, subtract, multiply or divide?
 What does $15.00 represent?
 Why is it $7.50?
 What does P mean?
 What is p + ½? 2p?
 What does it mean 50% of p? p/2? 0.5p?
 What are the different operations of the 2 answers not selected?
Use Power Point Presentation: We Love Mathematical Language
to develop a word wall.
For each slide model how you identify the key words. Circle the words and continue
developing the algebraic statement.
Have students copy the key words in their notebook. After the presentation, create a
word wall with all the key words you found.
RiverDeep Question #2 Use the SHOW ME function available with the problem to model
how to solve this problem.
CFU
Explain how the variable “n” represents the words “a number”
What are we adding to 3n?
Is 5 –3n the same as 3n-5?
How can we verify that the two are equivalent or not equivalent?
What is another way of saying less five?
What is another word that means “decreased by”
7 A&F 1.1 Lesson Plan
Lesson Design
Mathematics
RiverDeep Question #3
Use a clock to demonstrate that there are four 15minute periods in an hour?
CFU:
How many 15 min periods in ½ of an hour, and in 2 hours?
Use the SHOW ME function
CFU
What does “drain” mean?
What operation does “drain” imply?
What does 8y represent?
Guided Practice:
a. Initiate practice
activities under direct
teacher supervision – T.
works problem step-bystep along w/students
at the same time
b. Elicit overt responses
from students that
demonstrate behavior in
objectives
c. T. slowly releases
student to do more work
on their own (semiindependent)
d. Check for
understanding that
students were correct at
each step
e. Provide specific
knowledge of results
f. Provide close
monitoring
What opportunities will
students have to read,
write, listen & speak about
mathematics?
Closure:
a. Students prove that
they know how to do
the work
b. T. verifies that students
can describe the what &
why of the work
c. Have each student
perform behavior
3
Use Matching handout (7 AF 1.1 GP) with students and model the first four problems as
whole class. Give students ten minutes to complete pair/group then use whiteboards to
go over the worksheet. (Make a transparency of this handout)
Explain to students why you will start with A instead of # 1. Say” There are many ways
to translate 2n+2m so let’s start with letter A instead.
CFU:
As you work through the first four problems ask the students to identify key words and
show you using their whiteboards.
Use “How Many Ways” Worksheet (7 AF 1.1 GP) with students. Model one translation
from each problem, allow about ten minutes to complete and then share out using
popsicle sticks or equity cards. (Make a transparency of this handout)
Teacher Examples:
Problem 1. Three plus a number is less than five
Problem 2. Twice a number plus four equals six.
Problem 3. A number squared minus four.
CFU
Why did I use the word “plus”?
In what way would using “increased by” be different and similar to “plus”?
How else can we express “equals” in words.
Can you think of other words that mean a “numbered squared”?
Students will translate mathematical statements into verbal statements.
Students will orally share out their translations.
Ask and show students the following questions. Have them use whiteboards to show their
answers (this way you will know how much re-teaching needs to be done.)
1. Which algebraic expression represents 50 decreased by 3 times a number?
a) 50+3x b) 50-3x c) 3x d) 50-3-x answer is b
2. A plumber charges an hourly rate of $18.50. In addition, there is a service fee of
$35.00 per job.
7 A&F 1.1 Lesson Plan
Lesson Design
Mathematics
If she works h hours to complete a job, how much will she bill her customers in
dollars?
a) $35.-18.50h b) $35. 18.50 c) $35.+18.50 d) $35. 18.50
answer is c
3. A banker has six more dimes than nickels and eight fewer quarters than dimes. He
has forty coins altogether.
Which algebraic equation should the baker use to determine the number of
nickels in the banker’s coin collection?
a) n+n+6+n+6-8=40
b) n + d + q = 40
c) 6+d+q-8+n=40
d) 6d-8q+n=40
answer is a
4. When a number is doubled it equals 150.
Which equation represents this statement?
a) y-2=150 b) y+2=150 c) y/2=150 d)2y=150 answer is d
5. Which algebraic expression represents 30 less than a number?
a) x  30 b) x  30 c) x  30 d) 30x
answer is b
6. Which of the following expressions are equivalent to 3xy:
a) The product of triple a number and another number
b) The product of triple a number and triple another number
c) Triple the product of two numbers
d) Triple the product of three numbers
Answer are a and c

Independent Practice:
a. Have students continue
to practice on their own
b. Students do work by
themselves with 80%
accuracy
c. Provide effective, timely
feedback
Resources: materials
needed to complete the
lesson
4

Have students create one algebraic expression, equation and inequality and then give
three translations for each problem.
RiverDeep Worksheet: Translating Words Into Expressions (Your Turn)
#2-4.
Access to RiverDeep and LCD projectors, student whiteboards, and equity cards/popsicle
sticks, clock, We Love Mathematical Language PowerPoint presentation, RiverDeep
Your Turn worksheet that corresponds to tutorial, Matching Handout and How many ways
handout and transparencies of both handouts
7 A&F 1.1 Lesson Plan