Translate expressions (consecutive, sum)
Tape diagrams
Evaluate
7.EE.3: Solve multi-step real-life and mathematical problems posed with positive and
negative rational numbers in any form (whole number, fractions, and
decimals) using tools strategically. Apply properties of operations to calculate
with numbers in any form; convert between forms as appropriate; and assess
the reasonableness of answers using mental computation and estimation
strategies.
7.EE.4: Use variables to represent quantities in real-world or mathematical problem,
and construct simple equations and inequalities to solve problems by
reasoning about the quantities.
a. Solve word problems leading to equations of the form px + q = r and p(x +
q) = r, where p, q, and r are specific rational numbers. Solve equations of
these forms fluently. Compare an algebraic solution to an arithmetic
solution, identifying the sequence of the operations used in each approach.
7.3.7

Students understand that an equation is a statement of equality between two
expressions.

Students build an algebraic expression using the context of a word problem and
use that expression to write an equation that can be used to solve the word
problem.
WKSP
HW
Media
Student
Learning Goal
CC
Lesson
Standard
Pre Requisite
Understanding equations
#32
Spiral Review #9
Understanding equations
Find the unknown variable:
1. x – 4 = 8
2. 8y = 24
3. 9 + d = -2
Three Sisters
The ages of three sisters are consecutive integers. The sum of their ages is 45. Find
their ages.
a. Use a tape diagram to find their ages.
b. If the youngest sister is x years old, describe the ages of the other two sisters in
terms of x, write an expression for the sum of their ages in terms of x, and use that
expression to write an equation that can be used to find their ages.
c.
Determine if your answer from part (a) is a solution to the equation you wrote in
part (b).
Online Music Store
Sophia pays a $20 membership fee for an online music store.
a. If she also buys two songs from a new album at a price of $1 each, what is the total
cost?
b. If Sophia purchases n songs for $1 each, write an expression for the total cost.
c. Sophia’s friend has saved $118 but isn’t sure how many songs she can afford if she
buys the membership and some songs. Use the expression in part (b) to write an
equation that can be used to determine how many songs Sophia’s friend can buy.
d. Using the equation written in part (c), can Sophia’s friend buy 99 or 98 songs?
Understanding equations
Pens & Pencils
The total cost of four pens and seven mechanical pencils is $13.25. The cost of each
pencil is 75 cents.
a. Let the cost of a pen be 𝑝 dollars. Write an expression for the total cost of four pens
and seven mechanical pencils in terms of 𝑝.
b. Write an equation that could be used to find the cost of a pen.
c. Determine a value for 𝑝 for which the equation you wrote in part (b) is true.
d. Determine a value for 𝑝 for which the equation you wrote in part (b) is false.
Sum it Up
What is the process you used to create an equation? What did you build first?
Describe how to determine if a number is a solution to an equation.
Understanding equations
Name: __________________________________
Pre-Algebra
Date: ______
Exit Ticket
Andrew is trying to create a number puzzle for his younger sister to solve. He
challenges his sister to find the mystery number. ‘When 4 is subtracted from half
of a number, the result is 5.’
1. Write an equation to represent the mystery number: ____________________
2. Andrew’s sister’s first guess is 30. Is she correct? Why or why not?
3. What is the mystery number?
Understanding equations
Name: _______________________________________
Pre-Algebra
Date: _____
HW #32
Lesson Summary


1.
In many word problems, an equation is often formed by setting an expression equal to a
number.
To determine if a number is a solution to an equation, substitute the number into the
equation for the variable and check to see if the resulting number sentence is true.
The sum of three consecutive integers is 36.
a. Find the smallest integer using a tape diagram.
b. Let 𝑛 represent the smallest integer. Write an equation that can be used to find
the smallest integer.
c. Determine if each value of 𝑛 below is a solution to the equation in part (b).
n = 12.5
2.
n = 12
n = 11
Circle all the equations below:
1+x
x+x
5(x + 1) = 22.1
1+x=3
x=7
3(x + 2)
over 
Understanding equations
Review: Write the following in standard form.
3. 2(3x – 4)
4.
2 + (3x – 4)
5. 2 – (3x – 4)
6.
1
(4𝑥 − 8) − 𝑥
2
Factor the following expressions.
7. 3a + 18
8.
4a + (b + a) + 9b