Source: Wiggins, G., & McTighe, J. Understanding by Design.
Merrill Prentice Hall: 1998.
For further information about Backward Design refer to http://www.ubdexchange.org/
Title: Patterns & Relationships; Algebra Subject/Course: PreAlgebra Topic: Problem Solving; Equations Grade(s): 7 Designer(s):
Lillian
Laster 

Stage
1 – Desired Results 

Established
Goal(s) Students will demonstrate
understanding fundamental algebraic concepts.
Strand: Patterns
& Relationships QCC: 5 Topic: Expressions,
Equations, Inequalities Standard: Identifies
the use of a variable as a placeholder in an algebraic expression or
equation. QCC: 6 Topic:
Expressions Standard: Evaluates
algebraic expressions QCC: 7 Topic: Equations, Inequalities Standard: Writes
and solves onestep algebraic equations and inequalities using addition,
subtraction, multiplication, and division. QCC: 11 Topic: Expressions, Equations Standard: Translates
English phrases and sentences into mathematical expressions, equations, and
inequalities. QCC: 13 Topic: Problem solving, Equations Standard: Writes
and solves and equation for a given word problem. 

Understanding(s)
Students
will understand that... 1. An equation is a statement that two quantities are equal. 2. The solution to an equation is the number(s) which, when used as the value of the variable(s), makes the statement true. 3. In an equation if one side is changed in some way, the other side must be changed in exactly the same way in order to keep the two sides equal. 4. The same operations of arithmetic are used in algebra: addition, subtraction, multiplication, and division. 5. To solve for the unknown, the variables must be on one side of the equation and all the numbers on the other side of the equation. U 
Essential
Question(s) 1. How can a word phrase be written as mathematical
equation? 2. What can be used for the variable (x) to make the
statement true? 3. What is the inverse operation? 4. How are variables isolated to one side of an equation? Q 

Students will know... 1.
A variable is a letter that takes the place of a
number. 2.
A variable can be referred to as “unknowns” because
the values are unknown. 3.
Words can be translated into symbols: ·
Addition: sum of, plus, increased by, more than, add ·
Subtraction: the difference of, minus, decreased by,
subtracted from, less, less than, take away ·
Multiplication: the product of, times, multiplied by ·
Division: the quotient of, divided by, goes into ·
Equality: is, is equal to, equals, is the same as,
the result is ·
Inequality: is greater than, is less than, is greater
than or equal to, is less than or equal to, is at most, is at least, does not
equal K 
Students will be able to... 1.
To
find a replacement number for the variable that will make the equation a true
statement. 2.
Translate
statements into equations. 3.
Translate
statements into inequalities. 

Stage
2 – Assessment Evidence 


Performance
Task(s) Summary in G.R.A.S.P.S. form 1.
In
class have students change the following word phrases into math phrases: ·
Five
less than a number ·
Three
more than a number ·
Four
times a number ·
One
fifth of a number ·
The
difference between a number and three ·
The
product of eight and a number ·
The
sum of four and a number 2.
Divide
class into groups of 2 students. 3.
Partners
will collaborate together to determine operation needed to solve the
following word problems and compare answers. ·
A
number plus three is twelve. Find the
number ·
Four
times a number plus two is eighteen.
Find the number. ·
Two
times the larger of two consecutive integers is three more than three times
the smaller integer. Find both
integers. 4. Class extension exercise: To
show that percent problems can be solved using equations. Since two numbers are known, the third
number can be called the unknown’x’. A dress costs $75.33 after the tax is
added. If the tax is 8%, how much is
the dress? T 

Key Criteria: Students will participate in verbal responses and
questioning. Each cooperative group
will show and summarize all work.
Teacher observation 

Other
Evidence Learning activity, quiz 

Stage
3 – Learning Plan 
Learning
Activities Consider the W.H.E.R.E.T.O. elements. 
A rectangle has a perimeter of 76 inches. If its length is 8 inches more than its
width, find the length and width.
Note: Perimeter = 2 length x 2
width Draw the
rectangle. x + 8 x If x is the
width, then x + 8 is the length. Perimeter: 2x + 2(x + 8) = 76 Extension: A rectangle has a perimeter
of 76 inches. Its length is twice the
width. Find the area. 2x x If x is the
width, then 2x is the length. Perimeter: 2(2x) + 2(x) = 76 Area: length x width 