Source:  Wiggins, G., & McTighe, J. Understanding by Design. Merrill Prentice Hall: 1998.
                For further information about Backward Design refer to


Title: Patterns & Relationships; Algebra  Subject/Course: Pre-Algebra 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 one-step 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.


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?



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






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?



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





     If x is the width, then x + 8 is the length.

     Perimeter:  2x + 2(x + 8) = 76



     A rectangle has a perimeter of 76 inches.  Its length is twice the width.  Find the area.








    If x is the width, then 2x is the length.

    Perimeter:  2(2x) + 2(x) = 76

    Area:  length x width



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