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: Solving one-step equations (Understanding equality, isolating variable, reciprocals)    Grade(s): 7th         Designer(s): Mesha Rainey

Stage 1 Desired Results

Established Goal(s):

Students will demonstrate an understanding of basic operations and their relationships to each other; apply an understanding of rational numbers and their relationship to each other; Select the appropriate computational method; Demonstrate an understanding of variables, exponents, equations, and inequalities; and Model and develop methods for solving equations and inequalities.

Computation and Estimation

(Rational Numbers)


Adds, subtracts, multiplies and divides integers.


QCC #17



On-going throughout year.

On-going throughout year.

What are some differences and similarities in the rules for adding, subtracting, multiplying and dividing integers?

Patterns and Relationships/


(Order of Operations)

Uses order of operations to simplify numerical expressions.


QCC #8



On-going throughout year.

On-going throughout year.

How do you use the order of operations and why is it important?

Patterns & Relationships; Algebra



Writes and solves one-step algebraic equations (including formulas) and inequalities using addition, subtraction, multiplication, and division.


QCC #7



Ch. 7

Ch. 6

What are the four mathematical operations and which ones are inverses of one another?

What are the differences (based on operations) between a single-step and multi-step equation/inequality?


Understanding(s) Students will understand that...


1.   Equations model real world situations

2.   Equations provide a process to determine solutions involving an unknown/variable.

Essential Question(s)

  1.  Why do we bother with equations?

  2. Why does order matter and how does PEMDAS relate?

  3. Why do we need to show our work?

  4. What are inverse operations?




Students will know...

  • What equality means in math and how to manipulate around an equal sign

  • How to isolate the variable using inverse operations

  • How to combine like terms and the distributive property and apply it when solving equations

  • How to use their skills when solving equations in a chosen career



Students will be able to...


  • Solve one-step equations

  • Add, subtract, multiply, and divide fractions, decimals, and integers

  • Use inverse operations

  • Explain the concept of equality

  • Isolate variables in an equation


Stage 2 Assessment Evidence


Performance Task(s) Summary in G.R.A.S.P.S. form

1.       Students will choose a profession and research ways that math will be required. As an aside, they will also determine what types of math courses they will have to take to get to their profession. This will include high school and college level courses. Students will then be given a relevant math question for their chosen field and present their information to the class.

      Student Directions:
1. Choose a profession that you might be interested in. Record your choice next to your name on the class poster.
2. Using the computers, visit some of the listed web sites and research your profession. Think of at least two specific examples where you would have to use equations in your field.
3. Visit one of the continuing education sites listed and determine how much more math you will need to work in your field. Be sure to include future middle school and high school courses. Record the type of class and the number of semesters. (Example: Algebra I - 2 semesters, Business Calculus - 3 semesters) Enter the total number of semesters of math required and the highest level of math required next to your name on the class poster.
4. Choose the envelope with your name on it from the problem box. This will be a typical daily question from your field. Solve this problem. Be sure to write an equation, show your work, and draw a diagram if necessary.
5. Present your work to the class in an appropriate manner. You must have something visual. Your presentation should include: your profession, math required, your examples of typical questions, the problem that you were given and an explanation of your solution. Also include why this profession interests you and what you learned from this activity?

2.     Using the "Hands on Equations," students will demonstrate their ability to properly setup and solve variable equations. In addition, they will solve one- and two-step equations utilizing addition, subtraction, multiplication, and division.

      Student Directions:

      Given a word problem that suggests a variable equation, accurately setup the equation using the "Hands on Equation" blocks and scale.
Using the red (negative) and green (positive) blocks, place each piece onto the respective side of the scale. Once you have accomplished this, record your results on a sheet of paper.
Next, solve the variable equation (by addition, subtraction, multiplication, division, or combination) to determine the value
of the variable. Again, record your efforts onto a sheet of paper.

Key Criteria:

Setting up an equation following all relevant steps; Able to explain the relevance of those steps and choosing the correction operation to perform; Relating one-step equations to their chosen profession; Correctly modeling an equation using the Hands-On Equation kit. 

Other Evidence

Students will model an equation using the Hands-On Equation kit.  Students will be asked questions in class daily to check their understanding.  Students will also take a quiz to monitor their progress and test as a form of assessment.  Students will work in cooperative groups to check their in-class assignment (worksheet) and check their answers against others.  The students will be given a daily warm-up activity that reviews what was discussed previously.  In addition, students will complete problems on a small dry-erase board and will hold them up to be checked for a quick informal assessment. 



Stage 3 Learning Plan

Learning Activities Consider the W.H.E.R.E.T.O. elements.


1.      Students will write a journal entry, which discusses equality and what it means. 

2.  Students will model equations using the Hands-On Equation kit.  They will explain how we keep a scale balanced/equal and compare the scale to an equal sign.

3.  Students will discuss inverse operations and properties of equality.  Students will use these terms/concepts to show how to isolate a variable in a one-step equation.  Dry erase boards will be used to complete problems in order to check understanding.

4.  Students will take lecture notes about equality, inverse operations, and one-step equations, to include vocabulary terms. 




























**Information/ideas come from the "Understanding by Design" website.



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