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


Title: _Inputs and outputs____ Subject/Course: Algebra  Topic: _Variables_________ Grade(s): _8th___ Designer: ___Kevin Smith_____

Stage 1 Desired Results

Established Goal(s)

M8A3 Students will understand relations and linear functions.

.a Recognize a relation as a correspondence between varying quantities.

b. Recognize a function as a correspondence between inputs and outputs where

the output for each input must be unique.

e. Use tables to describe sequences recursively and with a formula in closed form.



Understanding(s) Students will understand that...

1.  There is a unique relationship between inputs and outputs of a function.


Essential Question(s)

1.      What is a function?

2.  Why is the relationship between the inputs and outputs unique?



Students will know...

1.  Definition of a function

2.  Definition of domain and range

3.  That variables can be used to determine patterns.  K

Students will be able to...

1. Represent data interchangeably in the forms of equations, tables, and graphs.



Stage 2 Assessment Evidence


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

1.  TI have a "number machine" that always affects in the same way whatever number I put in it. For example, when I put in 1, the machine gives me 6; when I put in 3, it gives me 10; when I put in 6, it gives me 16; and when I put in 9, it gives me 22. What will the machine give me if I put in 100? 


Students will work in groups of 3 and 4 to solve this problem.   S





Key Criteria:

Homework and quiz

Other Evidence

Teacher observations



Stage 3 Learning Plan

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



I have a number machine and it always affects every number I put into it in the same way.  If I put in 1, I get 6.  If I put in 3, I get 12.  If I put in 5, then I get 18.  If I put in 8, then what will the machine give me? 


Johnny went to the store and wanted to buy some comic books.  If he purchased one book, he would pay 2$.  If he buys two comic books, then he will pay 4$.  If he buys 3 books then he will pay 12$.  How much will he pay if he buys the whole set of 5? 


Jill has a garden and she is planting tomatoes.  If she plants three rows, she expects to have seventy tomatoes when the first ones are ready.  If she plants five rows, she expects to have 110.  How many tomatoes should she have if she plants 8 rows?  



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