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


Title: __Integers___________________ Subject/Course: Math/Pre Algebra___________ Topic: _Integers___________Grade(s): __7_____ Designer(s): _M. Rainey___________

Stage 1 Desired Results

Established Goal(s)

QCC #17:  (Computation and Estimation of Rational Numbers)  Adds, subtracts, multiplies, and divides integers.

QCC #35:  (Numbers Sense and Numeration)  Find the absolute value of any real number

QCC #22:  (Geometry and Measurement-Ordered Pair, Coordinate Plane) Identifies and graphs an ordered pair on a 4-Quadrant Coordinate Plane

Understanding(s) Students will understand that...

1.     positive and negative integers are used in many real-life applications, including temperature, acceleration, and altitude

2. coordinate planes are used as reference grids in many disciplines


Essential Question(s)

1.     How are negative numbers used today?

2. How would life be different if we didn't have negative numbers?




Students will know...

 Positive and negative numbers, additive inverse, opposite, coordinate plane, ordered pair, absolute value, quadrant, x-axis, y-axis, origin, graph


Students will be able to.

Read and write integers and find absolute value.  Compare and order integers.  Graph points on a coordinate plane.  Use integers to solve problems with various operations.


Stage 2 Assessment Evidence


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

1.      The student will design a picture using ordered pairs, utilizing their knowledge of positive and negative integers.


Given a piece of graph paper, label the x and y axis.  Draw a picture on the graph paper.  Write the list of ordered pairs on a piece of paper.  The student must write a minimum of 15 different points, which have to be in each of the 4 quadrants.  The student will exchange their list with another student.  The student will graph the other students ordered pairs and connect the dots to see what picture is created.

Key Criteria:

The student has a design on graph paper with 15 ordered pairs listed on a sheet of paper.  The display is neat and the list of ordered pairs is easy to read.  All parts of the graph are correctly labeled and the list of pairs is correct.

Other Evidence

E Worksheets, quiz, verbal observation, cooperative groups, student questioning technique.



Stage 3 Learning Plan

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


1.       PowerPoint presentation of the lesson

2. Students will play a game of review basketball.  The class will be divided into 4-5 teams.  They will be given a review problem to do.  Correct answers get a point.  If a team answers correctly, they earn a chance to shoot a piece of paper into the trash can for extra points. 

3. Students will be handed a variety of positive and negative numbers.  Students will create a human integer/number line with numbers handed to them, ordering themselves from least to greatest.

4. Students will watch the integer video to enhance their knowledge of integers and review for the test.

5. Students will use counters to model problems involving positive and negative numbers. 



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