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

Title: _________________________________    Subject/Course: ________________

Topic: ________________    Grade(s): _________   Designer(s): ________________

Stage 1 – Desired Results

Established Goal(s)

M5N4  Students will continue to develop their understanding of the meaning of common fractions and compute with them.

     c.  Find equivalent fractions and simplify fractions.

Understanding(s) Students will understand that...

1.    there are an infinite number of fractions that name the same sized "piece."

Essential Question(s)

1.      How can different fractions name the same size “piece?”

2.      How can you simplify fractions?



Students will know...

1.  the meanings of the terms numerator and denominator.

2.  the meanings of the terms halves, thirds, fourths, etc. 


Students will be able to...

1.  use pattern blocks to determine equivalent fractions.

2.  notice a pattern when using pattern block fractions.


Stage 2 – Assessment Evidence


Performance Task(s)

Explore the relationships between pattern blocks of different sizes.

Look for patterns based on the size and shape of a given block designated as one whole and its parts.  Use blocks to fill in a chart to compare fractions and their corresponding parts of a whole.

Notice that several fractions can name a specific sized pattern block. 



Other Evidence

Question students to lead them to notice the appropriate fraction names for the shapes or parts of blocks pictured on the chart.  Notice that some shapes have the same fraction name.




Stage 3 – Learning Plan

Learning Activities

Distribute pattern blocks of different sizes and colors.  Compare the blocks to each other in terms of size, how many will cover another.

Physically use the different blocks to assist in completing the chart:

  Ã=1 (half hexagon) = 1 t=1 p=1
(half hexagon)        
t(1/3 hexagon)        
(1/4 hexagon)        
p(1/6 hexagon)        
(1/8 hexagon)        

Discuss the chart's results, leading students to see that the same fraction names represent different sized block pieces.  Discuss how that could be, and the meanings of the numerators and the denominators. 

For the next lesson, use the chart's results and investigate what it means to simplify fractions and the methods involved.