Source: Wiggins, G., & McTighe, J. Understanding by Design.
Merrill Prentice Hall: 1998.
For further information about Backward Design refer to http://www.ubdexchange.org/
Title: Equivalent Fractions Subject/Course: Algebra I Topic: equivalent fractions Grade(s): 6
Designer(s): Pam Joseph 

Stage
1 – Desired Results 

Established
Goal(s): GPS M6N1 M6N1 Students will understand
the meaning of the four arithmetic operations as related to positive rational numbers and will use these concepts
to solve problems. a. Apply factors and multiples. b. Decompose numbers into their prime factorization
(Fundamental Theorem of Arithmetic). c. Determine the greatest common factor (GCF) and the
least common multiple (LCM) for a set of numbers. c. Add and subtract fractions and mixed numbers with
unlike denominators. e. Multiply and divide fractions and mixed numbers. f. Use fractions, decimals, and percents interchangeably. g. Solve problems involving fractions, decimals, and
percents. 

Understanding(s)
Students
will understand that... 1. when you know how to write equivalent fractions with different denominators, you can compare fractions U 
Essential
Question(s) 1.
How does one write
equivalent fractions with different denominators? 2.
How does one
compare fractions? Q 


Students will know... How to write equivalent fractions with different
denominators. K 
Students will be able to... Define the terms: fraction, numerator, and denominator;
Write a fraction which tells what part of a region is
shaded; Name the numerator and denominator of a fraction; Identify equivalent fractions; Write a fraction in lowest terms; Compare fractions. S 


Stage
2 – Assessment Evidence 


Performance
Task(s) Summary in G.R.A.S.P.S. form For assessment, students will be asked to perform the
following tasks: 1. Students
will identify numerator and denominator on the board. 2. Students
will fold a rectangular sheet of paper in half and color parts. Then they
will be asked to name the fraction of the paper that is colored (1/2). 3. They will
then be asked to refold the same paper and then fold it in half once again,
then unfold. How many equal parts now? (4)
What fraction is shaded? (2/4 or ½) This means that 2/4 = ½. 4. Students
will refold the papers and fold in half a third time. Unfold. Students will
be able to answer that the new fraction that is equal to ½ and 2/4 is 4/8 and
will be asked to explain why. 5. Repeat the
same activity with pieces of paper, demonstrating 1/4, ¾, 1/3, 2/3, 1/8. 6. Students
will show on the board that one way to create an equivalent fraction is to
multiply both the numerator and denominator by the same number. They will
also show that one can also use division to show that two fractions are
equivalent. 7. Ask what
lowest terms means. (AnswerA fraction is in lowest terms when the numerator
and denominator only have the number 1 as a common factor). 8. Students
will answer the following questions: What are unlike fractions? What are like
fractions? What does least common denominator mean? T 

Key Criteria: o
Students are able to answer important questions
about equivalent fractions. o
Students are able to fold papers and explain what
the resulting fractions are. o
Students are able to create equivalent fractions
using multiplication and division. 

Other
Evidence Other discussion about equivalent fractionsOE


Stage
3 – Learning Plan 
Learning
Activities Consider the W.H.E.R.E.T.O. elements. 
1. Write the
terms: fraction, unlike fraction, like fraction, numerator, and denominator
on the board. 2. Go over each
term and each definition. 3. Provide each
student with a rectangular piece of paper. 4. Fold the
paper in half. After folding the paper in half, instruct the students to do
the same. 5. Explain that
a fraction is part of a whole. You have divided a whole piece of paper into
two equal parts. 6. Unfold. The
students will color one of the equal parts. 7. Ask a
students to write ½ on a piece of paper to show that one out of the two equal
parts is now shaded. Instructor also writes this on the board. 8. Reintroduce
the vocabulary words numerator and denominator. The numerator is the number
of parts shaded and the denominator is the number of equal parts. 9. For those
students who have difficulty remembering which is the numerator and which is
the denominator, try this memory association technique In a fraction, one
number is UP above the line and one is DOWN below the line. The word
numerator has a “u” in it and so does up; the word denominator has a “d” in
it and so does down. 10. Repeat the
same activity with pieces of paper, demonstrating ¼, ¾, 1/3, 2/3, 1/8. 11. Each time,
the students should write the fractions down on paper and identify the
numerator and denominator. Have different students write it on the board each
time. 12. Ask students
to refold the same piece of paper and then fold it in half again. Unfold. 13. Ask “How
many equal parts now?” (4) Ask “What fraction is shaded (2/4 or ½). Say
“Since the amount of shading has not changed, this means that fraction ½ =
2/4. 14. Tell
students that ½ and 2/4 are two names for the same amount. Therefore, they
are equivalent. 15. Now have
students refold the papers and then fold in half a third time. Unfold. Ask
“What new fraction have they found that is equivalent to ½ and 2/4? (4/8)
These three fractions name the same amount. 16. Write all of
the factors of 24 and 100 on the board. Explain why 24/100, 12/50, 6/25 are
equivalent fractions. They are the same fractions, only the names change, not
the value. 17. Explain what
lowest terms meansA fraction is in lowest terms when the numerator and
denominator only have the number 1 as a common factor. 18. Write the
terms unlike fractions and like fractions on the board. Explain the
definitions. Now, go over the term least common denominator and explain. 