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


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


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


Essential Question(s)

1.      How does one write equivalent fractions with different denominators?

2.      How does one compare fractions?




Students will know...

How to write equivalent fractions with different denominators.



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.




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. (Answer-A 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?


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.       Re-introduce 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 means-A 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.