Objective
The student will be able to:

Evaluation Questions for each Objective

1. Define and describe equivalent fractions

2. Generate equivalent fractions

3. Identify if two fractions are equivalent

ENGAGEMENT

What the Teacher Will Do

Eliciting Questions/
Student Responses

What the Students Will Do

The teacher will display the “What Does Equivalent Mean?” transparency on the overhead.  Cover the bottom half of the transparency so students can only see the top half of the transparency.

The teacher will show the bottom half of the transparency.

What do you think the word “equivalent” mean?
Same
Equal

Are two groups of coins shown here the same? Why?
Yes and no
They are not the same because there are dimes and pennies on the left while on the right side are quarters and nickels.
They are the same because they both equal 35 cents.

We can say these two groups of coins are equivalent.  What does equivalent mean?  Be specific.
If two things are equivalent they have the same value.

What coins could I place on the right side so they would be equivalent to these 2 quarters?

The students will brainstorm the meaning of equivalent.

In pairs, students will discuss what combination of coins are equivalent to two quarters.

Selected students will share their answers.  The remaining students will confirm whether the answers presented are equivalent and why.

TRANSITION

That you know what equivalent means, you will explore what equivalent fractions are.

EXPLORATION

What the Teacher Will Do

Eliciting Questions/
Student Responses

What the Students Will Do

The teacher will facilitate students getting into groups of 4. The teacher will pass out the “Equivalent Fractions” worksheet to each student.

The teacher will model how to use the fraction bars to find equivalent fractions using ½ as an example.

Look at the 3 equivalent fractions you have written down: ½, 2/4, 3/6.  What patterns do you see among the fractions?
-The numerators count by 1’s and the denominators count by 2’s.
-There is a common factor  between the numerators and the denominators.  For example, 3 is three times bigger than 1 and 6 is three times bigger than 2. 

Without using your fraction bars, tell me some more fractions that are equivalent to ½.
4/8, 5/10, 10/20, 50/100

Is 35/70 equivalent to ½?
Why or why not?
-Yes, because like all the other fractions that are equivalent to ½ the denominator is twice as big as the numerator.
-Yes because 1 times 35 is 35 and 2 times 35 is 70.

Students will use their fraction bars to make fractions that are equivalent to ½ with the guidance of the teacher.   Students will record their fractions on their worksheet.

Students will use the patterns they have found to try to find fractions equivalent to ½ without using the fraction bars.

TRANSITION STATEMENT

You have done a good job finding fractions that are equivalent and looking for patterns in your fractions.  Now you will have an opportunity to share your results with your classmates.

EXPLANATION

What the Teacher Will Do

Eliciting Questions/
Student Responses

What the Students Will Do

The teacher will select students to share the results of their exploration.
Be intentional about who you choose to share; look for students who have found interesting and unique patterns as well as students with common misconceptions that need to be addressed with the entire class.

What fractions did you find that were equivalent to 2/3?
4/6, 6/9

What patterns did you see in the equivalent fractions?
-The numerators count by 2’s and the denominators count by 3’s.
--There is a common factor  between the numerators and the denominators.  For example, 6 is three times bigger than 2 and 9 is three times bigger than 3.

Without using your fraction bars, tell me some more fractions that are equivalent to 2/3.
8/12, 10/15, 20/30, 60/90

Is 14/21 equivalent to 2/3?
Why or why not?
-Yes because both the numerator and denominator of 14/21 are related by a factor of 7 to the original numerator and denominator of 2/3.

Continue using the same questions to explore fractions equivalent to ¾ and 1/3.

Selected students will share the results of the exploration.

TRANSITION STATEMENT

In the last activity you created your own equivalent fractions with fraction bars.  Now you will play the game “Memory” to practice identifying whether or not two fractions are equivalent.

ELABORATION

What the Teacher Will Do

Eliciting Questions/
Student Responses

What the Students Will Do

The teacher will hand out a set of “Equivalent Fractions Memory” cards and explain the directions.

The teacher will monitor students as they play “Memory.”  The teacher will observe the matches made by students to ensure correctness and identify any misconceptions.

After students have finished the game, the teacher will select some students to share one of their matches and tell how they knew it was equivalent.

How did you know these 2 fractions were a match?
-The fractions have the same value because if you color in ½ of a circle it is the same amount as if you color in 2/4 of a circle.
-I know 2/4 is equivalent to ½ because 2 is twice as big as 1 and 4 is twice as big as 2.

Give me an example of two fractions that are not equivalent.  How do you know they are not equivalent?
½ is not equivalent to 1/3 because they do not have the same value.  ½ is more than 1/3.

Students will play the game “Memory” in groups of 4.   Students lay all cards face down in rows on a desk or table.  On each student’s turn, he or she will turn over any 2 cards.  If the fractions represented on the cards are equivalent, then they are a match and the student keeps the cards. The student will tell how he or she knows the fractions are equivalent.  The other 3 players will confirm that the 2 cards are equivalent.  If the 2 cards are not equivalent, the student leaves the cards in place and turns them face down again.  Play continues until all the cards have been matched.  The player with the most matches wins.

Students will share their matches and explain how they knew the fractions are equivalent.

TRANSITION

You have created your own equivalent fractions and you have played a game in which you had to determine if fractions were equivalent.  Now you will have an opportunity  to show what you have learned.

EVALUATION

1. Use your fraction bars to find two fractions that have the same value as ½.  Draw your equivalent fractions and list them in the space provided. 

2.  What patterns do you notice in your equivalent fractions?

3.  Use the patterns you see to write down two more fractions you think are equivalent to ½.

____

____

4. Use your fraction bars to find two fractions that have the same value as 2/3.  Draw your equivalent fractions and list them in the space provided. 

5.  What patterns do you notice in your equivalent fractions?

6.  Use the patterns you see to write down two more fractions you think are equivalent to 2/3.

____

____

7. Use your fraction bars to find two fractions that have the same value as 3/4.  Draw your equivalent fractions and list them in the space provided. 

8.  What patterns do you notice in your equivalent fractions?

9.  Use the patterns you see to write down two more fractions you think are equivalent to 3/4.

____

____

10. Use your fraction bars to find two fractions that have the same value as 1/3.  Draw your equivalent fractions and list them in the space provided. 

11.  What patterns do you notice in your equivalent fractions?

12.  Use the patterns you see to write down two more fractions you think are equivalent to 1/3.

____

____