• Observe and ask questions during the pair activity in order to evaluate the level of students’ understanding.
• Read student math journal entries to further assess students’ comprehension of concepts.

“Today we are going to continue our work with fractions. We will be looking at fractions of a set. We will briefly review numerator and denominator and then play a fraction game.”

As an introductory activity, read Clean-Sweep Campers by Lucille Recht Penner to your students. Look at the pictures and talk about the children’s stay at camp. “Right now, I would like to read a book to you. Let’s look at the cover. What do you think our book will be about?” Take student suggestions and predictions about the book.

“The title of the book is Clean-Sweep Campers by Lucille Recht Penner.” If this book is unavailable, Fraction Action by Loreen Leedy is a good alternative. “As we read the story I want you to notice the strategies the children in the book use to solve their problems.”

As you read, ask students questions about the book and the groups of items on each page. Sample questions could include:

• “What did you learn from the book?”
• “What was the problem at the beginning of the story?”
• “How were fractions represented in the book?”
• “Give an example of equal sharing in the book. Explain.”
• “What happened at the end of the story?”

“We have been talking about fractions for a while now. Let’s review the parts of a written fraction.” Write a fraction on the board. Ask students to name the parts of the fraction and tell what they mean.

Review/discuss the meaning of fraction bar, numerator, and denominator.

Pattern Block Fraction of a Set Activity

Before the lesson, prepare a spinner (M-3-3-3_Spinner for Pattern Block Fraction of a Set.docx) and gather some pattern blocks in a bag to use in your demonstration. Say to students, “We are going to be describing a fraction of a set today. Let’s start with some pattern blocks. I am going to spin my spinner. I got the number 6. I need to reach into the bag and pull out six pattern blocks.”

These are the pattern blocks pulled from the bag:

“This is my set of pattern blocks. How many are triangles?” (three)

“Three out of six are triangles. We can write it like this:

Three out of six are triangles

or

 are triangles.”

Have students describe the rest of the set. Students can describe by color, size, shape, number of sides, etc. Try to write each observation students make in at least two different ways.

Sample ways to write what students describe might include:

• Two shapes out of six shapes are orange.
•  of the set are squares.
•  of 6 is 2 or  of 6 is 2.

After students have had time to describe the set, place the pattern blocks back in the bag. Repeat the process by spinning the spinner, selecting the blocks from the bag, and describing the set in multiple ways.

After students have participated in the activity as a class, split them up into partners to continue the activity with one additional step. Provide one spinner (M-3-3-3_Spinner for Pattern Block Fraction of a Set.docx) and one bag of pattern blocks for each student pair. Give each pair a divider as well. The divider is placed between the two partners so they cannot see what pattern blocks are being pulled from the bag.

“Maria, spin the spinner and tell the class what you got.” The student may say, for example, “My spinner is pointing at the four.”

“Now take four pattern blocks from your bag and place them on your side of the divider. While Maria is doing this, the rest of you will need to listen to the clues she gives you. You will then try to make a set of pattern blocks that matches hers. She can give you as many clues as you need in order to make the set.”

Then Maria may say, “My first clue is one out of four shapes is yellow.”

Students take a block and move it to their area. Maria shares another clue: “Three-fourths of the shapes has three sides.”

A student suddenly says, “I think I know what you have in your set. Do you have three green triangles and one yellow hexagon?”

Maria’s set is shown to the class and other students check to see if they correctly figured out the set of shapes. “You may now begin working with your partner.”

You will have opportunities to assess students while they are working with their partners on the Pattern Block Fraction of a Set Activity and through discussions and questions. Students may need to be pulled into small groups to further clarify understanding, or you can assess student learning at another time.

Some sample questions may include:

• “What do you notice about and ?”
• “What patterns do you notice?”
• “How did you know it was ?”
• “How would you write the fraction for this set?”
• “Do you think it is harder to figure out the set when there are more shapes?”
• “Which type of clue gives you the most information about the set?”
• “If my clue was  of the set is blue, how would you know how many shapes to place in your set?”
• “You have 10 shapes in your set. What is  of 10?”

Extension:

• Routine: Anytime a natural opportunity to describe a fraction of a set arises in class, use it to review this concept with students. For example, “One marker is red and three markers are blue. What fraction of the set of markers are red?” Or “It looks like we have 5 full sets of pattern blocks and 2 partial sets. What fraction of the sets are full sets?”
• Small Group: Place red, yellow, orange, and green counters in a bag. Reach in and pull out a small handful. Ask students to describe the set using fractions. Students can write their fractions on small dry-erase boards.
• Workstation: Give a pair of students eight two-colored counters. Students spill the counters on the table, observe the number of counters of each color, draw the results in their journals, and write the fractions for both colors. (See the example below.)

• Expansion Activity: The Fractions of a Set activity may be used with students requiring a greater challenge. Ask students to solve problems that involve fractions. You can use the Fraction of a Set Word Problems (M-3-3-3_Fraction of a Set Word Problems and KEY.docx). Give students one problem at a time and have them share their strategies with the class.
• Expansion Activity: The Number of a Set with Counters activity may be used with students looking to go beyond the standard requirements. Have students participate in an activity using 30, two-colored counters. (Additional information can be found at (http://www.etacuisenaire.com/search/searchdisplay?type=keyword&query=two-color+counters).Write an equation on the board with the same structure as the one below.

Students can answer your questions using the two-colored counters. Some sample questions might be:

• “How many groups do you need?”
• “How many counters show  of 18?”
• “What is the missing number in the equation?”
• “How can we relate multiplication to this problem?”