• Monitor and ask questions during the pair activity to evaluate the level of students’ understanding.
• Read student math journal entries to further assess students’ comprehension of this lesson’s concepts.

“Today we are going to continue our work with fractions. We will be making fraction strips. We will use them to make observations about fractions and play a fraction game.”

As an introductory activity, read the book Jump, Kangaroo, Jump! by Stuart J. Murphy to your students. Look at the pictures and talk about what is on each page.

“Before I give you a problem to solve, 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 Jump, Kangaroo, Jump! by Stuart J. Murphy. As we read the story I want you to notice the strategies the children in the book use to solve their problems.”

Ask students questions about the book and groups of items on each page as you read. 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?”

Fraction Strips Activity

Make copies of the color fraction strips page provided (M-3-3-2_Color Fraction Strips.doc) or have students make their own fraction strips (M-3-3-2_Blank Fraction Strips.doc). Have students cut the fractions apart. The only fraction strip that should not be cut is the One Whole. Instruct students to write their initials on the backs of the fraction strips so they will be able to keep them for future lessons.

“Each of us has made our own set of fraction strips. We will be using the fraction strips throughout the year. I’m going to give you a few minutes to explore your fraction strips. If you wish, you and a neighbor can put your pieces together and explore the fraction strips. Pay specific attention to patterns that you notice. For instance, can you find more than one way to represent the same fraction? What is true about fractions that are larger than ? How about fractions that are smaller than ? I will ask you to stop in a few minutes so we can regroup and discuss your observations.”

You may want to let students explore for about 10 to 15 minutes. Allow students to share observations they made while working with the fraction strips.

“Write down some observations you made in your math journal. What connections did you make? What surprised you? Did you see any relationships?” Give students about five minutes to write down their observations. Some students might use the fraction strips to help them clarify their thinking while they are writing. Walk around to groups of students and ask them to explain their work. Clarify any misunderstandings.

“Let’s hear some of your observations.”

(“Tom and I found that there are lots of ways to make . We put the  fraction strip on our desks. Then we put smaller fraction strips on top of the . We found that if we put two s on top of the , they are the same size.”)

“So  and  are equivalent? Is that what you mean?”

(“Yes. We also found that  and  are the same as .”)

Continue the discussion, allowing students to share their findings. Some sample questions might include:

• “How many sixteenths would be in ?” (8)
• “What does it mean if we say two fractions are equivalent?” (Two fractions have the same value or represent the same part of an object.)
• “How can you use your fraction strips to see if two fractions are equivalent?”
  (Set a smaller strip on top of a larger strip and see if they are the same size.)
• “What patterns do you notice?”
• “How do we show equivalent fractions when writing?” (Use the equal sign. Example: )
• “Use  or  strips to name a fraction that is larger than . Then name one that is smaller than .” Use comparison symbols when writing comparisons.  or .

“We will be using our fraction strips during the year, so I will hand out an envelope to everyone. Please write your name on the outside of the envelope and place your fraction strips inside.”

You will have opportunities to assess students while they are exploring the fraction strips and through discussions and questions. Students may need to be pulled into small groups to further clarify understanding.

Some sample questions include:

• “Are these two fractions equivalent? Explain.”
• “What do you notice about  and ?”
• “What patterns do you notice?”
• “How are the fraction strips helping you find equivalent fractions?”

Ask students to explain their thinking. When students share their answers, it is important to emphasize the equivalence of different representations.

Extension:

• Routine: With the Guess My Equivalent Fraction Activity, give students clues to find equivalent fractions. Say: “I am equivalent to . My denominator is 8.” Students listen to the verbal clues and use their fraction strips to find the equivalent fraction. Repeat as time allows. Students can also make up clues to share with the class.
• Small Group: Provide each student with a spinner (M-3-3-2_Fractions 3-in-a-Row Game Board.doc) and a paper clip to use with the spinner. Each student will also need one set of fraction strips (M-3-3-2_Color Fraction Strips.doc) and a Spin, Spin, and Compare recording sheet (M-3-3-2_Spin, Spin, and Compare Recording Sheet.doc). Decide who will be player 1.

Player 1 spins the spinner and makes the fraction using the fraction strips.

Player 2 spins the spinner and makes the fraction using the fraction strips.

Both players compare the two sets of fraction strips. If the fractions are equivalent, both players earn one point. If the fractions are not equivalent, the player with the larger fraction gets one point. The player with the most points after 10 rounds is the winner. Students should take turns recording equations on the recording sheet.

• Workstation: For each workstation, provide one Fractions 3-in-a-Row game board (M-3-3-2_Fractions 3-in-a-Row Game Board.doc) and a paperclip for the spinner. You will also need to place at each workstation two different-colored counters (centimeter cubes, disks, etc.)—15 of each color—and a sheet or poster listing the game rules:

1. Each player chooses a different set of colored markers. Decide which player will go first.
2. Player 1 spins the spinner. Look at the fraction on the spinner. Find an equivalent fraction on the game board. If the player has equivalent fractions on the spinner and the game board, s/he gets to place his/her counter on the game board.
3. Play continues with Player 2.
4. If players cannot find an equivalent fraction they lose their turn. If a player does not correctly find equivalent fractions, one of his/her markers is removed from the board. If the player doesn’t have any markers on the game board, play continues with the next player.
5. The first person to get three markers in a row is the winner.

• Expansion: For students who are going beyond the standard, show a fraction on the overhead projector. Students must find at least two equivalent fractions using their fraction strips and write equalities to show their work.

Students can write equations on the dry-erase boards.