<p>Students will get practice working with fractions within a set. Students are going to:&nbsp;<br>- Use counters and other manipulatives to learn about fractions of a set.</p>

<p>- What mathematical representations exist for relationships?&nbsp;<br>- How does effective communication benefit from mathematics?&nbsp;<br>- How do we represent, compare, quantify, and model numbers using mathematics?&nbsp;<br>- What does it mean to evaluate or estimate a numerical quantity?&nbsp;<br>- What qualifies a tool or strategy as suitable for a particular task?</p>

<p>- Denominator: The bottom number of a fraction. Tells the number of parts the whole is divided into.&nbsp;<br>- Equivalent Fractions: Fractions that have different numerators and denominators but reduce to the same value.&nbsp;<br>- Fraction: Part of a whole. A number written with the bottom part (the denominator) telling you how many parts the whole is divided into, and the top part (the numerator) telling how many you have.&nbsp;<br>- Numerator: The top number of a fraction. Tells how many parts of the whole you have.</p>

<p>- One bag of mixed pattern blocks per pair of students<br>- Spinner for Pattern Block Fraction of a Set (M-3-3-3_Spinner for Pattern Block Fraction of a Set), one assembled spinner for each pair of students<br>30, two-colored counters for each student<br>- Divider to place between two students (two-pocket folders work well), one divider for each pair of students<br>- Math journal or scrap paper for students to write on<br>- Fraction of a Set Word Problems (M-3-3-3_Fraction of a Set Word Problems and KEY)<br>- Lucille Recht Penner. (2000). <i>Clean-Sweep Campers</i>. Kane Press.<br>- Loreen Leedy. (1996). <i>Fraction Action</i>. Holiday House.</p>

<p>- Assess the students' comprehension level by watching and probing them during the pair exercise.&nbsp;<br>- To further gauge students' conceptual understanding, go through their math journal entries.</p>

<p>Modeling, Active Participation, and Scaffolding&nbsp;<br>W: Having seen and worked with fractions of a whole, students will now learn about fractions of a set.&nbsp;<br>H: Read the book Clean-Sweep Campers to the class. After reading, have a discussion about the narrative and the tactics the kids employed.&nbsp;<br>E: Students will describe a set using pattern blocks, which have many distinctive features. They will also use different fractions for different attributes.&nbsp;<br>R: By describing pattern block sets to one another in pairs and using descriptive sentences about the percentage of blocks that are a particular color, size, shape, etc., students will get experience and practice.&nbsp;<br>E: Keep an eye out for opportunities to reroute students who appear confused and monitor student pairs for understanding. Ask students to summarize what they learned in their math journals.&nbsp;<br>T: You can use the Extension suggestions listed at the end of the lesson to modify it to fit the needs of your class. Use the Expansion activities to increase the difficulty of the lesson. The Small Group activity may require students to practice in smaller groups if they require more time.&nbsp;<br>O: Students will practice identifying which numerical fraction, and vice versa, corresponds to a model of a fraction of a set during this lesson. Allow students to use counters to experiment and "see" what the fraction should look like if they are having trouble calculating the correct fraction given the model.</p>

<p><strong>"Today we will continue our work with fractions. We'll be studying fractions of a set. We are going to play a fraction game after quickly reviewing the numerator and denominator."</strong><br><br>Give your students a reading of Lucille Recht Penner's <i>Clean-Sweep Campers</i> as an introduction. Look at the picture and talk about the kids' camp experience.<strong> "I want to read a book to you right now. Now let's take a look at the cover. What do you think our book will be about ?" </strong>Consider the book's predictions and recommendations from the students.<br><br><strong>"The book is called </strong><i><strong>Clean-Sweep Campers </strong></i><strong>by Lucille Recht Penner." </strong>If you are unable to find this book, Loreen Leedy's <i>Fraction Action</i> is a reliable substitute.<strong> "As we read the story, please take note of the methods the kids in the book use to get out of their problems."</strong><br><br>Ask students questions about the book and the groups of objects on each page as you read. Possible sample queries are as follows:<br><br><strong>"What did the book teach you?"</strong><br><strong>"What was the problem at the story's beginning?"</strong><br><strong>"What was the book's representation of fractions?"</strong><br><strong>"Give an example of equal sharing in the book. Explain."</strong><br><strong>"What happened at the end of the story?"</strong><br><br><strong>"We have been discussing fractions for some time now. Let's go over the parts of a written fraction again." </strong>On the board, write a fraction. Ask students to identify the fraction's components and explain what they mean.<br>&nbsp;<img src="https://storage.googleapis.com/worksheetzone/images/Screen Shot 2024-04-02 at 16.02.09.png" width="410" height="113"><br>Review or go over the definitions of the terms <i>denominator</i>, <i>numerator</i>, and <i>fraction bar</i>.<br><br><strong>Pattern Block Fraction of a Set Activity.</strong><br><br>To&nbsp;use it in your demonstration, prepare a spinner (M-3-3-3_Spinner for Pattern Block Fraction of a Set.docx) and gather some pattern blocks in a bag before the lesson. Tell the students, <strong>"Today, we will be discussing a portion of a set. First, let's look at some pattern blocks. I'm going to start spinning my wheel. I was able to decipher 6. I have to take six pattern blocks out of the bag."</strong><br><img src="https://storage.googleapis.com/worksheetzone/images/Screen Shot 2024-04-02 at 16.02.22.png" width="397" height="68"><br>Here are the pattern blocks taken from the bag:<br><br><strong>"This group of pattern blocks is mine.&nbsp;</strong><br><strong>"How many triangles are there?" </strong><i><strong>(3)</strong></i><br><strong>"Triangles make up three of the six."</strong><br><br>This is how we could write it:<br><br><strong>There are three triangles among the six.&nbsp;</strong><br><br><strong>or&nbsp;</strong><br><br><strong>3/6&nbsp;are triangles.&nbsp;</strong><br><br>Ask students to explain the remaining pieces in the set. Students can describe themselves using terms like color, size, shape, number of sides, etc. Make an effort to record every observation your students make in two or more different ways.&nbsp;<br><br>Examples of ways to write what students describe could include:<br><br>Two out of six shapes are orange.<br><br>Squares make up 2/6 of the set.<br><br>Two is ⅓ of six,&nbsp;or 2/6 of six.<br><br>Repackage the pattern blocks in the bag once students have had a chance to describe the set. Spin the spinner, pick out some blocks from the bag, and give several descriptions of the set as you repeat the procedure.<br><br>Divide the class into pairs once the students have completed the activity to give them one more step to complete. For each pair of students, provide one bag of pattern blocks and one spinner (M-3-3-3_Spinner for Pattern Block Fraction of a Set). Assign a divider to every pair as well. To prevent the two partners from seeing which pattern blocks are being taken out of the bag, a divider is positioned between them.<br><br><strong>"Maria, show the class what you can do by spinning the spinner."</strong> For instance, the student might say, <i>"My spinner is pointing at the four."</i><br><br><strong>"Now, take out four pattern blocks from your bag and arrange them on the divider's&nbsp;side. The rest of you must pay attention to the hints Maria gives you while she is working on this. Next, you will attempt to create a matching set of pattern blocks. You can ask her for as many hints as you require to complete the set."</strong><br><br>"My first clue is that one out of four shapes is yellow," Maria might then utter.<br><br>After grabbing a block, the students move it to their spot. "Three-fourths of the shapes have three sides," says Maria, providing yet another hint.<br><br>Abruptly, one of the students says, “I believe I understand what you have in your set. Do you have one yellow hexagon and three green triangles?”<br><img src="https://storage.googleapis.com/worksheetzone/images/Screen Shot 2024-04-02 at 16.45.28.png" width="258" height="72"><br>The class sees Maria's set, and other students check to see if they correctly identified the set of shapes.<strong> "At this point, you can start working with your partner."</strong><br><br>Through conversations and questions, as well as while they are working with partners on the Pattern Block Fraction of a Set Activity, you will have the chance to evaluate the students. To further elucidate understanding, students might need to be divided into small groups. Alternatively, you could evaluate student learning at a later date.<br><br>Here are a few examples of possible questions:<br><br><strong>"What have you observed regarding 2/3&nbsp;and 4/6?"</strong><br><strong>"Do you see any patterns?"</strong><br><strong>"How did you figure that was 3/4?"</strong><br><strong>"How would you write this set's fraction?"</strong><br><strong>"Do you believe that when there are more shapes, it becomes harder to figure out the set?"</strong><br><strong>"Which kind of hint provides you with the most details about the piece?"</strong><br><strong>"If my clue was that 1/2&nbsp;of the set is blue, how would you know how many shapes to place in your set?"</strong><br><strong>"Your set consists of ten shapes. What is 1/5 of 10?"</strong><br><br><strong>Extension:</strong><br><br><strong>Routine:</strong> Review this idea with students whenever there's a chance to explain a fraction of a set in the classroom. For instance, "Three markers are blue, and one is red. How many red markers are there in the set?" Or, "It appears that we have two partial sets and five complete sets of pattern blocks. "What proportion of the sets are full?"<br><br><strong>Small Group:</strong> Pack a bag with the red, yellow, orange, and green counters. Insert your hand and take out a tiny handful. Using fractions, have students describe the set. On little dry-erase boards, students can write their fractions.<br><br><strong>Workstation: </strong>Provide eight counters with two colors for each pair of students. Pupils dump the counters onto the table, count how many of each color there are, sketch the findings in their diaries, and write the fractions for each color. (See the illustration below.)<br><img src="https://storage.googleapis.com/worksheetzone/images/Screen Shot 2024-04-02 at 16.46.06.png" width="514" height="361"><br>Expansion Activity: Students who need a more challenging task can use the Fractions of a Set activity. Assign students to work on fraction-related problems. M-3-3-3_Fraction of a Set Word Problems and KEY&nbsp;are the Fraction of a Set Word Problems that you can use. Assign each student a single problem, then ask them to present their solutions to the class.<br><br>Expansion Activity: Students who want to go above and beyond the requirements can use the Number of a Set with Counters activity. Give students a task to complete with 30,&nbsp;two-colored&nbsp;counters. (At&nbsp;<a href="http://www.etacuisenaire.com/search/searchdisplay?type=keyword&amp;query=two-color+counters">http://www.etacuisenaire.com/search/searchdisplay?type=keyword&amp;query=two-color+</a>counters), you can find more details.&nbsp;Using the same structure as the equation below, write an equation on the board.<br><img src="https://storage.googleapis.com/worksheetzone/images/Screen Shot 2024-04-02 at 16.46.36.png" width="203" height="52"><br>The two-colored counters allow students to respond to your questions. Here are a few examples of questions to ask:<br><br><strong>"How many groups are required?"</strong><br><strong>"How many counters show 2/3 of 18?"</strong><br><strong>"In the equation, what number is missing?"</strong></p>