<p>Students will study the concept of equivalent fractions. Students are going to:<br>- Use area models to investigate fractions (circles, rectangles, pattern blocks, etc.).<br>- Use sets to investigate fractions (chips).<br>- Use lengths to investigate fractions (fraction strips).<br>When presented symbolically, concepts can be confusing, so models aid students in understanding them.</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>- Seven different colored strips of paper that measure 2" × 8" per student<br>- (M-3-3-2_Color Fraction Strips) or the Blank Fraction Strips sheet (M-3-3-2_Blank Fraction Strips)<br>scissors<br>- Math journal or scrap paper for students to write on<br>- One set of fraction strips for each student (M-3-3-2_Color Fraction Strips)<br>- Envelopes, one for each student to store fraction strips<br>- Dry-erase boards and markers<br>- Fractions 3-in-a-Row (M-3-3-2_Fractions 3-in-a-Row Game Board)<br>- Paperclips for spinners<br>- Two different-colored markers (or centimeter cubes, disks, etc.); 15 of each color<br>- spinner for each player<br>- copies of the Spin, Spin, and Compare Recording Sheet (M-3-3-2_Spin, Spin, and Compare Recording Sheet)<br>- divider to place between two students (two-pocket folders work well)<br>- Stuart J. Murphy. (1998).<i> Jump, Kangaroo, Jump!</i> HarperCollins Publishers.<br>- Jerry Pallotta. (2003). <i>Apple Fractions.</i> Cartwheel.<br>- Jerry Pallotta and Robert C. Bolster. (2007). <i>Pizza Fractions.</i> Scholastic.</p>

<p>- As the students work in pairs, keep an eye on them and probe to find out how much they understand.&nbsp;<br>- Examine students' math journal entries to gauge their understanding of the concepts covered in this lesson.</p>

<p>Explicit instruction, modeling, scaffolding, and active engagement&nbsp;<br>W: Describe a fraction strip to the class and let them know that they will be creating one in order to compare various fractions and come to conclusions.&nbsp;<br>H: Tell the class about the book Jump, Kangaroo, Jump! and have a discussion about the tale. Involve students in the fractions story to get them excited about the lesson.&nbsp;<br>E: Use the Fraction Strips Activity to get students experimenting with fractions. This practice is particularly useful in helping students understand how two fractions with different denominators can represent the same amount. It also serves to reinforce the idea that all parts of a whole must be equivalent.&nbsp;<br>R: While students are examining fraction strips, keep an eye on them and pose questions. Use leading questions to elicit conclusions about equivalency, etc., if needed.&nbsp;<br>E: Talk to the class about the student fraction-strip observations. Ask pupils to write down in their math journals what they have learned about fraction strips and fractions.&nbsp;<br>T: Adapt the lesson using the ideas in the lesson's Extension section to fit the needs of your students. Students who would benefit from more practice or direction should use the Small Group section. Students seeking a challenge beyond the required coursework may find the Expansion section helpful. Throughout the year, the class may utilize the Routine section as a refresher on the lesson's concepts.&nbsp;<br>O: By using fraction strips, teachers can introduce students to equivalent fractions and common denominators visually. With the help of manipulatives, students must find equivalent fractions in the optional 3-in-a-Row activity.</p>

<p><strong>"We're going to carry on with our fractions work today. Fraction strips are what we're going to make. We'll use them to play a fraction game and make observations about fractions."&nbsp;</strong><br><br>Give your students a reading assignment that involves the book Jump, Kangaroo, Jump! by Stuart J. Murphy. Examine the images and discuss each page's contents.<br><br><strong>"I'd like to read you a book before I give you a problem to solve. Now let's look at the cover. What do you think our book will be about?"</strong> Consider the book's predictions and recommendations from the students. <strong>"The book is called Stuart J. Murphy's Jump, Kangaroo, Jump! Please take note of the methods the kids in the book use to solve their issues as we read the story."</strong><br><br>While reading, quiz students on the book and various groupings of objects on each page. Some examples of questions to ask would be:<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>Fraction Strips Activity</strong><br><br>Enable students to create their own&nbsp;fraction strips (M-3-3-2_Blank Fraction Strips) or make copies of the provided color fraction strips page (M-3-3-2_Color Fraction Strips). Give the students the fractions to cut apart. The One Whole is the only fraction strip that shouldn't be cut. For future lessons, tell students to write their initials on the back of the fraction strips so they can keep them.<br><br><strong>"We've all made a unique set of fraction strips. We'll be using the fraction strips all year. I'll give you some time to work with your fraction strips. If you'd like, you and your neighbor can put your pieces together and investigate the fraction strips. Take particular note of any patterns you observe. For example, can you represent the same fraction in more than one way? What is true about fractions that are larger than 1/2? What about fractions that are smaller than 1/2? In a short while, I'll ask you to stop so we can gather and talk about your observations."</strong><br><br>You might want to give students ten to fifteen minutes to explore. Permit students to present observations they came up with while using the fraction strips.<br><br><strong>"In your math journal, jot down some observations you made. What connections did you make? Why did it surprise you? Were there any relationships that you noticed?"</strong> Allow students to record their observations in writing for approximately five minutes. Fraction strips are a useful tool for some students to help them make sense of what they are thinking when writing. Approach student groups and request explanations of their work. Make sure that everything is clear.<br><br><strong>"Please share a few of your observations."</strong><br><br>(<i>"Tom and I discovered that there are lots of ways to make 1/2. On our desks, we placed the 1/2 fraction strip. Then we placed smaller fraction strips on top of the 1/2. We discovered that the 1/2 is the same size when two 1/4s are stacked on top of it."</i>)<br><br><strong>"So, and&nbsp;are equivalent? Is that what you mean?"&nbsp;</strong><br><br>(<i>"Yes. Furthermore, we discovered that and are identical to"</i>)<br><br>Let students present their findings as you carry on the conversation. Several examples of questions to ask could be:<br><br><strong>"How many sixteenths would be in 1/2?" </strong>(<i>8</i>)&nbsp;<br><strong>"If we say two fractions are equivalent, what does that mean?"</strong> (<i>Two fractions can denote the same component of an object or have the same value.</i>)&nbsp;<br><strong>"How can you determine whether two fractions are equivalent using your fraction strips?"</strong> (<i>To check whether two strips are the same size, place one smaller strip on top of the other.</i>)&nbsp;<br><strong>"What trends have you observed?"&nbsp;</strong><br><strong>"How do we write equivalent fractions?" </strong>(<i>Use the equals symbol. For instance, 1/2 = 2/4</i>)&nbsp;<br><strong>"To name a fraction larger than 1/2, use 1/6&nbsp;or 1/12&nbsp;strips. Next, give the name of one that is smaller than 1/2." </strong>(<i>When writing comparisons of 1/2&nbsp;&lt;&nbsp;6/8 or 9/12 &gt; 1/2, use the comparison symbols</i>.)<br><br><strong>"I will hand out an envelope to everyone since we will be using our fraction strips throughout the year. Put your fraction strips inside the envelope, and please write your name on the outside."</strong><br><br>Students' exploration of the fraction strips, as well as discussions and questions, will provide you with opportunities to assess them. It might be necessary to divide the class into smaller groups in order to better clarify the material.<br><br>Here are a few examples of sample questions:<br><br><strong>"Are the two fractions the same? Explain."</strong><br><strong>"What have you observed regarding and?"</strong><br><strong>"What trends have you observed?"</strong><br><strong>"How are you finding equivalent fractions with the help of the fraction strips?"</strong><br><br>Invite students to share their thought processes. Emphasize the equivalency of various representations when students present their answers.<br><br><strong>Extension:</strong><br><br><strong>Routine:</strong> Provide students with hints to locate equivalent fractions by using the Guess My Equivalent Fraction Activity. Declare, <strong>"I am comparable to... 8 is my denominator. "</strong> After hearing the spoken cues, students utilize their fraction strips to determine the matching fraction. As time permits, repeat. For the class to see, students can also invent their&nbsp;clues.<br><br>Each student should receive a spinner (M-3-3-2_Fractions 3-in-a-Row Game Board) and a paper clip to use with the spinner in small groups. Additionally, each student will require a Spin, Spin, and Compare recording sheet (M-3-3-2_Spin, Spin, and Compare Recording Sheet) and one set of fraction strips (M-3-3-2_Color Fraction Strips). Choose your player.<br><br>Use the fraction strips to create the fraction after Player 1 spins the spinner.<br><br>Use the fraction strips to create the fraction after Player 2 spins the spinner.<br><br>Both participants compare the two sets of fraction strips. Both players receive one point if the fractions are equal. The player with the larger fraction receives one point if the fractions are not equivalent. After ten rounds, the player with the most points wins. On the recording sheet, students should write equations in turns.<br><br><strong>Workstation:</strong> Give a Fractions 3-in-a-Row game board (M-3-3-2_Fractions 3-in-a-Row Game Board) and a paperclip for the spinner to each workstation. Additionally, you'll need to set up two distinct colored counters (centimeter cubes, disks, etc.) at each workstation, with fifteen of each color, along with a sheet or poster that contains the game's rules:<br><br>1. Every participant selects a unique set of colored markers. Choose a player to go first.<br>2. The first player spins the spinner. Check out the spinner's fraction. On the game board, locate a comparable fraction. The player gets to put their counter on the game board if the spinner and the game board have equivalent fractions on them.<br>3. Player 2 now plays.<br>4. Players forfeit their turn if they are unable to find an equivalent fraction. One of a player's markers is taken off the board if they are unable to identify equivalent fractions. Play moves on to the next player if there are no markers left on the game board.<br>5. The victor is the first person to get three markers in a row.<br><br><strong>Expansion: </strong>Use the overhead projector to display a fraction for students who are working beyond the curriculum. Using their fraction strips, students must identify at least two equivalent fractions, and they must write equalities to demonstrate their work.<br><br><img src="https://storage.googleapis.com/worksheetzone/images/Screen Shot 2024-04-02 at 15.56.59.png" width="594" height="146"><br><br>On the dry-erase boards, students can write equations.<br><br><img src="https://storage.googleapis.com/worksheetzone/images/Screen Shot 2024-04-02 at 15.57.09.png" width="497" height="41"></p>