Sunshine State Standard

MA.A.1.2.2

Materials

-Pictures of skyscrapers (photos, posters, a video clip, multimedia) if needed -White paper -Fraction tower manipulatives -Black- or whiteboard -Chalk or markers (alternately, an overhead and markers can be used) -Comparing Fractions worksheet -Comparing More Fractions worksheet -Overhead transparencies of both worksheets -Pencils COPYRIGHTED MATERIALS USED Comparing Fractions worksheet (by Conrad Deitrick) Comparing More Fractions worksheet (by Conrad Deitrick) Fraction Tower™ Cubes by Learning Resources® Note- the two worksheets used were made by me. I will gladly send them by email, but they are fairly simple and should be able to be recreated based on their description in the activity.

What to do

1. Grade Level: Third Grade 2. Subject: Math 3. Topic: Number Sense and Operations 4. Unit Rationale: The third-grade student can identify and name fractions. They also know how to compare numbers using symbols for greater than, less than, and equal to, although they have never applied the concept to fractions. In this lesson, they will bring the two ideas together and compare fractions using concrete manipulatives. This is a useful skill in the real-world, with applications in cooking, automotive skills (comparing sizes of wrenches, nuts, and bolts), and anywhere the English system of measurement (i.e., inches, feet, cups, gallons, etc.) is used. Furthermore, it is a skill that will be used in later grades as students begin learning to add, subtract, convert, multiply, and divide fractions. 5. Unit Goal: The student will understand the relative size of commonly-used fractions with the aid of concrete manipulatives. 6. Coded FL SSS with written Grade Level Expectation: MA.A.1.2.2.3.3: The student compares and orders commonly used fractions, including halves, thirds, fourths, fifths, sixths, and eighths, using concrete materials. 7. Lesson Objective: Given concrete manipulatives, the third-grade student will compare commonly-used unlike fractions (halves, thirds, fourths, fifths, sixths, eighths, tenths, and twelfths) and correctly identify them as greater than, less than, or equal to other fractions. DETAILED PROCEDURES 1) Gain Attention • “Class, I want to talk about cities for a minute. Big cities. Who here has been to a big city?” Let students talk about big cities they have been to. • “Okay, what kinds of buildings are there in big cities?” Any answer will do, but aim towards the biggest buildings. • If students do not know the meaning of the word “skyscraper,” teach it to them. Show pictures if necessary. • “Now we are going to make a city of our own, with skyscrapers. Take out your fraction tower manipulatives, and I’ll take out mine. We’ll also each need a sheet of paper.” (get materials) “The paper is a map of our city, and we are going to fill it with buildings to make a skyline.” • “We’ll start with one very large building in the middle of town, like we have in Tallahassee. Who knows the name of that building? (the capitol) Take the biggest fraction piece, the one that says ‘1’ on the side, and put it in the middle of the paper.” (students follow along) • “Now, we want another building that is smaller. Make a building that is smaller than the first one, using any pieces you want. Put it anywhere you want.” Students and teacher do this. • “Okay, who wants to tell me what they used for their building?” • Students can volunteer to share their buildings. At this point, any explanation will do. “Mine is two green pieces high” is just as good as “mine is two-fifths.” If a building does not fit the specifications, ask the student to measure their buildings against each other. • “Now, let’s try to make a building that is taller than the one we just made, but still smaller than the first one.” • Again, ask students to tell about their buildings. • Continue the process for two or three more buildings. It may be fun to have students vote on whether the next building should be shorter or taller than the previous one. They can act as a “zoning board.” • Every student’s city will look different. This is fine. 2) Check Prior Knowledge • Hold up a 1/3 piece of a fraction tower • “Who can tell me how much this is?” point to the number. • “Good.” Add another 1/3 piece. “Now, how much is this second piece? How many are they altogether? Can someone come write that on the board (or overhead) for me?” • Repeat with as needed with other pieces from the fraction tower set. • Ask students if any of them remember what “greater than” means, and what the symbol for it is. Discuss, and write examples on the board. • Repeat for “less than.” • Repeat for “equal to.” 3) State Objectives • Today we’re going to talk about fractions, and we’re going to compare them. By the end of our lesson, you will be able to tell me which fractions are greater than, less than, or equal to other fractions. 4) Present New Information with Examples a) Teacher Led Activity 1 • Hold up the last fraction piece used in the Check Prior Knowledge event. • “Now we are going to start comparing fractions. We will start with this piece (e.g., one third). Now, we need another piece to compare it to.” • Call on a student to pick a piece from the set to compare (e.g., one fifth). • “Now, everyone hold up one third and one fifth.” • “Are they the same? How do we know? Which is larger? Which is smaller?” • “Who can show me how to write this on the board using the ‘greater than’ symbol?” • “Now, let’s take more than one of the same kind of piece and put them together, like we did when we were making a city.” Ask for student suggestions. • “And then we need something to compare it to. Let’s pick two of the same piece again, but a different piece this time.” Ask for student suggestions. • “Everyone make two towers like the ones I’m holding now.” • “Are they the same? How do we know? Which is larger? Which is smaller?” • “Who can show me how to write this on the board using the ‘less than’ symbol?” • “Now we’re going to get a little bit crazy. We’re going to take one kind of fraction piece and put as many of them together as we want to. Then, we’re going to take another kind and put together as many as we want to.” Again, ask for student suggestions. • Again, “Everyone make two towers like the ones I’m holding now.” • “Are they the same? How do we know? Is one larger? Is one smaller?” • Hold up one tower. “Who can tell me the name of this fraction? Can you write it on the board?” • Hold up the second tower. “Now, who can tell me the name of the fraction that these pieces make? Can you write it on the board?” • “Who can compare these two numbers on the board using greater then, less than, or equal to symbols?” • Repeat the process as necessary with different fractions made with the fraction tower pieces, b) Teacher Led Activity 2 • “Let’s go back to the city we were making. We started with a building made of one kind of fraction tower piece. Who can tell me what it was?” • “Good, now what was the second building we made? Can anyone remember? What was the name of that fraction?” (e.g., 2/3) • Hold up both towers, and have the class follow along with their own manipulatives. • “Which one is larger?” • Put the first one (the whole) away for the moment. Invite the class to do the same. • Turn on the overhead and draw a table, with columns for greater than, less than, and equal to (using the symbols as well as the words). • “Now, starting with this second tower, we’re going to try to make as many fractions as we can that are the same height as 2/3. Please use only the same colors together; don’t mix different types of fractions together right now. We’ll be doing that next year.” • Give the students time to try to make equivalent towers. This could take more time than one would expect, but it gives them a chance to do some comparing and discovery on their own while still participating in a teacher-led activity. • “Who was able to make towers that were the same height as 2/3?” Ask for volunteers to share. With one, if it is correct, write it on the table in the equal-to column as an expression, e.g., 4/6=2/3. • Repeat with fractions greater than and then less than the original tower. Maximum student participation is desirable here. There are numerous possible answers for each column, so every student should have a chance to participate at least once. 5) Provide Practice & Feedback a) Student Centered Activity 1 • Group students into pairs. • “Now we’re going to practice comparing fractions on paper. I want you all to use your fraction towers to help you find the answers.” • Pass out Comparing Fractions worksheet. • “For each set of fractions, make a tower using your fraction tower set, compare them, and write the symbols for greater than, less than, or equal to in the empty square between them.” • Put a copy of the worksheet on the overhead projector. Work through the first problem on the worksheet as an entire class so they can see an example of what needs to be done. Work the second problem as well if absolutely necessary, but leave the rest for students to do in their groups. • Have students complete the assignment together (in pairs). • Move around the room, giving brief feedback and assistance (as needed) to the students as they work. b) Student Centered Activity 2 • Leave the students in pairs, or group them in new pairs, as appropriate. • “Remember when we made the table of fractions that were greater than, less than, or equal to our fraction tower? We’re going to do that again, but now you’re going to be able to do it on your own.” • Pass out Comparing More Fractions worksheet (one to each pair). • “Each group needs to make a fraction using the fraction tower using one of your sets of manipulatives. Any fraction and any height, but it should be made of just one color or type of fraction. We’re still not mixing them up yet.” • Put the overhead transparency of “Comparing More Fractions” on the overhead. • Allow the students time to make a fraction. • “Now, write your fraction down in the box where it says ‘Our Magic Fraction.’” • “When everyone is finished with that, I would like each group to take their fraction towers and find as many fractions as they can that are larger than their Magic Fraction. They will write them all down in the column beneath where it says ‘fractions that are greater than our magic fraction.” Point out the appropriate column on the overhead. • “I would also like each group to take their fraction towers and find as many fractions as they can that are equal to their Magic Fraction. They will write them all down in the column beneath where it says ‘fractions that are equal to our magic fraction.” Point out the appropriate column on the overhead. • “Finally, I would also like each group to take their fraction towers and find as many fractions as they can that are smaller than their Magic Fraction. They will write them all down in the column beneath where it says ‘fractions that are less than our magic fraction.” Point out the appropriate column on the overhead. • Illustrate what the students should do by showing an example on the overhead worksheet. • Have students complete the assignment together (in pairs). • Move around the room, giving brief feedback and assistance (as needed) to the students as they work. 6) Present Summary or Review • “Let’s go back to our city now. We made a city together at the beginning of the lesson, but during the lesson we learned some more about comparing fractions. Let’s see how we do with another city when I give more detailed instructions.” • Have the students put everything else away, get out their piece of paper again, and their fraction tower set. • “We need to start with one tall building. Can someone suggest just how tall our building should be by naming a fraction that we might have used already today?” Give students a chance to respond. Choose a relatively small fraction. Allow students to set up their building anywhere they want on their “city.” • “Good. Now I want our second building to be greater than our first building. Can anyone name a fraction that is greater than this first one. You can use your manipulatives to measure and see.” Allow students to respond, encouraging them to state the name of the fraction rather than describing the manipulatives by size or color. • Have students construct and place the new “building” in the city. • “Excellent. Now for our third building, I want another building that is equal to the last one. Who can make a building that is equal to the last one, and then tell me the fraction that it stands for.” Allow students to respond, encouraging them to state the name of the fraction rather than describing the manipulatives by size or color. • Have students construct and place the new “building” in the city. • Last, I want a building that is less than the last two. Who can make a building that is less than to the last two, and then tell me the fraction that it stands for.” Allow students to respond, encouraging them to state the name of the fraction rather than describing the manipulatives by size or color. • Conclude by asking questions. “Which building is the tallest? What is it’s fraction? Which building is the smallest? What fraction is it? Are any of the buildings the same? Which ones? What are their fractions? What do we call two numbers that are the same?” FORMAL ASSESSMENT For a formal assessment, the students would be given a paper-and-pencil test that resembled the Comparing Fractions worksheet. They would work alone, not in groups, but they would still be able to use fraction tower manipulatives.

Additional Information

This lesson plan template has been designed to embed the Six Instructional Events named by Robert Reiser & Walter Dick . The lesson plan template is ©2004 by J. Converso.

Submitted by

Conrad Deitrick

Leon County
Tallahassee, Florida
conrad.deitrick@us.army.mil