Equivalent+Fractions

__Title__: Matching Equivalent Fractions

__IEP Objective__: When given a “matching” worksheet the student will match equivalent simple fractions with 80% accuracy, four out of five times.

__Sunshine State Standard__: MA.4.A.6.3 – Generate equivalent fractions and simplify fractions.

I. __Lesson Objective__ Given a “matching” worksheet, students will match equivalent fractions with 80% accuracy by drawing graphical representations of each fraction.

II. __Procedures__ __ Opening __ //Gain Attention//: Using a PowerPoint slide project the text “I’m hungry! How do I know if I’m getting the same amount of pizza?” along with a picture of a delicious pizza. //Present Overview//: Make the PowerPoint slide go white by pressing “w” after the students have had sufficient time to read the slide, but before presenting the overview. “Today we will learn what ‘equivalent fractions’ are and how we can identify fractions that are equal to each other by drawing pictures.” //Share Rational//: Display the PowerPoint slide by pressing “w” again. “Pizzas are cut into slices, right? We’ve seen before, that if you eat a certain amount of slices out of a pizza, you eat a fraction of the pizza. Sometimes pizzas that are the same size are cut into different numbers of slices. If two pizzas of the same size are cut into different numbers of slices, how do you know how many slices you need to eat to get the same amount of pizza? You can solve this problem, and others like it, if you understand equivalent fractions!” //Review//: Make the PowerPoint slide go white by pressing “w" before moving on. Ask students to define a fraction (“how many parts we have out of a whole”), a numerator (“the top number, or how many parts we have”), and a denominator (“the bottom number, or how many parts make up a whole”). On the board write down the fraction “2/6” and ask students to identify which number shows how many parts are in the whole. Point to the correct answer.

__ Body __ 1. Define “equivalent fractions” as “fractions that use different numbers to represent that same value, or amount.” Ask students, “What part of the word ‘equivalent’ clues you in to what the word means?” (equ- is the beginning of the word “equal”) 2. Graphically show an example of equivalent fractions. On a PowerPoint slide show a bar cut into two sections, with one of the sections shaded. Point out that, “The bar is cut into two parts and one part is shaded in. This represents the fraction 1/2.” Using the “animations” feature, add dashed lines to cut each section into two. Emphasize that, “The whole is now cut into four pieces rather than two. This represents the fraction 2/4. Yet, the bar is still the same size and the same amount is shaded in. Are the two fractions equal?” (yes) 3. Display another slide that shows 1/2 and 2/4 numerically, with an equal sign between them, as well as graphical representations below. Emphasize that the fractions represent the same value and are equivalent. Ask students, “How does the picture help us understand that the fractions are equivalent?” (The shaded areas are the same size.) 4. Follow the same steps to graphically show a pizza starting as 1/4 and transitioning to 2/8. Ask students, “If the whole stays the same size, what must happen to the size of each part as we divide the whole into more parts?” Clarify that if the whole (or pizza) stays the same size, but we cut it into more parts (or slices), then the parts (or slices) must get smaller. 5. Display another slide that shows 1/4 and 2/8 numerically, with an equal sign between them, and graphical representations below. Emphasize that the fractions represent the same value and are equivalent. 6. Close the PowerPoint and show the same concept on the white board by drawing bars and circles to represent different equivalent fractions (2/5=4/10, 1/3 = 2/6 = 4/12). Be sure to take the students step by step and model how they should draw their own graphical representations. Label each bar or circle with the appropriate numerical representation as you go along.

__ Guided Practice __ 1. Write two columns of fractions on the board. There should be equivalent fractions in each column.
 * 1/2 || 2/6 ||
 * 1/3 || 3/6 ||
 * 3/4 || 4/6 ||
 * 2/3 || 6/8 ||

2. Model how the students should approach their independent practice by drawing a graphical representation of each fraction in the first column next to its numerical representation. (Students should already be familiar with this process from previous experience with fractions.) Ask students questions like “How many parts should this whole have?” and “How many parts should I shade in?” 3. Starting with 1/2 and going down the first column in sequence, model how to cut each part into more parts until you know which fraction in the second column is equivalent. Draw lines between equivalent fractions. 4. Repeat this process with a new set of numbers (see below) but instead of modeling how to draw pictures, ask students to come up to the board and divide and shade each previously outlined bar/circle themselves. Then ask students to come up and divide each part into more parts and draw lines between equivalent fractions.
 * 3/5 || 4/4 ||
 * 3/3 || 4/6 ||
 * 2/3 || 6/10 ||
 * 1/4 || 2/8 ||

__ Closure __ Tell students that they will go through the same exact same process in their independent practice. Ask one student to summarize the lesson by defining “equivalent fractions.” Allow for varied responses such as “fractions that show the same value,” “fractions that have more parts but are equal,” “fractions that have smaller parts but the same sized whole,” etc. until a complete definition has been given.

__ Independent Practice __ Hand out worksheets that have columns of equivalent fractions to match and empty bars and circles for students to divide and shade. Worksheet will be graded as evaluation.

III. __Questions__ · What is a fraction? (low level) · Which number shows how many parts are in a whole? (low level) · What part of the word ‘equivalent’ clues you in to what the word means? (high level) · If the whole stays the same size, what must happen to the size of each part as we divide the whole into more parts? (high level) · How many parts should this whole have? (low level) · Divide the bar/circle into ­[#] equal parts. (low level) · How many parts should I shade in? (low level) · Shade the correct amount of parts to represent [#/#]. (low level) · Did [name] represent the fraction correctly? How do you know? (high level) · Are the fractions equivalent? (high level) · How do you know that the fractions are equivalent? (high level)

IV. __Feedback__ //__ Correct response __// “That’s right [name], the denominator tells us how many parts make up a whole.” “You did a good job dividing the bar into five equal parts, [name].” //__ Incorrect response __// “Which number tells you how many parts to divide the circle in?” “Are you sure the fractions represent the same amount?” “Look at the picture we drew.”

V. __Materials__ PowerPoint software Computer, projector, and screen White board and dry erase markers Worksheet for each student

VI. __Evaluation__ If 40% of students complete worksheet with less than 80% accuracy, teacher will re-teach the lesson to the entire class and students will be re-evaluated. After 60% of the class reaches the objective, each student that did not reach 80% on the most recent evaluation will be assigned to the computer center during centers time to complete supplemental activities (described below) and then re-evaluated. If one or more students still do not reach objective in the most recent evaluation, the teacher will perform a small group re-teaching of the lesson during centers time and re-evaluate students until everyone reaches 80% accuracy.

VII. __Modifications/Adaptations__ During guided practice tell students that you will ask them to do a certain task (such as divide the bar into 3rds) ahead of time so they can be prepared when called on. Students that require more time to complete the problems will only have to complete one side of the worksheet (they choose which side) or can take the worksheet home to finish.

VIII. __Integration of Technology__ The computer center activity will include two related websites activities from which students can choose. [] This website allows students to graphically create equivalent fractions. Students can create two equivalent fractions for an automatically generated fraction or create three equivalent fractions on their own. [] This website allows students to choose which fraction is not equivalent. It has four levels of difficulty from which the student can choose.

Some aspects of this lesson plan were borrowed from: Bryan, Betty. (2010). Equivalent fractions lesson plan. Retrieved September 29, 2010 from CPALMS website: []

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