3rd Grade Fractions Unit Plan

Overview

Unit Objective SWBAT identify fractions as wholes and parts through pictures, models, and numbers and compare these identities with fractions of like denominators and those that are equivalent before performing mathematical operations on them.

Description of teachings in unit Fractions can be a complicated mathematical concept to understand and therefore, instruction must be thorough, explicit, and purposeful. The educator should supply children with meaningful practice and allow them to explore fractions through a variety of manipulative and pictorial representations for better mastery of the subject. With this being said, the teachings within this unit begin with the foundations of fractions in the sense of the meaning, parts, and the message they convey to the learner. Within the introductory set of lessons to teach fractions, students will be introduced to basic fractions including one half, one third, one fourth, one fifth, one sixth, one eighth, one tenth, and one twelfth. They will explore these fractions through the construction of their models and practice in identifying them in real contexts. To further students’ study of fractions, they will begin comparing them to one another with like numerator, denominators and as equivalents. These lessons are highlighted below and overall will be instructed through student centered activities of comparing fractions with greater and less than symbols and creating equivalent ones through multiplication. The capstone teaching in this unit will be comparing fractions with different numerators and denominators to assist students in addition and subtraction of fractions. Students must have an understanding before doing any operations with fractions, their sizes and in comparison to one another, as well as their equivalency to other fractions. Addressing fractions with unlike numerators and denominators is crucial as in real contexts; this is the way they appear. Furthermore, exploring unlike fractions provide the opportunity to instruct on finding a lowest common denominator which will also be used when students practice adding and subtracting fractions. All lessons employ unique instruction that had hands on practice and applications for students so as to better understand fractions in our daily lives.

Lesson Plans

Introduction The following lessons would be capstone lessons to the unit on fractions. These lessons come at the end of the unit as they require the foundational understandings of fractions as parts from holes and identifying fractions pictorially and numerically. These concepts should be taught at the beginning of the unit so that students are developmentally prepared to manipulate and compare fractions as in the lessons that follow.

Lesson 1- Comparing Fractions with Like Denominators Standards: Number and Operations—Fractions 3.NF

3. Explain equivalence of fractions in special cases, and comparefractions by reasoning about their size. d. Compare two fractions with the same numerator or the same

denominator by reasoning about their size. Recognize thatcomparisons are valid only when the two fractions refer to thesame whole. Record the results of comparisons with the symbols>, =, or <, and justify the conclusions, e.g., by using a visualfraction model.

Objectives: SWBAT compare and order fractions with like denominatorsTLWD comprehension and application of ordering fractions with like denominators by recognizing their numerical amounts as being greater than, less than or equal to one another.

Procedure: 1. Review with students the meanings of the numerator and denominator. What does each one tell? Identify with an example. It may help to write a fraction on the board (3/8) and label each part. (Numerator- tells how many fractional pieces there are. The fraction 3/8 indicates that there are three pieces.)(Denominator- tells how many pieces an object was divided into. The fraction 3/8 indicates that the whole object was divided into 8 pieces.)

2. Draw a representation of the wholes of two fractions with the same denominator and the fraction written underneath it. For practice, call on a student for each fraction to shade in the regions to make the fraction true. (i.e. draw a box with four regions and under one box write one fourth, under the other box write three fourths.)

3. Ask student to study the picture and choose the figure that has more space shaded in or the greater fraction. Call on a student to show which fraction is greater by putting in a greater than or less than symbol (>,<).

4. Repeat processes 2 and 3 two to three more times with different fractions. After a few trials, ask students what they observed about fractions with like denominators. You should be looking to see if students grasped the understanding that if two fractions have the same denominator, then the fraction with the largest numerator is the larger of the two fractions. Show this by erasing the denominators of the fractions you practiced shading with and ask if the greater then, less than and equal to signs still apply.

5. Further explain to students that this is so with your first example. Between 3/8 and 5/8, 5/8 is larger because out of eight pieces, five of them are accounted for as opposed to only three.

6. to have students practicing ordering fractions now that they know a method to finding whether they are greater than or less than one another, assign every student a denominator in which they must order on a number line or sentence strip. (i.e.: you assign a student with the denominator 5, so he/ she will order fractions 1/5, 2/5, 3/5, 4/5, 5/5, 6/5, 7/5, etc. up to ten in the numerator on a number line to be displayed in the front of the classroom.)

7. While students work on these lines, assess their understanding by asking how they are ordering their fractions. You should be looking for them to respond with consideration of the numerator and organizing them from least to greatest.

8. Extend students practice with the worksheet from the link that students will complete independently at their desks or if time does not permit this, for homework. - http://prek-8.com/3rdgrade/fractionCompare5.html

Assessment: Students will be assessed based on whether they ordered their fractions correctly on their number line/ sentence strip and could explain orally to you when going around the method for ordering this way being the consideration of greater or less than numerators. Accuracies on the worksheet will also be noted as an informal assessment.

Lesson 2- Comparing Fractions with like Numerators, Unlike DenominatorsStandards: Number and Operations—Fractions 3.NF

3. Explain equivalence of fractions in special cases, and comparefractions by reasoning about their size.

d. Compare two fractions with the same numerator or the samedenominator by reasoning about their size. Recognize thatcomparisons are valid only when the two fractions refer to thesame whole. Record the results of comparisons with the symbols>, =, or <, and justify the conclusions, e.g., by using a visualfraction model.

Objectives: SWBAT compare and order fractions with like numeratorsTLWD comprehension and application of ordering and comparing fractions with like numerators through recognition of their greater than, less than or equal sizes.

Procedure: 1. Review with students again review the meanings of the numerator and denominator. What does each one tell? Identify with an example. It may help to write a fraction on the board (3/8) and label each part. (Numerator- tells how many fractional pieces there are. The fraction 3/8 indicates that there are three pieces.)(Denominator- tells how many pieces an object was divided into. The fraction 3/8 indicates that the whole object was divided into 8 pieces.)

2. Review from yesterday that to find the greater of two fractions with the same denominator, you simply consider the number that is greater in the numerator because it states the number considered out of how many total parts.

3. On the over head projector, have a transparency of one fractional model (i.e. a circle) with the same numerator but a different denominator as another transparency (depicted by shaded regions, etc). Make sure that the fraction is written underneath the picture and that both picture and fraction are in two different colors.

4. Show them separately and survey student to see which one they think will be greater.

5. Place the transparencies over one another and have children see which color there is more of than the other.

6. Repeat this with different fractions and slowly work to seeing the two fractions separately, rather than overlapping one another. Have students continuing shading regions of overhead practice problems to solidify their understandings of fractional parts.

7. Finally, ask students what they observe. Students should be noticing that if the numerators of two fractions are the same, the fraction with the smaller denominator is the greater of the two. Explain that this is so because there are fewer holes to fill in pieces of. (I.e. 5/8 is larger than 5/16 because each fraction

says there are five pieces but if an object is divided into 8 pieces, each piece will be larger than if the object were divided into 16 pieces. Therefore, five larger pieces are more than five smaller pieces.)

8. Have students deal out fraction card to one another as if they were playing a card game. Students will alternate putting down a card of a fraction and the other student must put down a card higher than the one their opponent has put down. They must have the same numerator. The person with the most cards in the end wins. After a few rounds allow students to compete with same numerators and same denominators to practice comparing fractions with same denominator.

9. Students will complete a worksheet similar to the one in the previous lesson only with same numerators as independent class work practice or for homework.

Assessment: While students are playing the card game, walk around and ask the winner of the round how they knew they were the winner. The students should be able to respond that they knew they won because their denominator was smaller and thus their whole was divided into larger pieces. Also use the worksheet as an informal assessment and to check for accuracies in their work.

Lesson 3- Identifying equivalent FractionsStandards: Number and Operations—Fractions 3.NF

3. Explain equivalence of fractions in special cases, and comparefractions by reasoning about their size.

a. Understand two fractions as equivalent (equal) if they are thesame size, or the same point on a number line.b. Recognize and generate simple equivalent fractions, e.g., 1/2 =2/4, 4/6 = 2/3). Explain why the fractions are equivalent, e.g., byusing a visual fraction model.

Objectives: SWBAT identify and create equivalent fractionsTLWD comprehension and application of creating equivalent fractions with a student inquired method.

Procedure: 1. Tell students that today you will be in search of equivalent fractions and that equivalent fractions are fractions that have the same value or represent that same part of an object.

2. Students will be instructed to find fractions equivalent to one half. Tell students that they are to use fractions stacks and remove the one half stack and measure up all other stacks to the same height as one half.

3. Have the students record the fractions they have made from the stacks. 4. Gather students together to list the equivalent fractions that they found.5. Ask students if they notice anything about the fractions they listed to one half.

What is similar/dissimilar? Some students will see that whatever the numerator is multiplied by, the denominator is too by the same number.

6. Clarify and explain that fractions are equivalent when the numerator and denominator of one fraction are multiplied by the same number. Demonstrate this with all fractions equivalent to one half.

7. Put up another fraction (ie. one third or one fourth) and ask students to come up one by one and put an equivalent fraction for the fraction you have chosen. Instruct

them to not repeat any. After all students have had a turn, go through them and ask the child who wrote it why it is an equivalent fraction. What did they multiply the numerator and denominator by?

7. Have students with a partner play the equivalent fractions matching game. It is similar to memory but including remembering where each fraction was, they must also decide if the cards that they over turn are equivalent. http://www.superteacherworksheets.com/fractions/fractions-matching-game.pdf

8. For classwork or homework, students should work independently on the equivalent fractions worksheet where they must complete the missing fractions part to make it equivalent to the other. http://www.superteacherworksheets.com/fractions/equivalent-fractions.pdf

Assessment: Assess students informally as they play the game, by glancing at their cards and questioning them as to why the cards they matched were equivalent. Ask how they found their equivalency. You will know that students understand the concepts of equivalent fractions if they tell you they have found them through multiplying the numerator and denominator by the same number.

Unit Assessment

Description of assessment design The assessment was designed for students to showcase their mastered skills of the concepts of fractions that were instructed throughout the unit. The assessment begins with introductory questions to fractions including what they mean mathematically, identifying parts within wholes, and writing fractions properly with attention to the numerator and denominator. The problems through which students will demonstrate their mastery of this will be similar to the ones they have been given in homework or as class work. The purpose of any assessment is not to surprise students with new information. Thus the problems in this exam have children performing similar procedures to what they have done before. As the test progresses, problems become more complex just as in unit. Toward the middle of the test, students will practice concepts highlighted in the plans for this lesson: comparing fractions with like denominators and numerators and finding equivalent fractions. Students will be tested on this material in a similar way it was practiced. Students will compare fractions using greater than or less than symbols and will be asked how to find which fraction is greater for same denominator and same numerators. Also, students will have to explain how they find equivalent fractions, make them and determine if the ones given are equivalent. The final few components of the exam will consist of performing operations of addition and subtraction after solving problems that compared fractions with unlike denominators and unlike numerators. The test is structured so so that students could practice finding common denominators before using the information and method to solve. Students will perform comparing fractions with unlike numerator and denominators using greater than and less than symbols. They must also explain what a common denominator and show how to find one between two uncommon fractions. Using these tools, they must them solve addition and subtraction problems of fractions. Connection to Unit ObjectiveThe assessment connects to unit objectives as students are asked to identify fractions through representations and extend understanding of fractions by applying their knowledge of them to

compare them to one another, find their equivalencies and perform mathematical operations with them.

Specific criteria for assessment The assessment is composed of questions that cause students to explain their methods and processes for solving. This is important to ask so that the educator is aware of children’s methods as being effective or ineffective. Hence, in this assessment, students are asked explicitly how to compare fractions with like/ unlike numerators and denominators. Students are also asked more questions to developing the understandings to fractions and their operations in asking questions that include fraction vocabulary. It is detrimental for students to comprehend what they are working with before operating on it. Also in this assessment are open ended problems that students must solve mathematically and in more than one step. For almost every problem students must either compare problems to one another, to a figure, or determine a least common denominator before doing any addition, subtraction, or the placing of an inequality. With this, students must have prior knowledge and understanding of number sense, mathematical operations, greater than or less than terminology and form, and finally geometry in order to shade in regions or designated fractions. Overall, the concepts conveyed in this assessment are complex but reasonable for student to understand and work through problems with. This assessment requires multiple skills from children and for them to provide reason for their thinking so that we may better understand it and help us in designing future instruction.

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