“Fun with Fractions” Unit Outline

Day 1 Equal Shares

Brownie Challenge Objective: Fractions are used to describe parts of a whole

Vocab: numerator, denominator, whole, equal parts Day 2-3 Understanding Fractions

Exploring Fractions Centers: Making Fraction Strips, Using Fraction Circle to represent Story Problems

Objective: Read, write and identify fractions from wholes with more than 4 parts Vocab: numerator, denominator, whole, equal parts Day 4 Understanding Equivalent Fractions

Introduction to Equivalent Fraction- Fraction Memory Match and Fraction Flash Objective: Use models and number lines to identify equivalent fractions Vocab: equivalent fractions

Day 5 Exploring Equivalent Fractions

Finding Equivalent Fractions- Centers: Equivalent Fraction Challenge, Equivalent Fraction Number Lines

Objective: Use models and number lines to identify equivalent fractions and write fractions in simplest form Vocab: simplest form Day 6 Comparing Fractions

Comparing and Ordering Like Fractions & Unlike Fractions with the same Numerator Objective: Compare & order fractions using number line/ benchmark fractions Vocab: benchmark, like fractions, unlike fractions

Appendix

List of Handouts needed for the Unit

Brownie Equal Shares (Lesson 1)

Fraction Food Problems (Lesson 2)

Fraction booklet (Lesson 2)

Making Fraction Strips (Lesson 2)

Fraction Memory Match (Lesson 3)

Fraction Flash (Lesson 3)

Equivalent Fraction Challenge (Lesson 4)

Blank number line template (Lesson 4)

Comparing Fractions (Lesson 5)

Name: Emmy Burkhard_________ Date: 3/22/13_______

School: Haley Pilot School________ Grade: _3rd________ Starting and Ending Time: 10:00 to 11:00

OVERVIEW OF THE LESSON Common Core Standards: 3.NF.1 Understand a fraction 1/b as the quantity formed by 1 part when a whole is partitioned into b equal parts; understand a fraction as a/b as the quantity formed by a parts of size 1/b. Instructional Objective: When given a real life equal shares problem SWBAT problem solve in order to determine how to equally divide the whole into 4 parts, representing this fraction pictorially and numerically. Students will become familiar with the terms numerator and denominator, and begin to apply them when discussing the pieces of a fraction. Language Objective : SWBAT define and properly identify the numerator and denominator of a given fraction by correctly identifying and labeling each number in the fractions made during the whole class practice and beginning to use this vocabulary when discussing and identifying fractions. SWBAT demonstrate understanding of the terms whole and equal parts through their ability to make fractions when given real world equal share problems. Assessment:

• Assessment of the instructional objective: Students’ mastery of the instructional objectives will be measured by their performance on the worksheet from their brownie challenge and their ability to discuss their thinking and how they arrived at their answer.

• Assessment of the language objective: Students’ mastery of the terms numerator and

denominator will be measured by their ability to accurately define and identify the numerator and denominator of a given fraction. Students’ ability to verbally express their understanding of a fraction being a part of a whole in their explanation of their problem solving will be used to measure their understanding of the terms whole and equal parts.

Lesson 1: Equal Shares

Content:

- Understanding fractions as equal parts of a whole - Dividing a whole into 4 or more equal parts - Identifying and representing unit and non-unit fractions using models - Understanding how to write fractions as a part of a whole (numerator/denominator)

PROCEDURES FOR THE LESSON Opening (15 minutes): 1. Introduce new unit of study. Review lesson objective. 2. Present students with group exploration of equal shares: Brownie Challenge “When we are thinking about fractions we are thinking about equal parts of a whole. Each table will get 1 brownie. Your challenge is to figure out how you can divide the brownie into equal parts so that each table member gets the same amount?” Show students the sheet they are to fill out. 3. Students will work with their table groups to determine how they could cut the brownie so that each person gets an equal share and determine what fraction of the brownie each person will receive. On their worksheet students will record the cuts they would make, shade how much each person will get and record the fraction in numerical form

During Lesson (30 minutes): 1. Students will bring their worksheets to the meeting area, where the whole class will review the findings of their exploration. 2. Questioning if anyone divided the brownie differently or recorded a different fraction to represent the problem before proceeding. Share different groups strategies and dilemmas. 3. After reviewing the different ways that students have divided their brownie, ask students which way of dividing the brownie gives you a bigger piece of brownie. Challenge students to recognize that no matter what way you divide the brownie you are still receiving ¼, so the pieces are all equal. 4. Introduce vocabulary: whole, equal parts, numerator, denominator. 5. Explain to students that a fraction names equal parts of a whole. Returning to the fraction from their brownie exploration students will apply the vocabulary- the whole brownie has 4 equal parts, shading all parts of the shape write 1=4/4. Each equal part represents ¼ of the brownie. Identify and label the numerator and denominator of this fraction.

Closing (5 minutes): 1. Students will return to their seats and I will come around to cut their brownie as they would like. After making the first cut I will ask students how many equal parts the brownie has been divided into now, and ask students to represent one of these pieces as a fraction on their napkins. 2. After cutting the brownie into fourths as they have chosen the students will again represent the fraction they will receive on their napkins and then fill in the blank with a greater than or less than symbol, as they answer the question whether they would rather receive a piece of the brownie after the first cut or after the final cut (1/2 or ¼). They will then finally be able to enjoy their fourth of the brownie!

SUPPORTING ALL LEARNERS

Learner Factors: Adjust Grouping Formats Oral, Pointing, Signed

Responses Give Additional Examples Write Homework List Give Daily Progress Report Use of Braille or Large Print Give Student Copy of Directions Provide an Alternate Reading

Level for a Reading

Extend Time of Selected Work Reread Directions Use Assistive Devices to Respond Post visual picture or schedule Give Verbal Reminders Use of Interpreter Give Verbal Cues to Emphasize

Main Ideas Use Page Markers

Give More Frequent Breaks Handout Hard Copy of Board

Notes Word Processor/Computer Seating Near Advanced

Students Use Graphic Organizer Increase the Number of

Review Activities Pair Students

Specific Examples: Example 1: The students will first complete the group exploration and then as a whole class additional examples will be reviewed, modeling the picture representation and thinking aloud so that students are able to complete similar problems independently when given the independent practice worksheets. Example 2: The vocabulary words and objective will be posted and reviewed verbally while referencing the visual so that students are able to receive this information through both modes. The models for each fraction will also be written in numerical form as well as represented in a picture so that students are able to have multiple means through which to access the material. Example 3:For the group exploration students will be working with their table groups to figure out how to divide the brownie into equal shares, however each student will be responsible for completing a worksheet to show their thinking. This allows students to have the support of their peers but also holds them accountable for recording the information and reviewing it in our whole class review. Students will also be grouped during their centers to provide them with guided support.

FINAL DETAILS OF THE LESSON

Classroom Management: I will use our classroom management routine of 1,2,3 Magic to redirect students and correct inappropriate behavior, while also using praise and positive feedback to reward and encourage participation and engagement. I will use our classroom management routine of “compliments” to transition students to and from the meeting area. Materials:

- Brownies (napkins, 6 plastic knifes) - Equal Share Exploration guiding worksheet - Posted objective and vocabulary

Follow-up: This lesson is the first lesson in a unit on fractions. The concepts of this lesson are foundational skills necessary for comprehension of the remainder of the unit. Students must have this understanding of fractions in order to find equivalent fractions, and compare and order fractions, which are taught in the proceeding lessons.

Name: Emmy Burkhard________________ Date: 3/25/2013 & 3/26/2013

School: Haley Pilot School_______________ Grade: 3rd____________ Starting and Ending Time: 10:00 to 11:00

OVERVIEW OF THE LESSON Common Core Standards: 3.NF.1 Understand a fraction 1/b as the quantity formed by 1 part when a whole is partitioned into b equal parts; understand a fraction as a/b as the quantity formed by a parts of size 1/b. Instructional Objective: SWBAT read, write and identify fractions of wholes with more than 4 parts, by solving equal share problems with support in their small group learning centers and independently on their fraction quick check. SWBAT identify the numerator and denominator of a given fraction by correctly identifying each number in the fractions made during the whole class practice, during their group learning centers and on their fraction quick check. Language Objective : SWBAT define and properly identify the numerator and denominator of a given fraction by correctly identifying and labeling each number in the fractions made during the whole class practice and beginning to use this vocabulary when discussing and identifying fractions in their learning centers. SWBAT demonstrate understanding of the terms whole and equal parts through their ability to make fractions when given real world equal share problems.

Lesson 2: Understanding Fractions

Assessment:

• Assessment of the instructional objective: Students’ mastery of the instructional objective will be measured by their performance on the fraction quick check, which will serve as a quick assessment to gauge students’ level of understanding.

• Assessment of the language objective:

Students’ mastery of the terms numerator and denominator will be measured by their ability to accurately define and identify the numerator and denominator of a given fraction on their fraction quick check. Students’ ability to verbally express their understanding of a fraction being a part of a whole in their small group learning centers will be used to measure their understanding of the terms whole and equal parts. Content:

- Understanding fractions as equal parts of a whole - Dividing a whole into more than 4 equal parts - Identifying and representing unit and non-unit fractions using models - Understanding how to write fractions as a part of a whole (numerator/denominator)

PROCEDURES FOR THE LESSON Opening (15 minutes): 1. Review lesson objective and vocabulary. 2. Review “Recall Prior Knowledge” p. 113-115. During Lesson (40 minutes): 1. Students will be assigned to work in groups of 6 and will cycle through 2 learning centers. (Because there will be 4 groups in all, 2 groups will be working on the activity of each center simultaneously but in different locations)

Center 1: Fraction Strips- Students will make color coded fraction strips to represent 1 whole, ½, 1/3, ¼, 1/6, and 1/8. Students will cut the strips and label each with the matching fraction, then respond to the questions asking them to observe the relationship between the different colored strips.

Center 2: Fraction Circles- Students will practice applying fractions to real world

problems. Students will be presented with various scenarios and asked to represent the fraction using the fraction circles.

Closing (3 minutes): 1. Students will clean up their respective centers, ensuring that their fraction strips are in their labeled bag as the fraction strips will serve as a resource for these students throughout the unit. 2. Review anchor chart with word form of each fraction, having students repeat the word form after me.

SUPPORTING ALL LEARNERS Learner Factors: Adjust Grouping Formats Oral, Pointing, Signed

Responses Give Additional Examples Write Homework List Give Daily Progress Report Use of Braille or Large Print Give Student Copy of Directions Provide an Alternate Reading

Level for a Reading

Extend Time of Selected Work Reread Directions Use Assistive Devices to Respond Post visual picture or schedule Give Verbal Reminders Use of Interpreter Give Verbal Cues to Emphasize

Main Ideas Use Page Markers

Give More Frequent Breaks Handout Hard Copy of Board

Notes Word Processor/Computer Seating Near Advanced

Students Use Graphic Organizer Increase the Number of

Review Activities Pair Students

Specific Examples: Example 1: Students will be working in centers in order to allow them to further explore these concepts in small groups with the assistance and support of a teacher. The students will be divided into four groups of six students and each group will be working with a teacher to complete the activity for their station. Example 2: Because there are many steps in the making fraction strips center students will receive a copy of the directions listed clearly in a step-by-step format so that they are able to be successful completing this activity. This will help more advanced students to complete this task more independently, allowing more time to be spent supporting those students that may require more assistance, as well as providing all students with a hard copy of the directions and an additional mode of input. Example 3: The two different activities done at the two centers will provide students with an increased number of review activities. Providing them with exposure to the content in two different hands-on activities.

FINAL DETAILS OF THE LESSON

Classroom Management: I will use our classroom management routine of 1,2,3 Magic to redirect students and correct inappropriate behavior, while also using praise and positive feedback to reward and encourage participation and engagement. I will use our classroom management routine of “compliments” to transition students to and from the meeting area. Materials:

- Textbook 3B - Strips of different colored paper - Scissors - Making Fraction Strips worksheet - Fraction circles - Fraction Food Problems worksheet

Follow-up: This lesson is the second lesson in a unit on fractions. The concepts of this lesson are foundational skills necessary for comprehension of the remainder of the unit. Students must have this understanding of fractions in order to find equivalent fractions, and compare and order fractions, which are taught in the proceeding lessons. The fraction strips made during one of the centers will be used as a resource for students to use throughout the remainder of lessons.

Name: Emmy Burkhard_________________ Date: 3/27/13________

School: Haley Pilot School ______________ Grade: _3rd__________ Starting and Ending Time: 10:00 to 11:00

OVERVIEW OF THE LESSON MA Curriculum Standards : 3.NF.3 Explain equivalence of fractions in special cases, and compare fractions by reasoning about their size: a) Understand two fractions as equivalent (equal) if they are the same 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 they fractions are equivalent, e.g. by using a visual fraction model. Instructional Objective: SWBAT use models to determine whether or not two fractions are equivalent fractions during the partner matching game. Language Objective: SWBAT demonstrate their understanding of the vocabulary equivalent fractions by verbally explaining why two fractions are considered equivalent fractions and using an appropriate strategy (model, number line) to back up their reasoning. Assessment:

• Assessment of the instructional objective: Students’ mastery of the instructional objective will be measured by their ability to determine whether or not two fractions are equivalent during their partner matching game.

• Assessment of the language objective: Students’ understanding of the term equivalent

fractions will be measured by their ability to accurately identify equivalent fractions and verbally explain why two fractions are considered equivalent.

Lesson 3: Understanding Equivalent Fractions

Content:

- Identifying equivalent fractions - Using a model to find equivalent fractions - Representing a fraction on a number line by defining the interval from 0 to 1 as the whole - Using a number line to find equivalent fractions

PROCEDURES FOR THE LESSON Opening (5-7 minutes): 1. Introduce the lesson objective and vocabulary equivalent fractions to students. 2. Introduce the term equivalent fractions as fractions that name the same parts of a whole. Remind students of our brownie challenge, in which we found that if Charlotte divided the brownie the way that she wanted- into 8 small pieces so that each person received 2 pieces- the piece she received was equivalent to the piece they would receive if Owen divided the brownie the way that he wanted- into 4 large pieces so that each person received 1 piece, using fraction strips to model this on the board. 3. Emphasize to students that we can only find equivalent fractions when we are working with equal-sized wholes. If our brownies were different sized wholes would that be fair? If one group got a smaller brownie and still had to split it into 4 equal parts would the members get the same sized piece as the group with the larger brownie? Provide students with counter examples using different sized wholes. During Lesson (20-25 minutes): 1. Remind students of their making fraction strips station and the fractions represented by each color strip, reviewing the anchor chart. 2. Present students with ‘true or false?’ activity. Explain to students that we are going to prove or disprove the observations they noted during the making fraction strips station. 3. After reading each observation students will come up to the ELMO to prove or disprove their classmates’ observation using the fraction strips. 4. Students will also come up to the whiteboard to draw models to prove and disprove the noted observations. 5. Divide students into two activity groups in order to share the directions for their chosen partner game.

Closing (15- 25 minutes): 1. The directions for the two games will be explained for each group and a teacher and student will act as partners to model several turns.

- Fraction Memory Match: Students will receive a set of fraction circle cards with different fractions of the circles shaded, and the fraction written at the bottom of the card. The cards will be placed face down and students will take turns flipping over two cards to try to find a match (of equivalent fractions). If they turn over equivalent fractions they get to keep the match. If not, they must turn the cards back over, then wait for their partner to take their turn

- Fraction Flash: Students will receive a bag of fraction cards- the cards will have a fraction written in numerical form on one side and the pictorial representation on the backside. Students will pull two cards from the bag and looking at the number side their partner must determine whether or not the fractions are equivalent. Students can use their fraction strips, draw models or any other strategy that works for them. They can also use the picture support on the back side to check their answer.

2. Students will play their assigned game with their partner, recording their fractions on the worksheet as they play.

SUPPORTING ALL LEARNERS Learner Factors: Adjust Grouping Formats Oral, Pointing, Signed

Responses Give Additional Examples Write Homework List Give Daily Progress Report Use of Braille or Large Print Give Student Copy of Directions Provide an Alternate Reading

Level for a Reading

Extend Time of Selected Work Reread Directions Use Assistive Devices to Respond Post visual picture or schedule Give Verbal Reminders Use of Interpreter Give Verbal Cues to Emphasize

Main Ideas Use Page Markers

Give More Frequent Breaks Handout Hard Copy of Board

Notes Word Processor/Computer Seating Near Advanced

Students Use Graphic Organizer Increase the Number of

Review Activities Pair Students

Specific Examples: Example 1: Students will participate in one of the two activities designed to meet each student at the level they are currently at. Students that have a better number sense and seem to be more solid in their foundational understanding of fractions will be identifying whether or not two fractions given in number form are equivalent. These fraction cards will have picture supports on the back that students can use to check their answer. The students that appeared to be having more difficulty with fractions and/or make meaning through pictures rather than numbers will use picture fraction cards. These students will be comparing the pictures and questioning whether or not the pictures show the same shaded portion of the circle. Students will also be paired within their groups so that students can help one another and gain practice explaining their reasoning to their peers. Example 2: The directions for each game will be reviewed verbally and posted. The students will also receive a copy of the directions at the top of their worksheet. How to play each game will also be modeled so that students know what the game should look like and are more easily able to meet the expectations for each activity. Example 3: When reviewing the fraction strips center, students will have the visual of the anchor chart to refer to. The chart shows the fraction in pictorial, number and word form and uses colors to match the colors that the students used for their fraction strips, so that they are able to make this connection when using the fraction strips later in the lesson.

FINAL DETAILS OF THE LESSON

Classroom Management: I will use our classroom management routine of 1,2,3 Magic to redirect students and correct inappropriate behavior, while also using praise and positive feedback to reward and encourage participation and engagement. I will use our classroom management routine of “compliments” to transition students to and from the meeting area. Materials:

- Fraction strips - Posted objective and vocabulary - True or False? Worksheet - Memory matching fraction picture cards - Fraction Memory Match worksheet - Fraction Flash fraction cards - Fraction Flash worksheet

Follow-up: This is the third lesson in our fraction unit. Following this lesson, students will be learning to solve for equivalent fractions using number lines and multiplication and division. In the next lesson, students will learn how to find the simplest form of a fraction, which will further assess their understanding of equivalent fractions. It will be beneficial for students to have this conceptual knowledge of equivalent fractions in order to solve for equivalent fractions and the simplest form using multiplication and division.

Name: Emmy Burkhard________________ Date: _3/28/2013_______

School: Haley Pilot School______________ Grade: _3rd___________ Starting and Ending Time: 10:00 to 11:00

OVERVIEW OF THE LESSON MA Curriculum Standards: 3.NF.2 Understand a fraction as a number on the number line; represent fractions on a number line diagram: a) Represent a fraction 1/b on a number line diagram by defining the interval from 0 to 1 as the whole and partitioning it into b equal parts. Recognize that each part has size 1/b and that the endpoint of the part based at 0 locates the number 1/b on the number line 3.NF.3 Explain equivalence of fractions in special cases, and compare fractions by reasoning about their size: a) Understand two fractions as equivalent (equal) if they are the same 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. by using a visual fraction model. Instructional Objective: SWBAT use number lines in addition to other strategies (models, multiplication/division) to find equivalent fractions during the learning centers. Language Objective: SWBAT demonstrate their understanding of the vocabulary simplest form by verbally defining this term and accurately identifying and solving for the simplest form of fractions. Assessment:

• Assessment of the instructional objective: Students’ mastery of the instructional objective will be measured by their ability to participate fully in the learning centers with success. Their mastery of the content to date will be assessed with the quick-check at the

• Assessment of the language objective: Students’ mastery of the vocabulary simplest form

will be measured by their ability to accurately identify and solve for the simplest form of equivalent fractions.

Lesson 4: Exploring Equivalent Fractions

Content:

- Identifying and solving for equivalent fractions - Using models and number lines to find equivalent fractions - Using multiplication and division to find equivalent fractions - Identifying and using division to solve for the simplest form of a fraction

PROCEDURES FOR THE LESSON Opening (10 minutes): 1. Introduce lesson objective and vocabulary simplest form. 2. Review meaning of equivalent fractions and the methods previously practiced (model and multiplication) to solve for equivalent fractions. 3. Call on students to share one of the sets of equivalent fractions they found yesterday in their partner activity. Call on students to represent these fractions and show their equivalence using the methods previously learned. 4. Introduce the number line as an additional strategy to find equivalent fractions. Drawing a number line on the board explain to students that each fraction number line starts at 0 and ends at 1 because we are looking at parts of a whole. Remind students that equivalent fractions we must have equal-sized wholes. 5. Model how to represent fractions on a number line and show their equivalence. During Lesson (40 minutes): 1. Students will cycle through 2 stations (2 groups completing each task simultaneously) - Station#1 Equivalent Fraction Challenge Students will use the fraction bars to find, represent and record as many equivalent fractions to 1/2 as they can; when complete workbook p. 93-94 - Station #2 Equivalent Fraction Number lines: Students will receive additional instruction and examples of using number lines to find equivalent fractions and then practice this strategy by completing workbook p. 95-96. For extension students will practice plotting fractions on a blank number line template and finding equivalent fractions using the number line strategy. Closing (10 minutes): 1. Students will complete the fraction quick-check independently to assess their comprehension of the content thus far in the unit.

SUPPORTING ALL LEARNERS Learner Factors: Adjust Grouping Formats Oral, Pointing, Signed

Responses Give Additional Examples Write Homework List Give Daily Progress Report Use of Braille or Large Print Give Student Copy of Directions Provide an Alternate Reading

Level for a Reading

Extend Time of Selected Work Reread Directions Use Assistive Devices to Respond Post visual picture or schedule Give Verbal Reminders Use of Interpreter Give Verbal Cues to Emphasize

Main Ideas Use Page Markers

Give More Frequent Breaks Handout Hard Copy of Board

Notes Word Processor/Computer Seating Near Advanced

Students Use Graphic Organizer Increase the Number of

Review Activities Pair Students

Specific Examples: Example 1: The students will be paired into groups of 6 for the stations, which will provide them the opportunity to practice independently but with the assistance and scaffolding of a teacher as needed. The groupings will be assigned so that those students requiring additional support will be able to receive the attention they need within the small group setting. Example 2: After the instruction and modeling in the mini-lesson students will receive additional examples of using the number line strategy when they rotate to the number line station. The exposure to additional examples in a smaller group setting will enable more students to be more actively engaged in the lesson and provide all students with the repeated exposure that they require to comprehend a new idea more fully. Example 3: The students will cycle through two different stations to allow them the opportunity to practice using both models and number lines to find equivalent fractions. The students in the models stations will be reviewing a skill learned in yesterdays lesson and continuing to practice and apply this skill, in order to provide them with a deeper understanding and familiarity with equivalent fractions, which will help them to use the other strategies as their understanding, deepens.

FINAL DETAILS OF THE LESSON

Classroom Management: I will use our classroom management routine of 1,2,3 Magic to redirect students and correct inappropriate behavior, while also using praise and positive feedback to reward and encourage participation and engagement. I will use our classroom management routine of “compliments” to transition students to and from the meeting area. Materials:

- Individual student whiteboards, markers - Posted objective and vocabulary - Independent activity sheet

Follow-up: This lesson is the second lesson on equivalent fractions and the fourth lesson within the unit on fractions. Following this lesson students will be working with comparing and ordering fractions. It will be necessary for them to have a solid foundation of the concept of equivalent fractions in order to compare and order fractions.

Name: Emmy Burkhard________________ Date: __4/1/13 ______

School: Haley Pilot School______________ Grade: 3rd___________ Starting and Ending Time: 10:00 to 11:00

OVERVIEW OF THE LESSON MA Curriculum Standards: 3.NF.3 Explain equivalence of fractions in special cases, and compare fractions by reasoning about their size: d) Compare two fractions with the same numerator or the same denominator by reasoning about their size. Recognize that comparisons are valid only when the two fractions refer to the same whole. Record the results of comparisons with the symbols >, =, or < and justify the conclusions, e.g., by using a visual fraction model Instructional Objective: SWBAT use models and number lines to compare and order like and unlike fractions with the same numerator when completing their independent practice worksheet. Language Objective: SWBAT verbally define and identify like and unlike fractions and use their knowledge of these terms to help them determine which numbers to compare when comparing a set of fractions. Assessment:

• Assessment of the instructional objective: Students’ mastery of the instructional objective will be monitored throughout the mini-lesson and their independent practice.

• Assessment of the language objective: Students’ mastery of the terms like and unlike

fractions will be measured by their ability to verbally identify whether a fraction is like or unlike during the mini-lesson and then apply the appropriate strategy to compare and order the given set of fractions when working independently.

Lesson 5: Comparing Fractions

Content:

- Comparing like and unlike fractions - Ordering like and unlike fractions - Showing fractions as points or distances on a number line - Using models and number lines to represent and compare fractions - Understanding the pictorial representation of fractions as models or number lines

PROCEDURES FOR THE LESSON Opening (5 minutes): 1. Prior to introducing the new content of this lesson, review equivalent fractions. Review the anchor chart with the 3 strategies to find equivalent fractions (draw models, use number lines, multiply/divide).

During Lesson (20- 25 minutes): 1. Discovery (Like): Encourage students to think back to the brownie sharing activity on the first day of the unit. Remind students that they each split a brownie amongst their table group- each person receiving 1/4 of the brownie. Ask students to turn and talk with a partner to decide if they would rather have had 1/4 of the brownie or 2/4 of the brownie. Ask students to share back and explain their thinking. 2. Ask students how they could represent the fraction and show which fraction is bigger using a pictorial representation- model and number line. 3. Emphasize to students that fractions can be compared only if the wholes are equal-sized. (Just like with equivalent fractions) 4. Introduce vocabulary like fractions as fractions that have the same denominator. So we only compare the numerator- which number is bigger/smaller? 5. Discovery (Unlike, same numerator): Ask students turn and talk with a partner to decide if they would rather have 1/4 or 1/6 of their brownie. Ask students to share back and explain their thinking. 6. Ask students how they could represent the fraction and show which fraction is bigger using a pictorial representation- model and number line. 7. Introduce vocabulary unlike fractions as fractions with different denominator. 8. Group Practice: Give students a set of fractions (3/7, 5/7, 2/7; 1/3, 1/7, 1/4; etc.) and ask students to identify if the fractions are like or unlike. 9. Have students come up to the board to show how they can represent each fraction in order to compare them using a model or number line. 10. Explain to students that when we are working with unlike fractions if the numerator is the same (such as example) the fraction gets smaller as the denominator gets greater- refer back to brownie example, sharing with more people, you get a smaller piece. Closing (20-25 minutes): 1. Students will complete an independent practice worksheet.

SUPPORTING ALL LEARNERS Learner Factors:

Adjust Grouping Formats Oral, Pointing, Signed

Responses Give Additional Examples Write Homework List Give Daily Progress Report Use of Braille or Large Print Give Student Copy of Directions Provide an Alternate Reading

Level for a Reading

Extend Time of Selected Work Reread Directions Use Assistive Devices to Respond Post visual picture or schedule Give Verbal Reminders Use of Interpreter Give Verbal Cues to Emphasize

Main Ideas Use Page Markers

Give More Frequent Breaks Handout Hard Copy of Board

Notes Word Processor/Computer Seating Near Advanced

Students Use Graphic Organizer Increase the Number of

Review Activities Pair Students

Specific Examples: Example 1: The majority of students will complete the practice worksheets independently in order to assess their ability to compare like and unlike fractions with the same numerator on their own. The students that have been having difficulty working with fractions thus far in the unit and those that struggle with comparing numbers will work in small groups to help provide them with the additional support and instruction that they require. Example 2: Based on the student’s performance on the quick-check, I will begin the lesson by explicitly reviewing the strategies learned for finding equivalent fractions, referring to the posted anchor chart. Having the chart as a visual reminder and model of each strategy will help the students to see how to implement each strategy and remind them of the 3 learned strategies. Example 3: During the mini-lesson on comparing fractions students will have the opportunity to turn and talk to decide whether they would rather have 1/4 or 2/4 of the brownie, and then again comparing 1/4 and 1/6. Students will turn and talk with a partner in order to work together to make their decision, this will help to support students that are uncertain because their partner will have to explain it to them in a way that they understand so that they are certain of their decision.

FINAL DETAILS OF THE LESSON

Classroom Management: I will use our classroom management routine of 1,2,3 Magic to redirect students and correct inappropriate behavior, while also using praise and positive feedback to reward and encourage participation and engagement. I will use our classroom management routine of “compliments” to transition students to and from the meeting area. Materials:

- Posted objective and vocabulary - Equivalent Fraction anchor chart - Practice worksheet

Follow-up: This lesson is the fifth lesson in the fractions unit. The students will continue to compare and order fractions in the following lessons, however they will be exploring related and unrelated unlike fractions. The students will continue to use the strategies of using models and number lines as it helps them, while incorporating a new strategy- using benchmark fractions and matching the denominators (comparing to an equivalent fraction).