21
1 of 21 3.MATH.APT.Unit 4 Leadership and Learning Center. All rights reserved. Last Revised: June 2014 Greenfield/Rosedale/Fruitvale/Norris Rigorous Curriculum Design Engaging Learning Experiences Planner Subject Math Grade/Course 3 rd Grade Unit of Study Unit 4 - Fractions Duration of Unit 5 Weeks Engaging Scenario Directions : Incorporate the five elements of effective scenarios: current situation; student challenge; student role; intended audience; product or performance. The third grade classes are beginning a unit on basketball. We will need to use fractions to compare and find equivalent shooters. Over the next few weeks we will be making fractions and using fractions in games. Priority Standards 3.NF.2 Understand a fraction as a number on the number line; represent fractions on a number line diagram. 3.NF.3d COMPARE two fractions with the same numerator or the same denominator by REASONING about their size. RECOGINIZE 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 fractions model. Supporting 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 a/b as the quantity formed by a parts of size 1/b. 3.NF.2 Understand a fraction as a number on the number line; represent fractions on a number line diagram. 3.NF.2.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.2.b Represent a fraction a/b on a number line diagram by marking off a lengths 1/b from 0. Recognize that the resulting interval has size a/b and that its endpoint locates the number a/b on the number line. 3.NF.3 Explain equivalence of fractions in special cases, and compare fractions by reasoning about their size. 3.NF.3.a Understand two fractions as equivalent (equal) if they are the same size, or the same point on a number line. Recognize that equivalencies are only valid when the two fractions refer to the same whole. 3.NF.3.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. 3.NF.3.c Express whole numbers as fractions, and recognize fractions that are equivalent to whole numbers. Examples: Express 3 in the form 3 = 3/1; recognize that 6/1 = 6; locate 4/4 and 1 at the same point of a number line diagram. Geometry 3.G.2 Partition shapes into parts with equal areas. Express the area of each part as a unit fraction of the whole. For example, partition a shape into 4 parts with equal area, and describe the area of each part as 1/4 of the area of the shape.

Rigorous Curriculum Design Engaging Learning Experiences ...€¦ · Engaging Learning Experiences Planner Subject Math Grade/Course 3rd Grade Unit of Study Unit 4 - Fractions Duration

  • Upload
    others

  • View
    8

  • Download
    0

Embed Size (px)

Citation preview

Page 1: Rigorous Curriculum Design Engaging Learning Experiences ...€¦ · Engaging Learning Experiences Planner Subject Math Grade/Course 3rd Grade Unit of Study Unit 4 - Fractions Duration

1 of 213.MATH.APT.Unit 4

ⓒ Leadership and Learning Center. All rights reserved. Last Revised: June 2014Greenfield/Rosedale/Fruitvale/Norris

Rigorous Curriculum DesignEngaging Learning Experiences Planner

Subject MathGrade/Course 3rd GradeUnit of Study Unit 4 - FractionsDuration of Unit 5 Weeks

Engaging ScenarioDirections:Incorporate the five elements of effective scenarios: current situation; student challenge; student role;intended audience; product or performance.

The third grade classes are beginning a unit on basketball. We will need to use fractions to compare andfind equivalent shooters. Over the next few weeks we will be making fractions and using fractions in games.

Priority Standards3.NF.2 Understand a fraction as a number on the number line; represent fractions on a number linediagram.

3.NF.3d COMPARE two fractions with the same numerator or the same denominator byREASONING about their size. RECOGINIZE that comparisons are valid only when the two fractionsrefer to the same whole. RECORD the results of comparisons with the symbols >, =, or < andJUSTIFY the conclusions, e.g., by USING a visual fractions model.

Supporting Standards3.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 fractiona/b as the quantity formed by a parts of size 1/b.3.NF.2 Understand a fraction as a number on the number line; represent fractions on a number line diagram.3.NF.2.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 bequal 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 numberline.3.NF.2.b Represent a fraction a/b on a number line diagram by marking off a lengths 1/b from 0. Recognize that the resulting intervalhas size a/b and that its endpoint locates the number a/b on the number line.3.NF.3 Explain equivalence of fractions in special cases, and compare fractions by reasoning about their size.3.NF.3.a Understand two fractions as equivalent (equal) if they are the same size, or the same point on a number line. Recognize thatequivalencies are only valid when the two fractions refer to the same whole.3.NF.3.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.3.NF.3.c Express whole numbers as fractions, and recognize fractions that are equivalent to whole numbers. Examples: Express 3 inthe form 3 = 3/1; recognize that 6/1 = 6; locate 4/4 and 1 at the same point of a number line diagram.Geometry3.G.2 Partition shapes into parts with equal areas. Express the area of each part as a unit fraction of the whole. For example, partition ashape into 4 parts with equal area, and describe the area of each part as 1/4 of the area of the shape.

Page 2: Rigorous Curriculum Design Engaging Learning Experiences ...€¦ · Engaging Learning Experiences Planner Subject Math Grade/Course 3rd Grade Unit of Study Unit 4 - Fractions Duration

2 of 213.MATH.APT.Unit 4

ⓒ Leadership and Learning Center. All rights reserved. Last Revised: June 2014Greenfield/Rosedale/Fruitvale/Norris

Interdisciplinary ConnectionsWriting

“Unwrapped” Concepts(students need to know)

“Unwrapped” Skills(students need to be able to do)

DOKLevels

Understand 3.NF.2

Represent 3.NF.2

COMPARE 3.NF.3.b

REASONING 3.NF.3.b

RECOGNIZE 3.NF.3.b

RECORD 3.NF.3.b

JUSTIFY 3.NF.3.b

USING 3.NF.3.b

Fraction as a number on a numberline 3.NF.2

Fractions on a number line diagram3.NF.2

two fractions with samenumerator or the samedenominator 3.NF.3.b

about their size 3.NF.3.b

that comparisons are valid onlywhen the two fractions refer tothe same whole 3.NF.3.b

the results of comparisons withthe symbols >, =, or < 3.NF.3.b

the conclusions 3.NF.3.b

a visual fraction model 3.NF.3.b

3

3

1

2

2

1

3

2

Page 3: Rigorous Curriculum Design Engaging Learning Experiences ...€¦ · Engaging Learning Experiences Planner Subject Math Grade/Course 3rd Grade Unit of Study Unit 4 - Fractions Duration

3 of 213.MATH.APT.Unit 4

ⓒ Leadership and Learning Center. All rights reserved. Last Revised: June 2014Greenfield/Rosedale/Fruitvale/Norris

Corresponding Big Ideas Essential QuestionsFractional parts are equal shares of awhole or a whole set. 3.NF.2

Using a visual fraction model will allow youto compare fractions. 3.NF.3.b

Charts, tables, line plot graphs,pictographs, Venn Diagrams, and bargraphs may be used to display data andsolve problems. 3.MD.3

The scale increments used when making abar graph is determined by the scaleintervals being graphed. 3.MD.3

How could fractions be represented on anumber between 0 and 1? Explain yourreasoning. 3.NF.2

How can I fold paper strips to locatefractions on a number line? 3.NF.2

How do you determine which fraction islarger or smaller when they have likenumerators or denominators? 3.NF.3.b

How can you use data to create a graph tosolve problems? 3.MD.3

How would you decide what increments touse when creating a graph?3.MD.3

Unit Vocabulary Terms“Unwrapped” Priority Standards Concepts Supporting Standards Concepts and

Other Unit-Specific TermsUnderstandCompareReasoningRecognizingRecordJustifyUsingDrawSolve

RepresentRecognizeExplainGenerateExpress

Performance Task Synopses**You can switch tasks 2 and 3 depending on how you are teaching fractions in your classroom.

Task 1: Create a section fraction bars/strips. Use them to compare fractions with different numeratorsor denominators. Optional game

Task 2: With a partner, students will shoot 10 baskets (denominator of 10). Students will track basketsmade and compare them on a number line. They will then compare using symbols and justify theiranswers.

Task 3: Students will pick a card that will represent the number of baskets they will shoot (denominatorsof 12, 7, 5, 9) The number of baskets will determine their group. Students will track baskets made andcompare them on a number line within their group. They will then compare using symbols, justify theiranswers, and share with the class. (Teacher will prepare index cards with the denominators todetermine groups. Teacher can choose the denominators.)

Page 4: Rigorous Curriculum Design Engaging Learning Experiences ...€¦ · Engaging Learning Experiences Planner Subject Math Grade/Course 3rd Grade Unit of Study Unit 4 - Fractions Duration

4 of 213.MATH.APT.Unit 4

ⓒ Leadership and Learning Center. All rights reserved. Last Revised: June 2014Greenfield/Rosedale/Fruitvale/Norris

Performance Task # 1In Detail

S: Which standard(s) (priority/supporting) will the task address?

3.NF.2 Understand a fraction as a number on the number line; represent fractions on a number line diagram.

3.NF.3d COMPARE two fractions with the same numerator or the same denominator by REASONINGabout their size. RECOGINIZE that comparisons are valid only when the two fractions refer to the samewhole. RECORD the results of comparisons with the symbols >, =, or < and JUSTIFY the conclusions, e.g.,by USING a visual fractions model.

3.MD.3 Draw scaled picture graph and a scaled bar graph to represent a data set with several categories.Solve one-and two-step “how many more” and “how many less” problems using information presented inscaled bar graphs. For example, draw a bar graph in which each spare in the bar graph might represent 5pets.

Q: What essential Question(s) and corresponding Big Idea(s) will this task target?

How could fractions be represented on a number between 0 and 1? Explain your reasoning. – Fractionalparts are equal shares of a whole or a whole set.How can I fold paper strips to locate fractions on a number line? Using a visual fraction model will allow youto compare fractions.How do you determine which fraction is larger or smaller when they have like numerators or denominators?See aboveHow can you use data to create a graph to solve problems? Charts tables, line plot graphs, pictographs,Venn Diagrams, and bar graphs may be used to display data and solve problems.How would you decide what increments to use when creating a graph? The scale increments used whenmaking a bar graph is determined by the scale intervals being graphed.

U: Which “unwrapped” specific concepts and skills will this task target?“Unwrapped” Concepts(students need to know)

“Unwrapped” Skills(students need to be able to do)

DOKLevels

Understand 3.NF.2

Represent 3.NF.2

COMPARE 3.NF.3.b

REASONING 3.NF.3.b

RECOGNIZE 3.NF.3.b

RECORD 3.NF.3.b

Fraction as a number on a number line3.NF.2

Fractions on a number line diagram 3.NF.2

two fractions with same numerator orthe same denominator 3.NF.3.b

about their size 3.NF.3.b

that comparisons are valid only whenthe two fractions refer to the same whole3.NF.3.b

the results of comparisons with thesymbols >, =, or < 3.NF.3.b

3

3

1

2

2

1

Page 5: Rigorous Curriculum Design Engaging Learning Experiences ...€¦ · Engaging Learning Experiences Planner Subject Math Grade/Course 3rd Grade Unit of Study Unit 4 - Fractions Duration

5 of 213.MATH.APT.Unit 4

ⓒ Leadership and Learning Center. All rights reserved. Last Revised: June 2014Greenfield/Rosedale/Fruitvale/Norris

JUSTIFY 3.NF.3.b

USING 3.NF.3.b

Draw 3.MD.3

Represent 3.MD.3

Solve 3.MD.3

Using 3.MD.3

the conclusions 3.NF.3.b

a visual fraction model 3.NF.3.b

Scaled picture graph and bar graph

Data set with several categories 3.MD.3

One-and two-step “how many more” and“how many less” problems 3.MD.3

Information presented in scaled bargraphs.3.MD.3

3

2

1

2

2

2

A: How will the students apply the concepts and skills? What will they do and/or produce?Students will create fraction bars/strips in order to compare fractions with like numerators or likedenominators.

R: What resources, instruction, and information will students need in order to complete the task?Students will need paper and a pencil.

E: What evidence of learning will I look for to show that I know all of my students have conceptuallylearned the concepts and skills – the standard(s)?

1. Students meet “proficient” level or higher on Task 1 rubric2. Students respond to Essential Question with Big Idea in written or oral format.

D: How can I differentiate the application and/or evidence to meet the varying needs of my students?Students may work in small groups if necessary.

Task 1 Full Description:

Individually: Each student will create their own set of fraction bars/strips. When complete the teacher willdirect students to compare fractions using like numerators or like denominators.

Page 6: Rigorous Curriculum Design Engaging Learning Experiences ...€¦ · Engaging Learning Experiences Planner Subject Math Grade/Course 3rd Grade Unit of Study Unit 4 - Fractions Duration

6 of 213.MATH.APT.Unit 4

ⓒ Leadership and Learning Center. All rights reserved. Last Revised: June 2014Greenfield/Rosedale/Fruitvale/Norris

Performance Task # 1 Scoring Guide

Advanced or Exemplary All “Proficient” criteria plus: NONE

Proficient Correctly create fraction bars/strips Compare fractions and identify equivalent fractions

Progressing Meets _1_ of the “Proficient” criteria

Beginning Meets none of the “Proficient” criteria Task to be repeated after re-teaching Comments:

Teacher’s Evaluation: ______________________________________

Comments regarding student’s performance:

Interdisciplinary Connections andRelated Priority Standards

Specific to Task #1

21st Century Learning SkillsSpecific to Task #1

Writing Check all those that apply for each task:

❑ Teamwork and Collaboration❑ Initiative and Leadership❑ Curiosity and Imagination❑ Innovation and Creativity❑ Critical thinking and Problem Solving❑ Flexibility and Adaptability❑ Effective Oral and Written Communication❑ Accessing and Analyzing Information❑ Other

Page 7: Rigorous Curriculum Design Engaging Learning Experiences ...€¦ · Engaging Learning Experiences Planner Subject Math Grade/Course 3rd Grade Unit of Study Unit 4 - Fractions Duration

7 of 213.MATH.APT.Unit 4

ⓒ Leadership and Learning Center. All rights reserved. Last Revised: June 2014Greenfield/Rosedale/Fruitvale/Norris

Performance Task # 2In Detail

S: Which standard(s) (priority/supporting) will the task address?

3.NF.2 Understand a fraction as a number on the number line; represent fractions on a number line diagram.

3.NF.3d COMPARE two fractions with the same numerator or the same denominator by REASONINGabout their size. RECOGINIZE that comparisons are valid only when the two fractions refer to the samewhole. RECORD the results of comparisons with the symbols >, =, or < and JUSTIFY the conclusions, e.g.,by USING a visual fractions model.

3.MD.3 Draw scaled picture graph and a scaled bar graph to represent a data set with several categories.Solve one-and two-step “how many more” and “how many less” problems using information presented inscaled bar graphs. For example, draw a bar graph in which each spare in the bar graph might represent 5pets.

Q: What essential Question(s) and corresponding Big Idea(s) will this task target?How could fractions be represented on a number between 0 and 1? Explain your reasoning. – Fractionalparts are equal shares of a whole or a whole set.How can I fold paper strips to locate fractions on a number line? Using a visual fraction model will allow youto compare fractions.How do you determine which fraction is larger or smaller when they have like numerators or denominators?See aboveHow can you use data to create a graph to solve problems? Charts tables, line plot graphs, pictographs,Venn Diagrams, and bar graphs may be used to display data and solve problems.How would you decide what increments to use when creating a graph? The scale increments used whenmaking a bar graph is determined by the scale intervals being graphed.

U: Which “unwrapped” specific concepts and skills will this task target?“Unwrapped” Concepts(students need to know)

“Unwrapped” Skills(students need to be able to do)

DOKLevels

Understand 3.NF.2

Represent 3.NF.2

COMPARE 3.NF.3.b

REASONING 3.NF.3.b

RECOGNIZE 3.NF.3.b

RECORD 3.NF.3.b

JUSTIFY 3.NF.3.b

Fraction as a number on a number line3.NF.2

Fractions on a number line diagram 3.NF.2

two fractions with same numerator orthe same denominator 3.NF.3.b

about their size 3.NF.3.b

that comparisons are valid only whenthe two fractions refer to the same whole3.NF.3.b

the results of comparisons with thesymbols >, =, or < 3.NF.3.b

the conclusions 3.NF.3.b

3

3

1

2

2

1

3

Page 8: Rigorous Curriculum Design Engaging Learning Experiences ...€¦ · Engaging Learning Experiences Planner Subject Math Grade/Course 3rd Grade Unit of Study Unit 4 - Fractions Duration

8 of 213.MATH.APT.Unit 4

ⓒ Leadership and Learning Center. All rights reserved. Last Revised: June 2014Greenfield/Rosedale/Fruitvale/Norris

USING 3.NF.3.b

Draw 3.MD.3

Represent 3.MD.3

Solve 3.MD.3

Using 3.MD.3

a visual fraction model 3.NF.3.b

Scaled picture graph and bar graph

Data set with several categories 3.MD.3

One-and two-step “how many more” and“how many less” problems 3.MD.3

Information presented in scaled bargraphs.3.MD.3

2

1

2

2

2

A: How will the students apply the concepts and skills? What will they do and/or produce?Students will place numbers on a number line when the denominator is the same.

R: What resources, instruction, and information will students need in order to complete the task?Students will need paper, basket, and graph paper.

E: What evidence of learning will I look for to show that I know all of my students have conceptuallylearned the concepts and skills – the standard(s)?

1. Students meet “proficient” level or higher on Task 1 rubric2. Students respond to Essential Question with Big Idea in written or oral format.

D: How can I differentiate the application and/or evidence to meet the varying needs of my students?Students may work in small groups if necessary.

Task 2 Full Description:

Partner Work: Each partner will each shoot 10 baskets (trash can, basketball hoop, bucket, etc.) from thesame distance. Each student must keep track of the number of baskets that they make because this willbecome your numerator.

Individually: You will take the data that was collected on your basket tossing chart. You will plot the fractionson a number line that is represented between 0 and 1. Use <, >, or = to compare the fractions. Justify yourconclusions using words.

Page 9: Rigorous Curriculum Design Engaging Learning Experiences ...€¦ · Engaging Learning Experiences Planner Subject Math Grade/Course 3rd Grade Unit of Study Unit 4 - Fractions Duration

9 of 213.MATH.APT.Unit 4

ⓒ Leadership and Learning Center. All rights reserved. Last Revised: June 2014Greenfield/Rosedale/Fruitvale/Norris

Performance Task # 2 Scoring GuideAdvanced or Exemplary All “Proficient” criteria plus: NONE

Proficient Collect data from your partner Correctly place the fractions on a number line Use the correct symbol when comparing the fractions Answer justified in words

Progressing Meets _3_ of the “Proficient” criteria

Beginning Meets fewer than _3_ of the “Proficient” criteria Task to be repeated after re-teaching Comments:Teacher’s Evaluation: ______________________________________

Comments regarding student’s performance:

Interdisciplinary Connections andRelated Priority Standards

Specific to Task #2

21st Century Learning SkillsSpecific to Task #2

Check all those that apply for each task:

❑ Teamwork and Collaboration❑ Initiative and Leadership❑ Curiosity and Imagination❑ Innovation and Creativity❑ Critical thinking and Problem Solving❑ Flexibility and Adaptability❑ Effective Oral and Written Communication❑ Accessing and Analyzing Information❑ Other

Page 10: Rigorous Curriculum Design Engaging Learning Experiences ...€¦ · Engaging Learning Experiences Planner Subject Math Grade/Course 3rd Grade Unit of Study Unit 4 - Fractions Duration

10 of 213.MATH.APT.Unit 4

ⓒ Leadership and Learning Center. All rights reserved. Last Revised: June 2014Greenfield/Rosedale/Fruitvale/Norris

Performance Task # 3In Detail

S: Which standard(s) (priority/supporting) will the task address?

3.NF.2 Understand a fraction as a number on the number line; represent fractions on a number linediagram.

3.NF.3d COMPARE two fractions with the same numerator or the same denominator by REASONINGabout their size. RECOGINIZE that comparisons are valid only when the two fractions refer to the samewhole. RECORD the results of comparisons with the symbols >, =, or < and JUSTIFY the conclusions,e.g., by USING a visual fractions model.

3.MD.3 Draw scaled picture graph and a scaled bar graph to represent a data set with severalcategories. Solve one-and two-step “how many more” and “how many less” problems usinginformation presented in scaled bar graphs. For example, draw a bar graph in which each spare in thebar graph might represent 5 pets.

Q: What essential Question(s) and corresponding Big Idea(s) will this task target?How could fractions be represented on a number between 0 and 1? Explain your reasoning. – Fractional partsare equal shares of a whole or a whole set.How can I fold paper strips to locate freactions on a number line? Using a visual fraction model will allow you tocompare fractions.How do you determine which fraction is larger or smaller when they have like numerators or denominators?See aboveHow can you use data to create a graph to solve problems? Charts tables, line plot graphs, pictographs, VennDiagrams, and bar graphs may be used to display data and solve problems.How would you decide what increments to use when creating a graph? The scale increments used whenmaking a bar graph is determined by the scale intervals being graphed.

U: Which “unwrapped” specific concepts and skills will this task target?

“Unwrapped” Concepts(students need to know)

“Unwrapped” Skills(students need to be able to do)

DOKLevels

Understand 3.NF.2

Represent 3.NF.2

COMPARE 3.NF.3.b

REASONING 3.NF.3.b

RECOGNIZE 3.NF.3.b

RECORD 3.NF.3.b

Fraction as a number on a number line3.NF.2

Fractions on a number line diagram 3.NF.2

two fractions with same numerator orthe same denominator 3.NF.3.b

about their size 3.NF.3.b

that comparisons are valid only whenthe two fractions refer to the same whole3.NF.3.b

the results of comparisons with thesymbols >, =, or < 3.NF.3.b

3

3

1

2

2

1

Page 11: Rigorous Curriculum Design Engaging Learning Experiences ...€¦ · Engaging Learning Experiences Planner Subject Math Grade/Course 3rd Grade Unit of Study Unit 4 - Fractions Duration

11 of 213.MATH.APT.Unit 4

ⓒ Leadership and Learning Center. All rights reserved. Last Revised: June 2014Greenfield/Rosedale/Fruitvale/Norris

JUSTIFY 3.NF.3.b

USING 3.NF.3.b

Draw 3.MD.3

Represent 3.MD.3

Solve 3.MD.3

Using 3.MD.3

the conclusions 3.NF.3.b

a visual fraction model 3.NF.3.b

Scaled picture graph and bar graph

Data set with several categories 3.MD.3

One-and two-step “how many more” and“how many less” problems 3.MD.3

Information presented in scaled bargraphs.3.MD.3

3

2

1

2

2

2

A: How will the students apply the concepts and skills? What will they do and/or produce?Students will place fractions on a number line between 0 and 1 that have different denominators.

R: What resources, instruction, and information will students need in order to complete the task?Students will need graph paper.

E: What evidence of learning will I look for to show that I know all of my students have conceptuallylearned the concepts and skills – the standard(s)?

1. Students meet “proficient” level or higher on Task 3 rubric2. Students respond to Essential Question with Big Idea in written or oral format.

D: How can I differentiate the application and/or evidence to meet the varying needs of my students?Students may work in small groups if necessary.

Task 3 Full Description:

Partner Work: Each student will pull a card representing a denominator/group. Then each student will shoottheir given number of baskets. For example, if a student pulls an 8, they will shoot 8 baskets. Each studentmust keep track of the number of baskets that they make, because this will become the numerator.

Individually: You will take the group data that was collected at your basket tossing chart and plot the fractionson a number line that is represented between 0 and 1. Use <, >, or = to compare the fractions. Justify yourconclusions using words.

Group Mix: Students will be mixed so that multiple denominators are represented in each group. Now,students will plot the fractions on a number line that is represented between 0 and 1.

Page 12: Rigorous Curriculum Design Engaging Learning Experiences ...€¦ · Engaging Learning Experiences Planner Subject Math Grade/Course 3rd Grade Unit of Study Unit 4 - Fractions Duration

12 of 213.MATH.APT.Unit 4

ⓒ Leadership and Learning Center. All rights reserved. Last Revised: June 2014Greenfield/Rosedale/Fruitvale/Norris

Performance Task # 3 Scoring Guide

Advanced or Exemplary All “Proficient” criteria plus: NONE

Proficient Collect data from your group Correctly place the fractions on a number line Use the correct symbol when comparing the fractions Answer justified in words

Progressing Meets _3_ of the “Proficient” criteria

Beginning Meets fewer than _4_ of the “Proficient” criteria Task to be repeated after re-teachingComments:

Interdisciplinary Connections andRelated Priority Standards

Specific to Task #3

21st Century Learning SkillsSpecific to Task #3

Check all those that apply for each task:

❑ Teamwork and Collaboration❑ Initiative and Leadership❑ Curiosity and Imagination❑ Innovation and Creativity❑ Critical thinking and Problem Solving❑ Flexibility and Adaptability❑ Effective Oral and Written Communication❑ Accessing and Analyzing Information❑ Other

Page 13: Rigorous Curriculum Design Engaging Learning Experiences ...€¦ · Engaging Learning Experiences Planner Subject Math Grade/Course 3rd Grade Unit of Study Unit 4 - Fractions Duration

13 of 213.MATH.APT.Unit 4

ⓒ Leadership and Learning Center. All rights reserved. Last Revised: June 2014Greenfield/Rosedale/Fruitvale/Norris

Performance Task # 3In Detail

S: Which standard(s) (priority/supporting) will the task address?

3.NF.2 Understand a fraction as a number on the number line; represent fractions on a number linediagram.

3.NF.3d COMPARE two fractions with the same numerator or the same denominator by REASONINGabout their size. RECOGINIZE that comparisons are valid only when the two fractions refer to the samewhole. RECORD the results of comparisons with the symbols >, =, or < and JUSTIFY the conclusions,e.g., by USING a visual fractions model.

3.MD.3 Draw scaled picture graph and a scaled bar graph to represent a data set with severalcategories. Solve one-and two-step “how many more” and “how many less” problems usinginformation presented in scaled bar graphs. For example, draw a bar graph in which each spare in thebar graph might represent 5 pets.

Q: What essential Question(s) and corresponding Big Idea(s) will this task target?

How could fractions be represented on a number between 0 and 1? Explain your reasoning. – Fractional partsare equal shares of a whole or a whole set.How can I fold paper strips to locate fractions on a number line? Using a visual fraction model will allow you tocompare fractions.How do you determine which fraction is larger or smaller when they have like numerators or denominators?See aboveHow can you use data to create a graph to solve problems? Charts tables, line plot graphs, pictographs, VennDiagrams, and bar graphs may be used to display data and solve problems.How would you decide what increments to use when creating a graph? The scale increments used whenmaking a bar graph is determined by the scale intervals being graphed.

U: Which “unwrapped” specific concepts and skills will this task target?

“Unwrapped” Concepts(students need to know)

“Unwrapped” Skills(students need to be able to do)

DOKLevels

Understand 3.NF.2

Represent 3.NF.2

COMPARE 3.NF.3.b

REASONING 3.NF.3.b

RECOGNIZE 3.NF.3.b

RECORD 3.NF.3.b

JUSTIFY 3.NF.3.b

Fraction as a number on a number line 3.NF.2

Fractions on a number line diagram 3.NF.2

two fractions with same numerator or thesame denominator 3.NF.3.b

about their size 3.NF.3.b

that comparisons are valid only when the twofractions refer to the same whole 3.NF.3.b

the results of comparisons with the symbols>, =, or < 3.NF.3.b

the conclusions 3.NF.3.b

a visual fraction model 3.NF.3.b

3

3

1

2

2

1

3

Page 14: Rigorous Curriculum Design Engaging Learning Experiences ...€¦ · Engaging Learning Experiences Planner Subject Math Grade/Course 3rd Grade Unit of Study Unit 4 - Fractions Duration

14 of 213.MATH.APT.Unit 4

ⓒ Leadership and Learning Center. All rights reserved. Last Revised: June 2014Greenfield/Rosedale/Fruitvale/Norris

USING 3.NF.3.b

Draw 3.MD.3

Represent 3.MD.3

Solve 3.MD.3

Using 3.MD.3

Scaled picture graph and bar graph

Data set with several categories 3.MD.3

One-and two-step “how many more” and“how many less” problems 3.MD.3

Information presented in scaled bargraphs.3.MD.3

2

1

2

2

2

A: How will the students apply the concepts and skills? What will they do and/or produce?Students will place fractions on a number line between 0 and 1 that have different denominators.

R: What resources, instruction, and information will students need in order to complete the task?Students will need graph paper.

E: What evidence of learning will I look for to show that I know all of my students have conceptuallylearned the concepts and skills – the standard(s)?

3. Students meet “proficient” level or higher on Task 3 rubric4. Students respond to Essential Question with Big Idea in written or oral format.

D: How can I differentiate the application and/or evidence to meet the varying needs of my students?Students may work in small groups if necessary.

Page 15: Rigorous Curriculum Design Engaging Learning Experiences ...€¦ · Engaging Learning Experiences Planner Subject Math Grade/Course 3rd Grade Unit of Study Unit 4 - Fractions Duration

15 of 213.MATH.APT.Unit 4

ⓒ Leadership and Learning Center. All rights reserved. Last Revised: June 2014Greenfield/Rosedale/Fruitvale/Norris

Task 1

Fraction Strips

Materials:6 different colors of 12-by-18-inch construction papercut into 3-by-18-inch stripspaper cutter (can cut numerous strips at once)Thin marker (black) and a ruler

Directions:1. To begin the lesson, give students six precut strips of paper in six differentcolors. Specify one color and have students hold up the strip of this color. Tellstudents that this strip will represent the whole. Have students write "onewhole" on the fraction strip.

2. Next, ask students to pick a second strip, and fold it into two equal pieces.Ask students what they think each of these strips should be called (one-half or1/2). Have students label their strips accordingly, using both the word and thefractional representation. Ask students to highlight the fold marks, using a rulerand black marker.

3. Ask students to take a different color strip. Fold the strip into two equalparts. Next fold the strip in half again. Ask students to predict the number ofequal parts the strips will have. Open the strip and highlight the folds using amarker and a ruler. Ask students what they think each of these strips should becalled? (one-fourth or 1/4). Label the strips naming some parts as one-fourthand some of the sections as 1/4.

4. Continue the process of folding, marking, and naming strips for eighths,thirds, and sixths using words and fractional notation. What fraction of thewhole does one section of your strip represent?

5. Have students take out their “whole” and ask, “Which strip is 1/2 of thewhole?” How do you know? “Which strip is 1/4 of the whole?” How do youknow? Continue asking about 1/8, 1/3, and 1/6. Students should experimentwith the strips until they are consistently arriving at the correct answer.

6. Have students work in pairs to line up their fraction strips and find as manyrelationships as they can. Have students record these relationships on paper.When students have finished, have them share the relationships theydiscovered. Record relationships on chart paper and discuss. Students maynotice that one whole is the same as 2/2, 4/4, 8/8, 3/3, or 6/6. Students canalso fold strips to show equivalent strips.

Page 16: Rigorous Curriculum Design Engaging Learning Experiences ...€¦ · Engaging Learning Experiences Planner Subject Math Grade/Course 3rd Grade Unit of Study Unit 4 - Fractions Duration

16 of 213.MATH.APT.Unit 4

ⓒ Leadership and Learning Center. All rights reserved. Last Revised: June 2014Greenfield/Rosedale/Fruitvale/Norris

Examples of patterns you might discover:What fractions are equivalent to 1/2? How do you know? Students may foldfraction bars and discover the relationship between 1/2, 2/4, 4/8, and 3/6. Ask:“What do you notice about the fractions that are equivalent to 1/2?”Some may notice patterns within each fraction. (The numerator is always onehalf of the denominator – denominator designates the number of equal partsthe fraction strip has been divided into. The numerator designates the numberof parts we are referring to. For the fraction 4/8; the strip has been partitionedinto 8 equal parts and four of the 8 parts is equivalent to 1/2.) Tell studentsthat when fraction strips are the same length, they represent equivalentfractions.Did you find a fraction strip that does not have sections to equal one-half?(Fraction strip for thirds based on the pattern for 1/2, can you identify otherfractions that would be equivalent to 1/2? (Examples: 5/10; 6/12; 7/14;50/100; 500/1000; etc. (infinite number)What is the relationship between the numerator and the denominator?(Students should notice that the denominators are always double thenumerators or the numerator is always one-half of the denominator.)What do you notice about the denominator for fraction that equal 1/2?(Denominators are always even)

Thirds cannot equal a half. What are other fractions that cannot be dividedevenly into halves? Explain your reasoning. What is your proof?

Page 17: Rigorous Curriculum Design Engaging Learning Experiences ...€¦ · Engaging Learning Experiences Planner Subject Math Grade/Course 3rd Grade Unit of Study Unit 4 - Fractions Duration

17 of 213.MATH.APT.Unit 4

ⓒ Leadership and Learning Center. All rights reserved. Last Revised: June 2014Greenfield/Rosedale/Fruitvale/Norris

Optional Game:Get to a Whole

Materials: One set of fractions strips for each playerFraction strips must be cut into equal parts.Whole strip per player; halves into 2 parts and labeled; fourthsinto 3 parts and labeled; eighths into 8 equal parts and labeledDie or spinner 1/2, 1/4, 1/8, 1/8, 1/16, 1/16

Directions:The winner is the person who covers their whole strip first.

1. Take turns rolling the fraction die.2. The fraction that comes up on the die or spinner tells what

size piece to place on the whole strip.3. Check with partners to be sure he/she agrees with the

fractional part you place on the whole strip.4. Take turns rolling the die and placing a fractional piece on

the whole.5. If you only need 1/8 and you roll ½, you lose your turn.6. The first player to cover his or her whole strip exactly wins

the game.

Page 18: Rigorous Curriculum Design Engaging Learning Experiences ...€¦ · Engaging Learning Experiences Planner Subject Math Grade/Course 3rd Grade Unit of Study Unit 4 - Fractions Duration

18 of 213.MATH.APT.Unit 4

ⓒ Leadership and Learning Center. All rights reserved. Last Revised: June 2014Greenfield/Rosedale/Fruitvale/Norris

Task 2 Worksheet

Directions: Place your name and your partner’s name on the chart. Fill in thenumber of shots you will attempt and then tally mark the number of shots youmade. Once done, you will create a fraction that represents the number of shotsmade.

Students Number of Shots Shots Made Fraction

1.

2.

Directions: Use the fractions from above to place on the number line between 0and 1.

Student 1 _____________

Student 2 _____________

Directions: Use <, >, or = to compare the fractions. Justify your answer.

_____________________________________

_____________________________________

_____________________________________

_____________________________________

_____________________________________

Page 19: Rigorous Curriculum Design Engaging Learning Experiences ...€¦ · Engaging Learning Experiences Planner Subject Math Grade/Course 3rd Grade Unit of Study Unit 4 - Fractions Duration

19 of 213.MATH.APT.Unit 4

ⓒ Leadership and Learning Center. All rights reserved. Last Revised: June 2014Greenfield/Rosedale/Fruitvale/Norris

Task 3 Worksheet

Directions: Place names on the chart. Fill in the number of shots you willattempt and tally mark the number of shots you make. Once done, you will createa fraction that represents the number of shots made.

Students Number ofShots

Shots Made Fraction

1.

2.

3.

4.

Directions: Use the fractions from above to place on the number line between 0and 1.

Student 1 _____________

Student 2 _____________

Student 3 _____________

Student 4 _____________

Page 20: Rigorous Curriculum Design Engaging Learning Experiences ...€¦ · Engaging Learning Experiences Planner Subject Math Grade/Course 3rd Grade Unit of Study Unit 4 - Fractions Duration

20 of 213.MATH.APT.Unit 4

ⓒ Leadership and Learning Center. All rights reserved. Last Revised: June 2014Greenfield/Rosedale/Fruitvale/Norris

Directions: Use <, >, or = to compare your fraction with each member of yourgroup.

Extension: (optional)

Your teacher will mix your groups. Repeat the steps for task 3.

Directions: Place names on the chart. Fill in the number of shots you willattempt and tally mark the number of shots you make. Once done, you will createa fraction that represents the number of shots made.

Students Number ofShots

Shots Made Fraction

1.

2.

3.

4.

1. ___________________________

2. ___________________________

3. ___________________________

Page 21: Rigorous Curriculum Design Engaging Learning Experiences ...€¦ · Engaging Learning Experiences Planner Subject Math Grade/Course 3rd Grade Unit of Study Unit 4 - Fractions Duration

21 of 213.MATH.APT.Unit 4

ⓒ Leadership and Learning Center. All rights reserved. Last Revised: June 2014Greenfield/Rosedale/Fruitvale/Norris

Directions: Use the fractions from above to place on the number line between 0and 1.

Student 1 _____________

Student 2 _____________

Student 3 _____________

Student 4 _____________

Directions: Use <, >, or = to compare your fraction with each member of yourgroup.

1. ___________________________

2. ___________________________

3. ___________________________