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Mathematics INTERVENTION COMMON CORE Standards Plus ® Grade 3 SAMPLER

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www.standardsplus.org - 1.877.505.9152 © 2016 Learning Plus Associates

1

Mathematics

INTERVENTIONCOMMON CORE

Standards Plus® Grade

3

SAMPLER

INTERVENTIONCOMMON CORE

Standards Plus®

Available for Grades 1-8 Language Arts and Math

Great for: Small Group Instruction

Summer School ProgramsAfter School Programs

Special Ed - Academic IEP Goals

Mathematics

INTERVENTION

COMMON CORE

Standards Plus®

TEACHER EDITION A/B

Grade

3A/B

Topics:Operations & Algebraic ThinkingNumber & Operations - Fractions

Scaffolded lessons written to the Common Core Language Arts and Mathematics Standards.

Includes:

• Pre- and Post- Assessments for each set of instruction on a topic or idea

• Step-by-step direct instruction lessons that support student mastery of grade level standards

• Performance Tasks that provide students opportunities to apply their learning

2

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8+ Performance Tasks DOK 3-4

Students deepen and apply their skills

100+ Intervention LessonsDOK 1-2-3

Pre-AssessmentsUse assessment results to identify

and group students that need intervention

Scaffolded Intervention Lessons

Students learn the prerequisite skills necessary for the mastery

of grade-level standards

Post-Assessments

Administer a post-assessment to validate student progress

Standards Plus Intervention Includes

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Ready-To-Teach Direct Instruction Lessons

Standards Plus Intervention lessons are written in the Direct Instruction format because it is the most effective

research-based instructional delivery model and it is proven to increase student achievement.

Standards Plus Intervention works because teachers teach every lesson

Standards Plus® Common Core Intervention is not licensed for duplication. Copying is illegal. © 2014 Learning Plus Associates

Teacher Lesson Plan

124

Standards Plus® – Common Core Intervention Mathematics – Grade 3Domain:  Number & Operations – Fractions  Focus:  Equivalent Fractions  Lesson:  # 12

Lesson Objective:  Identify and represent equivalent fractions.  Introduction:  Today students will learn about equivalent fractions.   Instruction:  “We have learned how to show fractions as part of the whole and fractions as part of a group.  We have also learned about fractions that are equal to one.  Today we will learn about fractions that are equivalent.  Equivalent means that the fractions represent the same size and shape.  At the top of the page, we see two squares.  They are the same size and shape.  The square on the left is divided into two parts.  When we divide a shape into two equal parts, we have halves.  The fraction next to the square is one‐half.  There is one part shaded to show one‐half.  The square on the right is divided into four parts.  When a shape is divided into four equal parts, we have fourths.  The fraction next to the square is two‐fourths.  There are two parts shaded to show two‐fourths.  Even though the square is divided into a different number of parts, the area that is shaded is the same size and shape, so they are equivalent.”  Guided Practice:  “Today we will shade to show equivalent fractions.  Look at the example.  It shows two circles.  The circle on the left is divided into eight parts.  The circle on the right is divided into four parts.  Are the circles the same shape and size?  (Discuss.)  Because the circles are the same shape and size, we can use them to show equivalent fractions.  The fraction on the left says six‐eighths.  How many parts should we shade?  (6)  Let’s shade six parts.  (Pause.)  The fraction on the right should be equivalent to the fraction on the left.  Let’s shade to see.  The fraction on the right is three‐fourths.  How many parts will we shade?  (3)  Shade three parts.  (Pause.)  Notice that we shaded areas that were the same size and shape, so six‐eighths and three‐fourths are equivalent.”  Independent Practice:  “You will shade to show equivalent fractions two more times today.”  Review:  After 5 minutes, review the answers.  Shade as a model for the students to check their work.  Elicit student responses on how to say each fraction name.  Emphasize the th in each denominator to ensure that students hear it.  Closure:  “Today you shaded to show equivalent fractions.”    Answers:  1. Three parts shaded; one part shaded

2. Two parts shaded; four parts shaded 

 

St. Ed. Pg. B-20

Introduction

Instruction

Guided Practice

IndependentPractice

Review &Closure

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Using Standards Plus Intervention

1.  Use assessment results to identify students that need intervention

2.  If students are assessed online, our Standards Plus Platform will automatically group them for intervention lessons

3.  If students are assessed using print:• login on the dashboard• select intervention lessons • select topic • download lessons

4.  Teach direct instruction intervention lessons that scaffold the instruction of skills necessary for mastery of grade level standards

5.  Administer a post-assessment to validate student progress

Intervention Program

To access Intervention lessons:

Intervention Program

13

The entire Standards Plus Intervention Program is included as downloadable PDFs with your Standards Plus Program

Using Standards Plus Intervention Lessons: 1. Use assessment results to identify and group students that need intervention

2. Assign appropriate intervention lessons

3. Teach direct instruction intervention lessons that scaffold the instruction of skills necessary for mastery of grade level standards

4. Administer a post-assessment to validate student progress

5. Use performance tasks to provide students with opportunities to apply their learning.

6 www.standardsplus.org - 1.877.505.9152 © 2016 Learning Plus Associates

WHY STANDARDS PLUS INTERVENTIONINCREASES STUDENT ACHIEVEMENT

Students are provided the prerequisite skills necessary for mastery of grade level standards

Teachers:Teachers are the most important factor in student learning. That’s why every Standards Plus lesson is directly taught by a teacher.

Direct Instruction format:“Direct Instruction is a proven method of instruction that fosters the most significant gains in student achievement and results in deep and enduring understanding of the concept.” (Peladeau, Forget & Gagne, 2003).

Discrete learning targets:Each lesson has a clear learning objective, providing easily understood instruction which allows students to learn and retain the information in their long term memory.

Multiple exposures to prerequisite standards/skills: Each standard/skill is broken down and presented in multiple scaffolded lessons providing multiple opportunities to practice and develop a deep understanding of a specific skill allowing for long term retention.

Immediate feedback:“The most powerful single modification that enhances achievement is feedback.” (John Hattie, 1992)Every lesson provides immediate feedback to the students.

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Standards  Plus®  Common  Core  Intervention  –  Mathematics  –  Grade  3  Domain   Lesson   Focus   Standard(s)  References   TE  pg   St.  Ed.  pg   DOK  

Operatio

ns  &  Algebraic  Thinking  

Pre-­‐1   Pre-­‐Assessment-­‐Multiplication   3.OA.1,  3.  OA.5,  3.  OA.7,  3.  OA.9  

16   A-­‐3  

1-­‐2  

1   Commutative  Property  of  Multiplication  

Prerequisite  skills  and  scaffolded  instruction  to  build  readiness  for  grade  level  standards  

and  instruction.  

18   A-­‐4  

2   Associative  Property  of  Multiplication   20   A-­‐5  

3   Skip  Counting  –  by  2s   22   A-­‐6  

4   Skip  Counting  –  by  5s  and  10s   24   A-­‐7  

5   Multiplication  Facts:    2s   26   A-­‐8  

6   Multiplication  Facts:    5s  and  10s   28   A-­‐9  

7   Multiplication  Facts   30   A-­‐10  

8   Multiplication  Facts   32   A-­‐11  

9   Multi-­‐Digit  Multiplication   34   A-­‐12  

10   Multi-­‐Digit  Multiplication   36   A-­‐13  

11   Multi-­‐Digit  Multiplication   38   A-­‐14  

P1   Performance  Lesson  #1  –  How  to  Multiply  –  (3.OA.7)   40   A-­‐15   3  

Post-­‐1   Post-­‐Assessment-­‐  Multiplication   3.OA.1,  3.  OA.5,  3.  OA.7,  3.  OA.9  

42   A-­‐16   1-­‐2            

Pre-­‐2   Pre-­‐Assessment-­‐Multiplication  &  Division  in  Context   3.OA.2,  3.OA.3,  3.OA.7   44   A-­‐17  

1-­‐2  

12   Division  Facts  Prerequisite  skills  and  scaffolded  instruction  to  build  readiness  for  grade  level  standards  

and  instruction.  

46   A-­‐18  

13   Division  Facts   48   A-­‐19  

14   Division   50   A-­‐20  

15   Multiplication  in  Context   52   A-­‐21  

16   Division  in  Context   54   A-­‐22  

17   Multiple  Operations  in  Context   56   A-­‐23  

P2   Performance  Lesson  #2  –  Writing  Word  Problems  (3.OA.3,  3.OA.7)   58   A-­‐24   3  Post-­‐2   Post-­‐Assessment-­‐  Multiplication  &  Division  in  Context   3.OA.2,  3.OA.3,  3.OA.7   60   A-­‐25   1-­‐2  

         

Pre-­‐3   Pre-­‐Assessment-­‐Representing  &  Solving  Problems   3.OA.1,  3.OA.2,  3.OA.4,  3.OA.6,  3.OA.8  

62   A-­‐27  

1-­‐2  

18   Determining  the  Operation    

Prerequisite  skills  and  scaffolded  instruction  to  build  readiness  for  grade  level  standards  

and  instruction.  

64   A-­‐28  

19   Determining  the  Operation     66   A-­‐29  

20   Determining  the  Operation     68   A-­‐30  

21   Writing  Equations   70   A-­‐31  

22   Writing  Equations   72   A-­‐32  

23   Using  Unit  Conversions   74   A-­‐33  

24   Using  Unit  Conversions   76   A-­‐34  

25   Determining  Total  Cost   78   A-­‐35  

26   Determining  Total  Cost   80   A-­‐36  

P3   Performance  Lesson  #3  –  Writing  Equations  (3.OA.1,  3.OA.2,  3.OA.7,  3.OA.8)   82   A-­‐37   3  

Post-­‐3   Post-­‐Assessment-­‐  Representing  &  Solving  Problems   3.OA.1,  3.OA.2,  3.OA.4,  3.OA.6,  3.OA.8  

84   A-­‐38   1-­‐2            

Common Core Standards Plus® is not licensed for duplication. Copying is illegal.© 2013 Learning Plus Associates

Resources

3

Standards Plus Intervention - Math Grade 3 Lesson Index

8 www.standardsplus.org - 1.877.505.9152 © 2016 Learning Plus Associates

Standards  Plus®  Common  Core  Intervention  –  Mathematics  –  Grade  3  Domain   Lesson   Focus   Standard(s)  References   TE  pg   St.  Ed.  pg   DOK  

Num

ber  &

 Operatio

ns  –  Fractions    

Pre-­‐4   Pre-­‐Assessment-­‐Representing  Fractions   3.NF.1,  3.NF.2,  3.NF.2a,  3.NF.3c  

92   B-­‐3  

1-­‐2  

1   Identify  and  Write  Fractions  to    

Prerequisite  skills  and  scaffolded  instruction  to  build  readiness  for  grade  level  standards  

and  instruction.  

94   B-­‐4  

2   Part  of  the  Group   96   B-­‐5  

3   Part  of  the  Group   98   B-­‐6  

4   Part  of  the  Group   100   B-­‐7  

5   Part  of  the  Whole   102   B-­‐8  

6   Part  of  the  Whole   104   B-­‐9  

7   Equal  to  One   106   B-­‐10  

8   Equal  to  One   108   B-­‐11  

9   Fraction  Models   110   B-­‐12  

10   Finding  Fractions  on  a  Number  Line   112   B-­‐13  

11   Finding  Fractions  on  a  Number  Line   114   B-­‐14  

P4   Performance  Lesson  #4  –  Models  of  Fractions  (3.NF.1,  3.NF.3c)   116   B-­‐15-­‐16   3  

Post-­‐4   Post-­‐Assessment-­‐Representing  Fractions   3.NF.1,  3.NF.2,  3.NF.2a,  3.NF.3c  

120   B-­‐17   1-­‐2            

Pre-­‐5   Pre-­‐Assessment-­‐Equivalent  Fractions  &  Compare  Fractions   3.NF.1,  3.NF.3,  3.NF.3a-­‐b,  d   122   B-­‐19  

1-­‐2  

12   Equivalent  Fractions  

Prerequisite  skills  and  scaffolded  instruction  to  build  readiness  for  grade  level  standards  

and  instruction.  

124   B-­‐20  

13   Equivalent  Fractions   126   B-­‐21  

14   Equivalent  Fractions   128   B-­‐22  

15   Equivalent  Fractions   130   B-­‐23  

16   Comparing  Fractions   132   B-­‐24  

17   Comparing  Fractions   134   B-­‐25  

18   Comparing  Fractions   136   B-­‐26  

19   Comparing  Fractions   138   B-­‐27  

P5   Performance  Lesson  #5  –  Compare  Fractions  with  Models  (3.NF.1,  3.NF.3,  3.NF.3d)   140   B-­‐28-­‐29   3  

Post-­‐5   Post-­‐Assessment-­‐Equivalent  Fractions  &  Compare  Fractions   3.NF.1,  3.NF.3,  3.NF.3a-­‐b,  d   144   B-­‐30   1-­‐2  

Common Core Standards Plus® is not licensed for duplication. Copying is illegal. © 2013 Learning Plus Associates

Resources

4

Standards Plus Intervention - Math Grade 3 Lesson Index

www.standardsplus.org - 1.877.505.9152 © 2016 Learning Plus Associates

9

Standards  Plus®  Common  Core  Intervention  –  Mathematics  –  Grade  3  

Domain   Lesson   Focus   Standard(s)  References   TE  pg   St.  Ed.  pg   DOK  

Num

ber  &

 Ope

ratio

ns  in

 Bas

e  Te

n  

Pre-­‐6   Pre-­‐Assessment-­‐Rounding,  Add  &  Subtract   3.NBT.1,  3.NBT.2   14   C-­‐3  

1-­‐2  

1   Round  to  the  Nearest  10  

Prerequisite  skills  and  scaffolded  instruction  to  build  readiness  for  grade  level  standards  

and  instruction.  

16   C-­‐4  

2   Round  to  the  Nearest  100   18   C-­‐5  

3   Fact  Families   20   C-­‐6  

4   Fact  Families   22   C-­‐7  

5   Multi-­‐Digit  Addition     24   C-­‐8  

6   Adding  Whole  Numbers     26   C-­‐9  

7   Multi-­‐Digit  Addition   28   C-­‐10  

1-­‐2  

8   Adding  Whole  Numbers     30   C-­‐11  

9   Adding  Whole  Numbers     32   C-­‐12  

10   Multi-­‐Digit  Subtraction   34   C-­‐13  

11   Subtracting  Whole  Numbers   36   C-­‐14  

12   Multi-­‐Digit  Subtraction     38   C-­‐15  

13   Subtracting  Whole  Numbers     40   C-­‐16  

14   Subtracting  Whole  Numbers   42   C-­‐17  

P6   Performance  Lesson  #6  –  Addition  &  Subtraction  (3.NBT.2)   44   C-­‐18   3  Post-­‐6   Post-­‐Assessment-­‐  Rounding,  Add  &  Subtract   3.NBT.1,  3.NBT.2   46   C-­‐19   1-­‐2  

           

Geo

met

ry  

Pre-­‐7   Pre-­‐Assessment-­‐Shapes  &  Their  Attributes   3.G.1   52   C-­‐21  

1-­‐2  

1   Triangles,  Rectangles,  Squares,  Circles  

Prerequisite  skills  and  scaffolded  instruction  to  build  readiness  for  grade  level  standards  

and  instruction.  

54   C-­‐22  

2   Identify  &  Classify  Polygons   56   C-­‐23  

3   Identify  &  Classify  Polygons   58   C-­‐24  

4   Attributes  of  Polygons   60   C-­‐25  

5   Attributes  of  Polygons   62   C-­‐26  

6   Classifying  Quadrilaterals   64   C-­‐27  

7   Classifying  Quadrilaterals   66   C-­‐28  

8   Attributes  of  Quadrilaterals   68   C-­‐29  

9   Attributes  of  Quadrilaterals   70   C-­‐30  

10   Attributes  of  Quadrilaterals   72   C-­‐31  

P7   Performance  Lesson  #7  –  It’s  Classified  (3.G.1)   74   C-­‐32   3  Post-­‐7   Post-­‐Assessment-­‐  Shapes  &  Their  Attributes   3.G.1   76   C-­‐33   1-­‐2  

Common Core Standards Plus® is not licensed for duplication. Copying is illegal.© 2013 Learning Plus Associates

Resources

3

Standards Plus Intervention - Math Grade 3 Lesson Index

10 www.standardsplus.org - 1.877.505.9152 © 2016 Learning Plus Associates

Standards  Plus®  Common  Core  Intervention  –  Mathematics  –  Grade  3  

Domain   Lesson   Focus   Standard(s)  References   TE  pg   St.  Ed.  pg   DOK  

Mea

sure

men

t  &  D

ata  

Pre-­‐8   Pre-­‐Assessment-­‐Time   3.MD.1   84   D-­‐3  

1-­‐2  

1   Telling  Time  to  the  Hour  

Prerequisite  skills  and  scaffolded  instruction  to  build  readiness  for  grade  level  standards  

and  instruction.  

86   D-­‐4  

2   Telling  Time  to  the  Half  Hour   88   D-­‐5  

3   Telling  Time  to  the  Quarter  Hour   90   D-­‐6  

4   Telling  Time  to  the  Quarter  Hour   92   D-­‐7  

5   Telling  Time  to  Five  Minute  Intervals     94   D-­‐8  

6   Telling  Time  to  Five  Minute  Intervals   96   D-­‐9  

7   Determining  Intervals  of  Time   98   D-­‐10  

8   Determining  Intervals  of  Time   100   D-­‐11  

9   Elapsed  Time   102   D-­‐12  

P8   Performance  Lesson  #8  –  How  Long  Does  It  Take?  –  (3.MD.1)   104   D-­‐13   3  Post-­‐8   Post-­‐Assessment-­‐Time   3.MD.1   106   D-­‐14   1-­‐2  

           

Pre-­‐9   Pre-­‐Assessment-­‐Data   3.MD.3   108   D-­‐15  

1-­‐2  

10   Read  and  Interpret  a  Bar  Graph  

Prerequisite  skills  and  scaffolded  instruction  to  build  readiness  for  grade  level  standards  

and  instruction.  

110   D-­‐16  

11   Data  from  a  Bar  Graph   112   D-­‐17  

12   Data  from  a  Bar  Graph   114   D-­‐18  

13   Read  &  Interpret  a  Tally  Chart   116   D-­‐19  

14   Data  from  a  Tally  Chart   118   D-­‐20  

15   Data  from  a  Tally  Chart   120   D-­‐21  

16   Displaying  Data   122   D-­‐22  

17   Displaying  Data   124   D-­‐23  

P9   Performance  Lesson  #9  –  Analyze  &  Record  Data  (3.MD.3)   126   D-­‐24   3  Post-­‐9   Post-­‐Assessment-­‐Data   3.MD.3   128   D-­‐25   1-­‐2  

           

Pre-­‐10   Pre-­‐Assessment-­‐Length,  Perimeter,  &  Area   3.MD.4-­‐3.MD.8   130   D-­‐27  

1-­‐2  

18   Measuring  Length    

Prerequisite  skills  and  scaffolded  instruction  to  build  readiness  for  grade  level  standards  

and  instruction.  

132   D-­‐28  

19   Determining  Length   134   D-­‐29  

20   Determining  Length   136   D-­‐30  

21   Determining  Perimeter   138   D-­‐31  

22   Determining  Perimeter   140   D-­‐32  

23   Determining  Area   142   D-­‐33  

24   Determining  Area   144   D-­‐34  

25   Determining  Area   146   D-­‐35  

P10   Performance  Lesson  #10  –  Relating  Area  &  Perimeter  (3.MD.4,  3.MD.5,  3.MD.6,  3.MD.7)   148   D-­‐36   3  Post-­‐10   Post-­‐Assessment-­‐Length,  Perimeter,  &  Area   3.MD.4-­‐3.MD.8   150   D-­‐37   1-­‐2  

           

Common Core Standards Plus® is not licensed for duplication. Copying is illegal. © 2013 Learning Plus Associates

Resources

4

Standards Plus Intervention - Math Grade 3 Lesson Index

www.standardsplus.org - 1.877.505.9152 © 2016 Learning Plus Associates

11

Sample Lessons Included in this Booklet

Standards  Plus®  Common  Core  Intervention  –  Mathematics  –  Grade  3  Domain   Lesson   Focus   Standard(s)  References   TE  pg   St.  Ed.  pg   DOK  

Num

ber  &

 Operatio

ns  –  Fractions    

Pre-­‐4   Pre-­‐Assessment-­‐Representing  Fractions   3.NF.1,  3.NF.2,  3.NF.2a,  3.NF.3c  

92   B-­‐3  

1-­‐2  

1   Identify  and  Write  Fractions  to    

Prerequisite  skills  and  scaffolded  instruction  to  build  readiness  for  grade  level  standards  

and  instruction.  

94   B-­‐4  

2   Part  of  the  Group   96   B-­‐5  

3   Part  of  the  Group   98   B-­‐6  

4   Part  of  the  Group   100   B-­‐7  

5   Part  of  the  Whole   102   B-­‐8  

6   Part  of  the  Whole   104   B-­‐9  

7   Equal  to  One   106   B-­‐10  

8   Equal  to  One   108   B-­‐11  

9   Fraction  Models   110   B-­‐12  

10   Finding  Fractions  on  a  Number  Line   112   B-­‐13  

11   Finding  Fractions  on  a  Number  Line   114   B-­‐14  

P4   Performance  Lesson  #4  –  Models  of  Fractions  (3.NF.1,  3.NF.3c)   116   B-­‐15-­‐16   3  

Post-­‐4   Post-­‐Assessment-­‐Representing  Fractions   3.NF.1,  3.NF.2,  3.NF.2a,  3.NF.3c  

120   B-­‐17   1-­‐2            

Pre-­‐5   Pre-­‐Assessment-­‐Equivalent  Fractions  &  Compare  Fractions   3.NF.1,  3.NF.3,  3.NF.3a-­‐b,  d   122   B-­‐19  

1-­‐2  

12   Equivalent  Fractions  

Prerequisite  skills  and  scaffolded  instruction  to  build  readiness  for  grade  level  standards  

and  instruction.  

124   B-­‐20  

13   Equivalent  Fractions   126   B-­‐21  

14   Equivalent  Fractions   128   B-­‐22  

15   Equivalent  Fractions   130   B-­‐23  

16   Comparing  Fractions   132   B-­‐24  

17   Comparing  Fractions   134   B-­‐25  

18   Comparing  Fractions   136   B-­‐26  

19   Comparing  Fractions   138   B-­‐27  

P5   Performance  Lesson  #5  –  Compare  Fractions  with  Models  (3.NF.1,  3.NF.3,  3.NF.3d)   140   B-­‐28-­‐29   3  

Post-­‐5   Post-­‐Assessment-­‐Equivalent  Fractions  &  Compare  Fractions   3.NF.1,  3.NF.3,  3.NF.3a-­‐b,  d   144   B-­‐30   1-­‐2  

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Standards  Plus®  Common  Core  Intervention  –  Mathematics  –  Grade  3  Domain   Lesson   Focus   Standard(s)  References   TE  pg   St.  Ed.  pg   DOK  

Num

ber  &

 Operatio

ns  –  Fractions    

Pre-­‐4   Pre-­‐Assessment-­‐Representing  Fractions   3.NF.1,  3.NF.2,  3.NF.2a,  3.NF.3c  

92   B-­‐3  

1-­‐2  

1   Identify  and  Write  Fractions  to    

Prerequisite  skills  and  scaffolded  instruction  to  build  readiness  for  grade  level  standards  

and  instruction.  

94   B-­‐4  

2   Part  of  the  Group   96   B-­‐5  

3   Part  of  the  Group   98   B-­‐6  

4   Part  of  the  Group   100   B-­‐7  

5   Part  of  the  Whole   102   B-­‐8  

6   Part  of  the  Whole   104   B-­‐9  

7   Equal  to  One   106   B-­‐10  

8   Equal  to  One   108   B-­‐11  

9   Fraction  Models   110   B-­‐12  

10   Finding  Fractions  on  a  Number  Line   112   B-­‐13  

11   Finding  Fractions  on  a  Number  Line   114   B-­‐14  

P4   Performance  Lesson  #4  –  Models  of  Fractions  (3.NF.1,  3.NF.3c)   116   B-­‐15-­‐16   3  

Post-­‐4   Post-­‐Assessment-­‐Representing  Fractions   3.NF.1,  3.NF.2,  3.NF.2a,  3.NF.3c  

120   B-­‐17   1-­‐2            

Pre-­‐5   Pre-­‐Assessment-­‐Equivalent  Fractions  &  Compare  Fractions   3.NF.1,  3.NF.3,  3.NF.3a-­‐b,  d   122   B-­‐19  

1-­‐2  

12   Equivalent  Fractions  

Prerequisite  skills  and  scaffolded  instruction  to  build  readiness  for  grade  level  standards  

and  instruction.  

124   B-­‐20  

13   Equivalent  Fractions   126   B-­‐21  

14   Equivalent  Fractions   128   B-­‐22  

15   Equivalent  Fractions   130   B-­‐23  

16   Comparing  Fractions   132   B-­‐24  

17   Comparing  Fractions   134   B-­‐25  

18   Comparing  Fractions   136   B-­‐26  

19   Comparing  Fractions   138   B-­‐27  

P5   Performance  Lesson  #5  –  Compare  Fractions  with  Models  (3.NF.1,  3.NF.3,  3.NF.3d)   140   B-­‐28-­‐29   3  

Post-­‐5   Post-­‐Assessment-­‐Equivalent  Fractions  &  Compare  Fractions   3.NF.1,  3.NF.3,  3.NF.3a-­‐b,  d   144   B-­‐30   1-­‐2  

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Resources

4

Num

ber &

Ope

ratio

ns –

Fra

ction

s

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Pre-Assessment - Teacher Lesson Plan - Sample

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Teacher Lesson Plan

122

Standards Plus® – Common Core Intervention Mathematics – Grade 3 Domain: Number & Operations ‐ Fractions   Focus: Equivalent Fractions & Compare Fractions  Pre‐Assessment: 5

Procedure:  Each intervention assessment is designed to be completed independently by the students.  Read the directions aloud, and ensure that students understand how to mark their answer choices.   Review:  Review the correct answers with students as soon as they are finished.    

Answers:  1. 1 part shaded on the left; 2 parts shaded on the right. 2. 3 parts shaded in both figures.  Answers may vary:  They 

are not equivalent because the size and shape of the triangles are different. 

3. >; 7 parts shaded in both figures. 4. <; 3 parts shaded on the left; 4 parts shaded on the right. 5. =; 2 parts shaded in both figures. 

    

St. Ed. Pg. B-19

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Pre-Assessment - Student Page - Sample

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Student Page

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Standards Plus® – Common Core Intervention Mathematics – Grade 3 Domain: Number & Operations ‐ Fractions   Focus: Equivalent Fractions & Compare Fractions  Pre‐Assessment: 5

 

Directions: Shade to show equivalent fractions. 1. 

        13              

26  

 

Directions: Shade to show each fraction.  Explain why they are not equivalent on the lines below. 

2. 

38              

34  

 

 

 

 Directions:  Shade to show each fraction.  Use >, =, or < to compare the fractions.  Write the symbol on the line.  

3.  

79    _______  

712  

4. 

34    _______  

44  

5. 

27    _______  

27  

 

0

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Teacher Lesson Plan

124

Standards Plus® – Common Core Intervention Mathematics – Grade 3Domain:  Number & Operations – Fractions  Focus:  Equivalent Fractions  Lesson:  # 12

Lesson Objective:  Identify and represent equivalent fractions.  Introduction:  Today students will learn about equivalent fractions.   Instruction:  “We have learned how to show fractions as part of the whole and fractions as part of a group.  We have also learned about fractions that are equal to one.  Today we will learn about fractions that are equivalent.  Equivalent means that the fractions represent the same size and shape.  At the top of the page, we see two squares.  They are the same size and shape.  The square on the left is divided into two parts.  When we divide a shape into two equal parts, we have halves.  The fraction next to the square is one‐half.  There is one part shaded to show one‐half.  The square on the right is divided into four parts.  When a shape is divided into four equal parts, we have fourths.  The fraction next to the square is two‐fourths.  There are two parts shaded to show two‐fourths.  Even though the square is divided into a different number of parts, the area that is shaded is the same size and shape, so they are equivalent.”  Guided Practice:  “Today we will shade to show equivalent fractions.  Look at the example.  It shows two circles.  The circle on the left is divided into eight parts.  The circle on the right is divided into four parts.  Are the circles the same shape and size?  (Discuss.)  Because the circles are the same shape and size, we can use them to show equivalent fractions.  The fraction on the left says six‐eighths.  How many parts should we shade?  (6)  Let’s shade six parts.  (Pause.)  The fraction on the right should be equivalent to the fraction on the left.  Let’s shade to see.  The fraction on the right is three‐fourths.  How many parts will we shade?  (3)  Shade three parts.  (Pause.)  Notice that we shaded areas that were the same size and shape, so six‐eighths and three‐fourths are equivalent.”  Independent Practice:  “You will shade to show equivalent fractions two more times today.”  Review:  After 5 minutes, review the answers.  Shade as a model for the students to check their work.  Elicit student responses on how to say each fraction name.  Emphasize the th in each denominator to ensure that students hear it.  Closure:  “Today you shaded to show equivalent fractions.”    Answers:  1. Three parts shaded; one part shaded

2. Two parts shaded; four parts shaded 

 

St. Ed. Pg. B-20NOF - Teacher Lesson Plan - Sample

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Student Page

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Standards Plus® – Common Core Intervention Mathematics – Grade 3Domain:  Number & Operations – Fractions  Focus:  Equivalent Fractions  Lesson:  # 12

12              

24  

  

Example:  68

 

34  

Directions:  Shade to show each fraction. 

1.  

36

 

12  

2.  

25

 

410  

NOF - Student Page - Sample

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This Lesson Set Scaffolds Instruction for the following Grade 3

Numbers & Operations Fractions Standards...

The lesson set provides students multiple exposures

to prerequisite skills and grade level skills. This

guides learners toward the mastery of these

grade level 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.3 - Explain equivalence of fractions in special cases, and compare fractions by reasoning about their size.

3.NF.3a - Understand two fractions as equivalent (equal) if they are the same size, or the same point on a number line.

3.NF.3b - 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.3d - 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 conclu-sions, e.g., by using a visual fraction model.

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The Lessons Scaffold instruction for standards 3.NF.1, 3.NF.3, 3.NF.3a, 3.NF.3b, 3.NF.3d

Prerequisite Skills

Grade Level Skills

LESSONS12-13 LESSON

14

Identify and represent equivalent fractions.

LESSON OBJECTIVE:LESSON OBJECTIVE:Identify and

represent equivalent

fractions that are

equal to one.

LESSONS16-19LESSON

15

LESSON OBJECTIVE:LESSON OBJECTIVE:

Explain why given fractions are not

equivalent.

Demonstrate the ability

to use the symbols

<, >, = to compare

fractions.

InstructionStarts Here

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Post-Assessment - Teacher Lesson Plan - Sample

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Teacher Lesson Plan

144

Standards Plus® – Common Core Intervention Mathematics – Grade 3 Domain: Number & Operations ‐ Fractions   Focus: Equivalent Fractions & Compare Fractions  Post‐Assessment: 5

Procedure:  Each intervention assessment is designed to be completed independently by the students.  Read the directions aloud, and ensure that students understand how to mark their answer choices.   Review:  Review the correct answers with students as soon as they are finished.    

Answers:  1. 5 part shaded on the left; 10 parts shaded on the right. 2. 3 parts shaded in both figures.  Answers may vary:  They 

are not equivalent because the size of the rectangles is different. 

3. =; 5 parts shaded in both figures. 4. >; 7 parts shaded on the left; 1 part shaded on the right. 5. <; 2 parts shaded in both figures. 

    

St. Ed. Pg. B-30

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Post-Assessment - Student Page - Sample

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Student Page

145

Standards Plus® – Common Core Intervention Mathematics – Grade 3 Domain: Number & Operations ‐ Fractions   Focus: Equivalent Fractions & Compare Fractions  Post‐Assessment: 5

 

Directions: Shade to show equivalent fractions. 1. 

        56              

1012  

 

Directions: Shade to show each fraction.  Explain why they are not equivalent on the lines below. 

2. 

          35              

37  

 

 

 

 Directions:  Shade to show each fraction.  Use >, =, or < to compare the fractions.  Write the symbol on the line.  

3.  

511    _______  

511  

4. 

78    _______  

18  

5.  

29    _______  

23  

 

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Standards Plus® Common Core Interventi on – Mathemati cs – Grade 3Number & Operati ons - Fracti ons Performance Task #5

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Teacher Lesson Plan

140

Standards Plus® Common Core Intervention Mathematics – Grade 3Number and Operations – Fractions Performance Task #5 

Lesson Objective:  The students will draw models of fractions to compare them. 

Instruction:  “Today you will draw models of fractions.  Then you will compare each pair of fractions using less than, equal to, and greater than.” 

Guided Practice:  Point out the fractions for one‐fourth and five‐eighths on the student page.  “We need to have two models that are the exact same size overall.  We will divide one of the models into four equal parts.  We will divide the other model into eight equal parts.  Since we have a square, we can draw a vertical line to divide the square in half.  Then we can draw a horizontal line to divide the square into fourths.  Now we have fourths.  Let’s shade one of the fourths to show one‐fourth.  Look at the second square.  We need to divide it into eighths.  We can draw a vertical line and a horizontal line to make fourths.  Then we can draw two more lines.  We can draw two more vertical lines to split the fourths into eighths.  We can draw two horizontal lines to split the fourths into eighths.  We can also draw two diagonal lines to split the fourths into eighths.  I will draw diagonal lines from corner to corner to make this square show eighths.  Let’s shade five of the eighths to show five‐eighths.  Now we need to compare the fractions.  Is one‐fourth less than, equal to, or greater than five‐eighths?”  Use the less than (<) symbol to show that one‐fourth is less than five‐eighths.   

Independent Practice:  “You will draw lines to show each of the given fractions.  Shade to show each fraction.  Then compare them.  Write the comparison sign (<, =, >) to show how the two fractions compare.  For number three, you will need to draw the models yourself.  Make them as close to the same size as you can.  You may want to use a ruler to help you.” 

Review:  Review together as a class. 

 

 

 

 

St. Ed. Pg. B-28-29Performance Task - Teacher Lesson Plan - Sample

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Standards Plus® Common Core Interventi on – Mathemati cs – Grade 3Number & Operati ons - Fracti ons Performance Task #5

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Student Page 1 of 2

141

Standards Plus® Common Core Intervention Mathematics – Grade 3Number and Operations – Fractions Performance Task #5 

>               <               =        greater than             less than                 equal to 

14   ___________   

58  

 

1.                     15   ___________   

115  

 

 

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142

Standards Plus® Common Core Intervention Mathematics – Grade 3Number and Operations – Fractions Performance Task #5 

2.                     46   ___________   

56  

 

3.                     23   ___________   

49  

 

Standards Plus® Common Core Interventi on – Mathemati cs – Grade 3Number & Operati ons - Fracti ons Performance Task #5

Performance Task - Student Pages - Sample

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