What do the Common Core State Standards expect 5th grade students to know and be able to do, in regards to fractions?
Assessments usually fall into two major categories:
1. Summative- cumulative evaluations that might generate a single score, such as an end-of-unit test or a standardized test, such as EOG.
2. Formative- used to determine the point-in-time status of students' understanding, to preassess, or to attempt to identify students' naïve
understandings or misconceptions. The information is interpreted and used to provide feedback and make decisions about the next instructional steps. There are three key processes on formative assessment: 1) Establishing where the learners are in their learning, 2) Establishing where they are going, and 3) Working on how to get there.
Analogy: Formative assessment is like a digital snapshot, formative assessment is like a streaming video.
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Illustrative Mathematics
IXL
Instructional Principles, as described by the authors of Adding It Up (National Research Council, 2001), conclude that all students are best served when you give attention to the following three principles:
1. Learning with understanding is based on connecting and organizing knowledge around big conceptual ideas.
2. Learning builds on what students already know.
3. Instruction in school should take advantage of students' informal knowledge of mathematics.
These principles, also reflected in tenets of constructivist theory, apply that all learners and therefore are essential in making decisions about how you can adapt instruction to meet individual learners' needs through accommodations and modifications.
The CSA (Concrete, Semi-Concrete, Abstract) model,
also known as the CRA (Concrete, Representational, Abstract) model, has been used in mathematics education for years. Based on Bruner's
reasoning theory (1966), this model reflects a sequence that begins with an instructional focus on concrete representations (manipulatives
and tools), then moves to a semi-concrete representation (drawings and pictures) to a abstract representation (using only numerals or mentally solving problems) over time. Built into this approach is the return to visual models and concrete representations as needed or as students begin to explore new concepts or extensions of concepts previously learned. As students share reasoning that shows they are beginning to understand a mathematical concept, there can be a shift to semi-concrete representations. Then students can begin to articulate their thought processes using an appropriate model, which is evidence of the students' performance on targeted assessments. In the last component of the CSA model, students are capable of working with abstract aspects of the concepts without an emphasis on concrete or semi-concrete images.
NC DPI Lessons for Learning- not just fractions
Using Models to Add Fractions Video by Teacher Tube
Using Models to Multiply Fractions Video by Teacher Tube
Using Counters to Multiply Fractions Video by Teacher Tube
Marilyn Burns Fraction Kit: Cover Up and Uncover
Fraction Word Problems by Laura Candler
Adding and Subtracting Fractions with unlike denominators Math Pathways and Pitfalls by West Ed
Fractions of the Week- spiral and review
K-5 Teaching Resources: This page provides examples of 5th Grade Number Activities aligned with the Common Core State Standards. All activities are suitable for use in Math Centers, small group or whole class settings and are designed to elicit a range of responses and provide opportunities for students to communicate their reasoning and mathematical thinking. Instructions for each task are typed in large print and written in child-friendly language to enable students to work on activities independently after a brief introduction to the task.
NCTM Illuminations Fraction Tracks Game: This applet allows students to individually practice working with relationships among fractions and ways of combining fractions.
Modeling Fractions Videos with Thinking Blocks
Assessments usually fall into two major categories:
1. Summative- cumulative evaluations that might generate a single score, such as an end-of-unit test or a standardized test, such as EOG.
2. Formative- used to determine the point-in-time status of students' understanding, to preassess, or to attempt to identify students' naïve
understandings or misconceptions. The information is interpreted and used to provide feedback and make decisions about the next instructional steps. There are three key processes on formative assessment: 1) Establishing where the learners are in their learning, 2) Establishing where they are going, and 3) Working on how to get there.
Analogy: Formative assessment is like a digital snapshot, formative assessment is like a streaming video.
Learn Zillion- use your Google email account to log in
Illustrative Mathematics
IXL
Instructional Principles, as described by the authors of Adding It Up (National Research Council, 2001), conclude that all students are best served when you give attention to the following three principles:
1. Learning with understanding is based on connecting and organizing knowledge around big conceptual ideas.
2. Learning builds on what students already know.
3. Instruction in school should take advantage of students' informal knowledge of mathematics.
These principles, also reflected in tenets of constructivist theory, apply that all learners and therefore are essential in making decisions about how you can adapt instruction to meet individual learners' needs through accommodations and modifications.
The CSA (Concrete, Semi-Concrete, Abstract) model,
also known as the CRA (Concrete, Representational, Abstract) model, has been used in mathematics education for years. Based on Bruner's
reasoning theory (1966), this model reflects a sequence that begins with an instructional focus on concrete representations (manipulatives
and tools), then moves to a semi-concrete representation (drawings and pictures) to a abstract representation (using only numerals or mentally solving problems) over time. Built into this approach is the return to visual models and concrete representations as needed or as students begin to explore new concepts or extensions of concepts previously learned. As students share reasoning that shows they are beginning to understand a mathematical concept, there can be a shift to semi-concrete representations. Then students can begin to articulate their thought processes using an appropriate model, which is evidence of the students' performance on targeted assessments. In the last component of the CSA model, students are capable of working with abstract aspects of the concepts without an emphasis on concrete or semi-concrete images.
NC DPI Lessons for Learning- not just fractions
Using Models to Add Fractions Video by Teacher Tube
Using Models to Multiply Fractions Video by Teacher Tube
Using Counters to Multiply Fractions Video by Teacher Tube
Marilyn Burns Fraction Kit: Cover Up and Uncover
Fraction Word Problems by Laura Candler
Adding and Subtracting Fractions with unlike denominators Math Pathways and Pitfalls by West Ed
Fractions of the Week- spiral and review
K-5 Teaching Resources: This page provides examples of 5th Grade Number Activities aligned with the Common Core State Standards. All activities are suitable for use in Math Centers, small group or whole class settings and are designed to elicit a range of responses and provide opportunities for students to communicate their reasoning and mathematical thinking. Instructions for each task are typed in large print and written in child-friendly language to enable students to work on activities independently after a brief introduction to the task.
NCTM Illuminations Fraction Tracks Game: This applet allows students to individually practice working with relationships among fractions and ways of combining fractions.
Modeling Fractions Videos with Thinking Blocks