What do the Common Core State Standards expect 3rd 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.
Learn Zillion- use your google email account to log in
IXL
Illustrative Mathematics
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.
Bubble Gum Contest
3rd Grade Fraction Unit
Comparing Fractions with spinners
Equivalent Fractions Mix-n-Match by Laura Candler
Equivalent Fraction Pizza Fraction Fun by Laura Candler
Fraction Sorting: Comparing and Ordering by Laura Candler
Ordering Fractions by Laura Candler
K-5 Teaching Resources: This page provides examples of 3rd 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 Equivalent Fractions: Create equivalent fractions by dividing and shading squares or circles, and match each fraction to its location on the number line.
NCTM Illuminations Eggsactly with Fractions: In this unit, students explore relationships among fractions through work with the set model. This early work with fraction relationships helps students make sense of basic fraction concepts and facilitates work with comparing and ordering fractions and working with equivalency.
NCTM Illuminations Fun With Pattern Block Fractions: In this unit, students explore relationships among fractions through work with the region model. This early work with fraction relationships helps students make sense of basic fraction concepts and facilitates work with comparing and ordering fractions and working with equivalency. This unit consists of five lessons designed to help the students understand fractions when they are represented as a part of a region. Subsequent units develop understanding of other fraction models (e.g., set, area, and length). Representing fractions in a variety of ways helps students see relationships and develop understanding of later fraction concepts. It is important that students "see" a variety of concrete examples in addition to pictorial representations. The following lessons incorporate the use of physical and virtual manipulatives.
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
IXL
Illustrative Mathematics
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.
Bubble Gum Contest
3rd Grade Fraction Unit
Comparing Fractions with spinners
Equivalent Fractions Mix-n-Match by Laura Candler
Equivalent Fraction Pizza Fraction Fun by Laura Candler
Fraction Sorting: Comparing and Ordering by Laura Candler
Ordering Fractions by Laura Candler
K-5 Teaching Resources: This page provides examples of 3rd 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 Equivalent Fractions: Create equivalent fractions by dividing and shading squares or circles, and match each fraction to its location on the number line.
NCTM Illuminations Eggsactly with Fractions: In this unit, students explore relationships among fractions through work with the set model. This early work with fraction relationships helps students make sense of basic fraction concepts and facilitates work with comparing and ordering fractions and working with equivalency.
NCTM Illuminations Fun With Pattern Block Fractions: In this unit, students explore relationships among fractions through work with the region model. This early work with fraction relationships helps students make sense of basic fraction concepts and facilitates work with comparing and ordering fractions and working with equivalency. This unit consists of five lessons designed to help the students understand fractions when they are represented as a part of a region. Subsequent units develop understanding of other fraction models (e.g., set, area, and length). Representing fractions in a variety of ways helps students see relationships and develop understanding of later fraction concepts. It is important that students "see" a variety of concrete examples in addition to pictorial representations. The following lessons incorporate the use of physical and virtual manipulatives.
Modeling Fractions Videos with Thinking Blocks