All categories Categories All categories Not categorized Prioritized (G) Geometry (MD) Measurement and Data (NBT) Number and Operations in Base Ten (NF) Number and Operations - Fractions (OA) Operations and Algebraic Thinking

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# Geometry

## Narrative for the (G) Geometry

Grade 4 students describe, analyze, compare, and classify two-dimensional shapes by their properties, including explicit use of angle sizes and the related geometric properties of perpendicularity and parallelism.

By the end of Grade 4, students develop explicit awareness of and vocabulary for many concepts they have been developing, including points, lines, line segments, rays, angles (right, acute, obtuse), and perpendicular and parallel lines. Such mathematical terms are useful in communicating geometric ideas, but more important is that constructing examples of these concepts, such as drawing angles and triangles that are acute, obtuse, and right, help students form richer concept images connected to verbal definitions.

## Calculation Method for Domains

Domains are larger groups of related standards. The Domain Grade is a calculation of all the related standards. Click on the standard name below each Domain to access the learning targets and rubrics/ proficiency scales for individual standards within the domain.

#### MAT-04.G.02

4th Grade (MAT) Targeted Standard
(G) Geometry
Cluster: Draw and identify lines and angles, and classify shapes by properties of their lines and angles.

# Measurement and Data

## Narrative for the (MD) Measurement and Data

In Grade 4, students build on competencies in measurement and in building and relating units and units of units that they have developed in number, geometry, and geometric measurement.

Fourth graders learn the relative sizes of measurement units within a system of measurement4.MD.1 including: length: meter (m), kilometer (km), centimeter (cm), millimeter (mm); volume: liter (l), milliliter (ml, 1 cubic centimeter of water; a liter, then, is 1000 ml); mass: gram (g, about the weight of a cc of water), kilogram (kg); time: hour (hr), minute (min), second (sec).

Students learn to consider perimeter and area of rectangles, begun in Grade 3, more abstractly. Based on work in previous grades with multiplication, spatially structuring arrays, and area, they abstract the formula for the area of a rectangle.Students learn to apply these understandings and formulas to the solution of real-world and mathematical problems.

Students can use these skills to solve problems, including problems that arise from analyzing line plots. For example, with reference to the line plot above, students might find the difference between the greatest and least values in the data.

## Calculation Method for Domains

Domains are larger groups of related standards. The Domain Grade is a calculation of all the related standards. Click on the standard name below each Domain to access the learning targets and rubrics/ proficiency scales for individual standards within the domain.

#### MAT-04.MD.06

4th Grade (MAT) Targeted Standard
(MD) Measurement and Data
Cluster: Geometric measurement: understand concepts of angle and measure angles.

# Number and Operation in Base Ten

## Narrative for the (NBT) Number and Operation in Base Ten

At Grade 4, students extend their work in the base-ten system. They use standard algorithms to fluently add and subtract. They use methods based on place value and properties of operations supported by suitable representations to multiply and divide with multi-digit numbers. Visual representations such as area and array diagrams that students draw and connect to equations and other written numerical work are useful for this purpose. By reasoning repeatedly about the connection between math drawings and written numerical work, students can come to see multiplication and division algorithms as abbreviations or summaries of their reasoning about quantities.

Building on earlier work, students generalize place value understanding for multi-digit whole numbers to read, write, and compare whole numerals between 1,000 and 1,000,000. They also extend understanding of place value to include decimals to hundredths and fractional quantities 1/10 and 1/100.

## Calculation Method for Domains

Domains are larger groups of related standards. The Domain Grade is a calculation of all the related standards. Click on the standard name below each Domain to access the learning targets and rubrics/ proficiency scales for individual standards within the domain.

#### MAT-04.NBT.02

4th Grade (MAT) Targeted Standard
(NBT) Number and Operations in Base Ten
Cluster: Generalize place value understanding for multi­digit whole numbers. Limited to whole numbers less than or equal to 1,000,000.

#### MAT-04.NBT.04

4th Grade (MAT) Targeted Standard
(NBT) Number and Operations in Base Ten
Cluster: Use place value understanding and properties of operations to perform multi-­digit arithmetic.

#### MAT-04.NBT.05

4th Grade (MAT) Targeted Standard
(NBT) Number and Operations in Base Ten
Cluster: Use place value understanding and properties of operations to perform multi­-digit arithmetic.

#### MAT-04.NBT.06

4th Grade (MAT) Targeted Standard
(NBT) Number and Operations in Base Ten
Cluster: Use place value understanding and properties of operations to perform multi­-digit arithmetic.

# Number and Operations - Fraction

## Narrative for (NF) Number and Operations - Fractions

Grade 4 students learn a fundamental property of equivalent fractions: multiplying the numerator and denominator of a fraction by the same non-zero whole number results in a fraction that represents the same number as the original fraction. This property forms the basis for much of their other work in Grade 4, including the comparison, addition, and subtraction of fractions and the introduction of decimals.

Grade 4 students use their understanding of equivalent fractions to compare fractions with different numerators and different denominators. Students use area models and number line diagrams to reason about equivalence.  Students also compare decimals using the meaning of a decimal as a fraction, making sure to compare fractions with the same denominator. For example, to compare 0.2 and 0.09, students think of them as 0.20 and 0:09 and see that 0.20>0.09 because 20/100 > 9/100.

Using the understanding gained from work with whole numbers of the relationship between addition and subtraction, students add and subtract fractions with the same denominator. Students also compute sums of whole numbers and fractions, by representing the whole number as an equivalent fraction with the same denominator as the fraction. Grade 4 students also solve word problems involving multiplication of a fraction by a whole number.

## Calculation Method for Domains

Domains are larger groups of related standards. The Domain Grade is a calculation of all the related standards. Click on the standard name below each Domain to access the learning targets and rubrics/ proficiency scales for individual standards within the domain.

#### MAT-04.NF.02

4th Grade (MAT) Targeted Standard
(NF) Number and Operations - Fractions
Cluster: Extend understanding of fraction equivalence and ordering.

#### MAT-04.NF.03

4th Grade (MAT) Targeted Standard
(NF) Number and Operations - Fractions
Cluster: Build fractions from unit fractions by applying and extending previous understandings of operations on whole numbers.

##### MAT-04.NF.03 Understand a fraction a/b with a > 1 as a sum of unit fractions 1/b.
a. Understand addition and subtraction of fractions as joining and separating parts referring to the same whole.
b. Decompose a fraction into a sum of fractions with the same denominator in more than one way, recording each decomposition with an equation. Justify decompositions by using a visual fraction model or other strategies.
c. Add and subtract mixed numbers with like-denominators.
d. Using visual fraction models and equations, solve word problems involving addition and subtraction of fractions referring to the same whole and having like denominators.

#### MAT-04.NF.04

4th Grade (MAT) Targeted Standard
(NF) Number and Operations - Fractions
Cluster: Build fractions from unit fractions by applying and extending previous understandings of operations on whole numbers.

##### MAT-04.NF.04 Apply and extend previous understandings of multiplication to multiply a fraction by a whole number.
a. Understand a fraction a/b as a multiple of 1/b.
b. Understand a multiple of a/b as a multiple of 1/b, and use this understanding to multiply a fraction by a whole number.
c. Using visual fraction models and equations, solve word problems involving multiplication of a fraction by a whole number.

#### MAT-04.NF.07

4th Grade (MAT) Targeted Standard
(NF) Number and Operations - Fractions
Cluster: Understand decimal notation for fractions, and compare decimal fractions.

# Operations and Algebraic Thinking

## Narrative for the (OA) Operations and Algebraic Thinking

Algebraic thinking is about generalizing arithmetic operations and operating on unknown quantities.  It involves recognizing and analyzing patterns and developing generalizations about these patterns.  In algebra, symbols can be used to represent generalizations. Operations and Algebraic Thinking deals with the basic operations - addition, subtraction, multiplication, and division - the relationships they model, the kinds of problems they can be used to solve, as well as, their mathematical properties and relationships.

Fourth graders extend problem solving to multi-step word problems using the four operations posed with whole numbers.  Some problems might easily be represented with a single equation, and others will be more sensibly represented by more than one equation or a diagram and one or more equations. Consider two diving boards, one 40 feet high, the other 8 feet high. Students in earlier grades learned to compare these heights in an additive sense—“This one is 32 feet higher than that one”—using addition and subtraction to solve word problems. Students in Grade 4 learn to compare these quantities multiplicatively as well: “This one is 5 times as high as that one.”

Students reason about number or shape patterns, connecting a rule for a given pattern with its sequence of numbers or shapes. In examining numerical sequences and patterns, fourth graders can explore rules of repeatedly adding the same whole number or repeatedly multiplying by the same whole number.

Fourth graders also build upon earlier understandings about multiplication and division. Students examine various patterns in factor pairs by finding factor pairs for all numbers 1 to 100, and extend the idea of decomposition to multiplication and learn to use the terms multiple, prime number, composite number.

## Calculation Method for Domains

Domains are larger groups of related standards. The Domain Grade is a calculation of all the related standards. Click on the standard name below each Domain to access the learning targets and rubrics/ proficiency scales for individual standards within the domain.

#### MAT-04.OA.03

4th Grade (MAT) Targeted Standard
(OA) Operations and Algebraic Thinking
Cluster: Understand decimal notation for fractions, and compare decimal fractions.

# Geometry

## Narrative for the (G) Geometry

Grade 4 students describe, analyze, compare, and classify two-dimensional shapes by their properties, including explicit use of angle sizes and the related geometric properties of perpendicularity and parallelism.

By the end of Grade 4, students develop explicit awareness of and vocabulary for many concepts they have been developing, including points, lines, line segments, rays, angles (right, acute, obtuse), and perpendicular and parallel lines. Such mathematical terms are useful in communicating geometric ideas, but more important is that constructing examples of these concepts, such as drawing angles and triangles that are acute, obtuse, and right, help students form richer concept images connected to verbal definitions.

## Calculation Method for Domains

Domains are larger groups of related standards. The Domain Grade is a calculation of all the related standards. Click on the standard name below each Domain to access the learning targets and rubrics/ proficiency scales for individual standards within the domain.

#### MAT-04.G.01

Under Development

 MAT-04 Targeted Standards(G) Domain: GeometryCluster: Draw and identify lines and angles, and classify shapes by properties of their lines and angles. MAT-04.G.01 Draw points, lines, line segments, rays, angles (right, acute, obtuse), and perpendicular and parallel lines. Identify these in two-dimensional figures.

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## Proficiency (Rubric) Scale

 Score Description Sample Activity 4.0 Student is able to - 3.5 In addition to Score 3.0 performance, the student demonstrates in-depth inferences and applications regarding the more complex content with partial success. 3.0 “The Standard.” Student is able to - 2.5 No major errors or emissions regarding 2.0 content and partial knowledge of the 3.0 content. 2.0 Student is able to - 1.5 In addition to 1.0 content, student has partial knowledge of the 2.0 and/or 3.0 content. 1.0 Student is able to - 0.5 Limited or no understanding of the skill id demonstrated.

## Resources

### Vocabulary

• List

#### MAT-04.G.02

4th Grade (MAT) Targeted Standard
(G) Geometry
Cluster: Draw and identify lines and angles, and classify shapes by properties of their lines and angles.

#### MAT-04.G.03

Under Development

 MAT-04 Targeted Standards(G) Domain: GeometryCluster: Draw and identify lines and angles, and classify shapes by properties of their lines and angles. MAT-04.G.03 Recognize a line of symmetry for a two-dimensional figure as a line across the figure such that the figure can be folded along the line into matching parts. Identify line-symmetric figures and draw lines of symmetry.

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## Proficiency (Rubric) Scale

 Score Description Sample Activity 4.0 Student is able to - 3.5 In addition to Score 3.0 performance, the student demonstrates in-depth inferences and applications regarding the more complex content with partial success. 3.0 “The Standard.” Student is able to - 2.5 No major errors or emissions regarding 2.0 content and partial knowledge of the 3.0 content. 2.0 Student is able to - 1.5 In addition to 1.0 content, student has partial knowledge of the 2.0 and/or 3.0 content. 1.0 Student is able to - 0.5 Limited or no understanding of the skill id demonstrated.