# MAT-05 "I can ... statements"

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# Geometry

## Narrative for the (G) Geometry

By the end of Grade 5, competencies in shape composition and decomposition, and especially the special case of spatial structuring of rectangular arrays should be highly developed. Students need to develop these competencies because they form a foundation for understanding multiplication, area, volume, and the coordinate plane.

Students extend their spatial structuring in two ways. They learn to spatially structure in three dimensions; for example, they can decompose a right rectangular prism built from cubes into layers, seeing each layer as an array of cubes. They use this understanding to find the volumes of right rectangular prisms with edges whose lengths are whole numbers as the number of unit cubes that pack the prisms.  Second, students extend their knowledge of the coordinate plane, understanding the continuous nature of two-dimensional space and the role of fractions in specifying locations in that space.

Students in Grade 5 learn to analyze and relate categories of two-dimensional and three-dimensional shapes explicitly based on their properties. Based on analysis of properties, they classify two-dimensional figures in hierarchies.

Students also solve mathematical and real-world problems using coordinates. They graph connect ordered pairs of (whole number) coordinates to points on a grid, so that these coordinate pairs constitute numerical objects.  Students then interpret the results within the context of situation.

## 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-05.G.01

Under Development

 MAT-05 Targeted Standards(G) Domain: GeometryCluster: Graph points on the coordinate place to solve real­world and mathematical problems. MAT-05.G.01 Use a pair of perpendicular number lines, called axes, to define a coordinate system, with the intersection of the lines (the origin) arranged to coincide with the 0 on each line and a given point in the plane located by using an ordered pair of numbers, called its coordinates. Understand that the first number indicates how far to travel from the origin in the direction of one axis, and the second number indicates how far to travel in the direction of the second axis, with the convention that the names of the two axes and the coordinates correspond (e.g., x-axis and x-coordinate, y-axis and y-coordinate).

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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-05.G.02

Under Development

 MAT-05 Targeted Standards(G) Domain: GeometryCluster: Graph points on the coordinate place to solve real­world and mathematical problems. MAT-05.G.02 Represent real world and mathematical problems by graphing points in the first quadrant of the coordinate plane, and interpret coordinate values of points in the context of the situation.

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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-05.G.03

Under Development

 MAT-05 Targeted Standards(G) Domain: GeometryCluster: Classify two­dimensional figures into categories based on their properties. MAT-05.G.03 Understand that attributes belonging to a category of two-dimensional figures also belong to all subcategories of that category. For example, all rectangles have four right angles and squares are rectangles, so all squares have four right angles.

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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-05.G.04

 MAT-05 Targeted Standards(G) Domain: GeometryCluster: Classify two ­dimensional figures into categories based on their properties. MAT-05.G.04 Classify two-dimensional figures in a hierarchy based on properties.

## Student Learning Targets:

### Knowledge Targets

• I can identify attributes of two-dimensional shapes (square, rectangle, rhombus).

### Reasoning Targets

• I can classify shapes in a hierarchy based on their properties and attributes.

## Rubric / Proficiency Scale

 Score Description Sample Activity 4.0 Advanced Criteria is Under Development. In addition to Score 3.0 performance, the student demonstrates in-depth inferences and applications regarding the more complex content - 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 Student is able to classify a square, rectangle, and rhombus based on their common properties; and accurately classify shapes in a hierarchy. I can accurately classify shapes in a hierarchy based on their properties and attributes. I can identify the properties shared by squares, rectangles, and rhombuses and can accurately explain why they belong in the same category. - 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 identify attributes and properties of a square, rectangle, and rhombus and partially explain why they belong in the same category; and demonstrates partial understanding of how they are related; and is able to classify shapes in a hierarchy with partial success. I can classify some shapes in a hierarchy. I can identify the properties shared by squares, rectangles, and rhombuses and can partially explain why they belong in the same category. - 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 identify attributes and properties of a square, rectangle, and rhombus but is unable to explain how the shapes relate to one another. I can identify attributes of two dimensional shapes (square, rectangle, rhombus). - 0.5 Limited or no understanding of the skill is demonstrated.

## Resources

### Vocabulary

• classify
• category
• attribute - features
• subcategory
• hierarchy
• two dimensional
• properties
• polygon
• rectangle
• square
• rhombus
• parallelogram
• parallel sides
• right angles
• congruent

# Measurement and Data

## Narrative for the (MD) Measurement and Data

In Grade 5, students extend their measurement abilities from Grade 4 to express measurements in larger or smaller units within a measurement system.  The major emphasis for measurement in Grade 5 is volume. Volume not only introduces a third dimension and thus a significant challenge to students’ spatial structuring, but also complexity in the nature of the materials measured.

As students work with data in Grades K–5, they build foundations for their study of statistics and probability in Grades 6 and beyond, and they strengthen and apply what they are learning in arithmetic. Kindergarten work with data uses counting and order relations.  In Grades 3–5, work with data is closely related to the number line, fraction concepts, fraction arithmetic, and solving problems that involve the four operations.

By the end of Grade 5, students should be comfortable making line plots for measurement data and analyzing data shown in the form of a line plot. As in earlier grades, students should work with data in science and other subjects. Grade 5 students working in these contexts should be able to give deeper interpretations of data than in earlier grades.

## 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-05.MD.01

Under Development

 MAT-05 Targeted Standards(MD) Domain: Measurement and DataCluster: Convert like measurement units within a given measurement system. MAT-05.MD.01 Convert among different-sized standard measurement units within a given measurement system (e.g., convert 5 cm to 0.MAT-05.m), and use these conversions in solving multi-step, real world problems.

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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-05.MD.02

Under Development

 MAT-05 Targeted Standards(MD) Domain: Measurement and DataCluster: Represent and interpret data. MAT-05.MD.02 Make a line plot to display a data set of measurements in fractions of a unit (1/2, 1/4, 1/8). Use operations on fractions for this grade to solve problems involving information presented in line plots. For example, given different measurements of liquid in identical beakers, find the amount of liquid each beaker would contain if the total amount in all the beakers were redistributed equally.

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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-05.MD.03

Under Development

 MAT-05 Targeted Standards(MD) Domain: Measurement and DataCluster: Geometric measurement: understand concepts of volume and relate volume to multiplication and to addition. MAT-05.MD.03 Recognize volume as an attribute of solid figures and understand concepts of volume measurement.

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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-05.MD.03.a

Under Development

 MAT-05 Targeted Standards(MD) Domain: Measurement and DataCluster: Geometric measurement: understand concepts of volume and relate volume to multiplication and to addition. MAT-05.MD.03.a Recognize volume as an attribute of solid figures and understand concepts of volume measurement. A cube with side length 1 unit, called a unit cube, is said to have one cubic unit of volume, and can be used to measure volume.

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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.