Standards - Mathematics

2019 - Mathematics Course of Study Document
Mathematics (2019) Grade(s): 6

MA19.6.21

Identify, represent, and analyze two quantities that change in relationship to one another in real-world or mathematical situations.

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Knowledge

Students know:
  • Roles of dependent and independent variables.
  • Correct translation between verbally stated situations and mathematical symbols and notation.

Skills

Students are able to:
  • Represent real-world problems involving two quantities that change in relationship to one another using equations, graphs, and tables,
  • Use mathematical vocabulary to explain connections among representations of function contexts.
  • Analyze and interpret the relationship between the independent and the dependent variable in a given situation.

Understanding

Students understand that:
  • Equations with two variables represent mathematical relationships in which the value of the dependent variable varies with changes in the independent variable.
  • A symbolic or visual representation of relevant features of a real-world problem can aid in interpretation of the situation.
  • Translating between language, a table, an equation, or a graph represents the same relationship and provides a different perspective on the function.

Vocabulary

  • Dependent variables
  • Independent variables
  • Equations
Mathematics (2019) Grade(s): 6

MA19.6.21a

Use tables, graphs, and equations to represent the relationship between independent and dependent variables.

Mathematics (2019) Grade(s): 6

MA19.6.22

Write examples and non-examples of statistical questions, explaining that a statistical question anticipates variability in the data related to the question.

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Knowledge

Students know:
  • Characteristics of statistical and non-statistical questions.

Skills

Students are able to:
  • Justify the classification of mathematical questions as statistical or non-statistical questions.

Understanding

Students understand that:
  • Statistical questions have anticipated variability in the answers.
  • Data are the numbers produced in response to a statistical question.

Vocabulary

  • Statistical questions
  • Variability

Aligned Learning Resources

Michael Phelps.... or not?
Mathematics (2019) Grade(s): 6

MA19.6.23

Calculate, interpret, and compare measures of center (mean, median, mode) and variability (range and interquartile range) in real-world data sets.

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Knowledge

Students know:
  • Measures of center and how they are affected by the data distribution and context.
  • Measures of variability and how they are affected by the data distribution and context.
  • Methods of determining mean, median, mode, interquartile range, and range.

Skills

Students are able to:
  • Describe the nature of the attribute under investigation including how it was measured and its unit of measure using the context in which the data were collected.
  • Determine measures of center and variability for a set of numerical data.
  • Use characteristics of measures of center and variability to justify choices for summarizing and describing data.

Understanding

Students understand that:
  • Measures of center for a set of data summarize the values in the set in a single number and are affected by the distribution of the data.
  • Measures of variability for a set of data describe how the values vary in a single number and are affected by the distribution of the data.

Vocabulary

  • Data distribution
  • Measures of center
  • Measures of variability
  • Mean
  • Median
  • Mode
  • Interquartile range
  • Range

Aligned Learning Resources

Forecasting Statistics
Median StudyJam
Circle Graph StudyJam
Mean/Average StudyJam
Mode StudyJam
Choosing the Correct Graph StudyJam
Mathematics (2019) Grade(s): 6

MA19.6.24

Represent numerical data graphically, using dot plots, line plots, histograms, stem and leaf plots, and box plots.

Unpacked Content

Knowledge

Students know:
  • How to use graphical representations of real-world data to describe context, center, spread and shape from which they were collected.
  • Techniques for constructing line plots, stem and leaf plots, dot plots, histograms, and box plots.

Skills

Students are able to:
  • Organize and display data using dot plots, line plots, stem and leaf plots, histograms, and box plots.
  • Describe the nature of the attribute under investigation including how it was measured and its unit of measure using the context in which the data were collected.
  • Describe the shape of numerical data distribution including patterns and extreme values.
  • Use graphical representations of real-world data to describe and summarize the context from which they were collected.

Understanding

Students understand that:
  • Sets of data can be organized and displayed in a variety of ways, each of which provides unique perspectives of the data set.
  • Data displays help in conceptualizing ideas and in solving problems.
  • The overall shape and other significant features of a set of data, (e.g., gaps, peaks, clusters and extreme values) are important in summarizing numerical data sets.

Vocabulary

  • Dot plots
  • Histograms
  • Box plots
  • Stem and leaf plots
  • Line plots
  • Extreme values
  • Outliers
  • Gaps
  • Clusters
  • Symmetric
  • Skewed
  • Center
  • Spread
  • peaks
  • 5 number summary
  • Minimum
  • Maximum
  • Median
  • lower quartile
  • Upper quartile

Aligned Learning Resources

Forecasting Statistics
Double-Line Graph StudyJam
Mode StudyJam
Stem-and-Leaf Plots StudyJam
Creating and Interpreting Histograms - Age Distribution of Householders in the United States (Teacher Version)
Mathematics (2019) Grade(s): 6

MA19.6.24a

Analyze the graphical representation of data by describing the center, spread, shape (including approximately symmetric or skewed), and unusual features (including gaps, peaks, clusters, and extreme values).

Mathematics (2019) Grade(s): 6

MA19.6.25

Graph polygons in the coordinate plane given coordinates of the vertices to solve real-world and mathematical problems.

Unpacked Content

Knowledge

Students know:
  • Terminology associated with coordinate systems.
  • Correct construction of coordinate systems.

Skills

Students are able to:
  • Graph points corresponding to ordered pairs.
  • Represent real-world and mathematical problems on a coordinate plane.
  • Interpret coordinate values of points in the context of real-world and mathematical situations.
  • Determine lengths of line segments on a coordinate plane when the line segment joins points with the same first coordinate or the same second coordinate.

Understanding

Students understand that:
  • A variety of representations such as diagrams, number lines, charts, and graphs can be used to illustrate mathematical situations and relationships.
  • These representations help in conceptualizing ideas and in solving problems.
  • Distances on lines parallel to the axes on a coordinate plane are the same as the related distance on the axis (number line).

Vocabulary

  • Polygon
  • Coordinate plane
  • Vertices
  • X-coordinate
  • Y-coordinate
Mathematics (2019) Grade(s): 6

MA19.6.25a

Determine missing vertices of a rectangle with the same x-coordinate or the same y-coordinate when graphed in the coordinate plane.

Mathematics (2019) Grade(s): 6

MA19.6.25b

Use coordinates to find the length of a side between points having the same x-coordinate or the same y- coordinate.

Mathematics (2019) Grade(s): 6

MA19.6.25c

Calculate perimeter and area of a polygon graphed in the coordinate plane (limiting to polygons in which consecutive vertices have the same x-coordinate or the same y-coordinate).

Mathematics (2019) Grade(s): 6

MA19.6.26

Calculate the area of triangles, special quadrilaterals, and other polygons by composing and decomposing them into known shapes.

Unpacked Content

Knowledge

Students know:
  • Appropriate units for measuring area: square inches, square units, square feet, etc..
  • Strategies for composing and decomposing shapes to find area.

Skills

Students are able to:
  • Communicate the relationship between models of area and the associated real-world mathematical problems.
  • Use logical reasoning to choose and apply strategies for finding area by composing and decomposing shapes.
  • Accurately compute area of rectangles using multiplication and the formula.

Understanding

Students understand that:
  • The area of a figure is measured by the number of same-size unit squares that exactly cover the interior space of the figure.
  • Shapes can be composed and decomposed into shapes with related properties,
  • Area is additive.

Vocabulary

  • Right triangles
  • Special quadrilaterals
  • Polygons
  • Area
  • Decompose
  • Compose

Aligned Learning Resources

Area of Irregular Figures StudyJam
Area of a Triangle StudyJam
Compare and Contrast Information from Multiple Sources - Wolong's Pandas
Mathematics (2019) Grade(s): 6

MA19.6.26a

Apply the techniques of composing and decomposing polygons to find area in the context of solving real-world and mathematical problems.

Mathematics (2019) Grade(s): 6

MA19.6.27

Determine the surface area of three-dimensional figures by representing them with nets composed of rectangles and triangles to solve real-world and mathematical problems.

Unpacked Content

Knowledge

Students know:
  • Measurable attributes of objects, specifically area and surface area.
  • Strategies for representing the surface area of a 3-D shape as a 2-D net.

Skills

Students are able to:
  • Communicate the relationships between rectangular models of area and multiplication problems.
  • Model the surface area of 3-D shapes using 2-D nets.
  • Accurately measure and compute area of triangles and rectangles.
  • Strategically and fluently choose and apply strategies for finding surface areas of 3-D figures.

Understanding

Students understand that:
  • Area is additive.
  • Surface area of a 3-D shape is represented by the sum of the areas of the faces of the object.
  • Models represent measurable attributes of objects and help to solve problems.

Vocabulary

  • Nets
  • Surface area
  • Rectangular prism
  • Triangular prism
  • Square pyramid
  • Rectangular pyramid
  • Triangular pyramid

Aligned Learning Resources

Nets: Message in a Box
Determining Surface Area With Unit Blocks
Mathematics (2019) Grade(s): 6

MA19.6.28

Apply previous understanding of volume of right rectangular prisms to those with fractional edge lengths to solve real-world and mathematical problems.

Unpacked Content

Knowledge

Students know:
  • Measurable attributes of objects, specifically volume.
  • Units of measurement, specifically unit cubes.
  • Relationships between unit cubes and corresponding cubes with unit fraction edge lengths.
  • Strategies for determining volume.
  • Strategies for finding products of fractions.

Skills

Students are able to:
  • Communicate the relationships between rectangular models of volume and multiplication problems.
  • Model the volume of rectangles using manipulatives.
  • Accurately measure volume using cubes with unit fraction edge lengths.
  • Strategically and fluently choose and apply strategies for finding products of fractions.
  • Accurately compute products of fractions.

Understanding

Students understand that:
  • The volume of a solid object is measured by the number of same-size cubes that exactly fill the interior space of the object.
  • Generalized formulas for determining area and volume of shapes can be applied regardless of the level of accuracy of the shape's measurements (in this case, side lengths).

Vocabulary

  • Right rectangular prism
  • V = b h (Volume of a right rectangular prism = the area of the base x the height)

Aligned Learning Resources

Rumpelstiltskin Storybook Text: Fairy Tales Old and New
How Much Does It Take?
Mathematics (2019) Grade(s): 6

MA19.6.28a

Use models (cubes or drawings) and the volume formulas (V = lwh and V = Bh) to find and compare volumes of right rectangular prisms.

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