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Skills available for North Dakota sixth-grade math standards

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North Dakota Content Standards (adopted in 2023): Grade 6 North Dakota Content Standards (adopted in 2023): Grade 6
North Dakota Content Standards (adopted in 2023): Mathematical Practices North Dakota Content Standards (adopted in 2023): Mathematical Practices
North Dakota Content Standards North Dakota Content Standards
North Dakota Content Standards (Common Core) North Dakota Content Standards (Common Core)

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6.NO Number and Operations

6.NO.NS Number Systems
- 6.NO.NS.1 Explain and show the relationship between non-zero rational numbers and their opposites using horizontal and vertical number lines, including authentic problems. Use rational numbers to represent quantities in authentic contexts and explain the meaning of 0 in certain situations.
- 6.NO.NS.2 Write, interpret, and explain statements of order for rational numbers on a number line and in authentic contexts.
- Checkpoint opportunity
6.NO.O Operations
- 6.NO.O.1 Divide multi-digit whole numbers up to four-digit dividends and two-digit divisors using strategies or procedures.
  - Divide by 2-digit numbers (6)
- 6.NO.O.2 Add and subtract fractions and decimals up to the hundredths place, including authentic problems.
- 6.NO.O.3 Apply multiplication and division of fractions and decimals to solve and interpret problems using visual models, including authentic problems.
- 6.NO.O.4 Determine the greatest common factor of two whole numbers less than or equal to 100 and the least common multiple of two whole numbers less than or equal to 12.
- Checkpoint opportunity

6.AR Algebraic Reasoning

6.AR.RP Ratios and Proportional Relationships
- 6.AR.RP.1 Describe the concept of a ratio relationship between two quantities using ratio language and visual models.
- 6.AR.RP.2 Describe and calculate a unit rate when given a ratio relationship between two quantities using rate language and visual models.
  - Unit rates (6-S.11)
- 6.AR.RP.3 Make and use tables of equivalent ratios, tape diagrams, double number line diagrams, and equations to solve problems involving ratios, rates, and unit rates, including authentic problems.
- 6.AR.RP.4 Calculate a percent of a quantity as a rate per 100. Solve problems using ratio reasoning involving finding the whole when given a part and the percent.
- 6.AR.RP.5 Convert measurement units within and between measurement systems using ratio reasoning given conversion factors.
- Checkpoint opportunity
6.AR.EE Expressions and Equations
- 6.AR.EE.1 Read, write, and evaluate numerical expressions including expressions with whole number exponents and grouping symbols.
- 6.AR.EE.2 Read and evaluate algebraic expressions, including expressions with whole number exponents and grouping symbols. Write algebraic expressions to represent simple and authentic situations.
- 6.AR.EE.3 Identify when two expressions are equivalent. Apply the properties of operations to generate equivalent expressions.
- 6.AR.EE.4 Describe the concept of a solution of an equation and an inequality. Determine whether a given number is a solution to an equation or an inequality.
- 6.AR.EE.5 Write and solve equations of the form x + p = q and px = q for cases in which p and q are non-negative whole numbers or decimals, including authentic problems.
- 6.AR.EE.6 Write a statement of inequality of the form x > c or the form x < c to represent a constraint or condition. Recognize that inequalities of the form x > c or the form x < c have infinitely many solutions; represent solutions of such inequalities on number line diagrams.
- Checkpoint opportunity
  - Checkpoint: Numerical expressions with exponents (6-D.8)
  - Checkpoint: Understand and solve equations (6-AA.20)

6.GM Geometry and Measurement

6.GM.AV Area and Volume
- 6.GM.AV.1 Derive the relationship of the areas of triangles using the area of rectangles. Calculate the areas of triangles and quadrilaterals by composing and/or decomposing them into rectangles and triangles, including authentic problems.
- 6.GM.AV.2 Describe the concept of volume of a right rectangular prism. Apply given formulas to calculate the volume of right rectangular prisms, including fractional edge lengths, including authentic problems.
- Checkpoint opportunity
6.GM.GF Geometric Figures
- 6.GM.GF.1 Identify and position ordered pairs of rational numbers in all four quadrants of a coordinate plane.
- 6.GM.GF.2 Draw polygons in the coordinate plane given coordinates for the vertices. Determine the length of a side joining points with the same first or second coordinate, including authentic problems.
- 6.GM.GF.3 Represent three-dimensional figures using nets made up of rectangles and triangles (right prisms and pyramids whose bases are triangles and rectangles). Calculate the surface area of prisms with rectangular and triangular bases using nets, including authentic problems.
- Checkpoint opportunity

6.DPS Data, Probability, and Statistics

6.DPS.D Data Analysis
- 6.DPS.D.1 Write a statistical question that can be answered using measures of center or variability of a data set.
  - Identify statistical questions (6-JJ.1)
- 6.DPS.D.2 Calculate measures of center (median and mean) and variability (range and mean absolute deviation) to answer a statistical question. Identify mode(s) if they exist.
  - Calculate mean, median, mode, and range (6-JJ.2)
  - Calculate mean absolute deviation (6-JJ.6)
- 6.DPS.D.3 Identify outliers by observation and describe their effect on measures of center and variability. Justify which measures would be appropriate to answer a statistical question.
- 6.DPS.D.4 Display numerical data in plots on a number line, including dot plots and histograms. Describe any overall patterns in data, such as gaps, clusters, and skews.
- Checkpoint opportunity

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6.NO Number and Operations

6.NO.NS Number Systems

6.NO.NS.1 Explain and show the relationship between non-zero rational numbers and their opposites using horizontal and vertical number lines, including authentic problems. Use rational numbers to represent quantities in authentic contexts and explain the meaning of 0 in certain situations.

6.NO.NS.2 Write, interpret, and explain statements of order for rational numbers on a number line and in authentic contexts.

Checkpoint opportunity

6.NO.O Operations

6.NO.O.1 Divide multi-digit whole numbers up to four-digit dividends and two-digit divisors using strategies or procedures.

6.NO.O.2 Add and subtract fractions and decimals up to the hundredths place, including authentic problems.

6.NO.O.3 Apply multiplication and division of fractions and decimals to solve and interpret problems using visual models, including authentic problems.

6.NO.O.4 Determine the greatest common factor of two whole numbers less than or equal to 100 and the least common multiple of two whole numbers less than or equal to 12.

Checkpoint opportunity

6.AR Algebraic Reasoning

6.AR.RP Ratios and Proportional Relationships

6.AR.RP.1 Describe the concept of a ratio relationship between two quantities using ratio language and visual models.

6.AR.RP.2 Describe and calculate a unit rate when given a ratio relationship between two quantities using rate language and visual models.

6.AR.RP.3 Make and use tables of equivalent ratios, tape diagrams, double number line diagrams, and equations to solve problems involving ratios, rates, and unit rates, including authentic problems.

6.AR.RP.4 Calculate a percent of a quantity as a rate per 100. Solve problems using ratio reasoning involving finding the whole when given a part and the percent.

6.AR.RP.5 Convert measurement units within and between measurement systems using ratio reasoning given conversion factors.

Checkpoint opportunity

6.AR.EE Expressions and Equations

6.AR.EE.1 Read, write, and evaluate numerical expressions including expressions with whole number exponents and grouping symbols.

6.AR.EE.2 Read and evaluate algebraic expressions, including expressions with whole number exponents and grouping symbols. Write algebraic expressions to represent simple and authentic situations.

6.AR.EE.3 Identify when two expressions are equivalent. Apply the properties of operations to generate equivalent expressions.

6.AR.EE.4 Describe the concept of a solution of an equation and an inequality. Determine whether a given number is a solution to an equation or an inequality.

6.AR.EE.5 Write and solve equations of the form x + p = q and px = q for cases in which p and q are non-negative whole numbers or decimals, including authentic problems.

6.AR.EE.6 Write a statement of inequality of the form x > c or the form x < c to represent a constraint or condition. Recognize that inequalities of the form x > c or the form x < c have infinitely many solutions; represent solutions of such inequalities on number line diagrams.

Checkpoint opportunity

6.GM Geometry and Measurement

6.GM.AV Area and Volume

6.GM.AV.1 Derive the relationship of the areas of triangles using the area of rectangles. Calculate the areas of triangles and quadrilaterals by composing and/or decomposing them into rectangles and triangles, including authentic problems.

6.GM.AV.2 Describe the concept of volume of a right rectangular prism. Apply given formulas to calculate the volume of right rectangular prisms, including fractional edge lengths, including authentic problems.

Checkpoint opportunity

6.GM.GF Geometric Figures

6.GM.GF.1 Identify and position ordered pairs of rational numbers in all four quadrants of a coordinate plane.

6.GM.GF.2 Draw polygons in the coordinate plane given coordinates for the vertices. Determine the length of a side joining points with the same first or second coordinate, including authentic problems.

6.GM.GF.3 Represent three-dimensional figures using nets made up of rectangles and triangles (right prisms and pyramids whose bases are triangles and rectangles). Calculate the surface area of prisms with rectangular and triangular bases using nets, including authentic problems.

Checkpoint opportunity

6.DPS Data, Probability, and Statistics

6.DPS.D Data Analysis

6.DPS.D.1 Write a statistical question that can be answered using measures of center or variability of a data set.

6.DPS.D.2 Calculate measures of center (median and mean) and variability (range and mean absolute deviation) to answer a statistical question. Identify mode(s) if they exist.

6.DPS.D.3 Identify outliers by observation and describe their effect on measures of center and variability. Justify which measures would be appropriate to answer a statistical question.

6.DPS.D.4 Display numerical data in plots on a number line, including dot plots and histograms. Describe any overall patterns in data, such as gaps, clusters, and skews.

Checkpoint opportunity