The Common Core in Montana

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Skills available for Montana high school math standards

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Montana Common Core Standards: Algebra I Montana Common Core Standards: Algebra I
Montana Common Core Standards: Algebra II Montana Common Core Standards: Algebra II
Montana Common Core Standards: All High School Pathways Montana Common Core Standards: All High School Pathways
Montana Common Core Standards: Geometry Montana Common Core Standards: Geometry
Montana Common Core Standards: Mathematical Practices Montana Common Core Standards: Mathematical Practices
Montana Common Core Standards: Mathematics I Montana Common Core Standards: Mathematics I
Montana Common Core Standards: Mathematics II Montana Common Core Standards: Mathematics II
Montana Common Core Standards: Mathematics III Montana Common Core Standards: Mathematics III
Montana Content Standards: Algebra I with Probability Montana Content Standards: Algebra I with Probability
Montana Content Standards: Algebra II with Statistics Montana Content Standards: Algebra II with Statistics
Montana Content Standards: Geometry with Data Analysis Montana Content Standards: Geometry with Data Analysis
Montana Content Standards: Integrated Math I Montana Content Standards: Integrated Math I
Montana Content Standards: Integrated Math II Montana Content Standards: Integrated Math II
Montana Content Standards: Integrated Math III Montana Content Standards: Integrated Math III

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MT.HS.CORE.DATA Core Data Reasoning and Probability Standards

MT.HS.CORE.DATA.LIT Quantitative Literacy
- MT.HS.CORE.DATA.LIT.1 Distinguish between quantitative and categorical data and use representations and analysis techniques that are appropriate for each type.
- MT.HS.CORE.DATA.LIT.2 Ask a statistical question to determine whether there appears to be an association between two variables, design and carry out an investigation, and write a persuasive argument based on the results of the investigation.
- MT.HS.CORE.DATA.LIT.3 Distinguish between association and causation.
  - Correlation and causation (G)
MT.HS.CORE.DATA.INT Visualizing, Summarizing, and Interpreting Data
- MT.HS.CORE.DATA.INT.1 Use technology to organize data, including very large data sets, into a useful and manageable structure.
- MT.HS.CORE.DATA.INT.2 Represent the distribution of univariate quantitative data with plots on the real number line, choosing a format most appropriate to the data set, and representing the distribution of bivariate quantitative data with a scatter plot.
- MT.HS.CORE.DATA.INT.3 Understand that standard deviation measures the variability of a data distribution, and calculate standard deviation using technology.
  - Standard deviation of a sample (A1-II.7)
  - Standard deviation of a population (G)
- MT.HS.CORE.DATA.INT.4 Interpret differences in the shape, center, and spread of quantitative data distributions, in context, accounting for possible effects of outliers on measures of central tendency and variability.
  - Box plots (G)
  - Identify an outlier and describe the effect of removing it (G)
- MT.HS.CORE.DATA.INT.5 Compare and contrast two or more quantitative data distributions, using shape, center, and spread in context. This standard should incorporate cultural context relating to Montana Indigenous Peoples and local communities.
- MT.HS.CORE.DATA.INT.7 Analyze the relationship between two categorical variables in context. This standard should incorporate cultural context relating to Montana Indigenous Peoples and local communities by:
  - MT.HS.CORE.DATA.INT.7.a Summarizing categorical data for two categories in two-way frequency tables and visual representations.
    - Create and interpret two-way frequency tables (A1-JJ.1)
  - MT.HS.CORE.DATA.INT.7.b Interpreting relative frequencies for categorical data in context.
    - Create and interpret two-way frequency tables (A1-JJ.1)
  - MT.HS.CORE.DATA.INT.7.c Identifying possible associations and trends in categorical data.
    - Create and interpret two-way frequency tables (A1-JJ.1)
- Checkpoint opportunity
  - Checkpoint: Line plots, histograms, and box plots (G)

MT.HS.CORE.GEOM Core Geometric Reasoning Standards

MT.HS.CORE.GEOM.TRANS Transformations
- MT.HS.CORE.GEOM.TRANS.1 Represent transformations in the plane using a variety of methods.
- MT.HS.CORE.GEOM.TRANS.2 Define the congruence of two and show that two figures are congruent by finding a sequence of rigid motions that maps one figure to the other by:
  - MT.HS.CORE.GEOM.TRANS.2.a Using the definition of congruence in terms of rigid motions to show that two triangles are congruent if, and only if, corresponding pairs of sides and corresponding pairs of angles are congruent.
    - Prove triangles are congruent using rigid motions (G-L.1)
  - MT.HS.CORE.GEOM.TRANS.2.b Verifying that two triangles are congruent if, but not only if, the following groups of corresponding parts are congruent: angle-side-angle (ASA), side-angle-side (SAS), and side-side-side (SSS).
- MT.HS.CORE.GEOM.TRANS.3 Define the similarity of two figures in terms of similarity transformations by:
  - MT.HS.CORE.GEOM.TRANS.3.a Verifying that two triangles are similar if, and only if, corresponding pairs of sides are proportional and corresponding pairs of angles are congruent.
  - MT.HS.CORE.GEOM.TRANS.3.b Using the properties of similarity transformations to establish the angle-angle (AA) criterion for two triangles to be similar.
    - Similarity rules for triangles (G-M.8)
- Checkpoint opportunity
  - Checkpoint: Congruence transformations (G)
MT.HS.CORE.GEOM.ARG Geometric Arguments, Reasoning, and Proof
- MT.HS.CORE.GEOM.ARG.1 Investigate, conjecture, prove theorems, and communicate the proofs in a variety of ways by:
  - MT.HS.CORE.GEOM.ARG.1.a Prove theorems about lines and angles. Theorems include: vertical angles are congruent, when a transversal crosses parallel lines alternate interior angles are congruent and corresponding angles are congruent, and the points on the perpendicular bisector of a line segment are those equidistant from the segment's endpoints.
  - MT.HS.CORE.GEOM.ARG.1.b Prove theorems about triangles. Theorems include: the sum of the measures of the interior angles of a triangle is 180°, the Pythagorean Theorem, the base angles of isosceles triangles are congruent, and a line parallel to one side of a triangle divides the other two sides proportionally.
  - MT.HS.CORE.GEOM.ARG.1.c Prove theorems about parallelograms and other quadrilaterals. Theorems include: necessary and sufficient conditions for rectangles, parallelograms, rhombi, and kites.
  - MT.HS.CORE.GEOM.ARG.1.d Prove theorems about circles. Theorems include: the relationship between central, inscribed, and circumscribed angles, inscribed angles on a diameter are right angles, and the radius of a circle is perpendicular to the tangent where the radius intersects the circle.
- Checkpoint opportunity
MT.HS.CORE.GEOM.MEAS Measurement, Problem Solving, and Geometric Modeling
- MT.HS.CORE.GEOM.MEAS.1 Use the Pythagorean Theorem to calculate distance in the coordinate plane.
  - Distance formula (G-B.14)
- MT.HS.CORE.GEOM.MEAS.2 Derive the equation of a circle of a given center and radius using the Pythagorean Theorem.
  - Derive equations of circles using the Pythagorean theorem (G-Y.4)
- MT.HS.CORE.GEOM.MEAS.3 Use similarity to explore and define the sine ratio, cosine ratio, and tangent ratio in terms of right triangles by:
  - MT.HS.CORE.GEOM.MEAS.3.a Deriving and applying the trigonometric ratios in special right triangles.
  - MT.HS.CORE.GEOM.MEAS.3.b Using trigonometric ratios and the Pythagorean Theorem to solve right triangles.
- MT.HS.CORE.GEOM.MEAS.4 Use geometric shapes, their measures, and their properties to model objects and use those models to solve problems in context. This standard should incorporate cultural context relating to Montana Indigenous Peoples and local communities by:
  - MT.HS.CORE.GEOM.MEAS.4.a Modeling and solving problems with 2D shapes by using the perimeter and area of polygons, circles, and composite shapes with portions removed.
  - MT.HS.CORE.GEOM.MEAS.4.b Modeling and solving problems with 3D solids by using surface area and volume of solids, including composite solids and solids with portions removed.
  - MT.HS.CORE.GEOM.MEAS.4.c Deriving and applying the relationships between the lengths, perimeters, areas, and volumes of similar figures in relation to their scale factor.
  - Checkpoint opportunity

The Common Core in Montana

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MT.HS.CORE.DATA Core Data Reasoning and Probability Standards

MT.HS.CORE.DATA.LIT Quantitative Literacy

MT.HS.CORE.DATA.LIT.1 Distinguish between quantitative and categorical data and use representations and analysis techniques that are appropriate for each type.

MT.HS.CORE.DATA.LIT.2 Ask a statistical question to determine whether there appears to be an association between two variables, design and carry out an investigation, and write a persuasive argument based on the results of the investigation.

MT.HS.CORE.DATA.LIT.3 Distinguish between association and causation.

MT.HS.CORE.DATA.INT Visualizing, Summarizing, and Interpreting Data

MT.HS.CORE.DATA.INT.1 Use technology to organize data, including very large data sets, into a useful and manageable structure.

MT.HS.CORE.DATA.INT.2 Represent the distribution of univariate quantitative data with plots on the real number line, choosing a format most appropriate to the data set, and representing the distribution of bivariate quantitative data with a scatter plot.

MT.HS.CORE.DATA.INT.3 Understand that standard deviation measures the variability of a data distribution, and calculate standard deviation using technology.

MT.HS.CORE.DATA.INT.4 Interpret differences in the shape, center, and spread of quantitative data distributions, in context, accounting for possible effects of outliers on measures of central tendency and variability.

MT.HS.CORE.DATA.INT.5 Compare and contrast two or more quantitative data distributions, using shape, center, and spread in context. This standard should incorporate cultural context relating to Montana Indigenous Peoples and local communities.

MT.HS.CORE.DATA.INT.7 Analyze the relationship between two categorical variables in context. This standard should incorporate cultural context relating to Montana Indigenous Peoples and local communities by:

MT.HS.CORE.DATA.INT.7.a Summarizing categorical data for two categories in two-way frequency tables and visual representations.

MT.HS.CORE.DATA.INT.7.b Interpreting relative frequencies for categorical data in context.

MT.HS.CORE.DATA.INT.7.c Identifying possible associations and trends in categorical data.

Checkpoint opportunity

MT.HS.CORE.GEOM Core Geometric Reasoning Standards

MT.HS.CORE.GEOM.TRANS Transformations

MT.HS.CORE.GEOM.TRANS.1 Represent transformations in the plane using a variety of methods.

MT.HS.CORE.GEOM.TRANS.2 Define the congruence of two and show that two figures are congruent by finding a sequence of rigid motions that maps one figure to the other by:

MT.HS.CORE.GEOM.TRANS.2.a Using the definition of congruence in terms of rigid motions to show that two triangles are congruent if, and only if, corresponding pairs of sides and corresponding pairs of angles are congruent.

MT.HS.CORE.GEOM.TRANS.2.b Verifying that two triangles are congruent if, but not only if, the following groups of corresponding parts are congruent: angle-side-angle (ASA), side-angle-side (SAS), and side-side-side (SSS).

MT.HS.CORE.GEOM.TRANS.3 Define the similarity of two figures in terms of similarity transformations by:

MT.HS.CORE.GEOM.TRANS.3.a Verifying that two triangles are similar if, and only if, corresponding pairs of sides are proportional and corresponding pairs of angles are congruent.

MT.HS.CORE.GEOM.TRANS.3.b Using the properties of similarity transformations to establish the angle-angle (AA) criterion for two triangles to be similar.

Checkpoint opportunity

MT.HS.CORE.GEOM.ARG Geometric Arguments, Reasoning, and Proof

MT.HS.CORE.GEOM.ARG.1 Investigate, conjecture, prove theorems, and communicate the proofs in a variety of ways by:

MT.HS.CORE.GEOM.ARG.1.c Prove theorems about parallelograms and other quadrilaterals. Theorems include: necessary and sufficient conditions for rectangles, parallelograms, rhombi, and kites.

MT.HS.CORE.GEOM.ARG.1.d Prove theorems about circles. Theorems include: the relationship between central, inscribed, and circumscribed angles, inscribed angles on a diameter are right angles, and the radius of a circle is perpendicular to the tangent where the radius intersects the circle.

Checkpoint opportunity

MT.HS.CORE.GEOM.MEAS Measurement, Problem Solving, and Geometric Modeling

MT.HS.CORE.GEOM.MEAS.1 Use the Pythagorean Theorem to calculate distance in the coordinate plane.

MT.HS.CORE.GEOM.MEAS.2 Derive the equation of a circle of a given center and radius using the Pythagorean Theorem.

MT.HS.CORE.GEOM.MEAS.3 Use similarity to explore and define the sine ratio, cosine ratio, and tangent ratio in terms of right triangles by:

MT.HS.CORE.GEOM.MEAS.3.a Deriving and applying the trigonometric ratios in special right triangles.

MT.HS.CORE.GEOM.MEAS.3.b Using trigonometric ratios and the Pythagorean Theorem to solve right triangles.

MT.HS.CORE.GEOM.MEAS.4 Use geometric shapes, their measures, and their properties to model objects and use those models to solve problems in context. This standard should incorporate cultural context relating to Montana Indigenous Peoples and local communities by:

MT.HS.CORE.GEOM.MEAS.4.a Modeling and solving problems with 2D shapes by using the perimeter and area of polygons, circles, and composite shapes with portions removed.

MT.HS.CORE.GEOM.MEAS.4.b Modeling and solving problems with 3D solids by using surface area and volume of solids, including composite solids and solids with portions removed.

MT.HS.CORE.GEOM.MEAS.4.c Deriving and applying the relationships between the lengths, perimeters, areas, and volumes of similar figures in relation to their scale factor.

Checkpoint opportunity