Common Core Standards

Applying the Common Core Standards for High School Mathematics


To meet many of the Common Core Standards for geometry you can use Mathematics: A Very Short Introduction and Symmetry: A Very Short Introduction.

Geometry » Congruence

Experiment with transformations in the plane

  • CCSS.Math.Content.HSG-CO.A.1 Know precise definitions of angle, circle, perpendicular line, parallel line, and line segment, based on the undefined notions of point, line, distance along a line, and distance around a circular arc.

    Use the Mathematics: VSI Chapter 6 (Geometry) which describes angles, line segments, arcs, circles, and more.

Understand congruence in terms of rigid motions

  • CCSS.Math.Content.HSG-CO.B.6 Use geometric descriptions of rigid motions to transform figures and to predict the effect of a given rigid motion on a given figure; given two figures, use the definition of congruence in terms of rigid motions to decide if they are congruent.

    Use the Symmetry: VSI Chapter 3 (Types of symmetry) which describes ridged motion.

Prove geometric theorems

  • CCSS.Math.Content.HSG-CO.C.10 Prove theorems about triangles. Theorems include: measures of interior angles of a triangle sum to 180°; base angles of isosceles triangles are congruent; the segment joining midpoints of two sides of a triangle is parallel to the third side and half the length; the medians of a triangle meet at a point.

    Use the Mathematics: VSI Chapter 6 (Geometry), Chapter 3 (Proofs), and Chapter 5 (Dimensions). These chapters include the Pythagorean Theorem and information on the geometry of triangle that will help you meet this standard.

Geometry » Similarity, Right Triangles, & Trigonometry

Define trigonometric ratios and solve problems involving right triangles

  • CCSS.Math.Content.HSG-SRT.C.8 Use trigonometric ratios and the Pythagorean Theorem to solve right triangles in applied problems.

    Use the Mathematics: VSI Chapter 3 (Proofs) & Chapter 5 (Dimensions) which cover the Pythagorean Theorem.

Geometry » Circles

Understand and apply theorems about circles

Find arc lengths and areas of sectors of circles

Geometry » Expressing Geometric Properties with Equations

Translate between the geometric description and the equation for a conic section

Geometry » Modeling with Geometry

Apply geometric concepts in modeling situations

  • CCSS.Math.Content.HSG-MG.A.1 Use geometric shapes, their measures, and their properties to describe objects (e.g., modeling a tree trunk or a human torso as a cylinder).

    Use the Mathematics: VSI Chapter 6 (Geometry) and Chapter 1 (Modeling)

Statistics & Probability

To meet Common Core Standards for Statistics & Probability use Statistics: A Very Short Introduction and Probability: A Very Short Introduction.

Statistics & Probability » Interpreting Categorical & Quantitative Data

Summarize, represent, and interpret data on a single count or measurement variable

Statistics & Probability » Making Inferences & Justifying Conclusions

Understand and evaluate random processes underlying statistical experiments

Make inferences and justify conclusions from sample surveys, experiments, and observational studies

Statistics & Probability » Conditional Probability & the Rules of Probability

Understand independence and conditional probability and use them to interpret data

  • CCSS.Math.Content.HSS-CP.A.3 Understand the conditional probability of A given B as P(A and B)/P(B), and interpret independence of A and B as saying that the conditional probability of A given B is the same as the probability of A, and the conditional probability of B given A is the same as the probability of B.

    Use the Probability: VSI Chapter 2 (The workings of probability) which covers the Addition law, Multiplication Law, Independence, and more.
  • CCSS.Math.Content.HSS-CP.A.5 Recognize and explain the concepts of conditional probability and independence in everyday language and everyday situations. For example, compare the chance of having lung cancer if you are a smoker with the chance of being a smoker if you have lung cancer.

    Use the Probability: VSI Probability VSI Chapter 2 (The workings of probability) to understand the concepts and Chapter 6 (Games people play) and Chapter 7 (Applications in science, medicine, and operations research) to provide everyday situational examples.

Use the rules of probability to compute probabilities of compound events.