This summarizes the content of the Common Core State Standards for Mathematics, and highlights Expanding Horizons talks that address various elements of the standards. We also include links from some Expanding Horizons presentations back to the Common Core elements to which they relate. These connections are a work in progress, and we hope to highlight more connections over time.

### Standards for Mathematical Practice

1. Make sense of problems and persevere in solving them.
2. Reason abstractly and quantitatively.
3. Construct viable arguments and critique the reasoning of others.
4. Model with mathematics.
5. Use appropriate tools strategically.
6. Attend to precision.
7. Look for and make use of structure.
8. Look for and express regularity in repeated reasoning.

### Kindergarden

K.CC) Counting and Cardinality

• Know number names and the count sequence.
• Count to tell the number of objects.
• Compare numbers.

K.OA) Operations and Algebraic Thinking

• Understand addition as putting together and adding to, and understand subtraction as taking apart and taking from.

K.NBT) Number and Operations in Base Ten

• Work with numbers 11–19 to gain foundations for place value.

K.MD) Measurement and Data

• Describe and compare measurable attributes.
• Classify objects and count the number of objects in categories.

K.G) Geometry

• Identify and describe shapes.
• Analyze, compare, create, and compose shapes.

1.OA) Operations and Algebraic Thinking

• Represent and solve problems involving addition and subtraction.
• Understand and apply properties of operations and the relationship between addition and subtraction
• Add and subtract within 20.
• Work with addition and subtraction equations.

1.NBT) Number and Operations in Base Ten

• Extend the counting sequence.
• Understand place value.
• Use place value understanding and properties of operations to add and subtract.

1.MD) Measurement and Data

• Measure lengths indirectly and by iterating length units.
• Tell and write time.
• Represent and interpret data.

1.G) Geometry

• Reason with shapes and their attributes.

2.OA) Operations and Algebraic Thinking

• Represent and solve problems involving addition and subtraction.
• Add and subtract within 20.
• Work with equal groups of objects to gain foundations for multiplication.

2.NBT) Number and Operations in Base Ten

• Understand place value.
• Use place value understanding and properties of operations to add and subtract.

2.MD) Measurement and Data

• Measure and estimate lengths in standard units.
• Relate addition and subtraction to length.
• Work with time and money.
• Represent and interpret data.

2.G) Geometry

• Reason with shapes and their attributes.

3.OA) Operations and Algebraic Thinking

• Represent and solve problems involving multiplication and division.
• Understand properties of multiplication and the relationship between multiplication and division.
• Multiply and divide within 100.
• Solve problems involving the four operations and identify and explain patterns in arithmetic.

3.NBT) Number and Operations in Base Ten

• Use place value understanding and properties of operations to perform multi-digit arithmetic.

3.NF) Number and Operations—Fractions

• Develop understanding of fractions as numbers.

3.MD) Measurement and Data

• Solve problems involving measurement and estimation of intervals of time, liquid volumes, and masses of objects.
• Represent and interpret data.
• Geometric measurement: understand concepts of area and relate area to multiplication and to addition.
• Geometric measurement: recognize perimeter as an attribute of plane figures and distinguish between linear and area measures.

3.G) Geometry

• Reason with shapes and their attributes.

4.OA) Operations and Algebraic Thinking

• Use the four operations with whole numbers to solve problems.
• Gain familiarity with factors and multiples.
• Generate and analyze patterns.

4.NBT) Number and Operations in Base Ten

• Generalize place value understanding for multi-digit whole numbers.
• Use place value understanding and properties of operations to perform multi-digit arithmetic.

EH connections:

4.NF) Number and Operations—Fractions

• Extend understanding of fraction equivalence and ordering.
• Build fractions from unit fractions by applying and extending previous understandings of operations on whole numbers.
• Understand decimal notation for fractions, and compare decimal fractions.

4.MD) Measurement and Data

• Solve problems involving measurement and conversion of measurements from a larger unit to a smaller unit.
• Represent and interpret data.
• Geometric measurement: understand concepts of angle and measure angles.

4.G) Geometry

• Draw and identify lines and angles, and classify shapes by properties of their lines and angles.

5.OA) Operations and Algebraic Thinking

• Write and interpret numerical expressions.
• Analyze patterns and relationships.

5.NBT) Number and Operations in Base Ten

• Understand the place value system.
• Perform operations with multi-digit whole numbers and with decimals to hundredths.

EH connections:

5.NF) Number and Operations—Fractions

• Use equivalent fractions as a strategy to add and subtract fractions.
• Apply and extend previous understandings of multiplication and division to multiply and divide fractions.

5.MD) Measurement and Data

• Convert like measurement units within a given measurement system.
• Represent and interpret data.

5.G) Geometry

• Graph points on the coordinate plane to solve real-world and mathematical problems.
• Classify two-dimensional figures into categories based on their properties.

6.RP) Ratios and Proportional Relationships

• Understand ratio concepts and use ratio reasoning to solve problems.

6.NS) The Number System

• Apply and extend previous understandings of multiplication and division to divide fractions by fractions.
• Compute fluently with multi-digit numbers and find common factors and multiples.
• Apply and extend previous understandings of numbers to the system of rational numbers.

6.EE) Expressions and Equations

• Apply and extend previous understandings of arithmetic to algebraic expressions.
• Reason about and solve one-variable equations and inequalities.

6.G) Geometry

• Solve real-world and mathematical problems involving area, surface area, and volume.

EH connections:

6.SP) Statistics and Probability

• Develop understanding of statistical variability.
• Summarize and describe distributions.

EH connections:

7.RP) Ratios and Proportional Relationships

• Analyze proportional relationships and use them to solve real-world and mathematical problems.

7.NS) The Number System

• Apply and extend previous understandings of operations with fractions to add, subtract, multiply, and divide rational numbers.

7.EE) Expressions and Equations

• Use properties of operations to generate equivalent expressions.
• Solve real-life and mathematical problems using numerical and algebraic expressions and equations.

7.G) Geometry

• Draw, construct, and describe geometrical figures and describe the relationships between them.
• Solve real-life and mathematical problems involving angle measure, area, surface area, and volume.

EH connections:

• George Ashline
• Encountering the Great Problems from Antiquity: Hands-On Trisection, Duplication, and Quadrature
• Estimating the Circumference of the Earth – Following in the Shadow of Eratosthenes
• David Hathaway
• 3D Printing

7.SP) Statistics and Probability

• Use random sampling to draw inferences about a population.
• Draw informal comparative inferences about two populations.
• Investigate chance processes and develop, use, and evaluate probability models.

8.NS) The Number System

• Know that there are numbers that are not rational, and approximate them by rational numbers.

8.EE) Expressions and Equations

• Work with radicals and integer exponents.
• Understand the connections between proportional relationships, lines, and linear equations.
• Analyze and solve linear equations and pairs of simultaneous linear equations.

EH connections:

8.F) Functions

• Define, evaluate, and compare functions.
• Use functions to model relationships between quantities.

EH connections:

• George Ashline
• Exponential Functions in Snowflakes, Carpets, and Paper Folding

8.G) Geometry

• Understand congruence and similarity using physical models, transparencies, or geometry software.
• Understand and apply the Pythagorean Theorem.
• Solve real-world and mathematical problems involving volume of cylinders, cones, and spheres.

EH connections:

• George Ashline
• Encountering the Great Problems from Antiquity: Hands-On Trisection, Duplication, and Quadrature
• Estimating the Circumference of the Earth – Following in the Shadow of Eratosthenes
• Framing the Proof of the Pythagorean Theorem and Investigating Some Interesting Pythagorean Triple Properties
• David Hathaway
• 3D Printing

8.SP) Statistics and Probability

• Investigate patterns of association in bivariate data.

EH connections:

### HS – Number and Quantity

N-RN) The Real Number System

• Extend the properties of exponents to rational exponents
• Use properties of rational and irrational numbers

N-Q) Quantities

• Reason quantitatively and use units to solve problems

N-CN) The Complex Number System

• Perform arithmetic operations with complex numbers
• Represent complex numbers and their operations on the complex plane
• Use complex numbers in polynomial identities and equations

N-VM) Vector and Matrix Quantities

• Represent and model with vector quantities.
• Perform operations on vectors.
• Perform operations on matrices and use matrices in applications.

### HS – Algebra

A-APR) Arithmetic with Polynomials and Rational Expressions

• Perform arithmetic operations on polynomials
• Understand the relationship between zeros and factors of polynomials
• Use polynomial identities to solve problems
• Rewrite rational expressions

A-CED) Creating Equations

• Create equations that describe numbers or relationships

A-REI) Reasoning with Equations and Inequalities

• Understand solving equations as a process of reasoning and explain the reasoning
• Solve equations and inequalities in one variable
• Solve systems of equations
• Represent and solve equations and inequalities graphically

EH connections:

### HS – Functions

F-IF) Interpreting Functions

• Understand the concept of a function and use function notation
• Interpret functions that arise in applications in terms of the context
• Analyze functions using different representations

F-BF) Building Functions

• Build a function that models a relationship between two quantities
• Build new functions from existing functions

F-LE) Linear, Quadratic, and Exponential Models

• Construct and compare linear, quadratic, and exponential models and solve problems
• Interpret expressions for functions in terms of the situation they model

EH connections:

• George Ashline
• Exponential Functions in Snowflakes, Carpets, and Paper Folding

F-TF) Trigonometric Functions

• Extend the domain of trigonometric functions using the unit circle
• Model periodic phenomena with trigonometric functions
• Prove and apply trigonometric identities

### HS – Modeling

Modeling links classroom mathematics and statistics to everyday life, work, and decision-making. This area doesn’t have a separate set of “tagged” standards, but uses the basic modeling cycle, which involves:

1. identifying variables in the situation and selecting those that represent essential features,
2. formulating a model by creating and selecting geometric, graphical,tabular, algebraic, or statistical representations that describe
relationships between the variables,
3. analyzing and performing operations on these relationships to draw conclusions,
4. interpreting the results of the mathematics in terms of the original situation,
5. validating the conclusions by comparing them with the situation, and then either improving the model or, if it is acceptable,
6. reporting on the conclusions and the reasoning behind them.

Choices, assumptions, and approximations are present throughout this cycle.

### HS – Geometry

G-CO) Congruence

• Experiment with transformations in the plane
• Understand congruence in terms of rigid motions
• Prove geometric theorems
• Make geometric constructions

EH connections:

• George Ashline
• Encountering the Great Problems from Antiquity: Hands-On Trisection, Duplication, and Quadrature
• Estimating the Circumference of the Earth – Following in the Shadow of Eratosthenes
• Framing the Proof of the Pythagorean Theorem and Investigating Some Interesting Pythagorean Triple Properties

G-SRT) Similarity, Right Triangles, and Trigonometry

• Understand similarity in terms of similarity transformations
• Prove theorems involving similarity
• Define trigonometric ratios and solve problems involving right triangles
• Apply trigonometry to general triangles

EH connections:

• George Ashline
• Estimating the Circumference of the Earth – Following in the Shadow of Eratosthenes

G-C) Circles

• Understand and apply theorems about circles
• Find arc lengths and areas of sectors of circles

G-GPE) Expressing Geometric Properties with Equations

• Translate between the geometric description and the equation for a conic section
• Use coordinates to prove simple geometric theorems algebraically

G-GMD) Geometric Measurement and Dimension

• Explain volume formulas and use them to solve problems
• Visualize relationships between two-dimensional and three-dimensional objects

EH connections:

G-MG) Modeling with Geometry

• Apply geometric concepts in modeling situations

EH connections:

### HS Statistics and Probability

S-IC) Making Inferences and Justifying Conclusions

• Understand and evaluate random processes underlying statistical experiments
• Make inferences and justify conclusions from sample surveys, experiments and observational studies

EH connections:

S-CP) Conditional Probability and the Rules of Probability

• Understand independence and conditional probability and use them to interpret data
• Use the rules of probability to compute probabilities of compound events in a uniform probability model

S-MD) Using Probability to Make Decisions

• Calculate expected values and use them to solve problems
• Use probability to evaluate outcomes of decisions