St. Clare Mathematics Curriculum reflects the Common Core State Standards and Mathematical Practices

We emphasize mathematical practices as we approach each area of content.

**Mathematical Practices**

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

**Ratios and Proportional Relationships**

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

**The Number System**

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

**Expressions and Equations**

- Apply and extend previous understandings of arithmetic to algebraic expressions.
- Reason about and solve one-variable equations and inequalities.
- Represent and analyze quantitative relationships between dependent and independent variables.

**Geometry**

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

**Statistics and Probability**

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

**Ratios and Proportional Relationships**

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

**The Number System**

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

**Expressions and Equations**

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

**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.
- 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.

**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.
- Investigate patterns of association in bivariate data.

**The Number System**

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

**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.

**Functions**

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

**Seeing Structure in Expressions**

- Interpret the structure of expressions
- Write expressions in equivalent forms to solve problems

**Arithmetic with Polynomials and Rational Functions**

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

**Creating Equations**

- Create equations that describe numbers or relationships

**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