# Mathematics

## Standards for Mathematical Practice

- 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 an express regularity in repeated reasoning.

### Grade 5 Math - Overview

**Operations and Algebraic Thinking**

- ·Write and interpret numerical expressions.
- ·Analyze patterns and relationships.

**Number and Operations in Base Ten**

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

**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.

**The Number System**

- Gain familiarity with concepts of positive and negative integers.

**Measurement and Data**

- Convert like measurement units within a given measurement system.
- Represent and interpret data.
- Geometric measurement: Understand concepts of volume and relate volume to multiplication and to addition.

**Geometry**

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

### Grade 6 Math - Overview

**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.
- 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.

**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.

### Grade 7 Math - Overview

**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.

**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.

### Grade 8 Math - Overview

**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.

**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.

**Statistics and Probability**

- Investigate patterns of association in bivariate data