## MIDDLE SCHOOL MATHEMATICS 6-8 CURRICULUM

The pre-kindergarten through grade 8 content standards are organized by grade level and are grouped first by domain. Below is a chart that gives an overview of the domains that are addressed at each grade level. There are critical areas for instruction for each grade level, K-8. The critical areas are designed to bring focus to the standards at each grade by providing the big ideas that educators can use to build their curriculum and guide instruction. The grade level introductions include at least two and no more than four critical areas for each grade. The table below outlines the critical areas of instructions for grades 5-8 as well as the major clusters that have been identified by The Partnership for Assessment of Readiness for College and Careers (PARCC).

### The Critical Areas for Common Core Mathematics Instruction

5

#### Critical Areas of Instruction

1. Developing fluency with addition and subtraction of fractions, developing understanding of the multiplication of fractions and of division of fractions in limited cases (unit fractions divided by whole numbers and whole numbers divided by unit fractions).
2. Extending division to 2-digit divisors, integrating decimal fractions into the place value system and developing understanding of operations with decimals to hundredths, and developing fluency with whole number and decimal operation.
3. Developing understanding of volume.

#### PARCC Major Clusters

• Understand the place value system.
• Perform operations with multi-digit whole numbers and with decimals to hundredths.
• 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.
• Geometric measurement: understand concepts of volume and relate volume to multiplication and to addition.

6

1. Connecting ratio and rate to whole number multiplication and division and using concepts of ratio and rate to solve problem.
2. Completing understanding of division of fractions and extending the notion of number to the system of rational numbers, which includes negative numbers.
3. Writing, interpreting, and using expressions and equations.
4. Developing understanding of statistical thinking.
• Understand ratio concepts and use ratio reasoning to solve problems.
• Apply and extend previous understandings of multiplication and division to divide fractions by fractions.
• 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.
• Apply and extend previous understandings of numbers to the system of rational numbers.

7

1. Developing understanding of and applying proportional relationships.
2. Developing understanding of operations with rational numbers and working with expressions and linear equations.
3. Solving problems involving scale drawings and informal geometric constructions, and working with two- and three-dimensional shapes to solve problems involving area, surface area, and volume.
4. Drawing inferences about populations based on samples.
• Analyze proportional relationships and use them to solve real-world and mathematical problems.
• Apply and extend previous understandings of operations with fractions to add, subtract, multiply, and divide rational numbers.
• Use properties of operations to generate equivalent expressions.
• Solve real-life and mathematical problems using numerical and algebraic expressions and equations.

8

1. Formulating and reasoning about expressions and equations, including modeling an association in bivariate data with a linear equation, and solving linear equations and systems of linear equations.
2. Grasping the concept of a function and using functions to describe quantitative relationships.
3. Analyzing two- and three-dimensional space and figures using distance, angle, similarity, and congruence, and understanding and applying the Pythagorean Theorem.
• 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.
• Define, evaluate, and compare functions.
• Understand and apply the Pythagorean Theorem.
• Understand congruence and similarity using physical models, transparencies, or geometry software