# Grades 6-8 Mathematics Program Overview

In Grade 6, instructional time should focus on four critical areas:
1.  Connecting ratio and rate to whole number multiplication and division and using concepts of ratio and rate to solve problems.
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.
 Mathematical Practices 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.
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.
?In Grade 7, instructional time should focus on four critical areas:
?       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.
 Mathematical Practices 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.
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.
?In Grade 8, instructional time should focus on three critical areas:
?       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.
 Mathematical Practices 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.
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.