# Math Curriculum – Grade 6

The middle school Math program is closely aligned with the New York State Learning Standards for Mathematics and share the same goals to provide students with the knowledge and understanding of mathematics necessary to function in a world very dependent upon the application of mathematics. Focus in the curriculum is meant to give students an opportunity to understand concepts and practice with them in order to reach a deep and fluent understanding. Coherence in the curriculum means progressions that span grade levels to build students’ understanding of ever more sophisticated mathematical concepts and applications. Rigor means a combination of fluency exercises, chains of reasoning, abstract activities, and contextual activities throughout the module.

The Mathematics standards presented by the New York State Learning Standards describe varieties of expertise that mathematics educators at all levels should seek to develop in their students. These practices rest on important “processes and proficiencies” with longstanding importance in mathematics education.

The New York State Learning Standards include six instructional shifts to facilitate student proficiency in mathematics with a focus on shifting instructional methodology on the Practice Standards.  The Practice standards include:

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.

For additional information regarding state standards go to the NYS Learning Standards for Mathematics.

• In Grade 6, instructional time will focus on five critical areas:

1. Through their learning in the Ratios and Proportional Relationships domain, students:

• use reasoning about multiplication and division to solve ratio and rate problems about quantities;
• connect understanding of multiplication and division with ratios and rates by viewing equivalent ratios and rates as deriving from, and extending, pairs of rows (or columns) in the multiplication table, and by analyzing simple drawings that indicate the relative size of quantities; and
• expand the scope of problems for which they can use multiplication and division to solve problems, and they connect ratios and fractions.

2. Through their learning in the Number System domain, students:

• use the meaning of fractions and relationships between multiplication and division to understand and explain why the procedures for dividing fractions make sense;
• extend their previous understandings of number and the ordering of numbers to the full system of rational numbers, which includes negative rational numbers, particularly negative integers; and reason about the order and absolute value of rational numbers and about the location of points on a coordinate plane.

3. Through their learning in the Expressions, Equations, and Inequalities domain, students: • write expressions and equations that correspond to give situations, using variables to represent an unknown and describe relationships between quantities;

• understand that expressions in different forms can be equivalent, and use the properties of operations to rewrite and evaluate expressions in equivalent forms; and
• use properties of operations and the idea of maintaining the equality of both sides of an equation to solve simple one-step equations.

4. Through their learning in the Geometry domain, students:

• find areas of polygons, surface areas of prisms, and use area models to understand perfect squares; and
• extend formulas for the volume of a right rectangular prism to fractional side lengths and use volume models to understand perfect cubes.

5. Through their learning in the Statistics and Probability domain, students:

• learn to describe and summarize numerical data sets, identifying clusters, peaks, gaps, and symmetry, considering the context in which the data were collected; and
• understand the probability of a chance event and develop probability models for simple events.