# Math Curriculum – Grade 7

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 7, instructional time will focus on three critical areas:

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

• extend their understanding of ratios and develop understanding of proportionality to solve single- and multi-step problems;
• use their understanding of ratios and proportionality to solve a wide variety of percent problems; • solve problems about scale drawings by relating corresponding lengths between the objects or by using the fact that relationships of lengths within an object are preserved in similar objects;
• graph proportional relationships and understand the unit rate informally as a measure of the steepness of the related line; and
• distinguish proportional relationships from other relationships.

2. Through their learning in the Number System and the Expressions, Equations, and Inequalities domains, students:

• develop a unified understanding of number, recognizing fractions, decimals (that have a finite or a repeating decimal representation), and percents as different representations of rational numbers;
• extend addition, subtraction, multiplication, and division to all rational numbers, maintaining the properties of operations and the relationships between addition and subtraction, and multiplication and division;
• explain and interpret the rules for adding, subtracting, multiplying, and dividing with negative numbers by applying properties of operations, and view negative numbers in terms of everyday contexts; and
• use the arithmetic of rational numbers as they formulate expressions and equations in one variable and use these equations to solve problems.

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

• build on their previous work with single data distributions to compare two data distributions and address questions about differences between populations;
• begin informal work with random sampling to generate data sets and learn about the importance of representative samples for drawing inferences; and
• extend previous understandings of simple probabilities in grade 6 to calculate probabilities of compound events.