# Math

Our Middle School uses the *Connected Math Project* (*CMP3*) program, which is a natural extension of the constructivist curriculum from the Lower School. This program allows students to build their knowledge of mathematics through exploration of real-world problems, engaging math activities, and opportunities to construct their own understandings of mathematical concepts. The focus is not on rote memorization of algorithms, but rather on determining strategies and finding different routes to the solution of a problem. We encourage students to reason abstractly, persevere in problem solving, and explain their solutions clearly. Math is another lens through which to see the world as students explore questions that address authentic applications such as economics, statistics, and architecture as well as societal inequities and scientific analysis.

The four math strands that are taught throughout the Middle School years are:

- Number and Operation
- Geometry and Measurement
- Data Analysis and Probability
- Algebra and Functions

Each year builds upon what was learned in the prior year with the concepts and skills deepening as students progress. Teachers emphasize a growth mindset and encourage all students to consider themselves able to problem solve and persevere through complex problems.

**6th Grade**

Sixth graders explore the properties of numbers and the variety of ways that numerical comparisons can be made. They begin the year focusing on whole number properties, understanding prime factorization and the use of order of operations. Students study ratios, rational numbers, and equivalence. They deepen their familiarity with fractions and expand their ability to perform operations with fractions, decimals, and percents through working with number lines, examining rate tables, and making comparisons. Later in the year, sixth graders study geometry as they work with area, perimeter, and volume of two-dimensional and three-dimensional shapes.

**7th Grade**

Seventh graders spend the year analyzing concepts that are foundational for algebra, beginning with a geometry strand in which they use logical reasoning to analyze geometric attributes. They develop their understanding of similarity, congruence, and proportional relationships. Students’ grasp of proportional geometry transitions flexibly to grasping proportions, rates, ratios, and linear growth. Students embark on a study of integers and rational numbers, looking at order of operations and mathematical properties as a way to make computational sequences clear. They develop an understanding of the relationship between positive and negative numbers. Later in the year, seventh graders study probability through the creation of real-world activities that have fair and unfair outcomes.

**8th Grade**

Eighth graders spend the year developing their understanding of algebraic concepts, with units exploring linear, inverse, exponential, and quadratic functions. They learn to identify and represent each type of function in graphs, tables, and equations. Real-world connections are explored for each type of function, and students learn to understand the patterns in the world around them. Building upon their 6th and 7th grade exposure to variables, 8th graders look at the characteristics of quadratic relationships as they continue to explore algebraic concepts. Students who are interested in moving into advanced mathematics in high school are supported in preparation for taking the Algebra 1 Regents exam administered by NYC public high schools.

**Essential Questions**

*Why do we use variables?*

*How can I design a data investigation to answer a question?*

*What is the clearest way to represent numerical information?*

*How do you find the value of the unknown? *

*How can objects be represented and compared using geometric attributes?*

*What different interpretations can be obtained from a particular pattern or relationship?*

*How can math raise awareness of economic injustice and inspire social action?*

**Key Math Skills: Middle School **

- Analyze problems and persevere in solving them.
- Reason abstractly and quantitatively.
- Construct viable arguments and critique the reasoning of others.
- Use a mathematical framework to analyze a situation or pose a problem.
- Employ appropriate tools strategically.
- Attend to precision.