# Math

What does Math at CFS look like?

Concepts Develop from Concrete to Abstract
Mathematical concepts are introduced simply, concretely, and repeatedly, with complexity and abstraction developing over time. Students begin with concrete examples, and transition to diagrams and tables before relying exclusively on symbols to represent the mathematics they encounter. This is essential for middle school math students in order to successfully make the transfer to abstract (high school level) concepts.

Applying Mathematics in Real Life
Math students at CFS have opportunities to make connections to real-world contexts throughout the materials. Frequently, carefully-chosen anchor contexts are used to motivate new mathematical concepts, and students have many opportunities to make connections between contexts and the concepts they are learning. Additionally, most units include a real-world application lesson at the end. In some cases, students spend more time developing mathematical concepts before tackling more complex application problems, and the focus is on mathematical contexts.

Giving students opportunities to apply the mathematics they learn clarifies and deepens their understanding of core math concepts and skills and provides motivation and support. Mathematical modeling is a powerful activity for all students, regardless of learning profile. Each unit has a culminating activity designed to explore, integrate, and apply all the big ideas of the unit. Centering instruction on these contextual situations can provide students with disabilities an anchor with which to base their mathematical understandings.

Individual to Whole Class Progression
We provide students with time to think through a situation or question independently before engaging with others, and allow them to carry the weight of learning, with supports arriving just in time from the community of learners. This progression allows students to first activate what they already know, and continue to build from this base with others.

Consistent Lesson Structures
The structure of every lesson is the same: warm-up, activities, synthesis, cool-down. By keeping the components of each lesson similar from day to day, the flow of work in class becomes predictable for students. This reduces cognitive demand and enables students to focus on the mathematics at hand rather than the mechanics of the lesson.

### How Liz is working to make math more accessible in her classroom:

Processing Time
We are the opposite of a fast-paced, content-heavy, pressured math classroom. Increased time engaged in thinking and learning leads to mastery of grade level content for all students, including students with disabilities. Frequent switching between topics only creates confusion and does not allow for content to deeply embed in the mind of the learner. Mathematical ideas and representations are carefully introduced in the materials in a gradual, purposeful way to establish a base of conceptual understanding.

Peer Tutors
We use peers/mentors in our classroom! Peer tutors help struggling students access content and solve problems. This support keeps all students engaged in the material by helping students who struggle and deepening the understanding of both the peer mentor and the fellow student.

Eliminate Barriers
We aim to eliminate any barriers that students may encounter that prevent them from engaging with the important mathematical work of a lesson. Our classroom offers flexibility and a specified quiet area for students to have a calming and dedicated work zone. We pay attention to areas such as the physical environment of the classroom, access to tools, organization of lesson activities, and means of communication.

### CFS Math course area breakdown:

Pre-Algebra (students entering grades 6-8)
Pre-Algebra prepares students for the rigors of algebra and also teaches students problem-solving techniques to prepare them for high school level
mathematical concepts. Topics covered in the course include the properties of arithmetic, exponents, primes and divisors, fractions, equations and inequalities, decimals, ratios and proportions, unit conversions and rates, percents, square roots, basic geometry (angles, perimeter, area, triangles, and quadrilaterals), statistics, the coordinate plane, graph linear equations, probability, and more!

Algebra 1
Algebra 1 teaches the fundamentals of algebraic concepts and skills through incremental development. Students learn to manipulate signed numbers and exponents, graph equations on the rectangular coordinate system, and factor quadratic equations that have real roots. In the fall semester, instruction covers algebraic properties, fractions, factoring, signed exponents, properties of equalities, solutions of single and multivariable equations, abstract factions, and the slope- intercept formula. Students learn to factor quadratic equations, use the Pythagorean Theorem, derive an equation between two points, solve linear inequalities, factory binomials and trinomials, divide polynomials, simplify radical expression, and manipulate scientific notation. Word problems include rations, percentage, uniform motion, compound interest, and variation (indirect & indirect).

Geometry
The Geometry course includes an in-depth analysis of plane, solid, and coordinate geometry as they relate to both abstract mathematical concepts as well as real-world problem situations. Topics include logic and proof, parallel lines and polygons, perimeter and area analysis, volume and surface area analysis, similarity and congruence, trigonometry, and analytic geometry. Emphasis will be placed on developing critical thinking skills as they relate to logical reasoning and argument. Students will be required to use different technological tools and manipulatives to discover and explain much of the course content

Real Life Math
This unique course will introduces students to the decimals and percentages which are widely used in money and finances (think car loans, interest rates, balancing checking accounts, retirement savings accounts), as well as fractions, measurement, and conversions (think recipes for baking and cooking, budgeting cost per unit). Students will also learn how to set up and solve problems like this is a very useful mathematical concept that is applicable to real life situations. Lastly, students will also see data in common forms and will have to interpret data and graphs.