### Math

## Course Description

Our Core Connections math courses are a 3 year sequence of classes designed to prepare students for a rigorous college preparatory algebra course. All three years use a problem based approach with concrete models. The courses help students to develop multiple strategies to solve problems and to recognize connections between concepts. The lessons meet all of the content standards and embed the “Mathematical Practices of the Common Core State Standards released in June 2010.

Lessons are structured for student to collaborate actively by working in study teams. During class time, students work in study teams on challenging problems that introduce new material. The teacher provides guidance as needed and helps to consolidate topics. The homework for each lesson reinforces previously introduced skills and concepts and prepares students for new ones. The homework problems also allow students to apply previously learned concepts and skills in new contexts and deepen their understanding by solving the same type of problems in different ways.

**Course 1** - Upon completion of this course, students should be able to:

● Collect, organize and display data in multiple ways

● Analyze data using measures of central tendency

● Represent data sets using various methods and analyze how changes in data impact the representation.

● Represent and compare quantities using manipulatives, diagrams and number expressions.

● Represent multiplication using rectangular arrays.

● Model integers

● Make sense of multiple representations of portions (decimal, fraction, percent) and convert from one form to another.

● Compare fractions and generate equivalent fractions.

● Recognize rations in tables and graphs and solve corresponding problems.

● Use ratios to describe relationships with similar plane figures and other situations.

● Use models and standard algorithms for computations with fractions and decimals.

● Simplify variable expressions by combining like terms and using the Distributive Property.

● Evaluate variable expressions and solve simple equations and inequalities.

● Solve distance, rate and time problems. Solve percent problems including discounts, interest and tips.

● Compute area, surface area and volume of rectangular solids. Represent solids using nets.

**Course 2 **- Upon completion of this course, students should be able to:

● Model integers and operations with integers and rational numbers including using order of operations.

● Use linear models and equal ratios to represent part-whole relationships.

● Use percents and scale factors to determine percent increase or decrease, discounts and markups.

● Use variable expressions to represent quantities in contextual problems.

● Simplify variable expressions by combining like terms and using the Distributive Property.

● Solve linear equations including fractional coefficients and those with no solutions or infinite solutions.

● Solve and graph one-variable inequalities.

● Compare experimental and theoretical probabilities.

● Distinguish between dependent and independent events and calculate the probability of compound independent events.

● Represent probabilities of multiple events using systemic lists, charts or tree diagrams.

● Design, conduct and analyze surveys.

● Collect and compare data and describe the distribution of sets of data.

● Solve distance, rate and time problems.

● Compare ratios and calculate unit rates.

● Recognize and solve problems involving proportional relationships.

● Recognize and use the properties of similar shapes and scale factors to solve problems.

● Describe angles, angle pairs and their measures.

● Compute area and perimeter of standard and compound shapes. Compute the volume of a variety of solids.

**Course 3 **- Upon completion of this course, students should be able to:

● Represent a linear function with a graph, table, rule and context and should be able to find any representation when provided one of the others

● Solve systems of equations represented in tables and graphs.

● Symbolically manipulate expressions in order to solve problems including those with fractional coefficients.

● Solve contextual word problems using multiple strategies including making tables, looking for patterns, drawing diagrams and creating a table of guesses to assist with writing and solving a variable equation.

● Describe various transformations on a coordinate grid.

● Represent data using scatterplots and describe associations.

● Collect and analyze data and make predictions based on the trend of the data.

● Compare ratios, calculate unit rates and slope ratios.

● Analyze the slope of a line graphically, numerically and contextually.

● Recognize and solve problems involving proportional relationships.

● Graph and analyze non-linear functions.

● Recognize and use the properties of similar shapes to solve problems.

● Use the Pythagorean Theorem and its converse to solve problems in 2 and 3 dimensions.

● Use square and cube roots.

● Represent and simplify expressions using positive and negative exponents.

● Represent and compare large and small numbers using standard and scientific notation.

● Perform operations with numbers represented in scientific notation.

● Use the relationships between angles created by parallel lines with transversals and the triangle sum theorem to solve problems.

● Compute the volume of a variety of solids.

** Algebra** is the first course in a sequence of college preparatory mathematics that ends with Calculus. Students in Algebra use problem solving, critical analysis, evidence, and communicate justification of their thinking. Algebra aims to deepen and extend student mathematical understanding by focusing on developing fluency with solving linear equations and inequalities and systems; extending these skills to solving quadratic and exponential functions; exploring functions, and using regression techniques to analyze the fit of models to distributions of data.

*Math Support - 2 Advisory Periods a Week (offered for Course 1, Course 2, and Course 3)*

This course is an intervention course for students scoring at less than proficient levels on the CST standardized test. It is designed to provide students with the support necessary to be successful in their regular math course and master the grade-level concepts addressed in the Common Core State Standards. The six topic areas covered are: place value and basic number skills, fractions and decimals, ratios, rates, and percents, the core processes of mathematics, functions and equations and measurement.