# Skyview Middle School Seventh Grade Mathematics

• Core Connections, Course 2, is the second of a three-year sequence of courses designed to prepare students for a rigorous college preparatory algebra course. It uses a problem-based approach with concrete models. The course helps students to develop multiple strategies to solve problems and to recognize the connections between concepts. The lessons in the course meet all of the content standards and embed the mathematical practices of the Common Core state standards. 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 those with 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 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.

# Mathematics Department Overview

• Mathematics is the abstract study of topics such as quantity (numbers), structure, space and change. There is a range of views among mathematicians and philosophers as to the exact scope and definition of mathematics.

Mathematicians seek out patterns and use them to formulate new conjectures. Mathematicians resolve the truth or falsity of conjectures by mathematical proof. When mathematical structures are good models of real phenomena, then mathematical reasoning can provide insight or predictions about nature. Through the use of abstraction and logic, mathematics developed from counting, calculation, measurement, and the systematic study of the shapes and motions of physical objects. Practical mathematics has been a human activity for as far back as written records exist. The research required to solve mathematical problems can take years or even centuries of sustained inquiry.

Teaching mathematics is essential for all students as they grow to understand their world and become productive citizens. Mathematical models explain, celebrate, and analyze the world around us; from economic models on the stock market to musical models of symphonies, our world is mathematics. All Colorado students must understand mathematics and its relevance in their lives.

# Educational Content Areas

• The power of Colorado’s education improvement efforts lies in having a comprehensive system consisting of relevant and rigorous standards, aligned and meaningful assessments, excellent teachers and school leaders, and high-performing schools and districts. All aspects of the system are continuously improving to advance student learning and prepare students to succeed in an increasingly competitive workforce The Colorado Academic Standards are the expectations of what students need to know and be able to do at the end of each grade. They also stand as the values and content organizers of what Colorado sees as the future skills and essential knowledge for our next generation to be more successful. State standards are the basis of the annual state assessment.