# Skyview Middle School Sixth Grade Mathematics

• Core Connections, Course 1, is the first 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:
• 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 the other.
• Compare fractions and generate equivalent fractions.
• Recognize ratios 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 variables 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 those with discounts, interest and tips.
• Compute area, surface area and volume of rectangular solids.
• Represent solids using nets.

# 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.