Circle 6 Syllabus

Circle 6 is an engaging and comprehensive math course designed to prepare students for Pre-Algebra and Algebra, focusing on key concepts like ratios, proportions, exponents, and rational numbers. Aligned with Common Core Standards for Grades 6 and 7, this course introduces students to multi-step problem solving, including solving equations with inverse operations, tackling simple systems of equations, and applying the Pythagorean Theorem. Ideal for students ages 9 to 12 who are comfortable with four-digit arithmetic, squaring numbers, fraction operations, and working with negative numbers. Circle 6 incorporates problem-solving exercises, logic puzzles, and friendly competition-style challenges to keep young minds active, inspired, and ready for the next level in math!

Concepts, skills, and learning tools students see in this course include, but are not limited to:

• Exponents and Exponential Laws
• Rational Numbers, Percents and Decimals
• Ratios and Proportions
• Problem-solving skills, logic puzzles, algebraic and geometric thinking, competition-style problems

Upon completing the course, students will be able to:

• Advanced Expressions and Exponents: Simplify complex expressions with proper order of operations, apply laws of exponents (including negative and zero exponents), and use prime factorizations to find GCF and LCM.
• Operations with Fractions, Decimals, and Percentages: Perform all basic operations on fractions, decimals, and percentages, and set up and solve ratios, proportions, and percentage changes.
• Equations and Systems: Simplify and solve multi-step equations for single variables, solve simple systems of equations using substitution, and apply the Pythagorean Theorem.
• Geometry, Probability, and Statistics: Calculate perimeter and area of complex polygons, use counting principles to find probabilities, and interpret statistical data with central tendency and variability.

Students registering for this course should be comfortable with the following Math:‍

• Identifying and operating (addition, subtraction, multiplication, division) with integers (positive and negative whole numbers) up to 1 million
• Squaring numbers, finding areas and perimeters of complex polygonal shapes, identifying quadrilaterals by their properties
• Fractions with up to 3-digit numbers, including simplification, finding a common denominator and adding and subtracting fractions

• Integers and Powers (5 weeks): Develop foundational skills with integers, including addition, subtraction, multiplication, division, and introductory powers and roots.
• Fractions, Decimals, and Percents (7 weeks): Master operations with fractions, decimals, and percents, including conversions, adding/subtracting, multiplying/dividing, and applying percentage strategies.
• Expressions and Equations (7 weeks): Simplify and evaluate expressions, solve single and multi-step equations, explore exponential expressions, and work with simple systems of equations.
• Ratios, Proportions, and Statistics (7 weeks): Understand ratios, proportions, and percentage change; introduce graphing on the Cartesian plane; and cover central tendency, variability, counting principles, and basic probability.
• Geometry and the Pythagorean Theorem (6 weeks): Calculate perimeter, area, and volume of polygons and 3D shapes; explore the Pythagorean Theorem, its applications, and work with distances in 2D and 3D contexts.