Circle 5 Syllabus

Circle 5 is an engaging and challenging math course designed to expand your child’s understanding of factors, prime factorization, and powers—setting the stage for advanced number manipulation, fractions, and expressions. Aligned with Common Core Standards for Grades 5 and 6, Circle 5 builds on key concepts like order of operations and integers, and introduces probability through real-world applications. Ideal for students ages 8 to 11 who are confident with three-digit arithmetic, understand order of operations, and can add fractions with unlike denominators. The course incorporates problem-solving skills, logic puzzles, and friendly competition-style challenges to keep young minds active, inspired, and ready for their next math adventure!

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

• Understanding factors, primes, factorizations, and expanding powers
• Expand order of operations to include exponents, parentheses and absolute value
• Introducing integers, probability and counting principles
• Problem-solving skills, logic puzzles, algebraic and geometric thinking, competition-style problems

Upon completing the course, students will be able to:

• Advanced Number Operations: Master rounding up to 100,000,000s and to 1,000ths, and add/subtract fractions and decimals with ease.
• Multiplication and Division Skills: Multiply whole numbers and fractions, and perform division with remainders.
• Fraction and Integer Understanding: Deepen understanding of fractions, create equivalent fractions, and use integers and decimals in basic operations.
• Geometry and Probability: Explore perimeter and area of shapes (including triangles and circles) and learn foundational concepts in probability and counting principles.

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

• Identifying numbers up to 100,000,000
• Comfortable with arithmetic operations: addition and subtraction (3-digits), multiplication and division (both 2-digit operands)
• Adding simple fractions with one denominator being a multiple of the other denominator
• Simple order of operations with addition, subtraction, parentheses and multiplication

• Order of Operations, Multiplication, and Division (6 weeks): Master the order of operations, distributive property, multiplication techniques, powers, perfect squares, and division (including long division).
• Integers and Equations (5 weeks): Explore positive and negative numbers, absolute values, and solve one-step and two-step equations, including simple systems of equations.
• Fractions and Decimals (8 weeks): Convert between mixed and improper fractions, perform operations with fractions (addition, subtraction, multiplication, division with reciprocals), and work with decimals, including place value and rounding.
• Probability and Statistics (6 weeks): Learn probability basics, counting principles (addition and multiplication), and explore dependent and independent events using Venn diagrams and tree diagrams.
• Geometry (7 weeks): Study angles, calculate the area of various polygons, understand circles (circumference and area), and explore 3D concepts like surface area and volume of cylinders and cones.