# Mathematics Courses

Juni Mathematics is designed for students ages 7-18 to experience the power of critical thinking. In a world that’s changing drastically everyday, we help tomorrow's leaders apply their learnings to solve pressing real-world problems. Using rigorous Common Core and state standards as our starting point, we further build our students' understanding and discovery in Mathematics. Currently, we offer courses in Elementary Mathematics, Pre-Algebra, Algebra 1, Geometry, Algebra 2, Pre-Calculus & Trigonometry, and AP Calculus. Each course is divided into A and B halves, that each typically take 4-7 months to complete.

• ## Discovering Numbers, Operations, and Measurement

Ages 7-9

### Early Elementary A

This is an elementary-level course designed with 2nd grade math standards in mind. The course develops foundational skills in addition, subtraction, multiplication, and division, through hands-on activities designed to help students discover math. Early Elementary A covers Addition and Subtraction within 100 and within 1,000, Intuitive Thinking with Multiplication and Division, and Data and Measurement. After this course, students will continue to build their foundational knowledge of math in Early Elementary B.

• ## Exploring Arithmetic, Fractions, and Geometry

Ages 7-9

### Early Elementary B

This is an elementary-level course designed with 3rd grade standards in mind. The course strengthens students’ intuition in arithmetic, fractions, and geometric shapes, through interactive activities and projects. This course is designed to build on students’ prior understanding from Early Elementary A or equivalent. Early Elementary B covers Foundations of Multiplication and Division, Patterns in Arithmetic, Multiplication and Area, Fractions, and Geometry and Measurement. After this course, students will continue their in-depth knowledge of math in Late Elementary A.

• ## Investigating Multiplication, Division, and Geometry

Ages 9-11

### Late Elementary A

This is an elementary-level course designed with 4th grade standards in mind. The course advances students’ critical thinking in multi-digit multiplication and division, fractions, and geometry by applying their new skills to real-life quantitative problems. Late Elementary A covers Arithmetic Review, Fluency of Multiplication and Division, and Geometry. It’s designed to build on students’ prior understanding from Early Elementary B or equivalent. After this course, students will continue their exploration of math in the Late Elementary B course.

• ## Mastering Fractions, Decimals, Units, and Coordinates

Ages 9-11

### Late Elementary B

This is an elementary-level course designed with 5th grade standards in mind. The course drives mastery of fractions, decimals, units and coordinates through applying their new skills to problems inspired by the real world. Late Elementary B covers Fractions, Decimals, Unit Conversions, Whole Number Operations, and Patterns and the Coordinate Plane. This course is designed to build on students’ learnings from Late Elementary A or equivalent. After this course, students will continue their investigation of math in Pre-Algebra A.

• ## Pre-Algebra A

Ages 10-13

Pre-Algebra is an honors-level middle school course that prepares students for the study of Algebra 1. This course is suitable for mathematically advanced fifth and sixth graders, in addition to seventh and eighth graders who would like to build a strong foundation in Pre-Algebra concepts. Pre-Algebra A covers four broad topics: arithmetic review; fractions, decimals, percents, and ratios; arithmetic expressions; and exponents and radicals. The practice problems provided in this course range from fundamentals practice to complex word problems from previous AMC8 and MathCounts contests.

• ## Pre-Algebra B

Ages 10-13

Pre-Algebra is an honors-level middle school course that prepares students for the study of Algebra 1. This course is suitable for mathematically advanced fifth and sixth graders, in addition to seventh and eighth graders who would like to build a strong foundation in Pre-Algebra concepts. Pre-Algebra B is meant to be taken directly after Pre-Algebra A. It covers four broad topics: data and statistics, geometry, number theory, and probability and counting. The practice problems provided in this course range from fundamentals practice to complex word problems from previous AMC8 and MathCounts contests.

• ## Algebra 1A

Ages 12-15

Algebra 1 sets the foundation of algebra, focusing on working with linear and quadratic equations while building appropriate problem-solving skills. This course is suitable for students who have completed a Pre-Algebra course or equivalent, and after successful completion of Algebra 1, students are prepared to move onto Geometry. Algebra 1A covers three broad topics: solving linear equations, graphing linear equations, and solving systems of linear equations. The practice problems provided in this course range from fundamentals practice to complex word problems.

• ## Algebra 1B

Ages 12-15

Algebra 1 sets the foundation of algebra, focusing on working with linear and quadratic equations while building appropriate problem-solving skills. This course is suitable for students who have completed a Pre-Algebra course or equivalent, and after successful completion of Algebra 1, students are prepared to move onto Geometry. Algebra 1B is meant to be taken directly after Algebra 1A. It covers four broad topics: manipulating polynomials, solving quadratic equations, graphing quadratic equations, and functions. The practice problems provided in this course range from fundamentals practice to complex word problems.

• ## Geometry A

Ages 13-16

Geometry is a proof-based, high school level geometry course that emphasizes geometric concepts in two and three dimensions as they apply to points, lines, planes, circles, and polygons. This course is suitable for students who have completed an Algebra 1 course or equivalent, and after successful completion of Geometry, students are prepared to move onto Algebra 2. Geometry A covers five broad topics: geometry foundations, lines and angles, triangles, triangle dissection, and trigonometry. The practice problems provided in this course range from fundamentals practice to complex proof-based problems.

• ## Geometry B

Ages 13-16

Geometry is a proof-based, high school level geometry course that emphasizes geometric concepts in two and three dimensions as they apply to points, lines, planes, circles, and polygons. This course is suitable for students who have completed an Algebra 1 course or equivalent, and after successful completion of Geometry, students are prepared to move onto Algebra 2. Geometry B is meant to be taken directly after Geometry A. It covers four broad topics: quadrilaterals and polygons, circles, transformations, and three-dimensional shapes. The practice problems provided in this course range from fundamentals practice to complex proof-based problems.

• ## Algebra 2A

Ages 14-17

Algebra 2 is a high school level algebra course that builds fluency in understanding and analyzing complex functions. Students study the applications of different function types, including exponential, rational, and trigonometric functions, using these to model and draw conclusions about real-life situations. This course is suitable for students who have completed courses in Algebra 1 and Geometry or equivalent. After successful completion of Algebra 2, students are prepared to move onto Pre-Calculus & Trigonometry. Algebra 2A covers four broad topics: quadratic functions, polynomials, rational functions, and radical and piecewise functions.

• ## Algebra 2B

Ages 14-17

Algebra 2 is a high school level algebra course that builds fluency in understanding and analyzing complex functions. Students study the applications of different function types, including exponential, rational, and trigonometric functions, using these to model and draw conclusions about real-life situations. This course is suitable for students who have completed courses in Algebra 1 and Geometry or equivalent. After successful completion of Algebra 2, students are prepared to move onto Pre-Calculus & Trigonometry. Algebra 2B is meant to be taken directly after Algebra 2A. It covers five broad topics: exponents and logarithms, sequences, matrices, probability and statistics, and trigonometry.

• ## Pre-Calculus & Trigonometry A

Ages 15-18

Pre-Calculus & Trigonometry is a high school level course that prepares students for success in their studies of calculus. The course is designed to build on students’ prior understanding of Algebra and Geometry to learn rigorous concepts such as the binomial theorem, conic sections, trigonometry, and a brief introduction to calculus. This course is suitable for students who have completed courses in Algebra 2 and Geometry or equivalent. After successful completion of Pre-Calculus & Trigonometry, students will be prepared to move onto AP Calculus. Pre-Calculus & Trigonometry A covers four broad topics: polynomials; piecewise, rational, and logarithmic functions; sums, sequences, the binomial theorem; and conic functions.

• ## Pre-Calculus & Trigonometry B

Ages 15-18

Pre-Calculus & Trigonometry is a high school level course that prepares students for success in their studies of calculus. The course is designed to build on students’ prior understanding of Algebra and Geometry to learn rigorous concepts such as the binomial theorem, conic sections, trigonometry, and a brief introduction to calculus. This course is suitable for students who have completed courses in Algebra 2 and Geometry or equivalent. After successful completion of Pre-Calculus & Trigonometry, students will be prepared to move onto AP Calculus. Pre-Calculus & Trigonometry B is meant to be taken directly after Pre-Calculus & Trigonometry A. It covers five broad topics: trigonometry, applications of trigonometry, linear algebra, probability, and introduction to calculus.

• ## AP Calculus AB & BC

Ages 15-18

AP Calculus is a rigorous high-school level course that is designed to build students’ in-depth understanding of calculus. The course is aligned with College Board standards and is designed to prepare students for the AP Calculus AB or BC exam. This course is suitable for students who are taking AP Calculus concurrently in school or are studying for the exam independently. We require that students have completed Pre-Calculus / Trigonometry as a prerequisite to this course. Due to the length and rigor of this course, we strongly recommend all students enroll in this course with two classes per week or more. For students who are taking AP Calculus AB, the course will cover: Limits and Continuity, Differentiation, Applications of Derivatives, Integration and Accumulation of Change, Differential Equations, and Applications of Integrations. For students who are taking AP Calculus BC, this course will also cover Parametric Equations, Polar Coordinates, and Vector-Valued Functions.