Jamie York's Math Curriculum
Summary of Topics in the Math Academy
We believe in developing enthusiasm for learning, as well as independent and creative thinking. At the same time, we still, devote significant time to developing math skills. Our math program is rigorous, yet our goal is to support students to succeed. We aim to spark their interest in learning, and to develop problem-solving capacities they can use in real life.
A quarterly list of topics is below on this page.
For weekly topic lists, find the link in each quarterly list.
Middle School Curriculum Overview
Far too often in middle school (grades 6-8), schools treat math as if the central purpose is to “win” the race to get ahead. Students struggle with massive textbooks. Homework is onerous. The list of math topics to cover is enormous. There is no time for discovery. There is no time for thinking. Learning is superficial. The message is “Do what the teacher tells you or you will fall behind.”‘ There is too much fear.
Math skills are important, but developing the students’ mathematical thinking capacities is just as important.
Rather than slogging through a textbook that primarily drills skills, we believe teachers should inspire students to experience the wonders of mathematics.
High School Curriculum Overview
When students enter high school, their interest in math should be at its peak. High school is a time when their ability to think mathematically is growing the fastest. Developmentally speaking, 9th grade is the best time for students to really hone their algebra skills. Then, in contrast, 10th grade is a fantastic time for students to deepen their thinking. Studies like: Greek geometry (how did Archimedes figure out pi?), the origins of trigonometry, sequences and series, and the relationship between math and music, are opportunities for such deep engagement.
Math should be soul-expanding (not soul-crushing). Math should be an adventure!
Fifth Grade
Quarter #1
- Factors and multiples.
- (Common) Fractions: review and further work with 4th grade fractions
- Four processes. Vertical arithmetic (addition, subtraction, long multiplication, and long division).
- Freehand geometry (main lesson)
- Mental math and arithmetic facts using our Arithmetic Fact Speed Sheets.
- Problem solving, discovery, and puzzles.
Quarter #2
- Review of the U.S. measurement system.
- Wonder of Number (divisibility rules, prime numbers, patterns)
- Four processes. Vertical arithmetic (addition, subtraction, long multiplication, and long division).
- Mental math and arithmetic facts using our Arithmetic Fact Speed Sheets.
- Problem solving, discovery, and puzzles.
Quarter #3
- Decimal fractions and the metric system (main lesson)
- Four processes. Vertical arithmetic (addition, subtraction, long multiplication, and long division).
- Word problems.
- Mental math and arithmetic facts using our Arithmetic Fact Speed Sheets.
- Problem solving, discovery, and puzzles.
Quarter #4
- Four processes. Vertical arithmetic (addition, subtraction, long multiplication, and long division).
- Decimal fractions – continuation from main lesson.
- Wonder of Number (powers of two, square and triangular numbers, sum and difference theorems, aliquot sums and sequences).
- Mental math and arithmetic facts using our Arithmetic Fact Speed Sheets.
- Problem solving, discovery, and puzzles.
Sixth Grade
Quarter #1
- Geometric drawing and constructions (main lesson)
- Practice four processes, including long multiplication and long division.
- Practice all aspects of fractions.
- Practice all four processes with decimals.
- Exponents
- Divisibility rules
- Mental math and math tricks
- Problem solving, discovery, and puzzles.
Quarter #2
- Practice four processes, including long multiplication and long division.
- Practice all aspects of fractions.
- Practice all four processes with decimals.
- Divisibility rules
- Repeating decimals; Decimal/fraction conversions.
- Measurement – both US and metric
- Unit cost
- Mental math and math tricks
- Problem solving, discovery, and puzzles.
Quarter #3
- Business math (main lesson)
including an introduction to percents, (statistical) graphs, and formulas. - Practice four processes, including long multiplication and long division.
- Practice all aspects of fractions.
- Practice all four processes with decimals.
- Repeating decimals; Decimal/fraction conversions.
- Prime factorization.
- Divisibility rules
- Mental math and math tricks
- Problem solving, discovery, and puzzles.
Quarter #4
- Practice four processes, including long multiplication and long division.
- Practice all aspects of fractions.
- Practice all four processes with decimals.
- Repeating decimals; Decimal/fraction conversions.
- Mental math & math tricks (Casting out nines).
- Divisibility rules
- Prime factorization.
- Currency exchange rates.
- Measurement review & introduction to area.
- Ratios – brief introduction.
- Mental math and math tricks
- Problem solving, discovery, and puzzles.
Seventh Grade
Quarter #1
- Review of 6th grade math
- Geometric drawing & constructions (main lesson)
- Intro to the Pythagorean Theorem
- Measurement – US and Metric systems
- Word problems.
- Mental math and math tricks
- Problem solving, discovery, and puzzles
Quarter #2
- Measurement – US and Metric systems
- Ratios, including whole number and decimal form, and similar figures.
- Intro to Percents.
- Mental math and math tricks
- Problem solving, discovery, and puzzles
Quarter #3
- Percents, including percent increase and decrease.
- Intro to Algebra (main lesson)
- Ratios, including ratio in a circle (π).
- Mental math and math tricks
- Problem solving, discovery, and puzzles
Quarter #4
- Rates, including speed/distance/time and rate of pay problems.
- Geometry: rectangles, parallelograms, non-right triangles; the shear and stretch
- The square root algorithm
- Mental math and math tricks
- Problem solving, discovery, and puzzles
Eighth Grade
Quarter #1
- Geometry (main lesson),
including Stereometry (Platonic & Archimedean solids) and Loci (conic sections and Cassini curves). - Number Bases.
- Understanding the thinking behind computers (software and hardware).
- Square root algorithm.
- Pythagorean Theorem with calculations.
- Problem solving, discovery, and puzzles.
Quarter #2
- Pythagorean Theorem with calculations.
- Mensuration: Areas and volumes.
- Review of 7th grade percents.
- Problem solving, discovery, and puzzles.
Quarter #3
- Percents & Growth.
- Proportions & Dimensional analysis (including rates, ratios, density, and converting metric to/from US.)
- Problem solving, discovery, and puzzles.
Quarter #4
- Proportions & Dimensional analysis (including rates, ratios, density, and converting metric to/from US.)
- Algebra, including review of 7th grade algebra, order of operations; distributive property.
- Puzzles and Problem Solving Unit
- End-of-Year Review
Ninth Grade
Special Note: Advanced students may proceed through the below curriculum at a faster rate than what is indicated.
Quarter #1
- Descriptive Geometry (main lesson)
- Review middle school algebra
- Laws of exponents
- Arithmetic with polynomials
- Problem solving, discovery, and puzzles
Quarter #2
- Negative exponents
- Factoring polynomials
- Solving quadratic equations
- Word problems
- Problem solving, discovery, and puzzles
Quarter #3
- Word problems
- Solving systems of equations
- Review of percents, unit conversions, proportions
- Possibility & Probability (main lesson)
- Problem solving, discovery, and puzzles
Quarter #4
- The quadratic formula & al-Khwarizmi’s work
- Introduction to logarithms
- Fractional exponents
- Possibility & Probability practice
- Problem solving, discovery, and puzzles
- (for advanced students) simplifying square roots
- (for advanced students) rational expressions and equations
Tenth Grade
Quarter #1
- Greek Geometry and Deductive Proofs (main lesson)
- Geometry basics
- Circle geometry
Quarter #2
- The Geometry of the Triangle
- Writing proofs
- The works of Archimedes (sphere and π)
- Laws of proportionality (Euclid, Book V)
Quarter #3
- Intro to Trigonometry (main lesson)
- Mensuration (incl. volume & scale factors)
- Proof of Heron’s formula for triangle’s area
- Thorough review of 9th grade algebra
Quarter #4
- Sequences and Series
- Logarithms (building from 9th grade)
- Exponential growth, including the number e
- The Math of Music
Eleventh Grade
Quarter #1
- The Philosophy and Geometry of René Descartes (main lesson)
- Cartesian Geometry (graphing linear equations)
- Problem solving
Quarter #2
- Imaginary & Complex Numbers – Part I
- Cartesian Geometry (conic sections, systems of equations)
- Trigonometry (Right triangle trig, Law of Sines, Law of Cosines)
Quarter #3
- Introduction to functions
- Projective Geometry (main lesson)
- Problem solving
- Perm, Comb & Probability review and deepen
Quarter #4
- Trigonometry (Six Trig Functions, Law of Tangents, trig unit circle, radian measure)
- Cartesian Geometry (polynomial equations, systems of equations)
- Logarithms (building from 10th grade)
- Trigonometry (Six Trig Functions, Law of Sines, Law of Cosines, Law of Tangents, trig unit circle, radian measure)
- Imaginary & Complex Numbers – Part II
Twelfth Grade
Quarter #1
- Introduction to Calculus (main lesson)
Pre-Calculus Topics
- Analytical trigonometry (identities & equations)
- Graphing trigonometry functions
Quarter #2
Pre-Calculus Topics
- Graphing exp. & logarithmic functions
- Graphing rational functions (asymptotes)
Calculus Topics
- Review and furthering of ML material
- Chain rule and Implicit differentiation
- Related rate & max/min problems
Quarter #3
- Continued work on calculus topics
- Philosophy of Math
Quarter #4
- Philosophy of math & Gödel’s proof
- Fractal Geometry & Chaos (main lesson)
