 Quarter #1 (Sep 9 – Oct 4 and Oct 28 – Nov 22):

• Factors and multiples.
• (Common) Fractions: review and furthering from 4thgrade fractions
• Four processes. Vertical arithmetic (addition, subtraction, long multiplication, and long division).
• Freehand geometry (main lesson Nov 4-22)
• Mental math and arithmetic facts. Using ourArithmetic Fact Speed Sheets.

Quarter #2 (Dec 2-20 and Jan 6 – Feb 7):

• 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 ourArithmetic Fact Speed Sheets.

Quarter #3 (Feb 17 – April 10):

• Decimal fractions and the metric system (main lesson Feb 24 – Mar 13)
• Four processes. Vertical arithmetic (addition, subtraction, long multiplication, and long division).
• Word problems.
• Mental math and arithmetic facts. Using ourArithmetic Fact Speed Sheets.

Quarter #4 (April 20 – June 12):

• 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, perfect numbers, sum and difference theorems).
• Mental math and arithmetic facts. Using ourArithmetic Fact Speed Sheets.

Quarter #1 (Sep 9 – Oct 4 and Oct 28 – Nov 22):

• Geometric drawing and constructions (main lesson Nov 4-22)
• 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

Quarter #2 (Dec 2-20 and Jan 6 – Feb 7):

• 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

Quarter #3 (Feb 17 – April 10):

• Business math (main lesson Feb 24 – Mar 13)
including an introduction to percentages, (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

Quarter #4 (April 20 – June 12):

• 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

Quarter #1 (Sep 9 – Oct 4 and Oct 28 – Nov 22):

• Geometric drawing & constructions (main lesson Nov 4-22)
• Measurement – US and Metric systems
• Word problems.
• Mental math and math tricks

Quarter #2 (Dec 2-20 and Jan 6 – Feb 7):

• Measurement – US and Metric systems
• Ratios, including whole number and decimal form, and similar figures.
• Intro to Percents.
• Mental math and math tricks

Quarter #3 (Feb 17 – April 10):

• Percents, including percent increase and decrease.
• Intro to Algebra (main lesson Feb 24 – Mar 13)
• Ratios, including ratio in a square; ratio in a circle (π).
• Mental math and math tricks

Quarter #4 (April 20 – June 12):

• Rates, including speed/distance/time and rate of pay problems.
• Intro to the Pythagorean Theorem
• Rectangles, parallelograms, non-right triangles; the shear and stretch;
• The Square Root Algorithm
• Mental math and math tricks

Quarter #1 (Sep 9 – Oct 4 and Oct 28 – Nov 22):

• Geometry (main lesson Nov 4-22),
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.

Quarter #2 (Dec 2-20 and Jan 6 – Feb 7):

• Pythagorean Theorem with calculations.
• Mensuration: Areas and volumes.
• Review of 7th grade percents.

Quarter #3 (Feb 17 – April 10):

• Percents & Growth.
• Proportions & Dimensional analysis (including rates, ratios, density, and converting metric to/from US.)

Quarter #4 (April 20 – June 12):

• Proportions & Dimensional analysis (including rates, ratios, density, and converting metric to/from US.)
• Algebra, including review of 7thgrade algebra, order of operations; distributive property.
• Puzzles and Problem Solving
• End-of-Year Review

Special Note Advanced students may proceed through the below curriculum at a faster rate than what is indicated.

Quarter #1 (Sep 9 – Oct 4 and Oct 28 – Nov 22):

• Descriptive Geometry (main lesson Nov 4-22)
• Review middle school algebra
• Laws of exponents
• Arithmetic with polynomials

Quarter #2 (Dec 2-20 and Jan 6 – Feb 7):

• Negative exponents
• Factoring polynomials
• Word problems

Quarter #3 (Feb 17 – April 10):

• Word problems
• Solving systems of equations
• Review of percents, unit conversions, proportions
• Possibility & Probability (main lesson Feb 24 – Mar 13)

Quarter #4 (April 20 – June 12):

• Simplifying square roots
• Rational expressions and equations
• The quadratic formula & al-Khwarizmi’s work
• Introduction to logarithms
• Fractional exponents
• Possibility & Probability practice

Quarter #1 (Sep 9 – Oct 4 and Oct 28 – Nov 22):

• Greek Geometry and Deductive Proofs (main lesson Sept 16 – Oct 4)
• Geometry basics
• Circle geometry

Quarter #2 (Dec 2-20 and Jan 6 – Feb 7):

• The Geometry of the Triangle
• Writing proofs
• The works of Archimedes (sphere and π)
• Laws of proportionality (Euclid, Book V)

Quarter #3 (Feb 17 – April 10):

• Intro to Trigonometry (main lesson Feb 24 – Mar 13)
• Mensuration (incl. volume & scale factors)
• Proof of Heron’s formula for triangle’s area
• Thorough review of 9th grade algebra

Quarter #4 (April 20 – June 12):

• Sequences and Series
• Logarithms (building from 9th grade)
• Exponential growth, including the number e
• The Math of Music

Quarter #1 (Sep 9 – Oct 4 and Oct 28 – Nov 22):

• The Philosophy and Geometry of René Descartes (main lesson Sept 16 – Oct 4)
• Cartesian Geometry (graphing linear equations)
• Problem solving

Quarter #2 (Dec 2-20 and Jan 6 – Feb 7):

• Imaginary & Complex Numbers – Part I
• Cartesian Geometry (conic sections, systems of equations)
• Trigonometry (Right triangle trig, Law of Sines, Law of Cosines)

Quarter #3 (Feb 17 – April 10):

• Introduction to functions
• Projective Geometry (main lesson Feb 24 – Mar 13)
• Problem solving
• Perm, Comb & Probability review and deepen

Quarter #4 (April 20 – June 12):

• 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: Coming in 2021

Quarter #1 (Sep 9 – Oct 4 and Oct 28 – Nov 22):

• Introduction to Calculus (main lesson Sept 16 – Oct 4)

Pre-Calculus Topics

• Analytical trig (identities & equations)
• Graphing trig functions
• Graphing exp. & logarithmic functions
• Graphing rational functions (asymptotes)

Quarter #2 (Dec 2-20 and Jan 6 – Feb 7):

Calculus Topics

• Review and furthering of ML material
• Chain rule and Implicit differentiation
• Related rate & max/min problems

Quarter #3 and #4 (Feb 17 – April 10 and April 20 – June 12):

Possible Topics

• Business math topics (e.g., mortgage formula)
• Topics from economics
• Statistics in the media
• Introduction to Statistics
• Spherical trigonometry
• 3-D coordinate geometry
• Chaos theory & fractals
• Philosophy of math & Gödel’s proof