### Return to BEarth Academy: High School Edition: HERE

Return to BEarth Academy: Math Edition HERE

**Fifth Grade**

Enroll in BEarth Academy: Math Edition: Fifth Grade HERE

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

- Factors and multiples.
- (Common) Fractions: review and furthering from 4
^{th}grade 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 our
*Arithmetic 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 our
*Arithmetic 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 our
*Arithmetic 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 our
*Arithmetic Fact Speed Sheets*.

**Sixth Grade**

Enroll in BEarth Academy: Math Edition: Sixth Grade HERE

** 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

**Seventh Grade**

Enroll in BEarth Academy: Math Edition: Seventh Grade HERE

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

- Review of 6
^{th}grade math - 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

**Eighth Grade**

Enroll in BEarth Academy: Math Edition: Eighth Grade HERE

** 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 7
^{th}grade algebra, order of operations; distributive property. - Puzzles and Problem Solving
- End-of-Year Review

**Ninth Grade**

Enroll in the BEarth Academy: Math Edition: Ninth Grade HERE

__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
- Solving quadratic equations
- 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

**Tenth Grade**

Enroll in BEarth Academy: Math Edition Tenth Grade HERE

** 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

**Eleventh Grade**

Enroll in BEarth Academy: Math Edition: Eleventh Grade HERE

** 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