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 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.

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 6thgrade 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 7thgrade 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

 

 

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