Math is very important for productive members of society.

I think many homeschool parents are intimidated by teaching math, especially as kids get older and do more complicated work.

# Here’s how we do math in our homeschool – from preschool to high school.

## Primary curriculum is Singapore workbooks, Life of Fred, and VideoText.

## We do lots of supplemental work with games, manipulatives, and apps.

We love **notebooking** along with **workbooks** and **drill** to ensure our kids know their math facts and concepts well to move on to higher level math coursework.

We love keeping math journals. We do special math projects around seasons. We do fun math activities during the holidays like Valentine’s and Easter. I like to incorporate cross-curricular activities for further review. And we love playing with food. The kids like Montessori math games.

### Preschool

We focus on counting: cardinal and ordinal. We play and make math fun.

There is little writing. We draw, play with shapes, identify, play matching, games, sing songs, play apps.

Alex begged for a math workbook like his sisters. Luckily, I found Singapore K was just right for him!

He would beg to do *so many pages* each day that he completed both workbooks in just a few months!

### Elementary

I follow the natural transitions of my kids’ learning.

We’ve loved Singapore Primary Math since the beginning of our homeschool journey.

My children have been ready for the Book 1 Set by the time they were 5 years old.

A complete set of Singapore Primary Math for one grade level consists of two softcover textbooks and two consumable workbooks. There are also teacher manuals and homeschool schedule booklets.

We love notebooking with Life of Fred math.

I read the books aloud and the girls complete the Your Turn at the end of each chapter together with printable themed notebooking pages.

The elementary set of Life of Fred math are 10 books with titles beginning with the alphabet A through J.

Life of Fred is fun reading: it’s a narrative following the character Fred through adventures that entertain as we learn math concepts.

## Concepts learned in Life of Fred elementary:

**Apples**: Numbers that Add to 7, Circles, Ellipses, Reading 6:00 on a Clock, 5 + ? = 7, Days of the Week, Leap Years, Spelling February, Dressing for Cold Weather, 15 Degrees Below Zero (–15º), Deciduous Trees, Deciduous Teeth, Counting by Fives, 3x + 4x = 7x, Archimedes 287 B.C. Wrote The Sand Reckoner and Got Killed Being Rude, ante meridiem (a.m.), Donner and Blitz in German, One Million, Euclid Wrote The Elements, Squares, Pacific and Atlantic Oceans, Whales Are Not Fish, The “There Are Zero . . .” Game, Sets, the Popularity of Zero, Why Boats Are Cheaper to Rent in the Winter, Triangles, Herbivores and Carnivores, the Colors of the Rainbow, a King in Checkmate, the Story of the Titanic, ≠ (not equal), x + 4 = 7, One Thousand, Counting by Hundreds, Reading 3:05 on a Clock, Rectangles.

**Butterflies**: One Yard = 3 Feet, Numbers that Add to 9, Counting by twos, Reading 5:10 on a Clock, Facts about Butterflies, Chrysalis vs. Cocoon, Braces, Parentheses and Brackets, Christina Rossetti, Sheet Music for “But Not Alone,” Domenico Fetti’s Archimedes Thoughtful, Exclamation Points, Bad Things about Sugar, One Good Thing about Sugar, Marvin Stone’s Invention of the Paper Straw 1888, Orion’s Belt, Betelgeuse, Why Not Every Three Stars Can Make a Triangle, Collinear, Reading 5:55 on a Clock, Book Signings, Why You Can Not Walk In a Room, Deliberate vs. Inadvertent, How to Say Toenail in German, Ordinal Numbers, Yurts, Half Past Six, a Nebula is Not a Star, Light Years, the Alphabet Game, a Dozen, Perpendicular, p.m. (post meridiem), Syncope, Sheet Music for “The Crash of the Bell Tower,” Quotation Marks inside of Quotation Marks, A Baker’s Dozen, Spine of a Book, Naissance, Lie vs. Lay, Whole Numbers, Cardinal Numbers, Trillion, Quadrillion and Quintillion, Aleph-null, Kingie’s Brothers, States that Begin with the Letter M, ∞, Saying Thank You, Virgil’s Aeneid, History of Pizza, How to Set a Table.

**Cats**: Ursa Major (Big Bear), Commutative, Asterism, Vowels, Cardinality of a Set, Loud Talkers, Hiring Freeze, One Quarter, Numerals vs. Numbers, Counting by Threes, Hoodwinked, Finding Patterns, Sheet Music for “Happy”, Four Basic Emotions, Right Angles, Quarter and Half Notes, Obligate Carnivores, Adjectives and Verbs, Carbohydrates, a Quarter to Three, the Mariana Trench, 5280 Feet in a Mile, Ferdinand Magellan’s Trip, What Pacific Means, Bacteria, Rabies in 300 B.C., Treating Cat Scratches, Capital Letters Start Sentences, Five Vowel Words: Mat, Met, Mit, Mot, Mut, Twenty-Two English Words That Don’t Contain a Vowel: By, Cry, . . . , Tryst, and Why, Numbers Expressed as Hundreds, Tens and Ones, Sexagesimal and Decimal Systems, Numbers that Add to 13, Morse Code, Four Major Oceans of the World, Centuries, Centenarians, and Centurions, Homonyms, Square Feet, Prepositional Phrases, 71 English Prepositions, Volume, One Meter, the Three Countries of the World that Don’t Primarily Use the Metric System. What Mathematicians Do, Prime Numbers, Less Than (<).

**Dogs**: One Million, Our Place in the Dance of Life, π, the Game of Doubles, Fortnight, Digits in a Number, Two Dimes = 20 Cents, New Words in English, Anachronism, Middle English, Old English, Doubling 1 ➔ 2 ➔ 4 ➔ up to 1,267,650,600,228,229,401,496,703,205,376 (which is 100 doubles), 7 – z = 4, Making Choices in Life, Daniel Defoe’s Robinson Crusoe, Morse Code from A–Z, Functions, the Function Party Game, One Billion, Finding Patterns, What Can Cause Unclear Thinking, Rhyme Schemes, Tennyson’s In Memoriam, Eyes Adjusting to Bright Light, Consecutive Even Numbers, ATM Cards, Numbers that Add to 15, Guessing Functions, Right Angles, Rectangles, Constant Functions, Buying Books, One Day Without Reading, Sheet Music for “Borrowed Books”, Beautiful Handwriting, Numbers that Add to 17, Macronutrients, the Eight Planets, Seven Wonders of the Ancient World, Different Ways to Pick Out a Book to Read, Bar Graphs, Different Jobs You Might Choose, Adopting a Dog, Idioms, Spendthrifts, Adding two- and three-digit numbers, Art in Advertising, Carrying the One in Addition, Female and Male, Apartment Leases, Isotopes of Hydrogen, the Chemical Elements, Dog Games.

**Edgewood**: Dangling participles, Concurrent Lines, Christina Rossetti’s “A Chill,” Dealing with Troubles, Parallel Lines, Trapezoids, Right Angles, Facing Things You Don’t Want to Do, Functions, Rhombuses, Constant Functions, Tripoli, Eritrea, Median Average, Writing Larger Numbers with Commas, Using Logarithms to Solve 2x = 5, Birdie Rule for Logarithms, Finding Approximate values for log 5 on a Calculator, Bar Graphs, Math Poems, >, Couplets in Poetry, Strait does not mean Straight, Judging People by their Size, If Fred Were an Author, Numbers that Add to 8, 10, and 12, Population of the Earth, State Income Tax Rates as Percents, Definition of Polka Dots, Parallelograms, Rows and Columns of a Matrix, the Four Kinds of Sentences: Declarative, Interrogative, Imperative, and Exclamation, Pronouns, Quarter of an Hour, Importance of Seat Belts, Small, Medium, and Large Mistakes, Busted vs. Broken, Half Dozen, Gibbous Moons, Dusk, Two Kinds of Knowledge Errors, Firearm Safety, Symptoms of Hypothermia, Voluntary and Involuntary Actions of the Body, Lorentz Contraction, International Date Line, Treatment of Hypothermia, the Addition Game Using Playing Cards, Alright Is Not a Word, Playing Guess-A-Function, Six Examples of Functions: Add, Subtract, Multiply, Divide, Tangent, and Derivative, One Way to Feel Lonely, What It Means to Matriculate.

**Farming**: Why Many Dolls Have a Vacant Stare, Adding to 14, Litotes, Googol, Three Things in Order to be Great, Oxymorons, Percents, Adding to 16, Rows of a Matrix, Median Average, Collective Nouns, Union of Sets, All of Mathematics Generated by the Empty Set, Proof that the Set of Everything (the Universal Set) Cannot Exist, Cardinality of a Set, Cock-a-doodle-doo in Four Languages, Collinear Points, Numbers vs. Numerals, Borrowing One in Subtraction, Circumference of the World, What Iniquitous Means, the Second Sound Recording Ever Made, the Proof that Every Number is Interesting, Definition of Function, Domain, and Codomain, Flour Fights Are Fun, Rhetorical Questions, the Game of Questions, Caesura, Radius and Ulna, Humerus vs. Humorous, Dollars in Different Denominations.

**Goldfish**: Tulip Mania, Drawing Things to Scale, Digits in a Number, Similes, Being Pardoned Before Being Tried in 1974, What Is Rarely on a Doll’s Christmas List, the Whole Point of Math, Don’t Wave Your Money Around, the Advanced Form of the Game of Which of These Is Not Like the Others, Keeping Your Word, Picking Your Friends and Your Spouse, Polygons, Sequences, a Crocodile Smile, What to Remember If You Smoke, Comparative Forms of Adjectives, Superlative Forms of Adjectives, a Waning Moon, People’s Life Goals Are Different than Fish’s Life Goals, Definition of an Acre, What Gets Venerated, Meters vs. Yards, Four Countries That Are Nations of Immigrants, Kilograms vs. Pounds, How to Deal with a Duck Who Never Tells the Truth, Lacrimal Glands, Area of a Rectangle, Living in a City vs. Living in the Country, Volume of a Fish Tank, Cubic Feet into Gallons, Gallons of Water into Pounds, Multiplying by Ten, Hundred, and Thousand, One Ton = 2000 lbs., Anthropomorphizing Fish, Plastic Aquarium Plants Don’t Die, Decimal Point, Estimating Sums, Drawbacks to 180-gallon Fish Tanks, Physical Work vs. Mental Work, Tragedy of the Commons, a Fish in a Tank vs. Coalback in Jail, Talking to Your Goldfish, Kingie’s Favorite Composers, Practicing the Metric System with Dental Floss, Purchasing Foreign Products, Bar Graphs, Protein and Calcium for Growth.

**Honey**: A Real Education Is Both Broad and Deep, Thirty-six Shades of Blue, Commutative Law of Multiplication, Closed Under Addition, Having a Job that Matters, Quarter of an Hour, Cardinal Numbers, Developing Character, Time Zones in the U.S., d = rt, the Milky Way, One Trillion, Exponents, Protons in the Observable Universe, Atoms, Periodic Table of the Elements, Varieties of Houses, 1½ + 1½, Is This a Function?, Bragging, Mysteries in Life, Long Division, Fractions, Remainders, Dividing 56382 by 3, Hip Fractures, Changing 82614 feet into Yards, Three Reasons to Learn Long Division (Even Though Calculators Exist), 36 Quarters Equals How Many Dollars?, the Four Times Table, a Disadvantage to Being Married to a Calculator, Why English Teachers Have It Rougher Than Math Teachers, What Happens When You Squeeze Your Toothpaste Tube Four Times Harder Than Normal, Reading Graham Greene’s The Heart of the Matter in German, the Guess-a-Function Game, a Balance in Life, Four Answers to Where Honey Comes From, Four Answers to Where Do Bees Live, Hexagons and Octagons, Why Bees Don’t Make Honeycombs in the Shape of Squares, Smelting Iron Ore, What You Add to Iron to Make Steel, Buying Flash Cards vs. Making Them, How Far the Netherlands Is from Holland, Becoming an Apiarist, Farther vs. Further, Checklist for Starting a Business, Penciling out a Proposed Business, the Big Question in Arithmetic—Do I Add, Subtract, Multiply, or Divide?, Why Not to Become a Typewriter Manufacturer, the Drawbacks to Ignoring Reality, Why Fred Can’t Get a Credit Card, Looking Back at Mistakes We Have Made in Life, Division by Two-digit Numbers, the Past Tense of mimic, 7xyz + 8xyz, What Magic Really Means, Slope of a Line.

**Ice Cream**: One Use of Poetry, The Big Question in Arithmetic, Stationery vs. Stationary, Multiplying Two-digit Numbers, a Pound of Hamburger Weighs More Than a Pound of Gold, the Last Ten Multiplication Facts, How to Remember 7×8 = 56, Sigma Notation, Bibelots, Subtracting 12 oz. from 15 lbs., Forestland in the United States, Hyperbole, Bar Graphs, Ordered Pairs, Business Letters vs. Personal Letters, Capitalization in Closing Salutations, Elapsed Time, First and Second Coordinates, Using Honey Cards, Why Algebra Does Not Use the Times Sign (×), How to Polish Leather Shoes, Maps as Seen by Artists, War Historians, Mathematicians, Lovers of Cheese, and Literature Historians, a Poetical Meaning for “the Land of Milk and Honey,” Endoplasmic Reticulum, Finding Cyprus on a Map, the Cardinality of the Set of All Ice Cream Flavors that Begin with the Letter Alpha, Implicit vs. Explicit, the Two Major Countries on the Iberian Peninsula, Why You Can’t Find an Ibex in Kansas, Minutes and Hours in the Metric System, How to Have Ice in the Summer in Kansas in 1843, Improper Use of Seat Belts, Plotting Points on a Graph, Why You Shouldn’t Park on the Sidewalk, Michelangelo di Lodovico Buonarroti Simoni’s Painting, Perimeter, the One Reason for Mathematics, When Eating Ice Cream Can Be Torture, Irony, Hooke’s Law, Slope of a Line, Estimating Using Graphs, Changing the Scale on a Graph, Counting Back Change, Liberty vs. Freedom, the Commutativity of Set Union, Less Than (<) and Greater Than (>), Homogenized Milk, Why Use Soap, Cryogenics, What You Can Do If You Have Tons of Casual Cash (the answer: buy graph paper), Joe’s Stomach Has Only Finite Capacity, Why Brass Braces Are Better Than Regular Braces, Area of a Rectangle.

**Jelly Beans**: Little Babies Can’t Fritter Away Their Time, Finding One-third of a Number, Using Fisher’s Exact test, When the Possessive Case Is Indicated with Just an Apostrophe and No s, Prime Numbers, Fibonacci Numbers, Nouns, Fred’s Seven-word Speech, the Use of Segues, Can Dolls Grow Up?, Casting Out Nines, Seven to the One-thousandth Power in Three Steps, What Cows Don’t Think About, a Great Way to Rot Your Teeth, Intersection of Sets, Commutativity of Intersection, the Probability that Fred Will See Betelgeuse Become a Super Nova (the answer: one chance in ten thousand), Why Education Is So Important, Fever vs. Femur, Carburetors, Litotes, One Way to Avoid Evil, Decimal Points, Adding Decimals, Logs, Volume of a Box, Outline of the Plot of the First Three Acts of A Midsummer Night’s Dream, English Major vs. Math Major, Résumés, the Pinocchio Paradox, What Is a Tinker, Median Averages, Mean Averages, the Fad that Began March 3, 1939, Fifty Basic Survival Skills, Exponents, Set Subtraction, Reducing Fractions, Milli- and Kilo-, Monophagous and Monostich, Epigraphs, Tally Marks, Pie Charts, Five Things Your Income Depends On, the Biggest Happiness Killer, Mode Average, Subtracting Three Inches from Three Miles, Incisors, How to Prove You Are Not a Duck.

So, the math concepts in Life of Fred are interspersed with fun stories, life skills, cross-curricular information. We all love it!

We reinforce math concepts with fun storebought, printable, or homemade manipulatives.

Place value, money, and fractions are easier to grasp with visuals.

The girls love learning math with music, doing special activities around the holidays and seasons, and playing math apps on their iPad minis.

### Middle School

Singapore Math changes after Book 6, and I didn’t like the look of Books 7 and 8. I don’t like their two options for high school either.

These Life of Fred Intermediate books are a great new addition to our math shelf. They weren’t around when Liz was at this level.

I find it funny their titles continue the alphabet with KLM.

These offer a great transition to pre-Algebra and higher math.

Concepts in the intermediate Life of Fred books:

**Kidney**: Three Keys to Success, Charles Demuth’s “I Saw the Figure 5 in Gold,” Milliliters, Teachers’ Salaries, How to Carry Money on the Street, Writing Numerals in Checks ($4000 and Not $40.00), Idioms, Semibreves, Libraries State that Mccoy Comes Before Macdonald, Word Problems in Arithmetic, 100%, the Result of Years of Piano Practice, the Great Depression, Na + Cl → NaCl, Grams Vs. Ounces, Functions, Images of Elements of the Domain, Volumes, 115 Ounces = 7 Pounds and 3 Ounces, the Biggest Error in Thinking, What to Do in Life When You Hit a Wall, Perimeters, Definition of an Acre, How to Make a Million Dollars in Four Years, the Calculus Definition of Limit, the Economics of Free Things, Scores, Dozens, and Braces, Polar Form of Complex Numbers, Exponents, the Five Different Solutions to X5 = 32, Salaries of University Presidents, a Quarter after Two, Toiletries for Kids and Older People, Physical Exams, Ketones and Glucose, the Best Use of Leisure Time, Why We Have Two Kidneys, the Chief Use of Kidneys Is Not to Make Urine, Point-Segment-Square-Cube-Tesseract, Twelve Kinds of Set Theory, the Best Time in History to Become a Mathematician, Adumbration in Literature, Arithmetic Sequences and Series, the Difference Between the United Kingdom and Great Britain, the Four Different Reasons We Speak, Preview of the Fundamental Theorem of Calculus, Sigma Notation, Descartes’ Analytic Geometry, Why it Is Called a Solstice.

**Liver**: What to Pack for Camp, 1/4 + 1/4 +1/4 = 3/4, Why Blowing Your Nose and Wiping Your Eyes Is Not Commutative, I.e., E.g., Viz., Elapsed Time, the Two Rules of Survival, Passing the SAT Exam, Metaphors, the Three Angles of a Triangle Always Add to 180º, What Can Go Wrong with a Lifetime Guarantee, How To Be a Business Success, the Pythagorean Theorem, Finding Two-fifths of $400,000, Ordering Tjvjik, Ghapama and Satsivi at a Restaurant, Being a Hepatologist, Solving 2x – 7 = 11, What Livers Do, the Difference Between Saturnalia and Saturnine, Hypercholesterolemia, Pie Charts, Cirrhosis, the Drawbacks of Multitasking, Extradural Hemorrhage, Six-sevenths of 413, Four Drawbacks to Fred Living in a Castle in Germany, Verbs Often Used by People in Various Occupations, Treble and Bass Clefs, Electrical Use by U.S. Farms in 1925, How to Win at Bridge, Short Division, Quotients, Secant Lines, How to Have People like You, Changing Percents to Fractions—68 Completely Worked out Examples, Computing 2% of 550, Who Is Not Harmed by Watching Television All Day Long, the Difference Between Graffito and Graffiti, Pet Names Are Different than Names for Pets, How Not to Work Out in a Gym Weight Room, Functions, Domains, and Codomains, Brain Chatter and the Uses of Silence, Reducing Fractions, the First Step in Producing Great Art, What Three Units of a College Class Means, Reasonable Answers, the One Purpose of Great Universities, the Masthead of a Newspaper, Forming the Possessive of Words That End in S, Four Things That Are Important to Learn Earlier in Life, Finding an Average.

**Mineshaft**: Milligrams and Pounds, Rounding Numbers; a Trillion Pounds of Rice to Cuba; the Number of Stars in a Typical Galaxy; Three-eights of 19,416; Is a Quart less than (<) a Duck?; What to Do with Eleven Hours of Free Time Each Day; Six Is What Fraction of 24? Post Meridiem; Exponents; Extending the Domain of a Function; What Piece of Leather Made Feudalism Possible; Perpendicular Lines; Diminutives; Silent Letters; Rhombus; Can a Four-sided Figure Have Exactly Three Right Angles? Cardinality of Sets; Sectors; Most Horses Achieve Few Outstanding Things in Life; the Reason to Learn the Greek Alphabet; Square Knots; Inverse Operations; How Concrete Is Different than Cement; Prolix vs. Laconic; Freedom vs. Liberty; the Largest Cardinal Number Isn’t Six; Ounces, Gills, and Pints; Italicizing Book Titles; 30% of 270; Division by 100; Broiling vs. Pan Frying; Freud, Skinner, and Maslow; the Four Types of Sentences; Maslow’s Hierarchy of Needs; Pangolins; Mammals; Subtracting 3 oz. From 4 lbs. 2 oz.; Subtracting 7 Minutes 25 Seconds from 20 Minutes 10 Seconds; Subtracting 2 Gallons 1 Quart from 4 Gallons; Chords of a Circle; Three Definitions of Diameter; Steak for One-year-olds; Subtracting 40 Feet from 9 Miles; Fahrenheit to Celsius Conversions; Questions People Have at Different Stages in Life; Why You Won’t Bump into Moby Dick in Kansas; Does x < y Imply y > x? Converting 39 Inches into Feet; Indications Your Daughter Will Become an English Major; Finding the Sale Price after Taking 40% Off; the Image of an Element in the Domain of a Function; 63ºF = 17 2/9ºC.

I love the Intermediate and “Before High School” sets of Life of Fred.

Liz completed Fractions, Decimals and Percents, Pre-Algebra I with Biology, and Pre-Algebra 2 with Economics in two years.

Middle school Life of Fred math concepts:

**Fractions**: Less Than, Billion, Cardinal and Ordinal Numbers, Diameter and Radius, Savings and Expenses, Definition of a Fraction, Sectors, Comparing Fractions, Reducing Fractions, Adding and Subtracting Fractions, Common Denominators, Roman Numerals, Least Common Multiples, Improper Fractions, Lines of Symmetry, Division by Zero, Circumference, Multiplying Mixed Numbers, Commutative Law, Canceling, Definition of a Function, Area, Unit Analysis, Division of Fractions, Geometric Figures, Estimating Answers.

**Decimals and Percent**s: Number Systems, Adding and Subtracting Decimals, Multiplying by Ten, Functions and Inverse Functions, Pi, Multiplying Decimals, Whole Numbers, Squaring a Number, Subtracting Mixed Units, Sets and Subsets, Union and Intersection of Sets, Rules of Divisibility, Division of Decimals, Repeating Decimals, Bar Graphs, Prime and Composite Numbers, Consecutive Numbers, the Goldbach Conjecture, Area of a Circle, Dollars vs. Cents, Pie Charts, Conversion between Percents/ Fractions/ Decimals, 40% of 15, 30% off, Distance Equals Rate Times Time, 15% more, Area of a Triangle, Square Roots, Area of a Parallelogram, 13 Is What Percent of 52, Ratio, Ordered Pairs, Graphing, Negative Numbers, Elapsed Time, Probability.

**Pre-Algebra 0 with Physics**: Numerals, Making models, Nineteen conversion factor problems, Area of a rectangle, Friction independent of speed, Constants of Proportionality, Exact speed of light, Continuous and discrete variables, Story of the meter, Pendulums, Oblate spheroids, Krypton vs. kryptonite, Square roots, Pilgrims in Massachusetts in 1620, Hard c and soft c, Normal forces, Coefficient of friction, Solving d = rt for r, How ducks pronounce mu, Graphing points, Ordered pairs, Why rocks stop falling, Hunch-conjecture-theory-law, Simultaneity doesn’t exist, Inductive and deductive reasoning, How fossils and astronomy are connected, Hooke’s law, Four ways to stretch a spring, Three meanings of plastic, Static vs. kinetic friction, Nine forms of energy, Energy Cards game, Calamari spaghetti, Poetry of Christina Rossetti, Most filmed spot in the world, Getting grass stains out of pants, Experimentally finding the coefficient of static friction without knowing the weight of the object, How you know you have a liver, Resolving a vector into its components, Addition of vectors, Similar triangles, Slope, Physicists think that there isn’t any work in holding a bowling ball, Kelvin temperature, Law of conservation of energy, Perpetual motion machines, Kilowatt-hours, Photosynthesis, Metric system, Gregorian calendar, Two ways to measure mass, Definition of pi, Inertia, Newton’s first and second laws, Why cramming doesn’t work well, Definition of pressure, Exponents, Density of neutron stars, Computing the mass of an iron atom, Cavalieri’s principle, Pressure at a given depth, Special glass in auto windshields, Buoyancy, Finding the volume of a desk lamp, 80-pound rubber ducky, Official rules of golf, Advantages of cerebrospinal fluid, Air has mass, Why 35-foot straws don’t work, You are alive because ice floats, Gedankenexperiments, How water fountains work, Elliptical constructions, Galvani and dead frogs that twitch, Birds sitting on high-voltage power lines, How to buy a cafe, Placing question marks at the end of a quotation, Schematic drawings in electrical circuits, Electrons per second in an ampere, Why we wear clothes on days ending in y, Ohm’s law, Batteries in series, Computing resistance in parallel circuits, Dangers of electricity—Thomas Merton, Museums in New York City, History of the atom: Democritus, Isaac Newton, Henri Becquerel, J. J. Thomson, Ernest Rutherford, Niels Bohr, Principal quantum number, Arnold Sommerfeld, Louis de Broglie, C. J. Divisson and L. H. Germer, Orbital quantum number, Orbital magnetic quantum number, Spin magnetic quantum number, Wolfgang Pauli, Werner Heisenberg, Paul Dirac, Carl David Anderson, Positron.

**Pre-Algebra 1 with Biology**: Definition of Life, Sets, Fractions, Germination of Seeds, Area of a Rectangle, Volume of a Cube, Ordinal Numbers, Diameter and Circumference of a Circle, Definition of π, 2% of 500, Four Ways Plants Make New Plants, d = rt, 20% Discount, the Five Kingdoms, Phyla, Classes, Orders, Families, Genera, Species, Your Brain, Conversion Factors, Where the Non-Water Mass of a Plant Comes From—Plants Don’t Eat Dirt, Subsets of Sets, Digestion, Eyes, Negative Numbers, Dominant Genes, Genotypes, Phenotypes, Blood, Staying Alive, Solving Algebraic Equations, Volume of a Cylinder, Word Problems, Breathing, Chlorophyll vs. Hemoglobin vs. Hemocyanin, Avogadro’s Number, Stoichiometry, the Whole Numbers, a Proof that Division by Zero is Not Permitted, Bones, the Integumentary System, Epidermis and Dermis, Meiosis and Mitosis, Chromosomes, DNA, Alleles, Changing Your Phenotype.

**Pre-Algebra 2 with Economics:** Domain and codomain of a function, Conversion factors, Steps in Solving Word Problems, How Not to Bore Your Horse If You Are a Jockey, One-to-one Functions, Unit Analysis, Key to a Successful Business, Five Qualities that Money Should Have, the Tulip Mania in Holland, Definitions of Capitalism, Socialism, and Communism, Payday Loans, the Tragedy of the Commons, Partnerships, Cardinality of a Set, Four Ways to Kill Competition, Freedom vs. Liberty, Why We Have a High Standard of Living, Tariffs, Demand Curves, Venn Diagrams, Ricardo’s Law of Comparative Advantage.

Middle school is a rough time and we have to make sure all the basics are memorized and all the concepts are learned well. This is super important before moving on to high school math.

### High School

We love continuing Life of Fred math for high school. I have just purchased the last of the series for Liz as a supplement to her other math work: Beginning and Advanced Algebra, Geometry, and Trigonometry. I also purchased Calculus, which is listed as college-level, but it tells the story of Fred’s baby years and we wanna know! There are also books on Linear Algebra and Statistics.

High school Life of Fred Concepts:

**Beginning Algebra**: All of first-year high school algebra: Finite/Infinite Numbers, Natural numbers, Whole numbers, Integers, Adding signed numbers, Ratios, Multiplying signed numbers, Proportions, Inequalities in the integers, Continued Ratios, Adding like terms, Rectangles, Trapezoids, Sectors, Symmetric Law of Equality, Order of operations, Solving Equations, Rational numbers, Set builder notation, Distance-rate-time problems, Distributive law, Reflexive Law of Equality, Proof of the distributive law, Coin problems, Age problems, Transposing, Solving systems of equations by elimination, Work problems in two unknowns, Graphs, Plotting points, Averages, Graphing linear equations, Graphing any equation, Solving systems of equations by graphing, Solving systems of equations by substitution, Inconsistent and Dependent systems of equations, Factorial function, Areas and volumes, Commutative laws, Negative exponents, Multiplying polynomials, Solving quadratic equations by factoring, Common factors factoring, Easy trinomial factoring, Difference of squares factoring, Grouping factoring, Harder trinomial factoring, Solving fractional equations, Simplifying rational expressions, Adding and subtracting rational expressions, Multiplying and dividing rational expressions, Solving pure quadratic equations, Square roots, Pythagorean theorem, Real numbers, Irrational numbers, Fractional exponents, Solving radical equations, Rationalizing the denominator, Quadratic equations in everyday life, Solving quadratic equations by completing the square, Quadratic formula, Long division of polynomials, Functions, Slope, Finding slope of a line from its equation, Slope-intercept form of a line, Range of a function, Fast way to graph y = mx + b, Fahrenheit-Celsius conversions, Graphing inequalities, Why you can’t divide by zero, Absolute value, Solving inequalities in one unknown.

**Advanced Algebra**: Ratios, Median averages, Proportions, Dividing by zero, Cross-multiplying, Constants of proportionality, Inverse variation, Direct variation, Joint variation, Weight varies directly as the cube of the height, Area varies directly as the square of the height, Volume varies directly as the cube of the height, Laws of exponents, Rationalizing the denominator, Pythagorean theorem, Solving radical equations, Surface area of a cone, A Brief History of mathematics, Natural numbers, Whole numbers, Integers, Irrational numbers, Real numbers, Imaginary numbers, Complex numbers, Velocity, Conversion factors, Unit analysis, Venn diagrams, Union of sets, Disjoint sets, Subsets, Intersection of sets, Significant digits in addition and multiplication, Scientific notation, Exponential equations, Logarithms, Product, quotient, birdie, and power rules for logarithms, Using a scientific calculator, Finding antilogs, Three definitions of logarithms, Change-of-base rule for logarithms, Graphing, Abscissa, Ordinate, Quadrants, Slope, Slope given two points, Slope-intercept and double-slope forms of the line, Slopes of perpendicular lines, Multiplying binomials, Factoring binomials, Factoring a difference of squares, Factoring trinomials, Adding, subtracting, multiplying and dividing polynomial fractions, Complex fractions, Linear equations, Quadratic equations, Radical equations, Systems of Equations, Inconsistent, dependent and independent equations, Graphing planes in three dimensions, Cramer’s rule, Determinants, Ellipses, Circles, Reflective property of ellipses, Parabolas, Hyperbolas, Graphing inequalities, Definition of a function, Domain, Codomain, Range, Functional notation, One-to-one, Onto, Inverse functions, Ordered pairs, Long division of polynomials, Partial fractions, Proofs by math induction, Linear Programming, Arithmetic progressions, and series, Adding and multiplying matrices, Geometric sequences and progressions, Sigma notation, Fundamental principle of counting, Factorial, Permutations, Combinations, Binomial formula, Pascal’s Triangle.

**Geometry**: Thirteen regular chapters and six bonus honors chapters. Points and lines, Definition of when one point is between two other points, Definition of a triangle, Midpoint, Proof of a theorem in paragraph form, Tangent and secant lines, Area and volume formulas, Undefined terms, Hypothesis and conclusion, Contrapositives, Postulates, Euclid’s The Elements, Rays, Acute, obtuse, and right angles, Congruent angles, Linear pairs, Vertical angles, Supplementary angles, Perpendicular lines, SSS, SAS, ASA, Isosceles triangle theorem, Pons Asinorum, Parallel lines, Skew lines, Indirect proofs, Attempts to prove the parallel postulate, Exterior angles, Two proofs of the exterior angle theorem, Hypotenuse-leg theorem, Medians, Quadrilaterals: parallelogram, rhombus, trapezoid, kite, rectangle, square, Honor’s Problem of the century: If two angle bisectors are congruent when drawn to the opposite sides, then the triangle is isosceles, Definition of a polygon, Proofs of all the area formulas given only the area of a square (This is hard. Most books start with the area of a triangle as given.) Proofs of the Pythagorean theorem, Geometries with only three points, Similar triangles, Five manipulations of proportions, Angle bisector theorem, Symbolic logic, Truth tables, Circles, Inscribed angle theorem, Definition of a limit of a function, Inductive and deductive reasoning, Golden rectangles, 46 Ruler-and-compass constructions, Non-euclidean geometries, Solid geometry, Euler’s theorem, Geometry in high dimensions, Stereochemistry and homochirality, Complete chart up to the 14th dimension, Proofs using analytic geometry, Proof that a right angle is congruent to an obtuse angle using euclidean geometry, Flawless (modern) geoemtry which was invented about a hundred years ago.

**Trigonometry**: After Beginning Algebra, Advanced Algebra and Geometry, this book completes everything you need for calculus. Angles of elevation, Definition of the sine function, Angles of depression, Area of a triangle = ½ab sin θ, Heron’s formula, Review of graphing and significant digits, Discrete and continuous variables as illustrated in The Merchant of Venice, Tangent function, Why we create new mathematics, Limit of tan θ as θ approaches 90º, Ordinal and cardinal numbers, Cosine function, Graphing y = sin x, Identity function, Contrapositives, Domain and range of a function, Defining 6 to the pi power, Trig angles in standard position, Expanding the domain of a function, Periodic functions, Identities from algebra, Even and odd functions, Trig identities for sine and cosine, for tangent, for secant, Four suggestions for increasing success in solving trig identities, Trig identities for cotangent and cosecant, Nine tricks for solving trig identities, Shortcuts for graphing y = a sin (bx + c), Degrees, minutes, and seconds, Conversion factors, Radians, Videlicet, exempli. gratia, and id est, Area of a segment of a circle, Solving conditional trig equations, Related angles, Joseph Lister, Multiple angle formulas and their proofs, Symmetric law of equality, Probability of finding a right triangle, Law of Cosines, Florence Nightingale, Law of Sines, Inverse functions, One-to-one functions, Hyperbole, Principal values of the inverse trig functions, Ambiguous case for the law of sines, Why sin (2 Arctan 3) equals 3/5, Polar coordinates, Graphing a cardioid and a lemniscate, Codomain of a function, Official definition of the number one, Proof that the square root of 2 is irrational, Transcendental numbers, Complex numbers, Russell’s paradox, Malfatti’s problem and its solution in 1967, r cis θ, de Moivre’s theorem and its proof, The millionth roots of i, Review of the major parts of high school algebra and a preview of all of Calculus.

We use VideoText Algebra and Geometry for college prep high school.

The Algebra program gives these credits: **pre-algebra, algebra I, and algebra II**.

The Geometry program gives these credits: **geometry, trigonometry, and pre-calculus**.

It was always highly recommended by homeschoolers I knew for high school math. The videos are a little dry, but the lessons cover all the material needed. Both Videotext algebra and geometry can be completed in two years.

Liz went through VideoText Algebra in a little over a year. She and her dad worked through one lesson each school day.

We’re lucky that I’m a history/language arts/biology person and my husband is a math/chemistry guru.

Liz completes her video lesson and notes during the day and then she works through the text with Dad before dinner each evening. There are also quizzes and tests.

We teach to mastery, and review as needed.

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