Homeschooling Math
(Pre-Kindergarten through Grade Twelve)
The goal is to have the child learn some basic arithmetic skills and completely memorize the addition, subtraction, multiplication, and division facts. By age seven (or 7½), he or she begins to independently go through the Saxon Math series starting with Saxon Math 5/4 and progressing through Saxon Calculus. With this method, the child is likely to finish calculus by 14-16 years of age. Just because the results are impressive does not mean self-teaching is only for gifted children. The typical child can successfully learn by teaching him or herself. I learned the basic concept of self-teaching from Dr. Robinson and have successfully applied it to our homeschool. His approach is to have the child memorize the addition, subtraction, multiplication, and division facts and begin Saxon Math 5/4 at age seven (or 7½) without the beginner arithmetic that I include.
BEGINNER ARITHMETIC
From around the beginning of age four to the end of age six (K4, K5, and Grade One), we have chosen a seemingly accelerated, but relatively easy approach using the ABeka Arithmetic workbooks to keep us on track. I don’t make my child do every page in the workbooks. I am not interested in classroom style busy-work. The goal is to help the child learn and understand the concepts. This method can be applied regardless of your choice of beginner arithmetic curriculum or the amount of money you spend on homeschooling materials. In order to help your child learn the concepts, you can buy, borrow, substitute, or make many of the supplies. Work within your budget.
The chart below lists the five basic workbooks I use to loosely (or studiously) follow from around the beginning of age four to the end of age six (K4, K5, and Grade One). You may want to use both K4 and K5 workbooks in Pre-Kindergarten, work on K5 and Arithmetic 1 in Kindergarten, and work on Arithmetic 2 and 3 in Grade One. Some children may not be ready for arithmetic in Pre-Kindergarten, so skipping the first book (and even the second book) won’t be a problem. If the child is being homeschooled for the first time in grade one, then work on Arithmetic 1 and Arithmetic 2 throughout the year. Not finishing Arithmetic 3 won’t be a problem at all. Each ABeka workbook level also has a Curriculum Guide and Test and Speed Drill Booklet than can be added if desired.
________________________________________________________
Workbooks with Material to be Learned
ABeka ABC-123 K4
ABeka Numbers Skills K
ABeka Arithmetic 1 Workbook
ABeka Arithmetic 2 Workbook
ABeka Arithmetic 3 Workbook
Supplies to Help
ABeka Numbers Charts and Games K
ABeka Learning Games
ABeka Arithmetic 1 Charts and Games
ABeka Arithmetic Drill Card Sets ~ Memorize facts.
________________________________________________________
The following charts describe many of the skills that are covered in beginner arithmetic books and should be learned within the first few years of school. Begin gradually with counting, number recognition, and understanding the concepts of adding and subtracting. Continue to help your child build on this knowledge to include more and more of the following skills. The child does not have to understand everything in these charts by age seven or (or 7½), although much of it would be beneficial. Using the workbooks as guides will help you stay organized and keep up the pace.
________________________________________________________
Skill to be Learned ~ Numbers
Number concepts 1-100
Number sequences by ones
Using number words one-twenty and first-tenth
Number recognition, counting, and writing 1–100,000’s
Numbers largest and smallest 1-100
Numbers greatest and least 1–1,000
“Greater than”, “equals”, and “less than” symbols “< = >”
Concepts of equality and inequality
Before, after, between
Counting backwards
Simple number patterns
Odd and even
Rounding
Concepts of ordinal and cardinal numbers
Supplies or Ideas to Help
Numbers Concept Flashcards (ABeka)
Numbers Flashcards (ABeka)
Numbers counting chart
Counting manipulatives
________________________________________________________
Skill to be Learned ~ Skip Counting
Counting by 1’s, 2’s, 3’s (to 36), 4’s (to 48), 5’s, and 10’s
Before and after by 1’s, 2’s, 3’s (to 36), 4’s (to 48), 5’s, and 10’s
Supplies or Ideas to Help
Numbers counting chart
One Hundred Sheep: Skip Counting Songs from the Gospels CD
________________________________________________________
Skill to be Learned and Ideas to Help ~ Calendar
Months of the year
Chant
January, February…
March, April, May…
June… July… August….
September… October… November… December
Number of days per month
Poem
Thirty days hath September, April, June, and November.
All the rest have thirty-one,
Save February, which has twenty-eight,
‘Till leap year gives it twenty-nine.
Days of the week
Song
Sunday, Monday, Tuesday, Wednesday,
Thursday, Friday, Saturday
Date ~ day, month, date, year
Reading calendar
Magnetic calendar
________________________________________________________
Skill to be Learned ~ Telling Time
Tell time – hour, half-hour, quarter hour, fives, to the nearest minute
Recognize correct time from hand clocks and digital clocks
Put hands on clock (three o’clock, 7:45 P.M., etc.)
Supplies or Ideas to Help
Clock
Work sheets
Flashcards
________________________________________________________
Skill to be Learned ~ Math Facts
Addition facts through 18, column addition, four-digit addition with carrying
Subtraction facts through 18, four-digit subtraction with borrowing
Properties of sets and groups
Basic multiplication and division facts up to 12×12
Multiplication and division facts as inverse operations
Multiplication properties of 0 and 1
Multiple combinations
Supplies or Ideas to Help
ABeka Addition and Subtraction Animal Flashcards
ABeka Combination Dot Cards
Dominoes
Addition Flashcards (ABeka)
Subtraction Flashcards (ABeka)
Multiplication Flashcards (ABeka)
Division Flashcards (ABeka)
(Read math fact. Say answer. Look at back. Repeat from memory.)
Math Facts Practice Sheets (Work Sheet Factory)
________________________________________________________
Skill to be Learned ~ Place Value
Zero as a place holder
Place value to thousands
Decimal numeration system
Using 10 as a basic unit
Supplies or Ideas to Help
ABeka Place Value Concept Cards
Base ten blocks
________________________________________________________
Skill to be Learned ~ Measuring
Common customary and metric measures of:
time, weight, length, volume, shape, temperature
Concepts of quantity and size
Drawing and measuring lines to one-half inch
Understanding cm, inches, feet
Ounces, pounds
Reading a thermometer
Supplies or Ideas to Help
Ruler
Scale
Thermometer
________________________________________________________
Skill to be Learned ~ Fractions
Unit fractions
Using 1/2, 1/4, 1/3 appropriately
Fractions in daily life
Supplies or Ideas to Help
Fraction manipulatives
_______________________________________________________
Skill to be Learned ~ Money
Value of penny, nickel, dime, quarter, half-dollar, loonie, twoonie
Value of bills
Counting and combining coins and bills
Making change
Writing and recognizing money symbols $4.50, 30¢
Supplies or Ideas to Help
Real and/or pretend coins and bills
Play store
________________________________________________________
Skill to be Learned ~ Graphs
Number-line use
Reading pictographs, bar graphs, and line
graphs
________________________________________________________
Skill to be Learned ~ Roman Numerals
Recognition of Roman Numerals
Supplies or Ideas to Help
Flashcards
Poster
________________________________________________________
Skill to be Learned ~ Geometry
Recognizing geometric points, lines, shapes, patterns
Supplies or Ideas to Help
Puzzles
Activities
Geoboard/rubberbands
________________________________________________________
Skills to be Learned
Story problems
Basic concept of ratio
Estimation
Basic probability and chance
________________________________________________________
ROTE MEMORIZATION OF MATH FACTS
When your child is around 6½ to 7, place more emphasis on memorizing the math facts (addition, subtraction, multiplication, and division.)
________________________________________________________
Skill to be Learned ~ Math Facts
Rote memorization of math facts
Addition up to 9+9
Subtration up to 18-9
Multiplication up to 12×12
Division up to 144/12
Supplies or Ideas to Help
Addition Flashcards (ABeka)
Subtraction Flashcards (ABeka)
Multiplication Flashcards (ABeka)
Division Flashcards (ABeka)
(Read math fact. Say answer. Look at back. Repeat from memory.)
Math Facts Practice Sheets (Work Sheet Factory)
Quarter Mile computer program
Addition/Subtraction computer program
ABeka Rapid Calculation Drill
________________________________________________________
Once the math facts are completely memorized, and the child can read well, he or she is ready to start Saxon Math 5/4, usually by age 7 or 7½. Purchase the complete Saxon Math set for each level, including text, answer book, and test booklet.
There will be “those kind of days”, but for the most part, learning is steady and straightforward. When first beginning Saxon Math 5/4, the child may be ready to only complete 1/3 or 1/2 of a lesson. Eventually he or she will be able to finish at least one lesson per day, showing all work. Some parents require two hours of math per day or continuing math and Saturdays and/or throughout the year, both of which pick up the pace even more. The parent or the child can check the lessons, and the child makes any corrections by re-reading the lessons. If your child comes to you and says, “I can’t do that problem”, just help him locate the lesson where it should have been learned (indicated in sidebar of problem), and have him or her study the lesson again. The tests are unnecessary, but certainly can be used for review or parental reassurance. During the early years, have the child continue practicing math facts with flash cards review, completing Saxon Math Facts Practice sheets, and practicing ABeka Rapid Calculation Drills (with a parent).
If you are removing a child from school, have him or her memorize the math facts, regardless of age. Then use placement tests to determine which Saxon Math book to begin. It can take a couple months of deprogramming to get rid of the “need” for a teacher.
MATH / ALGEBRA / CALCULUS
Saxon Math 5/4
Saxon Math 6/5
Saxon Math 7/6
Saxon Math 8/7
Saxon Algebra 1/2
Saxon Algebra 1
Saxon Algebra 2
Saxon Advanced Math
Saxon Calculus
The child will usually finish Saxon Calculus by age 14-16. Then it is time to begin university level physics. If calculus is finished by age 13 or 14, he or she might be too young to start physics, so it might be better to do chemistry next. Otherwise, physics should always be done before chemistry.
PHYSICS
The Mechanical Universe (Olenick, Apos) (included in Robinson Curriculum)
Beyond the Mechanical Universe (Olenick, Apos) (included in Robinson Curriculum)
http://www.learner.org/resources/series42.html?pop=yes&vodid=607977&pid=548#
3-volume set of Richard Feynman Lectures for freshman and sophomore physics (text and perhaps audio recordings)
CHEMISTRY
Chemical Principles, Second Edition, (included in Robinson Curriculum) supplemented with
General Chemistry, Third Edition
As Dr. Robinson says, math should be learned before physics, physics before chemistry, and chemistry before biology. We have chosen a basic biology beginner course for grade nine, in order to have an extra credit, but I doubt it will be a problem even though it is an exception to this rule.
Upon completion of the above physics and chemistry materials, Robinson Curriculum also includes the following recommended texts that could be finished by the most gifted students before the age of 19.
Supplementary Physics Problems (Strong)
Thermodynamics (Lewis and Randall)
Statistical Mechanics (Norman Davidson)
At the time of writing these notes, my nine-year-old is in the fourth grade, and he is working on the Saxon Math 8/7 (grade eight/grade seven). My fourteen-year-old is in grade nine, and he is working on Advanced Math. They have done this without a teacher.
