# School in a Book: Basic Arithmetic and Measurement

Like reading and writing, math is a skill. For this reason, I limited the treatment of mathematics in this book to simple lists of concepts to master. In general, it’s a good idea to teach the concepts as they might be encountered in the real world–in other words, to present scenarios involving the process, then having the student create the equation that can be used to find the solution. Also that math does not have to be repetitive; no need to do long homework assignments. Learn the concept and move on, then revisit all sections several more times over a period of several years to commit them to memory.

Fortunately, math is more standardized than most subjects and most people won’t have trouble finding a comprehensive curriculum to follow. (If you are homeschooling, I recommend the nice video series from the Khan Academy, a free online school. For younger students, the hilarious Life of Fred series is great.)

One more note: If you’re teaching a young homeschooler and want to delay the more advanced arithmetic for a while, that shouldn’t be a major problem. However, math thinking does cause growth in places of the brain that other types of thinking do not. Instead of having your kids do long, repetitive math worksheets, I recommend math games and math puzzles, particularly those that emphasize spacial thinking. I didn’t realize how greatly those areas of my brain had been neglected after years of writing for a living till I took an aptitude test and totally failed the spacial thinking section. Don’t limit your kids’ options to become a mathematics professor, physicist or engineer.

Basic Arithmetic and Measurement Skills

Counting by twos, tens, fives and twenties
Understanding place value (ones, tens, hundreds, etc.)
Naming shapes, including three-dimensional shapes (cubes, cones, cylinders and spheres)
Rounding
Identifying Roman numerals
Multiplying (finding the product of two factors) and dividing (finding an unknown factor)
Using arrays
Understanding sets
Solving one-variable equations and inequalities
Adding, subtracting, multiplying and dividing fractions
Adding, subtracting, multiplying and dividing decimals
Adding, subtracting, multiplying and dividing negative numbers
Understanding integers, whole numbers, negative numbers, positive numbers
Solving story problems
Understanding absolute value
Using coordinate planes
Reading bar graphs, line graphs and grids
Measuring, including memorization of important conversions

Common English Measures

Distance

Inches (in) – 12 in = 1 ft
Feet (ft) – 3 ft = 1 yd
Yards (yd) – 1760 yd = 1 mi
Miles (mi) – 1 mi = 5280 ft

Weight

Ounces (oz) – 16 oz = 1 lb
Pounds (lb) – 2000 lb = 1 t
Tons (t) – 1 t = 2000 lb

Volume

Teaspoons (tsp) – 3 tsp = 1 tbsp
Tablespoons (tbsp) – 1 tbsp = 3 tsp
Fluid ounces (fl oz) – 8 fl oz = 1 cup
Cups (c) – 2 cups = 1 pt
Pints (pt) – 2pt = 1qt, 8 pt = 1 gal
Quarts (qt) – 4 qt = 1 gal
Gallons (gal) – 2 gal = 1 peck

Common Metric Measures

Distance

Millimeter (mm) – 1000 mm = 1 m
Centimeter (cm) – 100 cm = 1 m
Meter (m) – base unit (1)
Kilometer (km) – 1000 m = 1 km

Weight

Milligrams (mg) – 1000 mg = 1 g
Grams (g) – base unit (1)
Kilograms (kg) – 1000g = 1 kg, 1000 kg = 1 t
Metric ton (t) – 1000 kg = 1 t

Volume

Milliliters (mL) – 1000 mL = 1 L
Liters (L) – base unit (1)

Universal Measures of Time

Seconds (sec) – 60 sec = 1 min
Minutes (min) – 60 min = 1 hr
Hours (hr) – 24 hr = 1 day
Days – 7 days = 1 wk
Weeks (wk) – (about) 4 wk = 1 mo
Months (mo) – 12 mo = 1 yr
Years (yr) – 1 yr = 365 days
Centuries – 1 century = 100 yr
Millennium – 1 millennium = 1000 yr

Metric Prefixes

Nano – 1/1000000000
Micro – 1/1000000
Milli – 1/1000
Centi – 1/100
Deci – 1/10 