S k i l l i n A r i t h m e t i c
Sums less than 10. Sums equal to 10.
Sums between 10 and 20. Zero.
The Multiplication Table
Numeration of the Whole Numbers
Numerals versus numbers.
The names and numerals of the numbers
1 - 999.
||Reading and Writing Whole Numbers
The Powers of 10
How to read a whole number, however large.
Place value. Positional numeration.
Relationship between units of adjacent place value.
How to round off a whole number.
How to multiply a whole number by a power of 10.
The Meaning of Decimals
Cardinal and ordinal numbers.
Division into equal parts.
The decimal units.
The function of the decimal point.
How to write and how to read a decimal.
Trailing 0's. Leading 0's.
How to compare decimals.
||Multiplying and Dividing
by Powers of 10
The Meaning of Percent
How to multiply or divide a whole number by a power of 10.
How to multiply or divide a decimal by a power of 10.
Per centum -- For each 100.
How to take 1% of a number.
How to take 10%.
The metric system.
||More Elementary Addition
Composing a multiple of 10.
Adding by endings.
Adding from left to right by place value.
||Adding Whole Numbers and Decimals
Addition with Regrouping
||The Meaning of Subtraction
What number must we add?
Completing 100. Rounding off.
||Subtracting Whole Numbers and
Written calculation by adding to both numbers.
Written calculation by regrouping, or borrowing.
||The Meaning of Multiplication
The multiplier, the multiplicand, the product.
Factors and the order property.
How to multiply whole numbers that end
How to square a number mentally.
Decomposing the multiplier.
Decomposing the multiplicand:
The "distributive" property.
Multiply mentally by rounding off.
||Multiplying Whole Numbers and
How to find a percent of a number.
The area of a rectangle.
The Meaning of Division
The divisor, the dividend, and the quotient.
How to divide a number into equal parts.
Exact versus inexact division.
The division bar.
Decomposing the dividend.
The divisor a decimal.
Three properties of division.
What is short division?
The dividend a decimal.
How to round off a decimal.
How to express the quotient as a decimal.
The dividend less than the divisor.
Percent with a Calculator
Parts of Natural Numbers 1
What is a natural number?
The definition of a part of a number.
Percent -- parts of 100%.
Parts of Natural Numbers 2
Finding a part by decomposing.
How to divide by taking a part.
A mixed number of times.
Increase or decrease by a given part.
The percent that means a third.
Even and odd numbers.
Half of any number.
A fourth or 25% of a number.
5% of a
number -- 15%.
Ratio and Proportion
The definition of the ratio of two natural numbers.
Percents are ratios.
How to express the ratio of any smaller number to a larger.
The theorem of the common divisor.
The theorem of the same multiple.
How to find a percent by the method of proportions.
Lesson 20 What is a Fraction?
Common fractions, proper fractions, improper fractions, mixed numbers.
How to place a fraction on the number line.
How to change an improper fraction to a mixed number.
How to change a mixed number to an improper fraction.
How to compare fractions that have equal numerators
How to compare fractions that have equal denominators
||Unit fractions: Fractions with
Every fraction is a sum of unit fractions.
How to express a whole number as a fraction.
The complement of a proper fraction.
How to subtract a proper fraction from a whole number.
How to recognize equivalent fractions.
How to change denominators.
How to simplify or reduce a fraction.
How to clear a fraction of decimals.
||Lowest common multiple
How to compare fractions by cross-multiplying.
How to compare a fraction to ½.
Fractions into Decimals
What is a decimal fraction?
Frequent decimals and frequent percents: Half, quarters, eighths, thirds, fifths.
Exact versus inexact decimals.
||Adding and Subtracting Fractions
and Mixed Numbers
How to multiply a fraction by a whole number.
How to multiply a fraction by a fraction.
Dividing fractions compared to adding them.
||The Meaning of Multiplying Fractions
Parts of Fractions
The meaning of multiplying a number by
How to express a fraction as a percent.
How to take a part of a fraction.
The general definition of multiplication.
Percents are Ratios
The ratio to 100%.
Percent increase or decrease. Estimations.
Percent of a Number
How to find the Amount.
What ½% means.
How to find the Base.
||What Percent is One Number
The method of proportions.
Percent Increase or Decrease
"Difference" problems versus "out of"
||Prime Numbers and
The definition of a prime number.
Is there a last prime?
||Greatest Common Divisor
Lowest Common Multiple
How to find the GCD and the LCM of two numbers from their prime factorizations.
Continuous versus Discrete
| Appendix 2
||Triangular and Square Numbers
||The Sum of Consecutive Cubes
| Appendix 3
||The distributive property of multiplication
||The order property