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Introduction

Prologue 1     Elementary Addition

Sums less than 10.  Composing 10 itself.
Sums between 10 and 20.  Zero.

Prologue 2     The Multiplication Table

Lesson 1     Powers of 10

Which numbers are the powers of 10?
How do we read a whole number?  
What do we mean by the place value
of a digit?
How do we write a whole number in expanded form?
How do we round off a whole number to a given place?
How do we multiply a whole number by a power of 10?

Lesson 2    The Meaning of Decimals

Which numbers are the decimal units?  What is the function of the decimal point?
How do we read a decimal?  How do we compare decimals?

How do we multiply a decimal by a power of 10?  How do we divide a decimal by a power of 10?
When is a number written in "scientific notation"?
What does "percent" mean?
How can we take 1% of a number?

How do we add mentally by composing a multiple of 10?  How do we add by endings?  How do we add the units from left to right?  How can we add by rounding off?

How do we add whole numbers?  How do we add decimals?

What is the problem in subtraction?
How can we find the difference between a one-digit and a two-digit number?
How can we find the difference between two-digit numbers?
How do we complete 100?  How can we find the difference by rounding off?

How do we subtract by compensating?
How do we subtract by regrouping?

What is "multiplication"?
How do we multiply whole numbers that end in 0's?
What is the distributive property of multiplication, and how can we apply it to mental calculation?
How can we multiply mentally by rounding off?

In writing, how do we multiply whole numbers?  How do we multiply decimals?
How can we find a percent of a number?
How can we find the area of a rectangle?

Lesson 10    The Meaning of Division

The divisor, the dividend, and the quotient.
What is the problem in division?
What is a rate?
Exact versus inexact division.
The divisor a decimal.
How do we divide by decomposing the dividend?

Lesson 11    Short Division

How do we do short division?
How do we proceed when the dividend is a decimal?
How do we round off a decimal to a given number of decimal places?
How do we express the quotient as a decimal?
Calculator problems.

Lesson 12    Dividing Decimals  

When the divisor is a decimal, what must we do?

Lesson 13    Percent with a Calculator  

How do we use a calculator to solve a percent problem?  

Lesson 14    Parts of Natural Numbers 1  

Which numbers are the natural numbers?
What does it mean to say that a smaller number is a part of a larger number?
What does it mean to say that a smaller number is parts (plural) of a larger number?
Percents are parts of 100%.

Lesson 15    Parts of Natural Numbers 2  

What do we mean by a mixed number of times?
How can we find a part by dividing?
How can we find a fifth or 20% of a number?
What percent means a third?
How can we take half of any number?
How can we take a fourth or 25% of a number?
How can we multiply by 5 or 15?
Increase or decrease by a part.

Lesson 16    Ratio and Proportion  1  

What do we mean by the ratio of two natural numbers?   How do percents express ratios?
What is a proportion?
When is a ratio expressed with the lowest terms?
What is the Theorem of the Common Divisor?

Lesson 17    Ratio and Proportion  2  

What is the Theorem of the Alternate Proportion?  What is the Theorem of the Same Multiple?
What percent of 100 is any number?

Lesson 18    Proportionality  

What does it mean to say that two quantities are directly proportional?  How do we solve problems of proportionality?
What does it mean to say that two quantities are inversely proportional?

A fraction is a number that we need for measuring.
What is a common fraction?  What is a proper fraction?  How do we name the proper fractions?
What ratio has each fraction to 1?
What is a mixed number?   What is an improper fraction?

Lesson 20    Unit Fractions  

What is a unit fraction?
How can we express a whole number as a fraction?  
What do we mean by the complement of a proper fraction?
What kind of fraction does "out of" indicate?

Lesson 21    Equivalent Fractions  

What are equivalent fractions?  How can we know when fractions are equivalent?
How can we reduce a fraction to its lowest terms?  How can we reduce a fraction in which the numerator or denominator is a decimal?

Lesson 22    Comparing Fractions  

How can we compare fractions with the same numerator?  How can we compare fractions with the same denominator?
How can we find the lowest common multiple of two numbers?
How can we compare fractions when the numerators and denominators are different?
How can we know whether a fraction is more than or less than ½?

Lesson 23    Fractions into Decimals  

What is a "decimal"?  How can we change a fraction to a decimal?
Frequent decimals and frequent percents:     Half, thirds, quarters, fifths, eighths.
Complete versus incomplete decimals.

Lesson 24    Adding and Subtracting Fractions  

How do we add or subtract fractions?
What number should we choose as the common denominator?  
How do we add mixed numbers?
How do we subtract a mixed number from a whole number?

How do we multiply a fraction by a whole number?  How do we multiply a fraction by a fraction?  
How do we divide fractions?

Lesson 26   The Meaning of Multiplying Fractions
Parts of Fractions

What does it mean to multiply a number by a fraction?
How can we express a fraction as a percent?
How can we take a part of a fraction?

Lesson 27    Percents are Ratios  

How do percents express ratios?
Percent increase or decrease. Estimations.

Lesson 28    Percent of a Number  

How can we find the Amount?
What does ½% mean?
How can we find the Base?

How can we find the Percent by the method of proportions?
What is a general method for finding the Percent?

Lesson 30    Percent Increase or Decrease  

"Out of" problems and "difference" problems.
In a banking problem, what is the Amount and what is the Base?

Lesson 31    Prime Numbers  

What is a prime number?  How can we find the prime factorization of a number?
Is there a last prime?

How can we find the GCD and the LCM of two numbers from their prime factorizations?

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