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Number Sense
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Word Problems

Browse Middle School Number Sense/About Numbers
Stars indicate particularly interesting answers or good places to begin browsing.

Selected answers to common questions:
    About zero.
    Multiplying by zero.
    Casting out nines.
    Classifying numbers.
    Googol, googolplex.
    Number facts from the Web.
    Significant figures/digits.

What is Number Sense and How Can You Improve It? [08/29/2007]
What does the term 'number sense' refer to on standardized math test results? Is there any way to increase your number sense?

What is the Largest Named Number? [12/08/2004]
A discussion of various large numbers and how they are defined, including google, googleplex, and Moser, Skewes, and Graham numbers.

What Type of Number Are Zero and One? [11/08/2004]
If 1 and 0 are not considered prime or composite numbers, then what are they?

When Casting Out Nines Fails [11/29/2001]
To prove that casting out 9's worked, I intentionally used an incorrect quotient, but was shocked when the problem checked out correctly.

When in Rome, Know Your Place — Less a Written Notation for It [01/27/2015]
An adult wonders how Romans could have developed their rules for subtraction absent place value. Citing their use of the abacus, Doctor Peterson distinguishes between operating with the concept and representing it.

When Percentage Calculations are Inappropriate [02/11/2003]
How do I best calculate the percentage of goal when at least one of the numbers is a negative number?

Where Does Pi Come From? [11/04/1996]
If pi is a ratio of lengths that can be measured only so accurately, how can we know the value of pi so exactly?

Who Invented Integers? [11/29/2001]
And when were integers invented?

Whole Numbers and Multiples [09/11/2001]
My students and I have been trying to figure out what numbers are in the set of "Whole Numbers." Is zero a whole number?

Why Are All Repeating Decimals Classified Rational? [11/12/1997]
Please explain how .6 repeating can be a rational number when expressing it over 10's, 100's, etc.

Why Casting Out Nines Works [10/13/2008]
Can you explain in simple terms why the Casting Out Nines method works?

Why Commas after Every Three Places? [07/10/2001]
Why do we put commas after every three places in a number like 200,000?

Why does 0 factorial equal 1? [03/18/1998]
Why does 0! = 1? Is this like anything to the power of 0 equals 1?

Why Do We Have Leap Year ? [02/25/1998]
Why do we need to have one extra day each 4 years?

Why Do We Need to Study Rational Numbers? [04/22/2008]
My students want to know why they need to know what rational numbers are and what use they have in the real world.

Why Do We Use Order of Operations? [09/18/2008]
Why is it necessary to use order of operations? Why can't you just write a calculation from left to right, so 5+2^3*2 is just 2^3*2+5? Doctor Peterson shows how order of operations makes writing and understanding algebraic expressions quite simple.

Why Estimate? [08/16/2002]
Estimate to the nearest thousand a solution to Dave's subtraction problem. The numbers are: 6,107 - 2,980 = 4,127.

Why Estimate? [09/16/2002]
Why do we use estimation?

Why is 1 Not Considered Prime? [3/20/1995]
Just recently a grade six student asked me, "Why is 1 not considered prime?" I tried to answer, but as usual, could not since I do not understand this either. I thought the answer might lie in the fact that we aren't using the true definition or we are interpreting it wrong.

Why is Zero Not a Natural Number? [03/14/2001]
Can you explain why the natural numbers are {1, 2, 3...}? Also, is there a way to prove that zero is an integer?

Why Not Force Dividing by Zero? [10/22/2002]
Has there ever been an attempt to force dividing by zero just as it has been done so successfully by forcing the square root of -1 to be i?

Why Rules? [08/15/2001]
Why do we need to have rules for order of operations?

Why Study Prime and Composite Numbers? [01/25/2001]
My husband and I wonder why this is taught in school at all. Who uses this in the real world? Why does someone need to know whether a number is a prime number or not?

Why Two Odds Always Sum to an Even [03/21/2002]
Why do two odd numbers always equal an even number but two even numbers never equal an odd number?

Why Use Q and Z? [09/12/2001]
Why is the letter Q used for rational numbers and Z for integers?

Wondrous Numbers [02/07/2001]
What is a wondrous number?

Word for a 225th Birthday [07/10/2001]
This year America is celebrating its 225th birthday. As we celebrated the bicentennial in 1976, is there a term for 225 years?

Working in Base 7 [08/02/2007]
How do I add, subtract, multiply and divide in base 7?

Working with Different Bases [9/7/1995]
Please explain base 10 to me - then base 4.

Working with Sequences [11/14/1998]
Give the next two terms of the sequence: 1, 1, 2, 4, 3, 9, ....

Would Aliens Use Base 10? [05/13/2002]
If aliens had 6 fingers, would they use base 12?

Writing Numbers [11/24/2002]
Which words are okay to capitalize and when are hyphens used between words?

Writing Numbers in Words [09/15/1997]
Write each number in words: 1) 73.78007 2) 2.900087 (3) 34.4939.

Zero and One, Each Unique in Its Own Special Way [04/10/2013]
Zero is neither positive nor negative; 1 is neither prime nor composite. So how do we classify these numbers?

Zero and the Commutative Property of Multiplication [04/18/2003]
If we take 0x1, we get 0, and if we take 0x2, we still get 0, for it is still 0+0+0. But if we do it the other way round, why must it still be 0, if any number to the power of 0 = 1?

Zero Before the Decimal Point? [10/06/2000]
What is the merit of writing the zero before the decimal point in numbers less than one, for example 0.25?

Zero in the Denominator [8/14/1996]
What is the value of 4/0 * 0/4?

Zero Significance [10/27/2013]
Confused about the significance of the zeros on either side of a number such as 0.000, a student expresses doubts about manipulating them, and about representing integers in scientific notation. Doctor Peterson clears the air.

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