Natural Numbers 1 To 99: Activities

Math Backpacks Numbers-001-099-Activities.doc

Natural Numbers 1 to 99: Activities

Bob Albrecht & George Firedrake ●

This work is licensed under a Creative Commons Attribution-Noncommercial 3.0 license.

http://creativecommons.org/licenses/by-nc/3.0/

This is an activity unit for teachers about the set of natural numbers 1 to 99. {1, 2, 3, 4, 5, ..., 98, 99}

In this unit, we present activities related to our reference units

Natural Numbers 1 to 99 and Natural Numbers 1 to 99 – tables.

These number units are posted at www.curriki.org. Search for albrecht number.

PPP / UNDER CONSTRUCTION, but we will post it, warts and all, at Curriki.
Go to www.curriki.org and search for: albrecht number. / PPP

Natural numbers 1 to 99:

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20

21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40

41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80

81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99

The list of natural numbers from 1 to 99 occupies quite a chunk of space, and is a tad cumbersome to write. In a math textbook, you might see this set expressed in a shorthand list notation, like this:

The set of natural numbers 1 to 99 = {1, 2, 3, 4, 5, ..., 98, 99}

This notation begins with an opening curly brace, then the first few members of the set separated by commas, then an ellipsis ( ... ) followed by a comma, then the last one or two or more members of the set separated by commas, and finally a closing curly brace. Whew! That was a mouthful.

More set notation – we think it is called set-builder notation. Here are two versions:

The set of natural numbers 1 to 99 = {n | n is a natural number less than or equal to 99}

The set of natural numbers 1 to 99 = {n | n is a natural number and 1 ≤ n ≤ 99}

The phrase "The set of natural numbers 1 to 99" is a wee bit long, so let's give our set a name. In this unit, N99 is our name for the set of natural numbers 1 to 99.

N99 = {1, 2, 3, 4, 5, ..., 98, 99}

N99 = {n | n is a natural number and 1 ≤ n ≤ 99}

All aboard – here we go.

Natural Numbers 1 to 99: Questions, Activities, and Other Alakazams

N99 is our name for the set of natural numbers 1 to 99. The following questions, conjectures, activities, and other alakazams are about N99, and not about any other set. We have posted information about N99 at Curriki (www.curriki.org) in Microsoft Word files, including the units listed here:

Natural Numbers 1 to 99
Natural Numbers 1 to 99 – tables. / File name: Numbers-001-099.doc
File name: Numbers-001-099-tables.doc

To browse our number units, go to www.curriki.org and search for albrecht number.

We will suggest questions, conjectures, and other activities. Browse and (we hope) find one or two or more that you like. Pick easy items that your investigators can do quickly. Build confidence! As confidence accumulates, choose items that are slightly more difficult. Then go for more.

Divide the work. Divide your N99 investigators into teams of 2 or 3 or 4 members. If you have n teams, assign to each team approximately 1/n of the tasks that you choose from our list. Of course, you already knew that. Sorry.

Write your version of our stuff. Post it here and there. Write articles for your math teacher's periodical. If you do, please peruse the Creative Commons our Creative Commons license at

http://creativecommons.org/licenses/by-nc/3.0/

Post your version at Curriki (www.curriki.org). Tell us about your stuff. ().

Reminder:

· N99 is our name for the set of natural numbers 1 to 99.

· N99 = {1, 2, 3, 4, 5, ..., 98, 99}

· N99 = {n | n is a natural number and 1 ≤ n ≤ 99}

We will organize our questions in sets of questions (Question Set 01, 02, et cetera, et cetera) so that we can add or delete items in one question set without having to renumber everything following a change. We might list activities and conjectures related to a question set: For example, Question Set 02, Activity Set 01 (Q02A01) or Question Set ab, Conjecture Set cd (QabCcd).

Question sets, activities, conjectures, and other alakazams as of 2008-10-10.

Question Set 01 (Q01) Number of Numbers, Odd Numbers, Even Numbers

Question Set 01, Activity Set 01 (Q01A01)

Question Set 02 (Q02) Special Numbers

Question Set 02, Activity Set 01 (Q02A01)

Question Set 03 (Q03) Primes, Composites, Palprimes, and Emirps

More Questions, Activities, and Conjectures

PPP / A conjecture is true or false for N99. If a conjecture is true for N99, is it true for the whole shebang of natural numbers? / PPP

Question Set 01 (Q01) Numbers of Numbers, Odd Numbers, Even Numbers

PPP Boggled by a word or phrase? Browse the glossary way down yonder. PPP

1. How many numbers are in N99?

2. What is the first (smallest, least) number in N99?

3. What is the last (largest, greatest) number in N99?

4. How many natural numbers are not in N99?

5. How many odd numbers are in N99?

6. How many even numbers are in N99?

7. How many multiples of 2 are in N99?

8. On division of a number in N99 by 2, how many numbers have a remainder of 0?

9. On division of a number in N99 by 2, how many numbers have a remainder of 1?

10. How many multiples of 3 are in N99?

11. On division of a number in N99 by 3, how many numbers have a remainder of 0?

12. On division of a number in N99 by 3, how many numbers have a remainder of 1?

13. On division of a number in N99 by 3, how many numbers have a remainder of 2?

12. Your Turn. Add a question or two or more.

Question Set 01, Activity Set 01 (Q01A01)

PPP Ahoy teacher: In the following activities, YOU choose the value of n. PPP

1. Name n natural numbers that are not in N99.
2. Name n odd numbers that are not in N99.
3. Name n even numbers that are not in N99.
4. Name n multiples of 2 that are not in N99.
5. Name n multiples of 3 that are not in N99.
6. Name n numbers in N99 that, on division by 3, yield a remainder of 0.
7. Name n numbers in N99 that, on division by 3, yield a remainder of 1.
8. Name n numbers in N99 that, on division by 3, yield a remainder of 2.
9. Your Turn. Add an activity or two or more. / P Ahoy Teacher P
If you assign any of these activities to your students, choose a value of n that is appropriate for them.
We suggest n = 3 or a tad more, but your choice of the value of n is the best choice for your students.

Question Set 02 (Q02) Special Numbers

PPP Boggled by a word or phrase? Browse the glossary way down yonder. PPP

1. How many palindromic numbers are in N99?

2. How many uphill numbers are in N99?

3. How many flat numbers are in N99?

4. How many downhill numbers are in N99?

5. How many square numbers are in N99?

6. How many cubic numbers are in N99?

7. How many triangular numbers are in N99?

8. How many powers of 2 are in N99?

9. How many powers of 3 are in N99?

10. How many factorial numbers are in N99?

11. How many perfect numbers are in N99?

12. How many Fibonacci numbers are in N99?

13. Your Turn. Add a question or two or more.

Question Set 02 Activity Set 01 (Q02A01)

1. List the palindromic numbers in N99.
2. List the uphill numbers in N99.
3. List the flat numbers in N99.
4. List the downhill numbers in N99?
5. List the square numbers in N99.
6. List the cubic numbers in N99.
7. List the triangular numbers in N99.
8. List the powers of 2 are in N99?
9. List the powers of 3 are in N99?
10. List the factorial numbers are in N99?
11. List the perfect numbers in N99.
12. List the Fibonacci numbers are in N99?
13. Your Turn. Add an activity or two or more. / PP Ahoy Teacher PP
We suggest that your students list all palindromic numbers in N99, but you decide.
There are many uphill and downhill numbers in N99. Divide the work among n teams, where you choose the value of n.
We suggest that your investigators find all square numbers, cubic numbers, triangular numbers, powers of 2, powers of 3, factorial numbers, perfect numbers, and Fibonacci numbers in N99, but you decide.

Question Set 03 (Q03) Primes, Composites, Palprimes, and Emirps

1. How many prime numbers are in N99?
2. How many composite numbers are in N99?
3. How many palprimes are in N99?
4. How many emirps are in N99?
5. Your Turn. Add a question or two or more. / PP Ahoy Teacher PP
Palprime? Emirp? Browse the glossary way down yonder.

Question Set 03, Activity Set 01 (Q03A01)

1. List the prime numbers N99.
2. List the composite numbers in N99.
3. List the one-and-only number in N99 that is neither prime nor composite.
4. List the palprimes in N99.
5. List emirps in N99.
6. Your Turn. Add an activity or two or more. / PP Ahoy Teacher PP
Team 0: Find primes in 0 to 9.
Team 1: Find primes in 10 to 19.
Et cetera, et cetera.
Team 0: Find composites in 0 to 9.
Team 1: Find composites in 10 to 19.
Et cetera, et cetera.
Everybody find all palprimes and emirps.

Question Set 03, Conjecture Set 01 (Q03C01)

1. N99 has a first (smallest) number.
2. N99 does not have a first (smallest) number.
3. N99 has a last (greatest) number.
4. N99 does not have a last (greatest) number.
5. N99 has a finite number of numbers.
6. N99 has an infinite number of numbers.
7. N99 has more prime numbers than composite numbers.
8. N99 has more composite numbers than prime numbers.
9. N99 has the same number of prime numbers and composite numbers.
10. The number 1 is a prime number.
11. The number 1 is a composite number.
12. The number 1 is neither prime nor composite.
13. Your Turn. Add a conjecture or two or more. / PP Ahoy Teacher PP
A finite set has a first (smallest) number and a last (greatest) number.
The set of natural numbers has a first number (1), but does not have a last number. It goes on and on and on, never ending. .
The number 1 is unique. It is neither a prime number nor a composite number. Why is 1 neither prime nor composite? Look at the definitions of prime number and composite number in the Glossary down yonder.