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RULES. Classroom Rules No gum/food/drink No cell phone/computer No distracting other people First offense – verbal warning Second offense – 10 minute time out Third offense – eat dinner with adults. Homework Rules Weekly homework. How to count. WB Math Group.

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**RULES**• Classroom Rules • No gum/food/drink • No cell phone/computer • No distracting other people • First offense – verbal warning • Second offense – 10 minute time out • Third offense – eat dinner with adults • Homework Rules • Weekly homework**How to count**WB Math Group**Don’t we know how to count already?**• Not Really… • Ancient people could only count to three • But they know how to compare numbers that are larger than three • How to count huge numbers? Can’t use your fingers! • How to count tricky numbers? • Even majority of the adults don’t know how to count certain things**How many people are there?**• Warren • ~ 15,000 • Basking Ridge • ~ 21,000 • New Jersey • ~ 9,000,000 (6) • US • ~ 300,000,000 (8) • World • ~ 7,000,000,000 (9)**Some big numbers**• Number of Web Pages Google Searches ~ 50,000,000,000 (10) • Number of stars in the Milky Way Galaxy ~ 400 billion 400,000,000,000 (11) • Number of atoms in a drop of water ~ 2,000 billion billions (21) • Number of atoms in the universe 1,000… (80) • Number of Permutations of a 7x7 cube 1,000,…(160)**How to count natural numbers**• How many integers are between 1 ~ 100 ? • How many integers are between 1 ~ 100 inclusive? • How many integers are between 1 ~ 100 exclusive? • How many integers are between 1 ~ n inclusive? Natural numbers are positive integers**How to count natural numbers**• How many integers are between 234 ~ 1011 inclusive? • How many integers are between 234 ~ 1011 exclusive? • How many integers are between 0 ~ 50 inclusive? • How many integers are between r ~ r + n inclusive?**Deal with negative numbers**• How many integers are between -50 ~ 50 inclusive? • How many integers are between -50 ~ -10 inclusive?**Arithmetic sequence**An arithmetic (or linear) sequence is a sequence of numbers in which each new term is calculated by adding a constant value to the previous term • 2, 6, 10, 14, 18, 22, … • -5, -3, -1, 1, 3, 5 … • -1, 10, 21, 32, … • 1, 2, 4, 8, 16, …**Arithmetic sequence**a little algebra**Arithmetic sequence**• How many even numbers are between 2 ~ 200 inclusive? 2, 4, 6, …., 198, 200 • How many integers are in the sequence 3,6,9,…,300? • How many even numbers are between 50 ~ 199 inclusive?**Arithmetic sequence**• How many odd numbers are between 1 ~ 101, inclusive? 1, 3, 5, 7, 9, 11, …., 99, 101 1(2x1-1), 3(2x2-1), …, 99(2x50-1), 101(2x51-1) • How many odd numbers are between 3 ~ 123 inclusive? 3(2x2-1), 5(2x3-1), …., 121(2x61-1), 123(2x62-1) 3(2x1+1), 5(2x2+1), …, 121(2x60+1), 123(2x61+1) • How many numbers are in the following sequence: 5, 9, 13, 17, …, 401 ?**geometric sequence**A geometric sequence is a sequence of numbers in which each new term (except for the first term) is calculated by multiplying the previous term by a constant value. • 1, 2, 4, 8, 16, 32, 64, 128 • 1, 10, 100, 1000, 10000, • 1, 3, 9, 27, ??, ?? • 2, 3, 5, 9, 17, 33, 65, 129**geometric sequence**• 1, 2, 4, 8, … 1024 • 3, 6, 12, 24, 48, …, 300 • 64, 32, 16, 8, … ½, ¼ Slightly Trickier … • 4, 5, 7, 11, 19, …, 2051**Some exercises**• How many integers are there from 25 to 79 inclusive? • What is the 53rd integer in the sequence 86, 87, 88, …? • The largest of 123 consecutive integers is 307. What is the smallest? • The smallest of r consecutive integers is n, what is the largest integer? • The largest of r consecutive integers is k. what is the smallest? • How many integers are there in the sequence n, n+1, n+2, …, n+r ?

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