ARITHMETIC & NUMBERS

Transcription

1 MATH LEVEL 1 LESSON PLAN 1 ARITHMETIC & NUMBERS 2017 Copyright Vinay Agarwala, Revised: 12/19/17 Section 1: Arithmetic, Digits & Numbers 1. The word ARITHMETIC comes from Greek, ARITHMOS number + TECHNE skill. Arithmetic means number skill. 2. The first thing we learn in Arithmetic is counting. Counting starts with 1. The next count is always 1 more. Each count is called a NUMBER. 3. We use digits to write numbers just like we use letters to write words. In English there are 26 different letters that are used to write all possible words. In mathematics, there are ten digits: 0, 1, 2, 3, 4, 5, 6, 7, 8 and 9 to write all possible numbers. A DIGIT IS LIKE A LETTER. A NUMBER IS LIKE A WORD. How many digits make up the following numbers? (a) 536 (b) 72 (c) 3,532 (d) 6 (e) 652,900 (f) 1,000,000,000 Answer: (a) 3 (b) 2 (c) 4 (d) 1 (e) 6 (f) 10 Section 2: Counting Numbers 4. The counting starts from 1 and goes up to 9 as single-digit numbers. They make up the ONES place 1, 2, 3, 4, 5, 6, 7, 8, and 9 5. The counts after 9 are double-digit numbers from 10 to 99. As digits in ONES place cycle from 0 to 9, the digit in TENS place increase incrementally by 1 till it becomes 9. Therefore, the largest double-digit numbers is The counts after 99 are three-digit numbers from 100 to 999. As digits in TENS place cycle from 0 to 9, the digit in HUNDREDS place increase incrementally by 1 till it becomes 9. Therefore, the largest three-digit number is This gives us the following facts:

2 Zero (0) is a place holder when there is no count. There are 9 single-digit numbers from 1 to 9. There are 90 double-digit numbers from 10 to 99. There are 900 three-digit numbers from 100 to 999. (a) The largest 3-digit number is. (b) The smallest 4-digit number is. (c) The largest 4-digit number is. (d) The seven counts after 1095 are. Answer: (a) 999 (b) 1000 (c) 9999 (d) 1096, 1097, 1098, 1099, 1100, 1101, Section 3: The Group of ONES 8. Starting from the right, the place values are ONE-TEN- HUNDRED in a 3-digit number. Therefore, 395 = 3 HUNDREDS + 9 TENS + 5 ONES 9. Each place value is ten times the place value on its right. If ONES are like pennies, then TENS are like dimes, and HUNDREDS are like dollars. Therefore, we may write 395 cents = 3 dollars + 9 dimes + 5 pennies 10. The basic group of ONE-TEN-HUNDRED is called the Group of ONES. (a) Nineteen. (b) Ninety. (c) Ninety-nine. (d) Five hundred and two. (e) Three hundred and sixty-seven. (f) Nine hundred. (g) Nine hundred and twenty. Answer: (a) 19 (b) 90 (c) 99 (d) 502 (e) 367 (f) 900 (g) 920

3 Section 4: The Group of THOUSAND 11. The place values of ONE-TEN-HUNDRED repeat as groups. The group pf THOUSAND appears to the left of the group of ONES. We write the number four hundred eighty-seven thousand, six hundred and fifty-two as follows. (a) Four thousand and seven. (b) Nine thousand six hundred and five. (c) Fifty-five thousand and fifty-five. (d) Ninety thousand nine hundred and one. (e) One hundred and nine thousand. (f) Seven hundred and five thousand five hundred and seven. (g) Four hundred thousand and ninety. Answer: (a) 4,007 (b) 9,605 (c) 55,055 (d) 90,901 (e) 109,000 (f) 705,507 (g) 400,090 Section 5: The Group of MILLION 12. The group pf MILLION appears to the left of the group of THOUSAND. We write the number eight hundred sixty-five million and seven as follows. (a) Seven million seven hundred thousand seven hundred.

4 (b) Ninety-one million and nine. (c) Thirty-four million and fifty-six thousand. (d) Nine million four hundred thousand. (e) Fifty million fifteen thousand and fifty. (f) One hundred and forty million two thousand eight hundred. (g) One hundred and forty million and eight hundred. Answer: (a) 7,700,700 (b) 91,000,009 (c) 34,056,000 (d) 9,400,000 (e) 50,015,050 (f) 140,002,800 (g) 140,000,800 Section 6: The Group of BILLION 13. The group pf BILLION appears to the left of the group of MILLION. We write the number one hundred sixty-eight billion, two hundred ninety-five million, four hundred eighty-seven thousand, six hundred fifty-two as follows. (a) Six billion six hundred million seven thousand and thirty. (b) Sixty-nine billion and four thousand. (c) Forty billion seven hundred thousand two hundred and three. (d) One hundred billion nine hundred and thirty-three. (e) Eighty billion and ninety. (f) One hundred and seventy-five billion thirteen million two hundred and ninetynine. (g) One hundred and forty billion two hundred million, seventy-three thousand and ninety-four. Answer: (a) 6,600,007,030 (b) 69,000,004,000 (c) 40,000,700,203 (d) 100,000,000,933 (e) 80,000,000,090 (f) 175,013,000,299 (g) 140,200,073,094 Section 7: The Group of TRILLION 14. From right, the most used groups are ONES, THOUSANDS, MILLIONS, BILLIONS, and TRILLIONS as shown below. You separate these groups by commas.

5 We read this number as: 743 trillion, 168 billion, 295 million, 487 thousand, six hundred fifty-two. 15. We do not omit any place in a number. When a place value has no count, we place 0 there as a place holder. For example, we write the number 302 trillion, 4 billion, 865 million, and Seven as follows. In this number the count for THOUSANDS is altogether missing. 16. Since digit on the left is 10 times the digit to its right, we have. 1 THOUSAND = 10 HUNDREDS 1 MILLION = 10 HUNDRED THOUSAND 1 BILLION = 10 HUNDRED MILLION 1 TRILLION = 10 HUNDRED BILLION Place commas at the correct place in the following numbers (a) 8268 (c) (e) (b) (d) (f) Answer: (a) 8,268 (b) 82,682 (c) 6,032,650 (d) 15,973,037 (e) 76,098,305,009,023 (f) 801,000,006,000,759 Read the following numbers. (a) 52,762,869 (c) 75,765,532,658 (e) 409,008,007,006,834 (b) 273,045,008 (d) 30,006,000,074 (f) 590,000,060,000,001 Answer: (a) 52 million, 762 thousand, and 869 (b) 273 million, 45 thousand, and 8 (c) 75 billion, 765 million, 532 thousand, and 658 (d) 30 billion, 6 million, and 74 (e) 409 trillion, 8 billion, 7 million, 6 thousand, and 834 (f) 590 trillion, 60 million, and 1. (a) 304 thousand, and 516

6 (b) 45 million, 464 thousand, and 801 (c) 1 billion, 5 million, and 6 (d) 25 billion, 43 million, 60 thousand, and 50 (e) 43 trillion, 6 thousand, and 35 (f) 608 trillion, 45 million, and 529 Answer: (a) 304,516 (b) 45,464,801 (c) 1,005,000,006 (d) 25,043,060,050 (e) 43,000,000,006,035 (f) 608,000,045,000,529 Identify the place values of each digit in the following number. (a) 319,475,765,532,658 Answer: From left to right: (a) 3 hundred trillion, 1 ten trillion, 9 trillion, 4 hundred billion, 7 ten billion, 5 billion, 7 hundred million, 6 ten million, 5 million, 5 hundred thousand, 3 ten thousand, 2 thousand, 6 hundred, 5 ten, and 8. Lesson Plan 1: Check your Understanding 1. What are digits used for? How many digits are there? 2. How many real elephants are there in the room with you? What digit would you use to represent this number of elephants? 3. Give examples for (a) a single-digit number (b) a double-digit number (c) a three-digit number (d) a five-digit number. 4. How many double-digit numbers are there? 5. What are the three place values (from right to left) in a group? 6. What are the most used groups in a number from right to left? Check your answers against the answers given below. Answers 1) You use digits to write numbers. There are ten different digits. 2) Most likely there is no real elephant in the room with you. You will use the digit 0 in that case to represent the number of elephants. 3) Your example may differ: (a) 7 (b) 32 (c) 483 (d) 63,153 4) From 10 to 99 there are 90 double-digit numbers. 5) One-Ten-Hundred 6) Ones, Thousands, Millions, Billions, and Trillions