Objectives Chapter 1 Place Value Reading and Writing Whole Numbers Rounding Whole Numbers Addition with Carrying Addition of More Than Two Numbers Subtraction with Regrouping Regrouping with Zeros Multiplication with Carrying Division by One Digit Division with Remainders Division by Larger Numbers

Whole Numbers Unit 1 Pages 7 – 29

Page 7 Place Value Whole numbers are made up of the digits 0, 1, 2, 3, 4, 5, 6, 7, 8, & 9. The number 44 has two digits. The number 23,060 has five digits. The value of each digit is different because of its position in the number. Every position has a place value. The table on the next slide gives the names of the first ten places in our whole number system.

_, _ _ _, _ _ _, _ _ _ Place Value (Cont’d) one billions hundred millions ten millions one millions hundred thousands ten thousands one thousands hundreds tens ones Page 7 Place Value (Cont’d) _, _ _ _, _ _ _, _ _ _

Place Value – Example Page 7 Find the value of 5 in 85,406. The digit 5 is in the thousands place. It has a value of 5 thousands or 5,000.

Place Value – Group Work Page 8 Place Value – Group Work Use the number 985 to answer problems 1-3. Item one is done for you. 9 is in the hundreds place. 9 has a value of 900. 8 is in the _______ place. 8 has a value of ___. 5 is in the _______ place. 5 has a value of ___. There are 1,760 yards a mile. Use this number to answer problems 4-5. 1 is in the _______ place. 1 has a value of ___. 7 is in the _______ place. 7 has a value of ___. The digit 5 is in the thousands place. It has a value of 5 thousands or 5,000.

Reading & Writing Whole Numbers Page 8 Reading & Writing Whole Numbers Commas make numbers easier to read. Counting from the right, there is a comma after every three places. Large numbers are read in groups of three. At each comma we say the name of the group of digits that are set off by the comma.

Pages 8 – 9 R & W – Group Work Supply the missing words you need to read each number. 2,043,000 two million, forty-three thousand. 502 five _______ two. 4,080 four _______, eighty. 58,320 fifty-eight _______, three hundred twenty. Write words to show how to read each number 3,800 _______________________ 19,007,200 _______________________

Reading & Writing Whole Numbers Page 9 Reading & Writing Whole Numbers To write whole numbers from words, watch for places that must be held with zeros. Example: write three million, four hundred eight thousand, six hundred as a whole number. This number contains no ten thousands, no tens, and no ones (or units). Hold these places with zeros. 3,408,600

Pages 9 – 10 R & W – Group Work Write each of the following as a whole number. Three hundred eight _______ Ninety thousand, twenty-four _______ Eight hundred four thousand, five hundred _______ Sixty thousand, three hundred _______ Eleven million, two hundred seven thousand _______

Rounding Whole Numbers Page 10 Rounding Whole Numbers Rounding makes numbers easier to use when you don’t need exact values. To round a whole number: Underline the digit in the place to which you want to round. If the digit to the right of the underlined digit is 5 or more add 1 to the underlined digit. If the digit to the right of the underlined digit is 4 or less, do not change the underlined digit. Replace the digits to the right of the underlined digit with zeros.

Rounding – Examples Pages 10 – 11 Round 2,374 to the nearest hundred. Round 29,624 to the nearest thousand. 2,400 29,624

Rounding – Group Work Pages 10 – 11 Round each number: To the nearest ten: 38 542 295 To the nearest hundred: 863 59,848 4,082 To the nearest thousand: 6,174 39,723 3,279

Addition with Carrying Page 11 Addition with Carrying The answer to an addition problem is called the sum or total. When the sum of the digits in a column is a two- digit number, carry the digit at the left to the next column to the left. To add more than two numbers, find the total for each column.

Addition – Example Page 11 857 + 268 = 857 + 268 Step 1: If given in the horizontal format rewrite it in vertical format so that the place values line up. Step 2: Add the ones. (Remember: If the column of numbers results in a sum that is more than a single digit carry the second digit to the next column.) Step 3: Add the tens. Step 4: Add the hundreds. Carry on until the sum is reached. Answer: 1,125

Addition – Group Work Pages 12 – 13 44 + 57 = 15 + 88 = 68 + 46 = 341 + 59 = 48 + 485 = 101 103 114 400 533

Addition of More Than Two Numbers Page 14 Addition of More Than Two Numbers Commutative property of addition = changing the order of addends does not change the sum 4 + 2 = 2 + 4 Associative property of addition = changing the grouping of addends does not change the sum (2 + 3) + 4 = 2 + (3 + 4) Boils down to this you can an in any order that you want so add it in a way that makes it easiest for you.

Addition – Example Page 14 43 + 44 + 19 = 12 + 84 + 57 = Step 1: Line up the numbers and add the digits in the ones column Step 2: Add the digits in the tens column.

Addition – Group Work Pages 14 – 15 17 + 88 + 53 = 236 + 1,940 + 375 = 318 + 9,907 + 24,063 = 8,016 + 11,238 +127 = Don’s Music Shop sold 1,026 tapes in March, in April they sold 963 tapes, and in May they sold 1,372 tapes. What were the total sales for those three months? 158 2,551 34,288 19,381 3,361 tapes

Subtraction with Regrouping Page 16 Subtraction with Regrouping The answer to a subtraction problem is called the difference. When the bottom number in any column is too large to subtract from the top number, you must regroup the top number. You may know this operation as renaming or borrowing. Example: 85 – 39 = Step 1: 9 is too large to subtract from 5. Regroup the top number take 1 ten from the tens column and add it to the ones. Step 2: subtract the ones column. Step 3: subtract the tens column. 548

Subtraction – Group Work Pages 16 – 17 Subtraction – Group Work 58 – 29 = 811 – 243 = 6,175 – 496 = 4,236 – 1,448 = 683 people signed up to go on a trip to Miami. 506 people actually went on the trip. How many people who signed up did not go? 29 568 5,679 2,788 177 people

Regrouping with Zeros Page 18 To regroup with zeros, look at the first digit in the top number that is not zero. Example: 904 – 356 = Step 1: You cannot subtract 6 from 4. Take 1 hundred from the hundreds column. You now have 10 tens in the tens column. Step 2: Take 1 ten from the 10 in the tens column and add it to the ones column. Step 3: Subtract the ones column Step 4: Subtract the tens column Step 5: Subtract the hundreds column. 548

Subtraction – Group Work Pages 18 – 19 Subtraction – Group Work 801 – 236 = 706 – 267 = 4,000 – 1,256 = 7,000 – 1,270 = The town of Midvale wants to raise $850,000 to build a new health center. They have collected $473,260 so far. How much more money do they need? 565 439 2,744 5,730 $376,740

Multiplication With Carrying Page 20 Multiplication With Carrying The answer to a multiplication problem is called the product. When you multiply two digits, the product is often a two-digit number. You must carry the left digit to the next number you a re multiplying. Then add the digit you carry to the next product. Example: 76 x 29 = Step 1: 9 x 6 = 54. Write the 4 in the ones column, and carry the 5 to the next column Step 2: 9 x 7 = 63. Add the 5 that you carried. 63 + 5 = 68 Step 3: put a “place holder zero in the ones column in the partial products area. Step 4: 2 x 6 = 12. Write the 2 in the tens column, carry the 1 to the next column. Step 5: 2 x 7 = 14. Add the 1 that you carried. 14 + 1 = 15. Step 6: Add the partial products. 548

Multiplication – Group Work Pages 20 – 21 Multiplication – Group Work 74 x 6 = 778 x 63 = 24 x 866 = 48 x 30 = Rodney makes $370 a week. There are 52 weeks in a year. How much does Rodney make in one year? 444 49,014 20,784 1,440 $19,240

Division by One Digit Page 22 The answer to a division problem is called the quotient. To find a quotient, repeat the four steps listed below until you complete the problem. Divide Multiply Subtract and compare Bring down the next number.

Division – Example Pages 22 – 23 Long division = Writing every step out. Short division = writing out only the answer and the number you get by subtracting 1. Divide – can 6 go into 5? (no) 6 goes into 50? (8 times) write 8 above the zero. 2. Multiply – 8 x 6 = 48. Write 48 under the 50. 3a. Subtract – 50 – 48 = 2 & Compare – (to be sure that what you get by subtraction is less than what you divide by) 2 is less than 6 4. Bring down the next number – 4 5. Divide – 6 goes into 24? (4 times) write 4 above the 4 in 504 6. Multiply – 4 x 6 = 24 write 24 under the 24 7. Subtract – 24 – 24 = 0 & Compare – 0 is less that 6.

Division – Group Work Page 23 Three friends equally shared a raffle prize of $750. How much did each of them get? 47 77 79 276 $250

Division with Remainders Page 24 Division with Remainders If you do not get zero in the last subtraction step of a division problem, you will have a remainder. 96 r 3

Division – Group Work Page 25 1,542 ÷ 8 = 3,845 ÷ 6 = 2,183 ÷ 8 = 2,277 ÷ 5 = To make a climbing toy for her children, Mary is sawing pieces of wood each 4 feet long from a piece that is 19 feet long. How many pieces can Mary cut from the long piece? Assuming no waste, what will be the length of the remaining piece? 192 reminder 6 640 reminder 5 272 reminder 7 455 reminder 2 4 with 3 feet remaining

Division by Larger Numbers Page 26 Division by Larger Numbers To divide by two-digit and three-digit numbers, you must estimate how many times one number divides into another number. When you estimate, you make a guess. 48

Division – Group Work Page 27 1,616 ÷ 22 = 6,910 ÷ 85 = 1,412 ÷ 39 = 2,406 ÷ 91 = Last year the Melinos paid $7,440 in mortgage payments. There are 12 months in a year. How much did they pay each month? 73 R 10 (73.45 or 73.45454545) 81 R 25 (81.29 or 81.29411765) 36 R 8 (36.21 or 36.20512821) 26 R 40 (26.44 or 26.43.956044) $620.00