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Number and Operations

Number and Operations. Place value, reading and writing numbers, comparing and ordering numbers Laura Carter 4 th Grade. Vocabulary. Digit Period Place-value Standard form Expanded form Word form. Digit.

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Number and Operations

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  1. Number and Operations Place value, reading and writing numbers, comparing and ordering numbers Laura Carter 4th Grade

  2. Vocabulary Digit Period Place-value Standard form Expanded form Word form

  3. Digit • The number 916,823 has six digits. A digit is any symbol used to write a whole number.

  4. Period • A group of three digits is called a period. Commas separate the periods. At each comma, say the name of the period. periods ,

  5. Place-Value • The value a digit has because of its place in a number .

  6. Place Value • Example: 78,439 Place: hundreds Value: 400 How much a digit is worth based on what place it’s in. The position of a digit in a number

  7. Standard Form • Example: 184,800

  8. Expanded Form • Example: 100,000+80,000+4,000+800

  9. Word Form • Example: One hundred eighty-four thousand, eight hundred

  10. Real-World Example Scientists found that a gooney bird once traveled 24,983 miles in just 90 days. Identify the place of the underlined digit in 24,983. Then write its value. , . • The value of 4 is 4,000. • 4x1,000 • The value of 2 is 20,000. • 2x10,00 • The value of 9 is 900. • 9x100 The value of 8 is 80. 8x10 The value of 3 is 3. 3x1

  11. Watch me Model! 24,983 • Word Form: twenty-four thousand, nine hundred eighty three • Expanded form: 20,000+4,000+900+80+3 Write in standard form. • 10,000 +7,000 +800+60+4 • Eighty-six thousand, one hundred seventy-three

  12. Draw the Place value chart in your math notebook. Place Value Chart . ,

  13. Notebook Practice Write the place and value of each underlined digit. Write each number in standard, expanded and word form. • 104,002 • 62,574 • 38,035 Guided Practice

  14. Whiteboard Practice Write the place and value of the underlined digit. • 53,456 • 612,456 Write each number in standard form. • 500,000+1,000+30+3 • Twelve thousand four Write each number in expanded and word form. • 23,472 • 49,602

  15. Independent Practice • MB pg. 22 #s 13-37 odd only

  16. Decimals • Reading and writing decimal numbers

  17. Decimal • A number that uses place value, numbers, and a decimal point to show part of a whole. Ex: 17.32

  18. Decimal Place Value Poem Reading decimals is easy you’ll see. They have two names like you and me. First you say the name as if there were no dot. Then you say the name of the last place value spot. Example:0.28 First Name: twenty-eight Last Name: hundredths

  19. Real World Example • Watch http://connected.mcgraw-hill.com/connected/permLink.do?ced_pl_id=KHT9JMZNY8X2LDC3JDLRBNVRB8

  20. Write in your notes! Decimal Place Value Chart . Read these decimal numbers with me. 0.48 0.37 4.8 51.23

  21. Model: Write in your notes Write in standard form • Four tenths • Eighty-five hundredths • Four and three tenths • One and seven hundredths Write in word form. Name the value of the underlined digit. • 0.7 • 8.41 • 63.54

  22. Whiteboard Practice Write in standard form. • Nine tenths • One and seven tenths • Forty-three and eight hundredths

  23. Independent Practice Write in word form and expanded form. • 34,718 • 76.2 • 784,329 • 76,002 • 102,306 • 5.03 • 0.79 • 8,705.04

  24. Compare and Order Numbers

  25. Warm up: Real World Example • Watch http://connected.mcgraw-hill.com/connected/permLink.do?ced_pl_id=119@TQ8S@YY16Q9XB22QJ6VWW8

  26. Steps to compare and order whole numbers 1st: Line up the numbers by their place value 2nd: Compare from left to right. Let’s compare and order some numbers together in your notes!

  27. Work in your notes with me!

  28. Independent Practice • MB pg. 26 #s 9-25 odd only

  29. Comparing and Ordering Decimals When Will I Ever Do That???!!!

  30. McDonald’s Menu….I’m Lovin It!! • Double Cheeseburger: $ .99 • Big Mac Value Meal: $ 4.79 • Chicken McNuggetts Meal: $ 3.80 • Small Drink: $ .99 • McFlurry: $ 1.97 • Salad: $ 4.80 • 2 Cheeseburger Meal: $ 3.70 • Ice Cream Cone: $ .87

  31. Order Up!Least Expensive to Most Expensive • Ice Cream Cone .87 • Double Cheeseburger: .99 • Small Soft Drink: .99 • McFlurry: 1.97 • 2 Cheeseburger Meal: 3.70 • Chicken McNuggetts Meal: 3.80 • Big Mac Value Meal: 4.79 • Chicken Salad: 4.80

  32. What Do I Mean Compare Decimals? • When we compare we use terms such as: • Less than < • Greater than > • Equal to = • Comparing decimals is similar to comparing whole numbers. • 45<47 • 150>105 • When we compare decimals we use place value or a number line.

  33. Place Value Hundreds Ones Thousands Tens Tenths Hundredths Thousandths Ten-thousandths

  34. Half pipe Results • Compare Sara’s score with Danny’s score. • Line Up Decimal Points • Sara: 42.1 • Danny: 42.5 • Start at the left and find the first place where the digits differ. Compare the digits • 1<5 • 42.1<42.5 • This means Sara’s score was lower than Danny’s score.

  35. Let’s Try Using A Number Line 42.0 42.1 42.5 Numbers to the right are greater than numbers to the left. Since 42.5 is to the right of 42.1 we have: 42.5>42.1

  36. Equivalent Decimals • Decimals that name the same number are called equivalent decimals. • 0.60 and 0.6 • Are these the same???

  37. = 0.60 0.6

  38. Annexing Zeros • This means placing a zero to the right of the last digit in a decimal. • 0.6 0.60 • Although we added a zero, the value of the decimal did not change!! • Annexing or adding zeros is useful when ordering a group of decimals.

  39. Ordering Decimals • We can order decimals from least to greatest or we can order from greatest to least. • Let’s try an example: • Order 15, 14.95, 15.8, and 15.01 from least to greatest

  40. 15, 14.95, 15.8, 15.01 • First, line up the decimal points 15 14.95 15.8 15.01

  41. 15, 14.95, 15.8, 15.01 • Next, annex zeros so that each number has the same number of decimal places 15.00 14.95 15.80 15.01

  42. 15, 14.95, 15.8, 15.01 • Finally, use place value to compare the decimals. Always start from the left!! 15.00 14.95 15.80 15.01 • 14.95, 15, 15.01, 15.8

  43. Steps to Compare Decimals 1st Line up the decimal points. 2nd Compare the digits in each position. (add zeros to the right if needed) 3rd Compare and order using place value. Al the Alligator will eat the biggest number!

  44. One More Example • Order these numbers from greatest to least • 35.06, 35.7, 35.5, 35.849

  45. More practice Order greatest to least • 9.86, 9.8, 9.92, 9.09 • 0.12, 1.2, 1.21, 12.0 Compare using >,<,= 3. 0.2____0.6 4. 12.07_____1.207

  46. Estimate by Rounding NumbersI can estimate numbers by rounding.

  47. Vocabulary Estimate Round

  48. Estimate When you estimate, you find an answer that is close to the exact answer. One way to estimate is to round by changing the value of a number so that it is easier to work with.

  49. When would you Estimate? • About how many apples are in the bowl? • How many pieces of candy do you think are in the jar? • About how many days are there until Christmas break?

  50. Steps to Round 1st Underline the digit to be rounded. 2nd Look at the digit to the right of the place being rounded. 3rd. If the digit is 4 or less, do not change the underlined digit. If the digit is 5 or more, add 1 to the underlined digit. 4th Replace all digits after the underlined digit with zeros.

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