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Number 2

Number 2. Place value. LEVEL 3 : WRITE NUMBERS IN WORDS LEVEL 4 : MULTIPLY BY POWERS OF 10 ORDER WHOLE NUMBERS MULTIPLY BY MULTIPLES OF 10 LEVEL 5 : ROUND NUMBERS TO NEAREST 1, 10, etc ROUND NUMBERS TO ONE AND TWO DECIMAL PLACES. LEVEL 6 : ORDER DECIMAL NUMBERS

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Number 2

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  1. Number 2 Place value

  2. LEVEL 3: WRITE NUMBERS IN WORDS LEVEL 4: MULTIPLY BY POWERS OF 10 ORDER WHOLE NUMBERS MULTIPLY BY MULTIPLES OF 10 LEVEL 5: ROUND NUMBERS TO NEAREST 1, 10, etc ROUND NUMBERS TO ONE AND TWO DECIMAL PLACES LEVEL 6: ORDER DECIMAL NUMBERS APPROXIMATE DECIMALS TO A SENSIBLE DEGREE OF ACCURACY LEVEL 7: ESTIMATE TO 1, 2 AND 3 SIGNIFICANT FIGURES SF USE SF TO ESTIMATE CALCULATIONS LEVEL 8: SOLVE PROBLEMS USING STANDARD FORM Number 2 level descriptors

  3. ESTIMATE INTEGER MULTIPLY DIVIDE APPROXIMATE ROUNDING MULTIPLES PLACE VALUE POWERS ORDER DECIMAL PLACE SIGNIFICANT FIGURES STANDARD FORM KEY WORDS

  4. OBJECTIVE LEVEL 3: UNDERSTAND HOW TO WRITE NUMBERS IN WORDS SUCCESS CRITERIA WRITE NUMBERS OF INCREASING MAGNITUDE IN WORDS CONVERT NUMBERS WRITTEN IN WORDS INTO DECIMAL NUMBERS NUMBERS IN WORDS

  5. TYPES OF NUMBER • Counting numbers 1, 2, 3, 4, 5, … • Natural numbers 1, 2, 3, 4, 5, … • Odd numbers 1, 3, 5, 7, 9, … • Even numbers 2, 4, 6, 8, 10, … • Integers …,-2, -1, 0, 1, 2, … • Positive integers +1, +2, +3, +4, … • Negative integers -1, -2, -3, -4, -5, …

  6. Complete the table

  7. CREATE YOUR OWN whole numbers in words

  8. What does the 9 represent in each case

  9. What does the 9 represent in each case Nine tens or 90 Nine thousands or 9000 Nine units or 9 Nine million or 9000 000 Ninety million or 90 000 000

  10. Write out the decimal numbers in words Note: the most common mistake is to say 5.96 is five point ninety six. This is five point nine six

  11. Write out the decimal numbers in words Ninety eight point seven Two point nine four five Fifty two point eight seven Ninety six point seven zero nine Zero point zero zero nine Zero point zero six Note: the most common mistake is to say 5.96 is five point ninety six. This is five point nine six

  12. CREATE YOUR OWN decimal numbers in words

  13. What does the 4 represent in each case

  14. What does the 4 represent in each case Four tenths or 4/10 Four hundredths or 4/100 Four thousandths or 4/1000

  15. WRITE NUMBERS OF INCREASING MAGNITUDE IN WORDS CONVERT NUMBERS WRITTEN IN WORDS INTO DECIMAL NUMBERS IDENTIFY MAGNITUDE BY POSITION NUMBERS IN WORDS REVIEW

  16. OBJECTIVE LEVEL 4: UNDERSTAND HOW TO MULTIPLY AND DIVIDE BY POWERS OF 10 SUCCESS CRITERIA MULTIPLY BY 10 AND ADD A ZERO MULTIPLY BY 100 AND ADD TWO ZERO’S MULTIPLY A DECIMAL BY 10 AND THE NUMBERS MOVE TO THE LEFT DIVIDE A DECIMAL BY 10 AND THE NUMBERS MOVE TO THE RIGHT MULTIPLY AND DIVIDE BY POWERS OF 10

  17. Starter • 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 = • 5 + 5 + 5 + 5 + 5 + 5 + 5 + 5 + 5 + 5 = • 8 + 8 + 8+ 8 + 8 + 8 + 8 + 8 + 8 + 8 = • Is there a quick way to add the same number ten times?

  18. Modulus • MODULUS means size irrespective of sign |-4| = 4 |6| = 6 |-0.06| = 0.06

  19. The decimal point needs to be put back into the number

  20. The decimal point needs to be put back into the number

  21. Multiply numbers by ten • When a number is multiplied by ten the modulus of the number increases. • If a whole number is multiplied by 10 a zero is placed on the right hand end of the number 16 × 10 = 160 7 × 10 = 70 • If a decimal number is multiplied by 10 then the numbers move one place to the left of the decimal point and empty spaces are replaced by zero’s 2.76 × 10 = 27.6 0.62× 10 = 6.2

  22. Example 45 × 10 = 450 45 × 10 = 5 × 10 = 57 × 10 = 20 × 10 = 89 × 10 = 128 × 10 = 167 × 10 = 360 × 10 = Example 5.7 × 10 = 57 5.1 × 10 = 9.2 × 10 = 12.8 × 10 = 10.9 × 10 = 6.056 × 10 = 0.67 × 10 = 0.061 × 10 = 0.0074 × 10 = Multiply numbers by 10

  23. Example 45 × 10 = 450 45 × 10 = 450 5 × 10 = 50 57 × 10 = 570 20 × 10 = 200 89 × 10 = 890 128 × 10 = 1280 167 × 10 = 1670 360 × 10 = 300 Example 5.7 × 10 = 57 5.1 × 10 = 51 9.2 × 10 = 92 12.8 × 10 = 128 10.9 × 10 = 109 6.056 × 10 = 60.56 0.67 × 10 = 6.7 0.061 × 10 = 0.61 0.0074 × 10 = 0.074 Multiply numbers by 10

  24. Multiply numbers by one hundred • When a number is multiplied by one hundred the modulus of the number increases. • If a whole number is multiplied by 100 two zero’s are placed on the right hand end of the number 46 × 100 = 4600 8 × 100 = 800 • If a decimal number is multiplied by 100 then the numbers move two places to the left of the decimal point and empty spaces are replaced by zero’s 2.6 × 100 = 260 0.38 × 100 = 38

  25. Example 37 × 100 = 3700 89 × 100 = 9 × 100 = 27 × 100 = 60 × 100 = 49 × 100 = 524 × 100 = 973 × 100 = 940 × 100 = Example 5.7 × 100 = 570 8.1 × 100 = 3.2 × 100 = 16.8 × 100 = 14.9 × 100 = 8.056 × 100 = 0.95 × 100 = 0.039 × 100 = 0.0059 × 100 = Multiply numbers by 100

  26. Example 37 × 100 = 3700 89 × 100 = 8900 9 × 100 = 900 27 × 100 = 2700 60 × 100 = 6000 49 × 100 = 4900 524 × 100 = 52400 973 × 100 = 97300 940 × 100 = 94000 Example 5.7 × 100 = 570 8.1 × 100 = 810 3.2 × 100 = 320 16.8 × 100 = 1680 14.9 × 100 = 1490 8.056 × 100 = 805.6 0.95 × 100 = 95 0.039 × 100 = 3.9 0.0059 × 100 = 0.59 Multiply numbers by 100

  27. Divide numbers by 10 • When a number is divided by ten the modulus of the number decreases. • If a whole number is divided by 10 then the numbers move one place to the right of the decimal point and empty spaces are filled with zero’s 16 ÷ 10 = 1.6 8 ÷ 10 = 0.8 • If a decimal number is divided by 10 then the numbers move one place to the right of the decimal point and empty spaces are filled with zero’s 14.6 ÷ 10 = 1.46 0.46 ÷ 10 = 0.046

  28. Example 49 ÷ 10 = 4.9 89 ÷ 10 = 5 ÷ 10 = 87 ÷ 10 = 40 ÷ 10 = 39 ÷ 10 = 174 ÷ 10 = 925 ÷ 10 = 620 ÷ 10 = Example 9.5 ÷ 10 = 0.95 65.1 ÷ 10 = 43.2 ÷ 10 = 6.8 ÷ 10 = 4.9 ÷ 10 = 7.046 ÷ 10 = 0.51 ÷ 10 = 0.064 ÷ 10 = 0.0038 ÷ 10 = Divide numbers by 10

  29. Example 49 ÷ 10 = 4.9 89 ÷ 10 = 8.9 5 ÷ 10 = 0.5 87 ÷ 10 = 8.7 40 ÷ 10 = 4 39 ÷ 10 = 3.9 174 ÷ 10 = 17.4 925 ÷ 10 = 92.5 620 ÷ 10 = 62 Example 9.5 ÷ 10 = 0.95 65.1 ÷ 10 = 6.51 43.2 ÷ 10 = 4.32 6.8 ÷ 10 = 0.68 4.9 ÷ 10 = 0.49 7.046 ÷ 10 = 0.7046 0.51 ÷ 10 = 0.051 0.064 ÷ 10 = 0.0064 0.0038 ÷ 10 = 0.00038 Divide numbers by 10

  30. Divide numbers by 100 • When a number is divided by one hundred the modulus of the number decreases. • If a whole number is divided by 100 then the numbers move two places to the right of the decimal point and empty spaces are filled with zero’s 67 ÷ 100 = 0.67 4 ÷ 100 = 0.04 • If a decimal number is divided by 100 then the numbers move two places to the right of the decimal point and empty spaces are filled with zero’s 67.8 ÷ 100 = 0.678 0.86 ÷ 100 = 0.0086

  31. Example 49 ÷ 100 = 0.49 89 ÷ 100 = 63 ÷ 100 = 7 ÷ 100 = 90 ÷ 100 = 73 ÷ 100 = 714 ÷ 100 = 953 ÷ 100 = 630 ÷ 100 = Example 9.5 ÷ 100 = 0.095 9.1 ÷ 100 = 6.2 ÷ 100 = 46.8 ÷ 100 = 34.9 ÷ 100 = 7.056 ÷ 100 = 0.74 ÷ 100 = 0.062 ÷ 100 = 0.0094 ÷ 100 = Divide numbers by 100

  32. Example 49 ÷ 100 = 0.49 89 ÷ 100 = 0.89 63 ÷ 100 = 0.63 7 ÷ 100 = 0.07 90 ÷ 100 = 0.9 73 ÷ 100 = 0.73 714 ÷ 100 = 7.14 953 ÷ 100 = 9.53 630 ÷ 100 = 6.3 Example 9.5 ÷ 100 = 0.095 9.1 ÷ 100 = 0.091 6.2 ÷ 100 = 0.062 46.8 ÷ 100 = 0.468 34.9 ÷ 100 = 0.349 7.056 ÷ 100 = 0.07056 0.74 ÷ 100 = 0.0074 0.062 ÷ 100 = 0.00062 0.0094 ÷ 100 = 0.000094 Divide numbers by 100

  33. ÷ 10 × 10 ÷ 10 ÷ 10 ÷ 100 × 100 × 100 ÷ 10 ÷ 10 30 30000

  34. 300 30 × 100 ÷ 100 × 10 × 100 ÷ 10 ÷ 10 ÷ 10 ÷ 10 ÷ 10 × 100 3 3000 3000 3000 300 30 30000 30 300

  35. ÷ 10 × ÷ × 10 Create and complete your own snake name……………………….

  36. MULTIPLY BY 10 AND ADD A ZERO MULTIPLY BY 100 AND ADD TWO ZERO’S MULTIPLY A DECIMAL BY 10 AND THE NUMBERS MOVE TO THE LEFT OF THE DECIMAL POINT DIVIDE A DECIMAL BY 10 AND THE NUMBERS MOVE TO THE RIGHT OF THE DECIMAL POINT Multiply by Powers of 10 review

  37. OBJECTIVE LEVEL 4: UNDERSTAND HOW TO ORDER WHOLE NUMBERS SUCCESS CRITERIA ORDER NEGATIVE NUMBERS ORDER POSITIVE NUMBERS ORDER INTEGERS ORDER WHOLE NUMBERS

  38. Complete the Number lines

  39. Order whole numbers • We are often asked to place numbers in order of size. We must remember that: • Negative numbers are smaller than positive numbers • Zero lies between the positive and negative numbers • If in doubt – think of a number line

  40. Number lines

  41. ORDER POSITIVE INTEGERS • Example • Place the following numbers in order, smallest first 6, 8, 24, 17, 81, 12, 15 6, 8, 12, 15, 17, 24, 81

  42. Place the following sets of numbers in order, smallest first. 12, 83, 27, 1, 5 30, 41, 5, 17, 46 41, 1, 24, 56, 28 12, 91, 72, 8, 93 81, 93, 56, 34, 9 Place the temperatures in order, highest to lowest 760C, 210C, 260C 150C, 180C, 160C 910C, 120C, 390C 510C, 170C, 560C 190C, 160C, 730C ORDER POSITIVE INTEGERS EXTENSION – calculate the totals for each question 1

  43. Place the following sets of numbers in order, smallest first. 1, 5 , 12, 27, 83 5, 17, 30, 41, 46 1, 24, 28, 41, 56 8, 12, 72, 91, 93 9, 34, 56, 81, 93 Place the temperatures in order, highest to lowest 210C, 260C, 760C 150C, 160C, 180C, 120C, 390C, 910C 170C, 510C, 560C 160C, 190C, 730C ORDER POSITIVE INTEGERS EXTENSION – 128, 123

  44. ORDER NEGATIVE INTEGERS • Example • Place the following numbers in order, smallest first -6, -8, -4, -7, -18, -2, -5 -18, -8, -7, -6, -5, -4, -2

  45. Place the following sets of numbers in order, smallest first. -2, -8, -17, -1, -52 -3, -4, -8, -27, -16 -3, -18, -2, -76, -26 -7, -9, -2, -18, -28 -8, -56, -42, -37 -92 Place the temperatures in order, highest to lowest -150C, -20C, -160C -120C, -80C, -60C -90C, -150C, -190C -50C, -70C, -90C -120C, -60C, -80C ORDER NEGATIVE INTEGERS EXTENSION – calculate the totals for each question 1

  46. Place the following sets of numbers in order, smallest first. -52, -17, -8, -2, -1 -27, -16, -8, -4, -3 -76, -26, -18, -3, -2 -28, -18, -9, -7, -2 -92, -56, -42, -37 -8 Place the temperatures in order, highest to lowest -160C, -150C, -20C -120C, -80C, -60C -190C, -150C, -90C -90C, -70C, -50C -120C, -80C, -60C ORDER NEGATIVE INTEGERS EXTENSION – -80, -33

  47. ORDER INTEGERS • Example • Place the following numbers in order, smallest first 6, 0, -8, 4, 7, 8, -2, -5 -8, -5, -2, 0, 4, 6, 7, 8

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