NUMBER SENSE AT A FLIP

1. This is a powerpoint to teach number sense tricks. Credit goes to Jeff Boyd for its creation and placement in the public domain.Edited by pthornton52@hotmail.com on Nov. 3, 2017

2. NUMBER SENSE AT A FLIP

3. NUMBER SENSE AT A FLIP

4. Number Sense Number Sense is memorization and practice. The secret to getting good at number sense is to learn how to recognize and then do the rules accurately . Then learn how to do them quickly. Every practice should be under a time limit.

5. The First Step The first step in learning number sense should be to memorize the PERFECT SQUARES from 12 = 1 to 402 = 1600 and the PERFECT CUBES from 13 = 1 to 253 = 15625. These squares and cubes should be learned in both directions. ie. 172 = 289 and the 289 is 17.

6. The Rainbow Method Work Backwards 2x2 Foil (LIOF)23 x 12 Used when you forget a rule about 2x2 multiplication The last number is the units digit of the product of the unit’s digits Multiply the outside, multiply the inside Add the outside and the inside together plus any carry and write down the units digit Multiply the first digits together and add and carry. Write down the number 2(1) 2(2)+3(1) 3(2) 2 7 6 276

7. Consecutive Decades35 x 45 First two digits = the small ten’s digit times one more than the large ten’s digit. Last two digits are always 75 3(4+1)75 =1575

8. Ending in 5…Ten’s Digits Both Even45 x 85 First two digits = the product of the ten’s digits plus ½ the sum of the ten’s digits. Last two digits are always 25 4(8) + ½ (4+8)25 =3825

9. Ending in 5…Ten’s Digits Both Odd35 x 75 First two digits = the product of the ten’s digits plus ½ the sum of the ten’s digits. Last two digits are always 25 3(7) + ½ (3+7)25 =2625

10. Ending in 5…Ten’s Digits Odd&Even35 x 85 First two digits = the product of the ten’s digits plus ½ the sum of the ten’s digits. Always drop the remainder. Last two digits are always 75 3(8) + ½ (3+8)75 =2925

11. Squaring Numbers Ending In 5752 First two digits = the ten’s digit times one more than the ten’s digit. Last two digits are always 25 7(7+1)25 =5625

12. (1/8 rule) Multiplying By 12 ½ 32 x 12 ½ 32 Divide the non-12 ½ number by 8. Add two zeroes. 4+00 = 8 =400

13. (1/6 rule) Multiplying By 16 2/3 42 x 16 2/3 42 Divide the non-16 2/3 number by 6. Add two zeroes. 7+00 = 6 =700

14. (1/3 rule) Multiplying By 33 1/3 24 x 33 1/3 • Divide the non-33 1/3 number by 3. • Add two zeroes. 24 8+00 = 3 =800

15. (1/4 rule) Multiplying By 2532 x 25 32 Divide the non-25 number by 4. Add two zeroes. 8 +00 = 4 =800

16. (1/2 rule) Multiplying By 5032 x 50 32 Divide the non-50 number by 2. Add two zeroes. 16 = +00 2 =1600

17. (3/4 rule) Multiplying By 7532 x 75 Divide the non-75 number by 4. Multiply by 3. Add two zeroes. 32 = 8x3=24+00 4 =2400

18. (1/8 rule) Multiplying By 12532 x 125 Divide the non-125 number by 8. Add three zeroes. 32 4+000 = 8 =4000

19. Multiplying When Tens Digits Are Equal And The Unit Digits Add To 1032 x 38 First two digits are the tens digit times one more than the tens digit Last two digits are the product of the units digits. 3(3+1) 2(8) =1216

20. Multiplying When Tens Digits Add To 10 And The Units Digits Are Equal67 x 47 First two digits are the product of the tens digit plus the units digit Last two digits are the product of the units digits. 6(4)+7 7(7) =3149

21. Multiplying Two Numbers in the 90’s97 x 94 Find out how far each number is from 100 The 1st two numbers equal the sum of the differences subtracted from 100 The last two numbers equal the product of the differences 100-(3+6) 3(6) =9118

22. Multiplying Two Numbers Near 100109 x 106 First Number is always 1 The middle two numbers = the sum on the units digits The last two digits = the product of the units digits 1 9+6 9(6) = 11554

23. Multiplying Two Numbers With 1st Numbers = And A 0 In The Middle402 x 405 The 1st two numbers = the product of the hundreds digits The middle two numbers = the sum of the units x the hundreds digit The last two digits = the product of the units digits 4(4) 4(2+5) 2(5) = 162810

24. 10101 Rule Multiplying By 336718 x 3367 Divide the non-3367 # by 3 Multiply by 10101 18/3 = 6 x 10101= = 60606

25. 121 Pattern Multiplying A 2-Digit # By 1192 x 11 (ALWAYS WORK FROM RIGHT TO LEFT) Last digit is the units digit The middle digit is the sum of the tens and the units digits The first digit is the tens digit + any carry 9+1 9+2 2 = 1012

26. 1221 Pattern Multiplying A 3-Digit # By 11192 x 11 (ALWAYS WORK FROM RIGHT TO LEFT) Last digit is the units digit The next digit is the sum of the tens and the units digits The next digit is the sum of the tens and the hundreds digit + carry The first digit is the hundreds digit + any carry 1+1 1+9+1 9+2 2 =2112

27. 12321 Pattern Multiplying A 3-Digit # By 111192 x 111 (ALWAYS WORK FROM RIGHT TO LEFT) Last digit is the units digit The next digit is the sum of the tens and the units digits The next digit is the sum of the units, tens and the hundreds digit + carry The next digit is the sum of the tens and hundreds digits + carry The next digit is the hundreds digit + carry 1+1 1+9+1 1+9+2+1 9+2 2 = 21312

28. 1221 Pattern Multiplying A 2-Digit # By 11141 x 111 (ALWAYS WORK FROM RIGHT TO LEFT) Last digit is the units digit The next digit is the sum of the tens and the units digits The next digit is the sum of the tens and the units digits + carry The next digit is the tens digit + carry 4 4+1 4+1 1 = 4551

29. Multiplying A 2-Digit # By 10193 x 101 The first two digits are the 2-digit number x1 The last two digits are the 2-digit number x1 93(1) 93(1) = 9393

30. Multiplying A 3-Digit # By 101934 x 101 The last two digits are the last two digits of the 3-digit number The first three numbers are the 3-digit number plus the hundreds digit 934+9 34 = 94334

31. Multiplying A 2-Digit # By 100187 x 1001 The first 2 digits are the 2-digit number x 1 The middle digit is always 0 The last two digits are the 2-digit number x 1 87(1) 0 87(1) = 87087

32. Halving And Doubling52 x 13 Take half of one number Double the other number Multiply together 52/2 13(2) = 26(26)= 676

33. One Number in the Hundreds And One Number In The 90’s95 x 108 Find how far each number is from 100 The last two numbers are the product of the differences subtracted from 100 The first numbers = the small number difference from 100 increased by 1 and subtracted from the larger number 108-(5+8+1) 100-(5x8) = 9460

34. Fraction Foil (Type 1)8 ½ x 6 ¼ Multiply the fractions together Multiply the outside two number Multiply the inside two numbers Add the results and then add to the product of the whole numbers (8)(6)+1/2(6)+1/4(8) (1/2x1/4) = 531/8

35. Fraction Foil (Type 2)7 ½ x 5 ½ Multiply the fractions together Add the whole numbers and divide by the denominator Multiply the whole numbers and add to previous step (7x5)+6 (1/2x1/2) = 411/4

36. Fraction Foil (Type 3)7 ¼ x 7 ¾ Multiply the fractions together Multiply the whole number by one more than the whole number (7)(7+1) (1/4x3/4) = 563/16

37. (8-7)2 2 7x8 =21/56 Adding Reciprocals7/8 + 8/7 Keep the denominator The numerator is the difference of the two numbers squared The whole number is always two plus any carry from the fraction.

38. Percent Missing the Of36 is 9% of __ Divide the first number by the percent number Add 2 zeros or move the decimal two places to the right 36/9 00 = 400

39. Base N to Base 10 Of426 =____10 Multiply the left digit times the base Add the number in the units column 4(6)+2 = 2610

40. Multiplying in Bases4 x 536=___6 Multiply the units digit by the multiplier If number cannot be written in base n subtract base n until the digit can be written Continue until you have the answer = 4x3=12subtract 12Write 0 = 4x5=20+2=22subtract 18Write 4 = Write 3 = 3406

41. N/40 to a % or Decimal21/40___decimal Mentally take off the zero Divide the numerator by the denominator and write down the digit Put the remainder over the 4 and write the decimal without the decimal point Put the decimal point in front of the numbers . 5 25 21/4 1/4

42. Remainder When Dividing By 9867/9=___remainder Add the digits until you get a single digit Write the remainder 8+6+7=21=2+1=3 = 3

43. 421 Method Base 8 to Base 27328 =____2 Mentally put 421 over each number Figure out how each base number can be written with a 4, 2 and 1 Write the three digit number down 421 421 421 7 3 2 111 011 010

44. 421 Method Base 2 to Base 8 Of1110110102 =___8 Separate the number into groups of 3 from the right. Mentally put 421 over each group Add the digits together and write the sum 421 421 421 011 010 111 7 3 2

45. Cubic Feet to Cubic Yards3ftx 6ftx 12ft=__yds3 Try to eliminate three 3s by division Multiply out the remaining numbers Place them over any remaining 3s 3 6 12 3 3 3 1 x 2 x 4 = 4 Cubic yards

46. Cubic Feet to Cubic Yards44 ft/sec __mph Use 15 mph = 22 ft/sec Find the correct multiple Multiply the other number 22x2=44 15x2=30 mph Cubic yards

47. 25=32 subsets Subset Problems{F,R,O,N,T}=______ SUBSETS Subsets=2n Improper subsets always = 1 Proper subsets = 2n - 1 Power sets = subsets

48. ___ Repeating Decimals to Fractions.18=___fraction The numerator is the number Read the number backwards. If a number has a line over it then there is a 9 in the denominator Write the fraction and reduce 18 2 = 99 11

49. _ Repeating Decimals to Fractions.18=___fraction The numerator is the number minus the part that does not repeat For the denominator read the number backwards. If it has a line over it, it is a 9. if not it is a o. 18-1 17 = 90 90

50. Gallons Cubic Inches2 gallons=__in3 (Factors of 231 are 3, 7, 11) Use the fact: 1 gal= 231 in3 Find the multiple or the factor and adjust the other number. (This is a direct variation) 2(231)= 462 in3