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Mental Math in Math Essentials 11 by nye15450

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									  Mental Math
       in
Math Essentials 11

Implementation Workshop
   November 30, 2006
 David McKillop, Presenter
Mental Math Outcomes
 B1 Know the multiplication and
  division facts
 B2 Extend multiplication and division
  facts to products of tens, hundreds,
  and thousands by single-digit factors
 B3 Estimate sums and differences

 B4 Estimate products and quotients
Mental Math Outcomes
   B5 Mentally calculate 25%, 33⅓%, and
    66⅔% of quantities compatible with these
    percents
   B6 Estimate percents of quantities
    Why should students
    learn number facts?
 They are the basis of all mental math
  strategies, and mental math is the
  most widely used form of computation
  in everyday life
 Knowing facts is empowering
 Facilitates the development of other
  math concepts
  How is fact learning
  different from when I
      learned facts?
1. Facts are clustered in groups that can be
   retrieved by the same strategy.

2. Students can remember 6 to 8 strategies
   rather than 100 discrete facts.

3. Students achieve mastery of a group of
   facts employing one strategy before
   moving on to another group.
       General Approach
   Introduce a strategy using association,
    patterning, contexts, concrete materials,
    pictures – whatever it takes so students
    understand the logic of the strategy
   Practice the facts that relate to this strategy,
    reducing wait time until a time of 3 seconds,
    or less, is achieved. Constantly discuss
    answers and strategies.
   Integrate these facts with others learned by
    other strategies.
   IT WILL TAKE TIME!
          Facts with 2s:
          2 x ? and ? X 2
 Strategy: Connect to Doubles in
  Addition (Math Essentials 10)
 Start with 2 x ?




   Relate ? X 2 to 2 x ?
    Practice the Facts
 Webs
 Dice games

 Card games

 Flash cards
          Facts with 9s:
          ? X 9 and 9 x ?
   Nifty Nines               9 x 9 = 81
    Strategy: Two             8 x 9 = 72
    Patterns -Decade of       7 x 9 = 63
    answer is one less
    than the number of        6 x 9 = 54
    9s and the two            5 x 9 = 45
    digits of the answer      4 x 9 = 36
    sum to 9                  3 x 9 = 27
Practice the Facts
            Calculator
    Extend Nifty Nines
To 10s, 100s, 1000s   To estimating
 4 x 90               6.9 x $9

 9 x 60               9 x $4.97

 5 x 900              3.1 x $8.92

 9 x 700              7 x $91.25

 6 x 9 000            9 x $199

 9 x 3 000            4 x $889

                       8.9 x $898.50
    Extend Nifty Nines
To division:
 36 ÷ 9

 54 ÷ 9

 63 ÷ 9

 27 ÷ 3

 81 ÷ 9

 45 ÷ 5
            Facts with 5s
   The Clock
    Strategy: The
    number of 5s is like
    the minute hand on
    the clock – it points
    to the answer. For
    example, for 4 x 5,
    the minute hand on
    4 means 20
    minutes; therefore,
    4 x 5 = 20.
       Practice Strategy
           Selection
   Which facts can          3x5
    use The Clock            5x9
    Strategy?                8x2
   Which facts can          9x7
    use the Nifty Nines
    Strategy?                9x2
   Which facts can          2x5
    use the Doubles          7x5
    Strategy?                6x9
   Extend Clock Facts
To 10s, 100s, 1000s   To estimating
 5 x 80               4.9 x $5

 7 x 50               3 x $4.97

 5 x 400              3.89 x $50

 6 x 500              5 x $61.25

 9 x 5 000            7 x $499

 5 x 3 000            5 x $399

                       4.9 x $702.50
   Extend Clock Facts
To division:
 25 ÷ 5

 45 ÷ 5

 30 ÷ 5

 20 ÷ 4

 15 ÷ 3

 35 ÷ 5
            Facts with 0s
   The Tricky Zeros:          If you have 6 plates
    All facts with a zero       with 0 cookies on
    factor have a zero          each plate, how
    product.                    many cookies do
                                you have?
(Often confused with
  addition facts with
  0s)
           Facts with 1s
   The No Change             If you have 3 plates
    Facts: Facts with 1        with 1 cookie on each
                               plate OR 1 plate with 3
    as a factor have a
                               cookies on it, you have
    product equal to the       3 cookies.
    other factor.
            Facts with 3s
   The Double and
    One More Set
    Strategy. For
    example, for 3 x 6,
    think: 2 x 6 is 12
    plus one more 6 is
    18.
  Extend Threes Facts
To 10s, 100s, 1000s   To estimating
 5 x 80               4.9 x $5

 7 x 50               3 x $4.97

 5 x 400              3.89 x $50

 6 x 500              5 x $61.25

 9 x 5 000            7 x $499

 5 x 3 000            5 x $399

                       4.9 x $702.50
  Extend Threes Facts
To division:
 18 ÷ 3

 15 ÷ 3

 12 ÷ 3

 9 ÷ 3

 21 ÷ 3

 18 ÷ 6
            Facts with 4s
   The Double-
    Double Strategy.
    For example, for
    4 x 6, think: double
    6 is 12 and double
    12 is 24.
   Extend Fours Facts
To 10s, 100s, 1000s   To estimating
 4 x 40               3.9 x $4

 7 x 40               6 x $3.97

 8 x 400              3.89 x $80

 4 x 600              4 x $41.25

 8 x 4 000            7 x $399

 4 x 6 000            4 x $599

                       5.9 x $402.50
    Extend Fours Facts
To division:
 16 ÷ 4

 28 ÷ 4

 20 ÷ 4

 32 ÷ 4

 12 ÷ 4

 28 ÷ 7
     The Last Nine Facts
                         Using helping facts:
                          6x6=5x6+6
   6x6
                          7x6=5x6+2x6
   6 x 7 and 7 x 6
                          6x8=5x8+8
   6 x 8 and 8 x 6
                          7x8=5x8+2x8
   7x7
                          8x8=4x8x2
   7 x 8 and 8 x 7
                      •   Some know 8 x 8 is 64
   8x8                   because of a chess
                          board
                      •   What about 7 x 7?
   Extend Last 9 Facts
To 10s, 100s, 1000s   To estimating
 6 x 60               6.8 x $7

 7 x 80               6 x $5.97

 6 x 700              7.89 x $80

 7 x 700              7 x $61.25

 8 x 8 000            6 x $799

 4 x 6 000            8 x $699

                       5.9 x $702.50
   Extend Last 9 Facts
To division:
 36 ÷ 6

 42 ÷ 7

 64 ÷ 8

 49 ÷ 7

 56 ÷ 8

 42 ÷ 6
    Practice the Facts
 Flash cards
 Bingo

 Dice Games

 Card Games

 Fact Bee

 Calculators
    B3 Estimate sums and
         differences
 Using a front-end estimation strategy
 prior to using a calculator would
 enable students to get a “ball-park”
 solutions so they can be alert to the
 reasonableness of the calculator
 solutions.
Example: $42 678 + $35 987 would
 have a “ball-park” estimate of $40 000
 + $30 000 or $70 000.
    B3 Estimate sums and
         differences
 In other situations, especially where
 exact answers will not be found,
 rounding to the highest place value
 and combining those rounded values
 would produce a good estimate.
Example: $42 678 + $35 987 would be
 rounded to $40 000 + $40 000 to get
 an estimate of $80 000.
    About how many people live
    in the Maritime provinces?
    In the Atlantic provinces?
    About how many more
    people live in Nova than in
    New Brunswick?

Nova Scotia            936 760
Prince Edward Island   137 810
Saskatchewan           994 950
Newfoundland           520 340
New Brunswick          749 980
             Percents
 B5 Mentally calculate 25%, 33 ⅓%,
  and 66 2/3% of quantities compatible
  with these percents
 B6 Estimate percents of quantities
Visualization of
    Percent
           Find 3% of $800.

           Think: If $800 is
            distributed evenly in
            these 100 cells,
            each cell would
            have $8 – this is
            1%. Therefore,
            there is 3 x $8 or
            $24 in 3 cells (3%).
Visualization of 25
     Percent
             Find 25% of $800.

             Think: If $800 is
              distributed evenly in
              these 4 quadrants,
              each quadrant
              would have $800 ÷
              4 or $200.
              Therefore, 25% of
              $800 is $200.
Estmating Percent
         Estimate:
          25% of $35

          25% of $597

          26% of $48

          24% of $439

          26% of $118

          25% of $4378
Visualization of 33⅓%
       Percent
           Find 33⅓% of $69.
            Think: $69 shared
             among three equal
             parts would be
             $69 ÷ 3 or $23.
             Therefore, 33⅓% of
             $69 is $23.
Visualization of
    Percent
        Find 33⅓% of:
         $96

         $45

         $120

         $339

         $930

         $6309
Estimating Percent
         Estimate:
          33⅓% of $67

          33⅓% of $91

          33% of $180

          34% of $629

          32% of $1199

          33⅓% of $8999
Visualization of 66⅔
      Percent
          Find 66⅔% of $36.

          Think: $36 divided by
            3 is $12, so each
            one-third is $12,
            Therefore, 2-thirds
            is $24, so 66⅔% of
            $36 is $24.
Visualization of 66⅔
      Percent
          Find 66⅔% of:
           $24

           $60

           $120

           $360

           $660
Estimating Percent
         Estimate:
          67% of $27

          65% of $90

          68% of $116

          65% of $326

          67% of $894
      Parting words…
 It will take time.
 Build on successes.

 Always discuss strategies.

 Use mental math/estimation during all
  classes whenever you can.
 Model estimation before every
  calculation you make!

								
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