Mental Math in Math Essentials 11

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Mental Math in Math Essentials 11

• Implementation Workshop
• November 30, 2006
• David McKillop, Presenter

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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

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Mental Math Outcomes

• B5 Mentally calculate 25, 33?, and 66? of
  quantities compatible with these percents
• B6 Estimate percents of quantities

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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

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How is fact learning different from when I
learned facts?

• 1. Facts are clustered in groups that can be
  retrieved by the same strategy.
• 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.

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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!

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Facts with 2s2 x ? and ? X 2

• Strategy Connect to Doubles in Addition (Math
  Essentials 10)
• Start with 2 x ?
• Relate ? X 2 to 2 x ?

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17 facts
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Practice the Facts

• Webs
• Dice games
• Card games
• Flash cards

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Facts with 9s? X 9 and 9 x ?

• Nifty Nines Strategy Two Patterns -Decade of
  answer is one less than the number of 9s and the
  two digits of the answer sum to 9

• 9 x 9 81
• 8 x 9 72
• 7 x 9 63
• 6 x 9 54
• 5 x 9 45
• 4 x 9 36
• 3 x 9 27

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13 facts
30 Total
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Practice the Facts

• Calculator

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Extend Nifty Nines

• To 10s, 100s, 1000s
• 4 x 90
• 9 x 60
• 5 x 900
• 9 x 700
• 6 x 9 000
• 9 x 3 000

• To estimating
• 6.9 x 9
• 9 x 4.97
• 3.1 x 8.92
• 7 x 91.25
• 9 x 199
• 4 x 889
• 8.9 x 898.50

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Extend Nifty Nines

• To division
• 36 9
• 54 9
• 63 9
• 27 3
• 81 9
• 45 5

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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.

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13 new facts
43 Total
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Practice Strategy Selection

• Which facts can use The Clock Strategy?
• Which facts can use the Nifty Nines Strategy?
• Which facts can use the Doubles Strategy?

• 3 x 5
• 5 x 9
• 8 x 2
• 9 x 7
• 9 x 2
• 2 x 5
• 7 x 5
• 6 x 9

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Extend Clock Facts

• To 10s, 100s, 1000s
• 5 x 80
• 7 x 50
• 5 x 400
• 6 x 500
• 9 x 5 000
• 5 x 3 000

• To estimating
• 4.9 x 5
• 3 x 4.97
• 3.89 x 50
• 5 x 61.25
• 7 x 499
• 5 x 399
• 4.9 x 702.50

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Extend Clock Facts

• To division
• 25 5
• 45 5
• 30 5
• 20 4
• 15 3
• 35 5

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Facts with 0s

• The Tricky Zeros All facts with a zero factor
  have a zero product.
• (Often confused with addition facts with 0s)

• If you have 6 plates with 0 cookies on each
  plate, how many cookies do you have?

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19 facts
62 Total
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Facts with 1s

• The No Change Facts Facts with 1 as a factor
  have a product equal to the other factor.

• If you have 3 plates with 1 cookie on each plate
  OR 1 plate with 3 cookies on it, you have 3
  cookies.

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13 new facts
75 Total
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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.

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9 new facts
84 Total
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Extend Threes Facts

• To 10s, 100s, 1000s
• 5 x 80
• 7 x 50
• 5 x 400
• 6 x 500
• 9 x 5 000
• 5 x 3 000

• To estimating
• 4.9 x 5
• 3 x 4.97
• 3.89 x 50
• 5 x 61.25
• 7 x 499
• 5 x 399
• 4.9 x 702.50

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Extend Threes Facts

• To division
• 18 3
• 15 3
• 12 3
• 9 3
• 21 3
• 18 6

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Facts with 4s

• The Double-Double Strategy.
• For example, for 4 x 6, think double 6 is
  12 and double 12 is 24.

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7 facts
91 Total
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Extend Fours Facts

• To 10s, 100s, 1000s
• 4 x 40
• 7 x 40
• 8 x 400
• 4 x 600
• 8 x 4 000
• 4 x 6 000

• To estimating
• 3.9 x 4
• 6 x 3.97
• 3.89 x 80
• 4 x 41.25
• 7 x 399
• 4 x 599
• 5.9 x 402.50

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Extend Fours Facts

• To division
• 16 4
• 28 4
• 20 4
• 32 4
• 12 4
• 28 7

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The Last Nine Facts

• Using helping facts
• 6 x 6 5 x 6 6
• 7 x 6 5 x 6 2 x 6
• 6 x 8 5 x 8 8
• 7 x 8 5 x 8 2 x 8
• 8 x 8 4 x 8 x 2
• Some know 8 x 8 is 64 because of a chess board
• What about 7 x 7?

• 6 x 6
• 6 x 7 and 7 x 6
• 6 x 8 and 8 x 6
• 7 x 7
• 7 x 8 and 8 x 7
• 8 x 8

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The 100 Facts
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Extend Last 9 Facts

• To 10s, 100s, 1000s
• 6 x 60
• 7 x 80
• 6 x 700
• 7 x 700
• 8 x 8 000
• 4 x 6 000

• To estimating
• 6.8 x 7
• 6 x 5.97
• 7.89 x 80
• 7 x 61.25
• 6 x 799
• 8 x 699
• 5.9 x 702.50

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Extend Last 9 Facts

• To division
• 36 6
• 42 7
• 64 8
• 49 7
• 56 8
• 42 6

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Practice the Facts

• Flash cards
• Bingo
• Dice Games
• Card Games
• Fact Bee
• Calculators

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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.

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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.

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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
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Percents

• B5 Mentally calculate 25, 33 ?, and 66 2/3 of
  quantities compatible with these percents
• B6 Estimate percents of quantities

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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).

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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.

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Estmating Percent

• Estimate
• 25 of 35
• 25 of 597
• 26 of 48
• 24 of 439
• 26 of 118
• 25 of 4378

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Visualization of 33? Percent

• Find 33? of 69.
• Think 69 shared among three equal parts would
  be 69 3 or 23. Therefore, 33? of 69 is
  23.

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Visualization of Percent

• Find 33? of
• 96
• 45
• 120
• 339
• 930
• 6309

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Estimating Percent

• Estimate
• 33? of 67
• 33? of 91
• 33 of 180
• 34 of 629
• 32 of 1199
• 33? of 8999

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Visualization of 66? Percent

• Find 66? of 36.
• Think 36 divided by 3 is 12, so each one-third
  is 12, Therefore, 2-thirds is 24, so 66? of
  36 is 24.

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Visualization of 66? Percent

• Find 66? of
• 24
• 60
• 120
• 360
• 660

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Estimating Percent

• Estimate
• 67 of 27
• 65 of 90
• 68 of 116
• 65 of 326
• 67 of 894

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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!