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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
   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

   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
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
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
you have?
(Often confused 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
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.
in the Maritime provinces?
In the Atlantic provinces?
people live in Nova than in
New Brunswick?

Nova Scotia            936 760
Prince Edward Island   137 810
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
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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