# Everyday Math Algorithms by xiaoyounan

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```									    Computation
Algorithms

Everyday Mathematics
Computation Algorithms in
Everyday Mathematics
Instead of learning a prescribed (and limited)
set of algorithms, Everyday Mathematics encourages
students to be flexible in their thinking about
numbers and arithmetic. Students begin to realize
that problems can be solved in more than one way.
They also improve their understanding of place value
and sharpen their estimation and mental-
computation skills.
The following slides are offered as an
extension to the parent communication from your
child’s teacher. We encourage you to value the
thinking that is evident when children use such
algorithms—there really is more than one way to
solve a problem!
Before selecting an algorithm, consider
how you would solve the following
problem.
48 + 799
We are trying to develop flexible thinkers who recognize that
One way to approach it is to notice that 48 can be renamed
as 1 + 47 and then
48 + 799 = 47 + 1 + 799 = 47 + 800 = 847
An algorithm consists of a precisely specified sequence of steps
that will lead to a complete solution for a certain class of problems.

Important Qualities of Algorithms
• Accuracy
–    Does it always lead to a right answer if you do it right?
• Generality
–    For what kinds of numbers does this work? (The larger the set of
numbers the better.)
• Efficiency
–    How quick is it? Do students persist?
• Ease of correct use
–    Does it minimize errors?
• Transparency (versus opacity)
–    Can you SEE the mathematical ideas behind the algorithm?
Hyman Bass. “Computational Fluency, Algorithms, and Mathematical Proficiency: One
Mathematician’s Perspective.” Teaching Children Mathematics. February, 2003.
Partial Sums
Partial Products
Partial Differences
Partial Quotients
Lattice Multiplication
Click on the algorithm you’d like to see!
Click to proceed
speed!             735
+ 246
Add the hundreds (700 + 200)
900
Add the tens        (30 + 40)
70
Add the ones (5 + 6)
+11
(900 + 70 + 11)            981
356
+ 247
Add the hundreds (300 + 200)
500
Add the tens        (50 + 40)
90
Add the ones (6 + 7)              +13
(500 + 90 + 13)
603
429
+ 989
1300
100
+ 18
1418
Click to proceed
56
speed!
× 82
50 X 80                 4,000
50 X 2                    100
6 X 80                    480
6X2                   +   12
products                  4,592
How flexible is your
thinking? Did you notice
that we chose to multiply      52
in a different order this    × 76
time?
70 X 50                   3,500
70 X 2                      140
6 X 50                     300
6X2
+   12
products                    3,952
A Geometrical Representation
of Partial Products         52
(Area Model)

50   2
× 46
2,000
40              2000    80       300
80
6                 300   12        12
2,392
Students complete all regrouping
before doing the subtraction. This
11 13
can be done from left to right. In    6 12
this case, we need to regroup a
100 into 10 tens. The 7 hundreds is   72 3
45 9
now 6 hundreds and the 2 tens is
now 12 tens.

2 64
Next, we need to regroup a 10 into
10 ones. The 12 tens is now 11
tens and the 3 ones is now 13
ones.
Now, we complete the subtraction. We have 6
hundreds minus 4 hundreds, 11 tens minus 5 tens,
and 13 ones minus 9 ones.
9 12       13 16
7 10        8 14
80 2         94 6
27 4         56 8
5 28         3 78
73 6
– 2 45
Subtract the hundreds
(700 – 200)      500
Subtract the tens                  10
1
(30 – 40)
Subtract the ones
(6 – 5)

(500 + (-10) + 1)     491
41 2
– 3 35
Subtract the hundreds
(400 – 300)        100
Subtract the tens                           20
3
(10 – 30)
Subtract the ones
(2 – 5)

(100 + (-20) + (-3))       77
19 R3
I know
10 x 12 will
Click to proceed
speed!
12 2 31
work…

1 20 10
1 11
Students begin
quotients, and
by choosing
60 5
record the
partial quotients
quotient along
that they
51
with the
recognize!
remainder.
48 4
3 19
85 R6
32 27 26
1 6 0 0 50
Compare the    11 26
partial quotients
used here to the
80 0 25
ones that you     32 6
chose!
3 20 10
6 85
Click to proceed
53
5    3
speed!

× 72
3× 7 2 × 7 7         3500
3 55     3
1          Compare
100
1 × 2 0× 2 2
5    3                210
to partial
8 0         6                 6
products!
+
the
6
on the diagonals.
3816
16
1    6    × 23
0    1 2   200
2    2    30
0    1 3   120
3 3      8 + 18
6    8     368