# Everyday Math and Algorithms

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```					Getting to Know Everyday Mathematics
Andy Barlow
Chrissy Thonet
Math Specialists
Jenkins School
Everyday Math
and
Algorithms

Taking a journey
in completing the
Focus Algorithms
Did You Know?
   40% of adults hated math in school

   84% of middle schoolers would
rather do “anything” other than math
homework
Everyday Mathematics in the
Classroom
   Developed by the University of Chicago
School Mathematics Project

   Based on research about how children
learn and develop mathematical power

background needed in the 21st century
Everyday Math Lesson
1.Getting Started-Mental Math, Math Message

2. Introduce Content

3.Ongoing Learning & Practice

4. Differentiation Options
~Enrichment
~Extra Practice
What are the main messages of

Everyday Mathematics
regarding computation?
Everyday Mathematics
takes a moderate position,
combining elements from both the

child-centered,
invented-algorithm approach

and the
During the early phases
of learning an operation,
Everyday Mathematics
encourages students to
invent their own procedures.

Students are asked to solve problems
in real-life contexts
before they learn systematic procedures
for solving such problems.
After students have had plenty of
opportunities to experiment with
computational strategies of their own,
EDM introduces several algorithms for
each operation.

EDM also designates one of the
alternative algorithms as the
Focus Algorithm.
Important Qualities of Algorithms
An algorithm consists of a precisely specified sequence of
steps that lead to a complete solution for a certain class of
problems.
Accuracy
• Does it always lead to a right answer if you do
it right?
Efficiency
• Does the student get bogged down with many
steps or lose track of logic?
Flexibility
• Is the student able to choose an appropriate
strategy for the problem? Can the student use
one method to solve and another to check?
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
Focus Algorithms
+ Partial Sums
x Partial Products
÷ Partial Quotients

Partial Differences
Lattice Multiplication
Partial Sums
Algorithm
268
+ 483
Add the hundreds (200 + 400)     600
Add the tens (60 +80)            140
Add the ones (8 + 3)           + 11
(600 + 140 + 11)          751
785
+ 641
Add the hundreds (700 + 600)    1300
Add the tens (80 +40)            120
Add the ones (5 + 1)           +    6
(1300 + 120 + 6)         1426
329
+ 989
1200
100
+ 18
1318
The partial sums algorithm for addition is particularly
useful for adding multi-digit numbers. The partial
sums are easier numbers to work with, and students
feel empowered when they discover that, with
practice, they can use this algorithm to add number
mentally.
An alternative subtraction
algorithm
12
12
2
In order to subtract, the top
number must be larger than                     9   3    2
the bottom number.
- 3     5    6
To make the top number in the ones
column larger than the bottom number
trade 1 ten for 10 ones. You now have 2
tens and 12 ones.
5   7    6
Move to the tens column. I cannot subtract 5
from 2. To make the top number in the tens
column larger than the bottom number, trade
1 hundred for 10 tens. You now have 8
hundreds and 12 tens.

Now subtract column by column in any order
Let’s try another one                              11
6   12   15
together.
7   2    5
This time we will trade from left to
right.                                       - 4   9    8
Move to the tens column. I cannot subtract 9
from 2. To make the top number in the tens     2   2    7
column larger than the bottom number, trade
1 hundred for 10 tens. You now have 6
hundreds and 12 tens.

Move to the ones column. To make the top
number in the ones column larger than the
bottom number trade 1 ten for 10 ones. You
now have 11 tens and 15 ones.

Now subtract column by column in any order
13
8    14   12
Now, do this one on
- 2   8    7
6    5    5
Be careful! It’s tricky!          9
6    10   13
Watch out for the O!        7    0    3
- 4   6    9
2    3    4
Partial Differences
736
– 245
Subtract the hundreds
(700 – 200)      500
Subtract the tens                 10
1
(30 – 40)
Subtract the ones
(6 – 5)

(500 + (-10) + 1)     491
Try Another One
412
– 335
Subtract the hundreds
(400 – 300)        100
Subtract the tens                   20
-3
(10 – 30)
Subtract the ones
(2 – 5)

(100 + (-20) + (-3))      77
Partial Products Algorithm
for Multiplication
Focus Algorithm
Partial Products
To find 24 x 13, think of 24 as 20 + 4
and 13 as 10 + 3. Then multiply each
part of one sum by each part of the           Build an array
showing
24                                    24 x 13 !
x 13                                       20            4

12           3x4
60           3 x 20              10
200       40

40           10 x 4
+200
____           10 x 20             3        60       12

312
To find 67 x 53, think of 67 as 60 + 7
and 53 as 50 + 3. Then multiply each
part of one sum by each part of the
other, and add the results                 67
X 53
Calculate 50 X 60
3,000
Calculate 50 X 7
350
Calculate 3 X 60
180
Calculate 3 X 7
+ 21
3,551
Let’s try another
one.                   14
X 23
Calculate 10 X 20    200
Calculate 20 X 4       80
Calculate 3 X 10       30
Calculate 3 X 4
+ 12
322
Do this one on
Let’s see if
you’re right.        X 79
Calculate 30 X 70   2,100
Calculate 70 X 8      560
Calculate 9 X 30      270
Calculate 9 X 8
+ 72
Partial        Standard
Products        Algorithm
21              21
X 23           X 23
3 3x1
60 3 x 20      63
20 20 x 1
420
+____
___ 20 x 20
+400
483             483
1. Create a grid. Write one
factor along the top, one
digit per cell.
Write the other factor
along the outer right side,
one digit per cell.

2. Draw diagonals
across the cells.             0       2       1
3.Multiply each digit
in the top factor by
each digit in the side
6       4       8
factor. Record each
cell, placing the tens
digit in the upper half       0       3       2
of the cell and the
ones digit in the
bottom half of the                8       2       4
cell.

diagonal and record
any regroupings in the
next diagonal
0       2       1
6       4       8
0       3       2
8       2       4
3       1       1
5       5       0

4       2       1
9       1       4
The lattice algorithm for multiplication has been traced to
India, where it was in use before A.D.1100.
Many Everyday Mathematics students find this particular
multiplication algorithm to be one of their favorites. It
helps them keep track of all the partial products without
having to write extra zeros – and it helps them practice
their multiplication facts
Partial Quotients
A Division Algorithm
The Partial Quotients Algorithm uses a series of “at least,
but less than” estimates of how many b’s in a. You might
begin with multiples of 10 – they’re easiest.

There are at least ten 12’s in
158 (10 x 12=120), but fewer                12       158
than twenty. (20 x 12 = 240)                               10 – 1st guess
Subtract - 120
There are more than three                             38
(3 x 12 = 36), but fewer than                               3 – 2nd guess
four (4 x 12 = 48). Record 3 as           Subtract - 36
the next guess

2     13
Since 2 is less than 12, you can stop
estimating. The final result is the sum
Sum of guesses
of the guesses (10 + 3 = 13) plus what
is left over (remainder of 2 )
Let’s try another one

36       7,891
Subtract - 3,600    100 – 1st guess
4,291
Subtract - 3,600    100 – 2nd guess
691
- 360    10 – 3rd guess
331
- 324    9 – 4th guess

7      219 R7
Sum of guesses
Now do this one on your
own.
43         8,572
Subtract    - 4,300    100 – 1st guess
4272
Subtract     -3870    90 – 2nd guess
402
- 301    7 – 3rd guess
101
- 86      2 – 4th guess
199 R 15
15
Sum of guesses
Everyday Mathematics Games

•Provide frequent practice

•Fun and flexible

•Played regularly
Name That Number!

Target Number

8 x 2 = 16
Possible
Solutions     10 + 8 – 2 = 16
Include…

7 x 2 + 10 – 8 = 16
8 / 2 + 10 + 7 – 5 = 16
Math Projects and Math Word Wall
Set of Data…………… Minimum &Maximum
Range
Mode   Median
Graphing the Data
Parental Involvement
Classroom Volunteering
•

Parent Letters
•

•

Play games at home
•

Practice fact triangle cards
•

•

Apply math practice to every day situations
•
Jenkins Math Website

http://www.scituate.k12.ma.us/schools-jenkins-
elementary-mathematics.htm

Study Island
http://www.studyisland.com

Symphony Math
http://symphonylearning.com/
Thank You for being here for your child!

Please email or call with questions!
abarlow@scit.org
cthonet@scit.org
781-545-4910 (Jenkins School)

Visit www.WrightGroup.com
Thanks
For joining us!

on the journey!

```
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