Transcript 4.2 Written Algorithms For Whole

4.2 Written Algorithms For WholeNumber Operations
Algorithms for Multiplying Whole-Numbers
An Overview of the Topics
 Define what an algorithm is.
 Discuss the importance of place value and distributivity in whole number operations.
 Explain the main algorithms for multiplying whole-numbers.
 Explain the differences between the various algorithms.
 View a problem a student has with using a multiplicative algorithm.
 Practice using these algorithms through class activities.
 Handout out worksheets and handouts for you to refer back on.
 Discuss your questions.
What is an algorithm anyway?
 An algorithm is simply the step-by-step procedure you use to find an answer.
 Here is an analogy. Suppose you need to brush your teeth. What are the steps
you take and what order do you take them in?
 Do you open the bathroom door? Do you open a drawer to grab your
toothbrush? Do you squeeze just a little of the toothpaste on your brush?
 What order do you take those steps in?
 It is just like a staircase.You take your first step to reach your second step until
you have reached the top. At the top, you will find your answer.
Place Value and Distributivity
 When you multiply 10 by 16, when do you use place value? When
do you use distributivity?
 If we separate the 16 into its separate place values, we have the
following:
 10 + 6 = 16
 Now we can bring back the original 10 from our problem.
 10(10) + 10(6) =
 Then if we distribute the 10, we have the following:
 100 + 60 = 160
Algorithms For Multiplying Whole
Numbers
 There are 2 main algorithm for multiplying whole numbers:
 The standard algorithm.
 The lattice algorithm.
 The standard algorithm takes the sets of numbers you are
multiplying and places one under the other. Then, you
multiply each digit in the bottom set by each digit in the top
set.
Examples Using The Standard
Algorithm
 Multiply 2 by 517. If we use the standard algorithm, we get
the following. Keep in mind the importance of place value.
1
517
x 2
14
20
+ 1000
1034
is the same as
517
x 2
1034
The Lattice Algorithm
 The lattice algorithm uses lattice figures to multiply whole-
numbers.
 The basic idea of using the lattice algorithm is finding the
products in the intersecting rows and columns.You separate
each digit in the answer by placing the ten’s digit in the top
left triangle and the ones digit in the bottom left triangle. If
there is a hundreds digit in your answer or any other place
value, you carry it over to the next column to the left, as if
you were adding. Then, you just add the numbers diagonally.
Examples Using The Lattice Algorithm
 Multiply 52 by 673. Use the lattice provided to complete this
problem.

6
7
3
3 3
1
5
0 5 5
1 1
0
2
2 4
6
Now, add the diagonals.
6
9
9
4
3
=
3
4
9
9
6
=
34,996
The Differences Between the Standard
Algorithm and the Lattice Algorithm
Standard Algorithm
 Uses multiples of ten to
obtain answer by use of
placing zeros.
Lattice Algorithm
 Uses lattice to place digits in
the appropriate place value.
 Is more time consuming
 Is quicker when writing
down the problem.
because lattice is not usually
available for each problem.
Place Value Is A Problem
 For my research, I
interviewed a 5th grade
student. After completing
some worksheets asking him
to use the different
algorithms, I found that he
missed some problems.
 The majority of the problems
he missed revolved around
place value.
 He tried the following
problem and solved it the
following way:
His Way:
Correct:
3
462
x105
2307
0000
+ 4620
6927

31
462
x 105
2310
0000
+ 46200
48510
Now It’s Your Turn
 Complete problem #3 from
your handout using the standard
algorithm. Then, as a class we
will complete it together.
3
3
25
x 67
175
+ 1500
1675

 Is the answer
A. 1500
B. 4670
C. 0
D. 1675
More Practice Using Algorithms
 Please use your handout to
complete problem number 4.
485
x 398
3880
43650
+ 145500
193030
 Is the answer:
A. 193030

B. 359490
C. 493990
D. 5895
Are There Any Questions?