Download Section 3.4

Section 3.4
Algorithms for Multiplication and Division
Mathematics for Elementary School Teachers - 4th Edition
O’DAFFER, CHARLES, COONEY, DOSSEY, SCHIELACK
Linda Roper
9 x 12 = ?
•
How does a child who does not know
the multiplication fact 9 x 12, but knows
some other facts, figure out the answer?
Developing Algorithms for Multiplication:
Using Paper-and-Pencil
Developing Algorithms for Multiplication:
Using the Area Model
 Factors are the length and width of the
rectangle.
 The product is the area of the rectangle,
possibly found using partial products.

Example: 13 × 24 = 312
13 x 24
x
13
24
x
13
24
x
13
24
x
13
24
10 x 20
10 x 4
3 x 20
3x4
24
x 13
12
60
40
200
312
3x4
3 x 20
10 x 4
10 x 20
Add the partial products
Developing Algorithms for Multiplication:
Using Paper-and-Pencil
2. 15 x 21
Use the area model to solve the
multiplication problem.
Example: 6 × 345
 Expanded algorithm:
 Standard algorithm:
Other Ways to Multiply
 A spreadsheet is a powerful way to find the
product of a large set of numbers and a single
factor.
 Lattice multiplication is an algorithm that
reduces multidigit calculations to a series of
basic multiplication facts followed by a series
of simple sums.


The diagonals correspond to place values.
Partial products are found using the distributive
property.
Example
Use lattice multiplication to find 247 × 681.
Read the final product from the top down and to the right: 168,207.
Developing Algorithms for Division:
Using Paper-and-Pencil
 The expanded algorithm for division features
repeated subtraction to find the quotient,
which is simple to use but can be quite
inefficient.
 The standard algorithm for division has
several steps and is based on the sharing
interpretation of division.
Developing Algorithms for Division:
Using Paper-and-Pencil
Developing Algorithms for Division:
Using Models as a Foundation
 Use base-ten blocks to model the sharing interpretation for division:
105 ÷ 15
 Trade 1 hundred for 10 tens, then trade 10 tens for 100 ones.
 There are 105 ones, which we can divide into 15 equal groups. Seven
ones can go into each of the groups, so 105 ÷ 15 = 7.
Standard Algorithm for Division
Step 1: Set up the problem
 Model
 Algorithm
Standard Algorithm for Division
Step 2: Decide where to start
 Model
 Algorithm
Standard Algorithm for Division
Step 3: Divide the hundreds
 Model
 Algorithm
Standard Algorithm for Division
Step 4: Divide the tens
 Model
 Algorithm
Standard Algorithm for Division
Step 5: Divide the ones
 Model
 Algorithm
312 ÷ 2
312 ÷ 2
312 ÷ 2
312 ÷ 2
312 ÷ 2
312 ÷ 2
312 ÷ 2
312 ÷ 2
312 ÷ 2 = 156
The End
Section 3.4
Linda Roper