*Relearning to Teach Arithmetic, Susan Jo Russell. 1999.
Everett Public Schools, 2005
Powerful Procedures and Strategies for Multiplication–
Please note that students may use
larger numbers or chunks once they are more confident with their understanding with number.
Also, the recording of the numbers is to
explain
how they solved the problem and can look
tedious. Many of the steps can be done
mentally
with some keeping track on paper if necessary.
Multiplication by breaking numbers apart*
(using landmarks)
12 x 14
10 x 14 = 140
2 x 14 = 28
140 + 28 = 168
Multiplying each place, starting with the largest place*
(related to the traditional partial product algorithm)
29 x 4
29 x 12
20 x 4 = 80
20 x 12 = 240
9 x 4 = 36
9 x 12 = (9 x 10) + (9 x 2) = 90 + 18 = 108
80 + 36 = 116
240 + 108 = 348
Breaking up one of the numbers into parts that are easier to multiply*
(landmarks other than 10’s)
29 x 4
128 x 32
(25 x 4) + (4 x 4)
(125 x 32) + (3 x 32)
25 x 4 = 100
125 x 32 = (125 x 10) + (125 x 10) + (125 x 10) + (125 x 2)
4 x 4 = 16
= 1250 + 1250 + 1250 + 250 = 4000
100 + 16 = 116
3 x 32 = 96
96 + 4000 = 4096
Rounding the numbers up or down, then compensating*
29 x 12
32 x 96
29 x 12 = (30 x 12) – (1 x 12)
32 x 96 = (32 x 100) – (32 x 4)
30 x 12 = 360
= 3200 – 128 = 3072
360 – 12 = 348
It is important that students eventually learn to read all common notations, including both vertical and
horizontal notations for addition, subtraction, and multiplication, as well as the various notations for
division. However, they need to be secure enough to interpret these notations correctly while still relying
on their own mathematically sound procedures to solve problems notated in any of these ways.*
For example:
2 + 4 = 6
32 – 27 = 5
5 = 32 - 27
2
32
12
12 x 7 = 84
+4
- 27
x 7
6
5
84
6
24 ÷ 4 = 6
24/4 = 6
4)24
*Relearning to Teach Arithmetic, Susan Jo Russell. 1999.
Everett Public Schools, 2005
Area/Array Model
X 20
7
30 600 210
34 x 27 = (600
4
+ 200) + (80 + 10 + 28)
80
28
= 800 + 118
= 918
X
tens
ones
tens
ones