Fourth and Fifth Grade Strategies – *Multiplication and
Division Multi-Digit Problems
Strategies the students will be using will vary depending on the size of the number. The focus is on grouping
numbers and not counting by ones.
* Fourth grade students focus on continuing to become proficient in the basic multiplication/division
combinations and apply those strategies to more complex problems – many which can be done mentally.
They should have at least two efficient ways to solve multi-digit problems mentally or with some
recording for multiplication and division.
Multiplication:
Multiplication by breaking numbers apart
(using landmarks)
12 x 14
12 x 14
12
(another way to keep track)
10 x 14 = 140
10 x 10 = 100
x 14
2 x 14 = 28
2 x 10 = 20
100
140 + 28 = 168
4 x 10 = 40
20
2 x 4 =
8
40
= 168
8
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
Half and double
12 x 14
12 x 45 =
12 x 7 = 84
6 x 90 =
84 + 84 = 168
= 540
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
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.
Division:
Subtracting groups of the divisor
159 ÷ 13
159
29 OR Use the Big 7 method of recording (see below)
10 x 13 = 130 -130
-26
2 x 13 = 26
29
3
12 r3
Breaking the problem into parts
150 ÷ 48 = (50 ÷ 48) + (50 ÷ 48) + (50 ÷ 48) = 3 r 6
(There is one 48 with 2 left over in each 50)
OR
159/13
Break into 130 + 29, 130 divided by 13 is 10; 29 divided by 13 is 2 with 3 remaining
Transferring the problem into an equivalent problem that is easier to solve.
1400 ÷ 35 = 200 ÷ 5 (divide both numbers by 7)
928/16 = 464/8 = 232/4 = 116/2 = 58
Solving and easier related problem, then compensating
247 ÷ 13
Solve 260 ÷ 13 (There are 20 thirteens in 260, but 247 is 13 less than 260. So there are only 19 thirteens in 247)
Dealing out into groups*
159/13
Give 10 to each group; that uses up 130; 29 is left
Give 1 more to each group; that uses up 13; 16 is left
Give 1 more to each group; 3 is left.
The result is 12 in each group, remainder 3
Big 7
– (looks like a big 7) method of recording to keep track of repeated subtraction.
7 )293
-70
7 x 10
223
-140
7 x 20
83
-70
7 x 10
13
-7
7 x 1
6
41 R 6
Fourth Grade Computation Expectations:
At least two efficient strategies for multiplying and dividing multi-digit
numbers.
Fifth Grade Computation Expectations
are the same as fourth with continued practice and refinement of efficient
strategies.