Study Guide
Math Unit—Multiplication
Learning Targets
At the end of this unit—
1) I can understand models and patterns of multiplication so I can recall
multiplication facts.
2) I can create and use models—sets, number lines, and arrays—of
multiplication.
3) I can answer basic multiplication facts from the 2’s through the 12’s tables.
4) I can solve multiplication problems with one factor 99 or less and the second
factor 5 or less.
5) I can identify the identity and commutative properties in multiplication.
Vocabulary
factor—the numbers that are multiplied together
Example: In the equation 3 x 5 = 15, 3 and 5 are factors.
product—the answer when you multiply numbers
Example: In the equation 3 x 5 = 15, 15 is the product.
identity property—a number that is multiplied by 1 equals the same number
Example: 5 x 1 = 5
commutative property—factors can be multiplied in either order and the product
will be the same
Example: 2 x 6 = 12 and 6 x 2 = 12
fact family—collection of 4 related facts—2 multiplication and 2 division—using
the same numbers
Example:
2 x 7 = 14
7 x 2 = 14
14 ÷ 2 = 7
14 ÷ 7 = 2
Strategies for multiplying
Students need to be able to quickly recall the answer to basic multiplication facts.
In addition to rote practice, there are strategies and “tricks” that may help
students learn these facts.
array—an arrangement of objects or symbols in even rows and columns that show a
multiplication fact
Example: * * * * * *
******
******
******
There are 4 rows and 6 columns. It is a 4 by 6 array. This array shows the
multiplication fact 4 x 6 = 24.
skip counting—counting by a number other than 1
Example:
counting by 2’s—2 4 6 8 10 12 14 16 18 20
repeated addition—adding the same number repeatedly is the same as multiplying
Example: 3 + 3 + 3 + 3 = 12
3 x 4 = 12
Strategies by table
2’s tables:
1. Count by 2’s: 2 4 6 8 10 12 14 16 18 20
2. Use doubles facts in addition.
Example: 2 x 7 = _____ Find the answer to 7 + 7.
3’s tables:
1. Count by 3’s:
3
12
21
30
6
15
24
9
18
27
Try to remember the numbers in “chunks”:
Three 1-digit numbers: 3 6 9
Three numbers with 1 in the tens place: 12 15 18
Three numbers with 2 in the tens place: 21 24 27
2. Do the doubles addition fact (as you would for the 2s tables), then add that
number to it. Multiplying by 3 is doing a “triple”.
Example: To find 3 x 6, add 6 + 6, then add 6 to that
sum.
6 + 6 = 12, 12 + 6 = 18 or 6 + 6 + 6 = 18
3 x 6 = 18
4’s tables:
1. Use what you know about the 2’s tables, then double the answer.
Example:
4 x 7 = ________
Think “What is 2 x 7?”, then double that answer.
2 x 7 = 14, and 14 + 14 = 28, so 4 x 7 = 28.
2
x7
14
* * * *
* * *
* * * *
* * *
4
x7
28
* * * *
* * *
* * * *
* * *
* * * *
* * *
* * * *
* * *
5’s tables:
1. Count by 5’s: 5 10 15 20 25 30 35 40 45 50
2. The pattern in the ones place is 0 5 0 5 0 5.
3. When you multiply an even number by 5, the product is an even number (a
product that ends with 0).
Example: 4 x 5 = 20
4. When you multiply an odd number by 5, the product is an odd number (a
product that ends with 5).
Example: 7 x 5 = 35
6’s tables:
1. If you have already learned the 2’s, 3’s, 4’s, and 5’s tables, these are the only
facts you still need to learn:
6x6
6x7
6x8
6 x 9 (use the nines trick)
Use what you know about the 3’s tables, then double the answer.
Example:
6 x 7 = _______
Think “What is 3 x 7?”, then double that answer.
3 x 7 = 21, and 21 + 21 = 42, so 6 x 7 = 42.
3
x7
21
* * * *
* * *
* * * *
* * *
* * * *
* * *
6
x7
42
* * * *
* * *
* * * *
* * *
* * * *
* * *
* * * *
* * *
* * * *
* * *
* * * *
* * *
2. Remember that if you multiply 6 times an even number, the product ends with
that digit.
Examples: 6 x 4 = 24
6 x 8 = 48
7’s and 8’s tables:
1. If you learned the other multiplication tables, you learned all of the 7’s and 8’s
facts except:
7 x 7 = 49
7 x 8 = 56
8 x 8 = 64
Students need to practice these three facts until they have them memorized.
9’s tables:
1. When you multiply a number times 9:
-The tens digit is one less than the original number.
Examples: 9 x 4 = 36
9 x 7 = 63
-The tens digit plus the ones digit equals nine.
Examples: 9 x 6—the tens digit = 5
5+4= 9
9 x 6 = 54
The sum of the tens and ones digits is always 9.
Examples:
9 x 2 = 18
1+8=9
9 x 3 = 27
2+7=9
9 x 4 = 36
3+6=9
2. Use the 9’s tables finger “trick”. Put your hands on a table, palms down and
fingers spread. Your fingers are numbered 1 through 10, left to right. When you
multiply a number times 9, put down that finger. The total fingers to the left of the
finger that is down equal the digit in the tens place of the product. The total fingers
to the right of the finger that is down equal the digit in the ones place of the
product.
Example: 9 x 4
A) Put down the index finger of your left hand.
B) There are 3 fingers to the left of your index finger, so
the tens digit of the product will be 3.
C) There are 6 fingers (counting all fingers on both
hands) to the right of your index finger, so the ones digit
of the product will be 6.
9 x 4 = 36