Study Guide
Math Unit—Division
Learning Targets
At the end of this unit—
1) I can understand models and patterns of multiplication and use those
patterns to answer division facts.
2) I can create and use models—sets, number lines, and arrays—of division.
3) I can answer basic division facts from the 2’s through the 12’s tables.
Vocabulary
divide—separate into equal groups; “fair sharing”
Example:
There are 12 marbles. The marbles are divided equally into 3 groups. There are 4
marbles in each group.
divisor—the number you divide by
Example: In the problem 12 ÷ 3 = 4, 3 is the divisor.
dividend—the amount you want to divide into equal groups
Example: In the problem 12 ÷ 3 = 4, 12 is the dividend.
quotient—the answer when you divide
Example: In the problem 12 ÷ 3 = 4, 4 is the quotient.
dividend ÷ divisor = quotient
Strategies for dividing
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
repeated subtraction—subtracting the same number repeatedly is the same as
division
Example: 12 – 3 = 9
9–3=6
6–3=3
3–3=0
Three has been taken away (subtracted) 4 times, so there are 4 groups of 3 in 12.
array—an arrangement of objects or symbols in even rows and columns that show a
multiplication and division fact
Example:
24 ÷ 4
Draw an array, making rows of 4. Count each object or symbol that is put in the
array until there are a total of 24.
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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
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4
x7
28
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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
* * * *
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* * * *
* * *
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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