Helping students make their own
Helping Students make their own chart:
multiplication chart
Links for Multiplication charts
www.math-aids.com
http://www.mathsisfun.com/multipli
cation-table-bw.html
http://www.helpingwithmath.com/p
rintables/tables_charts/cha0301mult
iplication144.htm
Words in Math that are clues to
operation required…..
Symbol
Words Used
+
Addition, Add, Sum, Plus, Increase, Total,
All together
-
Subtraction, Subtract, Minus, Less,
Difference, Decrease, Take Away, Deduct
×
Multiplication, Multiply, Product, By, Of,
Times, Lots Of, All Together
÷
Division,
Divide, Quotient, Goes Into, How Many
Times, Groups of, Goes into
Divisibility Rules 2 - 3
Divisible by 2 IF
The last digit is even (0,2,4,6,8)
Example:
128 is129 is not
∞∞∞∞
Divisible by 3 IF
The sum of the digits is divisible by 3
Example:
381 (3+8+1=12, and 12÷3 = 4) Yes
217 (2+1+7=10, and 10÷3 = 3 1/3) No
Divisibility Rules 4 - 5
DIVISIBLE BY 4 IF
The last 2 digits are divisible by 4
EXAMPLE
1312 is (12÷4=3)
7019 is not
∞∞∞∞
DIVISIBLE BY 5 IF
The last digit is 0 or 5
EXAMPLE: 175 is AND 809 is not
∞∞∞∞
Divisibility Rules 6 - 7
DIVISIBLE BY 6 IF
The number is divisible by both 2 and 3
114 (it is even, and 1+1+4=6 and 6÷3 = 2) Yes
308 (it is even, but 3+0+8=11 and 11÷3 = 3 2/3) No
∞∞∞∞
DIVISIBLE by 7 IF
If you double the last digit and subtract it from the rest of the number and
the answer is: 0, or divisible by 7 (Note: you can apply this rule to that
answer again if you want)
672 (Double 2 is 4, 67-4=63, and 63÷7=9) Yes
905 (Double 5 is 10, 90-10=80, and 80÷7=11 3/7) No
∞∞∞∞
Divisibility Rules 8 - 9
DIVISIBLE 8 IF
The last three digits are divisible by 8
109816 (816÷8=102) Yes
216302 (302÷8=37 3/4) No
∞∞∞∞
DIVISIBLE 9 IF
The sum of the digits is divisible by 9
(Note: you can apply this rule to that answer again if you want)
1629 (1+6+2+9=18, and again, 1+8=9) Yes
2013 (2+0+1+3=6) No
Divisibility Rules 10 - 12
DIVISIBLE BY 10 IF
The number ends in 0
220 is
BUT
221 is not
∞∞∞∞
DIVISIBLE BY 11 IF
If you sum every second digit and then subtract all other digits and the
answer is: 0, or divisible by 11
EXAMPLES: 1364 ((3+4) - (1+6) = 0) Yes
3729 ((7+9) - (3+2) = 11) Yes
25176 ((5+7) - (2+1+6) = 3) No
∞∞∞∞
DIVISIBLE BY 12 IF
The number is divisible by both 3 and 4
EXAMPLE: 648 (By 3? 6+4+8=18 and 18÷3=6 Yes. By 4? 48÷4=12 Yes) Yes
524 (By 3? 5+2+4=11, 11÷3= 3 2/3 No. Don't need to check by 4.) No
Divisibility Rules links
http://www.mathaids.com/Division/Divisibility_Test_Handout.ht
ml
http://www.helpingwithmath.com/by_subject/
division/div_divisibility_rules.htm
Common & Least Common Multiples
A common multiple is a number that is a
multiple of two or more numbers. The
common multiples of 3 and 4 are 0, 12, 24, ....
The least common multiple (LCM) of two
numbers is the smallest number (not zero)
that is a multiple of both.
Least Common Multiples
Least Common Multiple
The least common multiple, or LCM, is another
number that's useful in solving many math
problems. Let's find the LCM of 30 and 45.
One way to find the least common multiple of
two numbers is to first list the prime factors of
each number.
30 = 2 × 3 × 5
45 = 3 × 3 × 5
Then multiply each factor the greatest number of times it occurs in
either number. If the same factor occurs more than once in both
numbers, you multiply the factor the greatest number of times it
occurs.
Then multiply each factor the greatest number of times it occurs in
either number. If the same factor occurs more than once in both
numbers, you multiply the factor the greatest number of times it
occurs.
2: one occurrence
3: two occurrences
5: one occurrence
2 × 3 × 3 × 5 = 90 <— LCM
After you've calculated a least common multiple, always check to be
sure your answer can be divided evenly by both numbers.
EXAMPLES
3, 9, 21
Solution: List the prime factors of each.
3: 3
9: 3 × 3
21: 3 × 7
Multiply each factor the greatest number of times it occurs in any of the
numbers. 9 has two 3s, and 21 has one 7, so we multiply 3 two times, and
7 once. This gives us 63, the smallest number that can be divided evenly
by 3, 9, and 21. We check our work by verifying that 63 can be divided
evenly by 3, 9, and 21.
∞∞∞∞
12, 80
Solution: List the prime factors of each.
12: 2 × 2 × 3
80: 2 × 2 × 2 × 2 × 5 = 80
Multiply each factor the greatest number of times it occurs in either
number. 12 has one 3, and 80 has four 2's and one 5, so we multiply 2 four
times, 3 once, and five once. This gives us 240, the smallest number that
can be divided by both 12 and 80. We check our work by verifying that 240
can be divided by both 12 and 80
Find the LCM with a calculator!!
http://www.calculatorsoup.com/calc
ulators/math/lcm.php
Finding Equivalent Fractions:
Equivalent Fraction Links
http://www.dr-mikes-math-games-forkids.com/equivalent-fractions-calculator.html
http://www.helpwithfractions.com/fractioncalculator/
Teaching Squares and Square Roots
Squares and Square Roots
Fact Family
Fact Family
The numbers along the left side and top are
factors. The numbers inside are products
To use the multiplication table to find the product of 3 and 9,
locate 3 in the first column and then find 9 in the top row.
Follow the 3 row to where it meets the 9 column. The number
in the square where the column and row meet is the product.
See the shaded area in the table below.
3 x 9 = 27
Another way to find the product of 3 and 9 on the multiplication table is
to locate 9 in the first column and then 3 in the top row. See the shaded
area in the table below.
3 x 9 = 27
A multiplication table can also be used to find missing factors in multiplication
and division sentences. Finding a missing factor in multiplication is similar to
finding a quotient in division.
Use the multiplication table below to find
the missing factor in5 x n = 20.
Locate 5 in the first column and move
across the row to 20. The number in the
square at the top of the column is the
missing factor.
5 x 4 = 20
To find the quotient in 20 ÷ 5 = n, follow the same steps as for 5 x 4 =
20 above. The number in the square at the left end of the row is the quotient.
20 ÷ 5 = 4
Making the connection
between missing factors
in multiplication
sentences and
quotients in division will
help students better
understand the
relationship between
the two operations.
A multiplication table can also be used to reinforce students' understanding
of other math concepts, such as the Commutative Property of Multiplication
and inverse operations. Look at the multiplication table below.
The table shows 3 x 6 = 18.
It also shows 6 x 3 = 18
Because the
Commutative Property of
Multiplication states that changing
the order of the factors does not
change the product.
The inverse, or opposite, of
multiplication is division. So the
table also shows
18 ÷ 3 = 6 and 18 ÷ 6 = 3. These four
number sentences each use the
same three numbers: 3, 6, and 18.
Related number sentences
that use the same numbers
are called a fact family
Some fact families have only two related number sentences. The
multiplication table below shows the fact family for 7 and 49.
The fact family for 7 and 49 is
7 x 7 = 49 and
49 ÷ 7 = 7.
There is only one
multiplication sentence in
this fact family because the
factors are the same
number. There is only one
division sentence because
the divisor and quotient are
the same number.
http://www.vertex42.com/Files/pdfs/2
/school-reward-chart.pdf
Click the link above.
The progress chart can be
printed and used to graph
goals in math.