Multiplication Tablex 0 1 2 3 4 5 6 7 8 9 10 11 12
0 0 0 0 0 0 0 0 0 0 0 0 0 0
1 0 1 2 3 4 5 6 7 8 9 10 11 12
2 0 2 4 6 8 10 12 14 16 18 20 22 24
3 0 3 6 9 12 15 18 21 24 27 30 33 36
4 0 4 8 12 16 20 24 28 32 36 40 44 48
5 0 5 10 15 20 25 30 35 40 45 50 55 60
6 0 6 12 18 24 30 36 42 48 54 60 66 72
7 0 7 14 21 28 35 42 49 56 63 70 77 84
8 0 8 16 24 32 40 48 56 64 72 80 88 96
9 0 9 18 27 36 45 54 63 72 81 90 99 108
10 0 10 20 30 40 50 60 70 80 90 100 110 120
11 0 11 22 33 44 55 66 77 88 99 110 121 132
12 0 12 24 36 48 60 72 84 96 108 120 132 144
Multiplication and Division of Whole Numbers
There are 3 major types of Multiplication and Division problems.
They are:– Additive (Sometimes Equal
Groups)– Comparison– Combination
Additive (Equal Groups)
• This involves a given number of ______ , each set having the same number of __________________.
• The goal is to find the number of _______________________.
• UNKNOWNS– ________________ Unknown– Size of __________Unknown– Number of Groups Unknown
sets
objects
objects
Whole
Groups
Equal Groups: Whole Unknown• Mark has 4 bags of apples.
There are 6 apples in each bag.
• How many apples does Mark have altogether?
Number sentence:
6+6+6+6=
Equal Groups: Size of Groups Unknown
• Mark has 24 apples.
• He wants to share them equally among his friends.
• How many apples will each friend receive?
• What type of problem is this?– PARTITION DIVISION
Equal Groups: Number of Groups Unknown
• Mark has 24 apples.
• He put them into bags containing 6 apples each.
• How many bags did Mark use?
• What type of problem is this?– MEASUREMENT DIVISION
These problems can be represented using:
– Objects (like M&M’s)
– Pictures of Objects
– Number Sentences 2+2+2+2= 8; 4x2= 8
Examples
• There are 4 packages of muffins.• There are 3 muffins in each
package.• How many muffins in all?
DRAW THIS and then show MODEL, then write number sentence
• What is the number sentence? 3+3+3+3= 12
Comparison
• When figuring out comparison problems, one is comparing an amount or __________________ difference
• UNKNOWNS
– __________________ Unknown•
– ________ ______Unknown
– _______________________ Unknown
quantity
Product
Set size
Multiplier
Comparison: Product Unknown
• Jill picked 6 apples.
• Mark picked 4 times as many apples as Jill.
• How many apples did Mark pick?
• What type of problem is this?
• MULTIPLICATION
Comparison: Set Size Unknown
• Mark picked 24 apples.
• He picked 4 times as many apples as Jill.
• How many apples did Jill pick?
• What type of problem is this?
• PARTITION DIVISION
Comparison: Multiplier Unknown
• Mark picked 24 apples, and Jill picked only 6.
• How many times as many apples did Mark pick as Jill did?
• What type of problem is this?
• MEASUREMENT DIVISION
EXAMPLE
• Nolan had 5 M&M’s. Breanna had 4 times as many as Nolan. How many M&M’s did Breanna have?
• DRAW and MODEL
Combination Problems
• In combination problems, the problem is to count the number of possible ___________________ that can be made between sets.
• The product consists of _______ of things.
combinations
pairs
Combination Unknowns
– __________________ Unknown
– ________________ Unknown
Product
Size of a Set
Combinations: Product Unknown
• Sam bought 4 pairs of pants and 3 jackets and they can all be worn together.
• How many different outfits consisting of a pair of pants and a jacket does Sam have?
Combinations: Size of a Set Unknown
• Sam bought some new pants and jackets.
• He has a total of 12 different outfits.
• If he bought 4 pairs of pants, how many jackets did Sam buy?
EXAMPLES
• You have 3 colors of regular M&M’s and 4 colors of Peanut ones.
• How many combinations can you make to have one of each in each combination?
• DRAW and MODEL
Review
• How many main types of Multiplication and Division problems are there?
• Which problems are multiplication problems? Division?
• Which type of problem has only 2 unknowns? Why?
Review
• What kind of problem is it when it involves counting the number of possible pairings that can be made between two sets?
• What kind of problem is it when you are fair sharing?
• What kind of problem when it says: “he had 4 times as many…”?