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…”?