1. Multiplication Table x 1 2 3 4 5 6 7 8 9 10 11 12 14 16 18 20 22 24 151 2 3 4 5 6 7 8 9 10 11 12 14 16 18 20 22 24 15 21 27 30 33 36 28 32 40 44 48 25 35 45 50 55 60 42 54 66 72 49 56 63 70 77 84 64 80 88 96 81 90 99
108
100
110
120
121
132
144

2. Multiplication and Division of Whole Numbers
There are 3 major types of Multiplication and Division problems.
They are:
Additive (Sometimes Equal Groups)
Comparison
Combination

3. 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

4. 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: =

5. 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

6. 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

7. These problems can be represented using:
Objects
(like M&M’s)
Pictures of Objects
Number Sentences
= 8; 4x2= 8

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?
= 12

9. Comparison
When figuring out comparison problems, one is comparing an amount or __________________ difference
UNKNOWNS
__________________ Unknown
________ ______Unknown
_______________________ Unknown
quantity
Product
Set size
Multiplier

10. 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

11. 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

12. 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

13. 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

14. 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

15. Combination Unknowns __________________ Unknown Product
Size of a Set

16. 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?

17. 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?

18. 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

19. 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?

20. 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…”?