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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 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…”?