Relationship between multiplication and division

Use this PhET Simulator to see how factors and products will help you think about your division facts.

An Interactive Multiplication Model

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Multiplication may be the most powerful operation because it makes order out of huge sets and tiny objects. There are three common types of multiplication:

1. Groups of objects (3 boxes and each box has 8 milks, so there are 24 milks)
2. Arrays of objects (3 rows of 8 desks, so there are 24 desks)
3. Areas of rectangles (3 inches by 8 inches, is 24 square inches)
4. Comparisons (A book costs $8 and a dictionary costs 3 times as much. The dictionary costs $24.)

Memorizing all the multiplication facts is a critical skill for every student. Students hopefully have skip counting skills they can use initially to count out loud to find 3 eights or 8 threes. Then, students will memorize more familiar facts like “2 times”, “5 times”, and “10 times.”

The rest of the table can be worked with by doubling the memorized facts. Or, students can skip count from a known fact. The facts in the bottom right corner will be the most challenging and may require traditional memorization techniques (flash cards, self-quizzing, etc.).

Some multiplication questions

• Alice bought 4 sheets of stamps. Each sheet had 5 stamps. How many stamps did Alice buy?
• Berto brought 8 packs of water bottles. Each pack has 6 water bottles. How many water bottles did Berto buy?
• Cara brought 8 packs of hot dogs to a family reunion. Each pack has 8 hot dogs. How many hot dogs did Cara bring?
• David is planning a flower garden. He wants to plant twice as many roses as sunflowers.
• If he plants 10 sunflowers, how many roses would he plant?
• Eva buys 6 times as many flowers as trees. How many flowers should she buy if she bought 4 trees?
• A school club has twice as many boys as girls. There are 10 boys in the club. How many girls are in the club?
• The high temperature is twice as high in L.A. as Olympia, Washington today. Today’s high temperature in Olympia, Washington is 44ºF. What is the high temperature in L.A. today?

Some pictures of multiplication

Retro Multiplication

Have some time? Check out this 30 minute Schoolhouse Rock exploring multiplication ideas. You will enjoy gems like “My Hero Zero”!

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