Lesson 3: Multiplication and Its Properties

Getting Started

Questions to Explore

  • What are some strategies we can use to multiply and divide?
  • How do we write and speak in mathematical language?

Facts and Definitions

  • Commutative property of multiplication: math law that states that the order of the numbers doesn't matter when multiplying; a × b = b × a
  • Identity property of multiplication: math law that states that when multiplying a number by one, the product is always the number itself; also called the one property of multiplication
  • Zero property of multiplication: math law that states that when multiplying a number by zero, the product is always zero
  • Associative property of multiplication: math law that states that when multiplying more than 2 numbers, it doesn't matter which numbers you multiply first
  • Distributive property of multiplication: math law that states that when given a multiplication problem, it's possible to break a factor down into easier numbers, find the products of the other factor with those easier numbers, and then add those products together to find the product of the original problem


  • Represent verbal statements of multiplicative comparisons as multiplication equations
  • Identify properties of multiplication


  • 3 small plastic zipper bags
  • colored pencils
  • counters (kit)
  • fine point dry-erase markers (kit)
  • glue or glue stick
  • index cards (kit)
  • Interactive Notebook
  • multiplication flashcards (kit)
  • permanent marker
  • scissors
  • whiteboard (kit)


Materials: 3 small plastic zipper bags, counters (kit), fine point dry-erase markers (kit), index cards (kit), Interactive Notebook, multiplication flashcards (kit), permanent marker, whiteboard (kit)
Write 5×6 on an index card, and give your child the whiteboard, a dry-erase marker, and a large handful of counters (at least 30). Ask, "How many ways can you model this problem using these materials?" He may draw a picture (such as an array) or number line and may make groups using the counters. Ask, "What does 5×6 mean in words?" Make sure that he is able to explain that this multiplication sentence means that there are five groups with six in each group ("five groups of six"). Now, ask, "Once you know the answer, how would you say the whole problem?" ("five times six is thirty")

If needed, repeat this process with 9×4 and 10×3. Also, reverse the process with you giving the groups and your child providing the multiplication sentence. Ask your child to write a multiplication sentence for "7 groups of 3" (7×3) and "8 times 4" (8×4).
Now, provide time for your child to work with his multiplication flashcards. He should shuffle them and divide them in half. He will work with just one of the sets right now. (He can put the other set aside for now.) As he goes through the first set, he should make 3 piles: 1) facts that he knows immediately, 2) facts that take him a few seconds to figure out, and 3) facts that he doesn't recall. Explain that he will spend time during this lesson reviewing the facts that end up in the second and third piles. Ask, "Which facts do you recall most easily?" and "Which facts are harder for you?"

Give your child the "Multiplication Table" sheet, and tell him to color the facts on it that he knows immediately. He should look back to the first pile he made to determine which spaces to color on the table. For example, if he knows 2×4, then he should color "8" where 2 and 4 meet (starting from the left side of the table with 2 and from the top with 4). When he finishes coloring all of the facts that he knows, he can store this sheet in his Interactive Notebook. He should also store each of his current "fact piles" in three separate bags labeled "Know," "Working On," and "Don't Know" to indicate which piles they include.

NOTE: If your child's "Working On" and "Don't Know" bags have a lot of cards in them, you may stretch this exercise out over several days instead of just the two days of this lesson.