🔢 MathGrade 2Lesson 19
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Understand Multiplication as Groups

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Learning Objectives

  • 1Read a multiplication expression as "__ groups of __"
  • 2Match a multiplication expression to the correct dot-group picture
  • 3Connect multiplication to the matching repeated addition sentence
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Mini Lesson

We know how to write repeated addition. Now we meet a shortcut: the multiplication sign x. Instead of writing 4 + 4 + 4, we write 3 x 4 — which means "3 groups of 4."

Reading a multiplication expression

  • In 3 x 4, the first number (3) is the number of groups and the second number (4) is the group size.
  • Read it aloud as: "3 groups of 4."
  • The repeated addition is: 4 + 4 + 4 = 12.
  • So 3 x 4 = 12.

Three ways to show the same fact

  • Dot picture: three groups, four dots each.
  • Repeated addition: 4 + 4 + 4 = 12.
  • Multiplication: 3 x 4 = 12.

More examples

  • 2 x 5 = "2 groups of 5" -> 5 + 5 = 10.
  • 4 x 3 = "4 groups of 3" -> 3 + 3 + 3 + 3 = 12.
  • 5 x 2 = "5 groups of 2" -> 2 + 2 + 2 + 2 + 2 = 10.
Three ways to show 3 groups of 4A diagram linking the multiplication 3 x 4 = 12, the dot picture of three groups of four, and the repeated addition 4 + 4 + 4 = 12.Multiplication3 x 4 = 12Dot picture3 groups of 4Repeated addition4 + 4 + 4= 12same answer!=3 (groups) x 4 (group size) = 12Read: "3 groups of 4"
Three connected representations of the same fact — the expression 3 x 4 = 12, the dot picture, and 4 + 4 + 4 = 12.
Four multiplication expressions with repeated addition and totalsFour rows: 2x5=10 (5+5), 3x4=12 (4+4+4), 4x3=12 (3+3+3+3), 5x2=10 (2+2+2+2+2).Multiplication = Repeated Addition2 x 5 = 102 groups of 5 -> 5 + 5 = 103 x 4 = 123 groups of 4 -> 4 + 4 + 4 = 124 x 3 = 124 groups of 3 -> 3 + 3 + 3 + 3 = 125 x 2 = 105 groups of 2 -> 2+2+2+2+2 = 10
Four color-coded rows linking each multiplication expression to its "groups of" reading and repeated addition sentence.
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Ask yourself: "What is the number of groups? What is the group size? Can I draw the dots and count them?"

Vocabulary
Multiplication
A shortcut for repeated addition of equal groupse.g. 3 × 4 = 12 is multiplication.
Times
The word we read for the multiplication sign ×e.g. We read 3 × 4 as three times four.
Number of groups
The first number in a multiplication, telling how many groupse.g. In 3 × 4, the number of groups is 3.
Group size
The second number in a multiplication, telling items in each groupe.g. In 3 × 4, the group size is 4.
Product
The answer to a multiplicatione.g. The product of 3 × 4 is 12.
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