Math Background

Lesson: Multiplication by Two-Digit Numbers
Developing the Concept

Now that your students have created their own multiplication fact chart and acquired an initial understanding of using the Distributive Property to solve multiplication problems involving multiplying by one-digit numbers, it is time to expand their understanding by having them use the Distributive Property to multiply by two-digit numbers.

Materials: model multiplication fact charts from the first lesson.

Preparation: Post your model multiplication fact chart where students can see it.

  • Say: Take out your multiplication fact charts, because we are going to refer to them as needed when we solve some multiplication problems.

    Write 14 x 26 on the board in horizontal form.

  • Ask: How can I rewrite 14 x 26, using the Distributive Property?
    Someone will probably respond, “14 x (20 + 6).” On the board, write 14 x 26 = 14 x (20 + 6).
  • Ask: Can anyone show us how to use the Distributive Property of Multiplication to solve 14 x 26?
    Direct your students to solve 14 x 26 as follows: 14 x 26 = 14 x (20 + 6) = (14 x 20) + (14 x 6) = 280 + 84 = 364. Write this on the board. Explain how the Distributive Property distributes 14 to each part of the expanded form of 26.
  • Say: I am going to show you how the Distributive Property can be used to multiply 14 by 26 in the vertical form of the standard multiplication algorithm.
    Write 14 x 26 on the board in vertical form (see below).
    multiplication problem
  • Say: (while pointing to each partial product) Notice how the Distributive Property breaks each of the partial products into problems that involve basic facts.

    Write 14 x 26 on the board in vertical form to the right of the problem above (see below).

    multiplication problem
  • Say: (while writing the solution, using regrouping) You can also solve this problem by using regrouping.
  • Ask: How can 34 x 326 be solved by using the vertical form of the standard multiplication algorithm?
    Direct your students to solve 34 x 326 in this manner.
    multiplication problem
  • Ask: How would your answer change if the problem were 34 x $3.26?
    Students should be able to say that the solution would include a dollar sign and a decimal point; otherwise, nothing else changes. Insert the dollar sign and the decimal point into the problem (34 x 326) already on the board; then insert a dollar sign and a decimal point into the answer.

    Give your students these problems: 16 x 84; 54 x 764; 24 x 306; and 79 x $4.78. Ask them to find the products. Tell students to refer to their multiplication fact charts when necessary.

Wrap-Up and Assessment Hints
Create several completely solved multiplication problems, including those with money amounts, that show the algorithm with some missing numbers (see below). Ask students to fill in the missing numbers. This activity will encourage your students to slow down and think about each step in the multiplication process.

multiplication problem

Houghton Mifflin Math Grade 5