## Multiplication by Two-Digit Numbers: Tips and Tricks

- Provide your students with grid paper. Write a multiplication problem (8 x 19) on the board. Have your students model this multiplication problem by drawing a rectangular array (8 by 19 squares). Then have your students shade their arrays to express the multiplication problem by using the Distributive Property (8 x 10 squares and 8 x 9 squares).
- Write 8 x 19 on the board. Have one of your students begin writing the problem by using the Distributive Property [8 x 19 = 8 x (10 + 9)] and then have a second student complete the property [8 x 19 = 8 x (10 + 9) = (8 x 10) + (8 x 9) = 80 + 72 = 152].
- On the board, write a multiplication problem using the Distributive Property with some of the numbers missing [ x 19 = 8 x ( + 9) = (8 x 10) + ( x 9)]. Have one of your students volunteer to fill in the missing numbers [8 x 19 = 8 x (10 + 9) = (8 x 10) + (8 x 9)].
- Have students begin each lesson in this chapter with a different 30-second, 10-problem, drill of basic multiplication facts. The goal is to increase, each day, the number of correct answers given in 30 seconds.
- Have students write their vertical multiplication problem on a large grid, one digit per grid square, to help them keep their computations and regrouping in proper alignment.
- Have groups of students solve similar problems (8 x 29; 8 x 209; 8 x 219). Then have group members take turns explaining to the class why the products are
*not*the same (8 x 29 = 232; 8 x 209 = 1,672; 8 x 219 = 1,752). Note that students frequently make errors when multiplying by a number that contains zero (8 x 209 = 1,672) either by ignoring its place value (8 x 209 232) or by multiplying by 0 as though they were multiplying by 1 (8 x 0 8; 8 x 209 1,752). - State a number (30). Ask students to raise their hands if they believe it is a multiple of 10 (yes). Repeat for other numbers (590, yes; 39, no; 400, yes).
- Challenge students to write three multiplication problems—one involving a number times a multiple of 10 that has more than one 0 in its product; one involving a number times a multiple of 100 that has more than two 0s in its product; and one involving a number times a multiple of 1,000 that has more than three 0s in its product. (5 x 20 = 100; 5 x 800 = 4,000; and 80 x 2,000 = 160,000)
- At the board, have one of your students compute 8 x 132 (1,056) while another computes 20 x 132 (2,640) and a third computes 28 x 132 (3,696). Have a volunteer explain how the three problems are related (8 x 132 and 20 x 132 are the partial products of 28 x 132). Repeat with other related multiplication problems.
- Most students enjoy learning fun number tricks. You may want to show your class this trick for multiplying any number by 11—for example, 11 x 43,872. First, multiply the number by 10 (note that this step can be done mentally): 10 x 43,872 = 438,720. Then add the number and the result from the above step: 43,872 + 438,720 = 482,592. You may even want to challenge your students to explain why this works. If necessary, suggest to students that they use the Distributive Property to solve the problem:
11 x 43,872 = (10 + 1) x 43,872 = (10 x 43,872) + (1 x 43,872) = 438,720 + 43,872, or 482,592.

- Provide your students with word problems that have the operation clue words already highlighted or the operation underlined. Discuss with students the operations these clues indicate. Have students solve the problems.
- Have students highlight or underline operation clue words in word problems as each problem is read as a class. Have students solve the problems.