Discuss the word “commute” and point out that parents commute — or travel back and forth — to work. Call two volunteers to the front of the classroom and announce their names, left to right. Have the pair switch places and announce their names again, left to right. Point out that they are still the same two students, even though their positions changed. The commutative property works the same way: when you multiply two numbers, the product is the same, regardless of order. Both 7 x 8 and 8 x 7 equal 56.
Discuss the word “associate” and ask students who their associates are during recess. On an overhead projection, display three pictures of people cut from a magazine and call them "Matt," "Ben" and "Al." Place parentheses around Matt and Ben. Tell the students Matt and Ben are associating, or talking, and Al is on the sideline. Change the parentheses so they are now around Ben and Al with Matt on the sideline. Emphasize they are the same three boys, even though the grouping changed. The associative property works the same way: when three or more numbers are multiplied, the product is the same, regardless of grouping. (5 x 3)4 equals 60, and 5(3 x 4) also equals 60.
This property is reviewed at the fourth grade level, yet students may confuse it with the zero property of multiplication. Ask for a volunteer and announce his name. Tell him to take off his shoes and ask if he still has the same identity — if he is the same “one.” The identity property works this way: the product of any number and one is that number. 6 x 1 = 6.
Create an array, showing 2 x 3. Lay three rows of cubes, two in each row. Explain that the array shows three times two or six. Ask students how to depict 4 x 0 or 0 x 4. This visual representation shows nothing is in the array; any number times zero equals zero.
Some school districts include the distributive property at the fourth grade level. Teach boys and girls the basic concept of distributing multiplication over addition. Ask them to quickly give the answer to 5 x 34. Demonstrate that the mental process is faster if you first multiply 5 x 30, then multiply 5 x 4 and add the answers together: 150 + 20 = 170. You are “distributing” the 5 over the 34. Do several more examples. Transfer that concept to problems such as 2(4x5) = (2 x 4) + (2 x 5).