When adding more than two numbers, the associative property of addition states that the grouping of addends does not affect the sum. An example of the associative property is: 7 + (3 + 2) = (7 + 3) + 2. Each side of the equality still adds to 12 and is not dependent on the parentheses. Adapt the property to finding perimeters. Instruct students to group the longest sides of a rectangle in parentheses, adding the group of the two shorter sides, and find the sum. Ask the students to find the perimeter of the same rectangle by first grouping the top and left sides, adding them to the group containing the bottom and right sides to find the sum. Compare the two sums to display the associative property. Adapt to multiplication by finding the area.
In a combined addition and multiplication problem, the distributive property applies by multiplying the number outside the parentheses by both numbers being added within them and calculating the sum of the two findings. An example of the distributive property is 5 x (3 + 2) = (5 x 3) + (5 x 2), both equaling 25. Finding the area of two rectangles at the same time that share one side is an activity using the distributive property. Multiply the width of the rectangle by both the lengths of the two attached rectangles and add the products to find the total area.
The commutative property in elementary mathematics states that addends can be arranged in any order and will arrive at the same sum. For example: 2 + 1 = 1 + 2, both being the sum of three. An activity to communicate the commutative property of addition is to pair students and give each person 10 pennies. Challenge the students to place any number of the 10 pennies into one hand and the remainder into the other. No matter how many pennies are in the first hand or the second hand, there are still 10 pennies total. The commutative property is also adapted to multiplication.
The zero property of multiplication suggests that any zero is the product of any number and zero. As an example: 9 x 0 = 0 as well as 0 x 3 = 0. Give students a handful of counters and challenge them to make no groups of nine counters or nine groups of no counters. The directions may confuse some students because when you construct zero groups of a number or any number of groups of zero, you have no groups and no items.