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Multiplicative Identity Property
According to the multiplicative identity property, any number multiplied by itself is that number. For example, 20 * 1 = 20. Explain to fourth graders that multiplication is a short-form of addition and that writing a number times itself just means that you're not adding anything at all to that number, which is why the answer is the number itself. Compare 20 * 1 to 20 * 2, which means to add 20 together twice, to further illustrate the multiplicative identity property. Once children master the commutative property for multiplication, you can tell them that division also has a commutative property, so any number divided by itself is also the number itself. Show fourth graders several examples.
Commutative Property of Multiplication
When multiplying two numbers together, it doesn't matter which number you multiply first and which you multiply second. For example, 2 * 10 = 20 and 10 * 2 also equals 20. When teaching fourth graders the commutative property of multiplication, have them complete a worksheet with two columns. In the first column, have them complete simple two number multiplication problems such as 2 * 10, 4 * 2, 10 * 1, 9 * 8 and 16 * 2. In the adjacent column, have them multiply the numbers in reverse order such a 10 * 2, 2 * 4, 1 * 10 and 8 * 9. Give a gold star to any child whose answers in both columns match.
Associative Property of Multiplication
When you're multiplying together a string of three or more numbers, you can group the numbers in any order and get the same answer. For example, 4 * 2 * 1 is 8 just as 1 * 2 * 4, 1 * 4 * 2, 4 * 1 * 2, 2 * 4 * 1 and 2 * 1 * 4 are all 8. Talking to fourth graders about grouping numbers, which means pairing two numbers together to multiply them. In the example above in 4 * 2 * 1, you can group (4 * 2) together or (4 * 1) together. In whatever combination you group these numbers for multiplying, you will always get 8. Write a multiplication problem on the board such as 1 * 2 * 3 * 4. Show the children how you solve this problem by grouping (1 * 2) and multiplying to get two and (3 * 4) to get 12 and multiplying 12 * 2 to get 24. Challenge the children to get a different answer by grouping the numbers differently. Have each child try to stump you by having you group the numbers differently, and amaze them at always arriving at the correct answer of 24.
Zero Property of Division
There are two parts to the zero property of division. First, zero divided by any number is zero. Second, dividing a number by zero is impossible. Explain to fourth graders that division is also a short form of addition by explaining the relationship between multiplication and division. Explain that division is also just a short form of addition. 14 / 7 is 2 because you're really asking, how many times must I add together 7 to equal 14? Because 7 + 7 = 14, the answer is 2. In 14 / 0, you're really asking, how many times must I add together zero to equal 14? It doesn't matter how many times you add zero to itself, you will never get 14. Zero divided by 12 is always 0 because 0 / 12 asks, how many times must I add 12 together to get zero? f you don't add it at all, you get 0, so zero divided by any number is always zero.