Fourth Activity The commutative property says that you can switch the order of the numbers for a given operation and still get the same result. Now let’s look at another property. Are these true? ? ? ? 4 + (5 + 6) = (4 + 5) + 6 1 + (8 + 3) = (1 + 8) + 3 9 + (7 + 2) = (9 + 7) + 2 (To the teacher: The above is formatted using a borderless table.) 1) If you replaced the numbers with different numbers would it still be true? Justify your answer? 2) Can you find an example that won’t work? 3) This called the associative property. It says, we can group numbers differently and still get the same result. Describe how this definition of the property is related to the three examples you worked with. Try this property with the other three operations. Do you think the associative property is true of subtraction? Why or why not? Subtraction: Test it out: ? 4 (5 6) = (4 5) 6 – – – – Multiplication: Do you think the associative property is true of subtraction? Why or why not? Test it out: ? 4 (5 6) = (4 5) 6 ∗ ∗ ∗ ∗ Division: Do you think the associative property is true of subtraction? Why or why not? Test it out: ? 4 (5 6) = (4 5) 6 What connections do you see the operations that the associativity property holds true for and among those that it doesn’t? How would you explain this connection?
Fourth Activity The commutative property says that you can switch the order of the numbers for a given operation and still get the same result. Now let’s look at another property. Are these true? ? ? ? 4 + (5 + 6) = (4 + 5) + 6 1 + (8 + 3) = (1 + 8) + 3 9 + (7 + 2) = (9 + 7) + 2 (To the teacher: The above is formatted using a borderless table.) 1) If you replaced the numbers with different numbers would it still be true? Justify your answer? 2) Can you find an example that won’t work? 3) This called the associative property. It says, we can group numbers differently and still get the same result. Describe how this definition of the property is related to the three examples you worked with. Try this property with the other three operations. Subtraction: Do you think the associative property is true of subtraction? Why or why not? Test it out: ? 4 – (5 – 6) = (4 – 5) – 6 Multiplication: Do you think the associative property is true of subtraction? Why or why not? Test it out: ? 4 ∗ (5 ∗ 6) = (4 ∗ 5) ∗ 6 Division: Do you think the associative property is true of subtraction? Why or why not? Test it out: ? 4 (5 6) = (4 5) 6 What connections do you see the operations that the associativity property holds true for and among those that it doesn’t? How would you explain this connection?