Thursday, September 1, 2016

Year’s First Foray Into Math, And Then Some


Source: Pixabay CC0 Public Domain

Yesterday during homeroom and first period my students and I spent the whole time going over all those pesky start of the year forms and handbooks each new school year brings. By the time we were done with that there was no time left over to talk math.

In my other 3 classes, since we didn’t have to go over any of that bureaucratic paperwork, we were able to delve into some math. The math we touched on was rather basic, consisting primarily of a review of elementary concepts.

Okay, so the ‘yesterday’ of paragraph one has become two days ago and my classes have not only touched on some basic concept review, we’ve begun the curricular lessons.

Prior to beginning our trip up and down the number line learning about integers tomorrow (Hurricane Hermine permitting) we did several group activities today to renew our familiarization with several mathematical properties.

Our first activity involved the Associative Properties of Addition and Multiplication. For those of you who might not remember, the Associative Properties are the Properties where parentheses are used to group operations that are to be done first when evaluating an expression. For instance, to simplify an expression like (x+3)+5 you would regroup by moving the parentheses to get the expression x+(3+5). Now you can combine the two like terms, 3 and 5 to get 8. The simplified expression would be x+8.

The first activity also included the Commutative Property. Using the Commutative Property, you can change the order of the addends in an addition only expression or the factors in a multiplication only expression. For example, to simplify an expression like (5+y)+7, you would first commute the 5 and the y so the new expression would read (y+5)+7. Then you would apply the Associative Property to get y+(5+7). The simplified expression would be y+12.

In the second activity, students used the Properties of Zero and One to simplify expressions. Both Multiplication and Addition have a Zero Property, though they work quite differently.

In Multiplication, 0 times any number results in a product of 0. In Addition, adding 0 to any number changes the number not at all. This is sometimes called the Additive Identity Property.

Multiplication also has an Identity Property When you multiply any number by 1, the value of the number does not change. This comes in handy when finding equivalent fractions or common denominators.

Tomorrow we will be putting these Properties to work when we begin learning about using the four basic arithmetic operations with Integers. We will if Hurricane Hermine lets us get in a full school day.

As always, I remain,

The Exhausted Educator

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