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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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