Math Operations vocab of what means addition, subtraction, multiplication, and division
Make sure to glue the '1/2 sheet' of math word phrases that we associate with each of the four basic operations -- into your spiral notebook (SN)
Use a "LET STATEMENT"
Let n = the number
That is the simplest "LET STATEMENT. You are defining your variable!
We can use the same mathematical expression to translate many different word phrases
Five less than a number n
The number n decreased by five
The difference when five is subtracted from a number n
All three of those phrases can be translated into the variable expression
n - 5
The product of a number and 3 3n
4 times a number 4n
The quotient of 3 and a number 3/n
The quotient of a number y divided by ten becomes y/10. It may look like only a fraction to you-- but if you read y/10 as always " y divided by 10" you have used the proper math language.
Twelve more than three times a number m
Wait-- where are you starting from... in this case you are adding 12 to 3m so you must write
3m + 12
Not all word phrases translate directly into mathematical expressions. Sometimes we need to interpret a situation.. we might need to use relationships between to help create our word phrase.
10 less than a number is n-10
a number increased by 9 n + 9
9 more than a number is also n + 9
In writing a variable expression for the number of hours in w workdays, if each workday consists of 8 hours...
8w would be our expression
Some everyday words we use to so relationships with numbers:
consecutive whole numbers are whole numbers that increase by 1 for example 4, 5, 6
So the next consecutive whole number after w is w + 1.
A preceding whole number is the whole number that is 1 less and the next whole number is the whole number that is 1 greater.
So the number which precedes x would be x - 1.
The next number after n is n + 1
What if I asked what is the next consecutive EVEN number after the even number "m"
It would be m + 2
What would it be if I asked what was the next consecutive odd number, after the odd number x?
x + 2
What if I asked what is the next consecutive EVEN number after the even number "m"
It would be m + 2
What would it be if I asked what was the next consecutive odd number, after the odd number x?
x + 2
Let's look at those relationships like the workdays from Monday's lesson... We are going to find another strategy to use for some of the more complicated expressions...
First set up a T chart- as discussed in class
put the unknown on the left side of the T chart... The unknown is always the one that reads like " w workdays"
so in this case
w workdays on the left side and under it you put
1
2
3
On the right side put the other variable-- in this case hours
under hours put the corresponding facts you know-- the relationship between workdays and hours as given in this case
hours
8
16
24
all of those would be on the right side of the T chart.
Now look at the relationships and ask yourself--
"What do you do to the left side to get the right side?"
and in this case, specifically...
What do you do to 1 to get 8?
What do you do to 2 to get 16?
What do you do to 3 to get 24?
Do you see the pattern?
For each of those the answer is "Multiply by 8" so
what do you do to w-- The answer is Multiply by 8
so the mathematical expression in this case is "8w."
What about writing an expression for how many dimes are in x dollars?
Use your T- chart
x dollars dimes
1..................10
2..................20
3..................30
x...................10x
Put 3 known relationships and then ask yourself "What did I do to the left side to get the right side"
What did I do to 1 to get 10? ... answer multiply by 10
What did I do to 2 to get 20? ... answer multiply by 10
What did I do to 3 to get 30? ... answer multiply by 10
So What must I do to x? it must be the same ... answer multiply by 10 so 10x is what I am looking for!
How many dollars do we have in n nickles?
set up-- unknown on the left!
n nickles dollars
20....................1
40....................2
60....................3
n......................?
Again, Ask yourself "What did I do to the left side to get the right side"
What did I do to 20 to get 1? ... divide by 20
What did I do to 40 to get 2? ... divide by 20
What did I do to 60 to get 3? ... divide by 20
So what must I do to n? it must be the same ... divide by 20 so n/20
The number of feet in i inches
i inches is the unknown... so that goes on the left side of the T chart... with feet on the right
i inches ___feet
12...............1
24...............2
36...............3
I filled in three known relationships between inches and feet Now, ask your self those questions again...
"What do you do to the left side to get the right side?"
and in this case, specifically...
What do you do to 12 to get 1?
What do you do to 24 to get 2?
What do you do to 36 to get 3?
In each of these, the answer is divide by 12
so What do you do to i? the answer is divide by 12
i inches ___feet
12...............1
24...............2
36...............3
i................i/12
and it is written i/12
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