1/13/2016 mathematical modeling various ways to represent the same mathematical expression or...
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04/21/23
Mathematical Modeling
Various ways to represent the same mathematical expression or situation
04/21/23
Compare to Vocabulary
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Cést Domage = that’s too badcierra la boca por favor = close your mouth pleasea lot = plethora = myriad = surfeit
Now let’s look at math terms – copy these in your notebook, please.
plus + Is less than < Is greater than > two times a number 2A The next 2 are “switcheroos” – they go at the end of the
expression less than - 7 less than 12 12-7 more than + 4 more than 5 5+4
More terms - copy these also, por favor.
Addition Subtraction Multiplication Division
Plus Minus Times Divided by
The sum of The difference of
The product of The quotient of
Increased by Decreased by Multiplied by Per
Total Fewer than of
Is more than Is less than
Added to Subtracted from
Take it one step at a time 4 more than 3 times a number
4 more than --> +4
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Keep Going
4 more than 3 times a number 4 more than +4
3 times a number
let A represent “a number”
3A 3
Put it all together now4 more than 3 times a number
4 more than +4 3 times a number 3A new model 3A +4 4+3A this would give you the
correct math answer but would NOT be written correctly. Remember more than is a switcheroo!
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Multiple ways to graph the same information
1st Qtr2nd Qtr3rd Qtr4th Qtr
0
10
20
30
40
50
60
70
80
90
1st Qtr 2nd
Qtr
3rd Qtr 4th Qtr
East
West
North
0
20
40
60
80
100
120
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160
180
1st Qtr 2nd Qtr 3rd Qtr 4th Qtr
North
West
East
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1st Qtr 2nd Qtr 3rd Qtr 4th QtrEast 20.4 27.4 90 20.4West 30.6 38.6 34.6 31.6North 45.9 46.9 45 43.9
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Change a word problem to a math expression
A taxi charges 4.95 for the first 1/10 of a mile
and .95 for each additional 1/10 of a mile.
Write a math expression to indicate
a taxi trip of “n”miles
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A taxi charges 4.95 for the first 1/10 of a mile
and .95 for each additional 1/10 of a mile.
Follow the steps.
a taxi trip of “n”miles = $
A taxi charges 4.95 for the first 1/10 of a mile
and .95 for each additional 1/10 of a mile,
First 1/10 of a mile = 4.95
4.95 +
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How many tenths of a mile do we have?
A taxi charges 4.95 for the first 1/10 of a mile
and .95 for each additional 1/10 of a mile.
.95 for each additional 1/10 of a mile
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10N = tenths of a mile
How many additional 1/10 of miles do we have?
A taxi charges 4.95 for the first 1/10 of a mile
and .95 for each additional 1/10 of a mile.
.95 for each additional 1/10 of a mile
(10n-1) --> We were charged 4.95 for thevery first 1/10 of a mile.
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.95 for each additional 1/10 of a mile
A taxi charges 4.95 for the first 1/10 of a mile
and .95 for each additional 1/10 of a mile
(10n-1) .95# of tenths of a mile times .95
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A taxi charges 4.95 for the first 1/10 of a mile
and .95 for each additional 1/10 of a mile.
Put it all together now.
$ = 4.95 + (10n-1).95or
cost for n miles = $4.95 + .95(10n-1)
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-3 -2 -1 0 1 2 3
X < 2
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Mathematical Modeling
Various ways to represent the same mathematical expression or situation
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