1/13/2016 mathematical modeling various ways to represent the same mathematical expression or...

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

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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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