High School Mathematics at Work Essays and Examples for the Education of All Students (1998) / Chapter Skim
Currently Skimming:
Part Three: Curricular Considerations
Part Three: Curricular Considerations
Pages 91-126
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From page 93... ...
_ J :::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::: V~ rr r ~ 4- ^~ e ~ ^~ e ~ e ~ f ~ ~rat 18;;W;27 U1 ~UIL111~UIL.
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From page 94... ...
· ~ rat OI such
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From page 95... ...
· ~ To I i ~ fit ~ ~· ~ ~· ~· ~ CELOCO warns that the statement 'CStudents should be
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From page 98... ...
arrot it has been felt p In Chica o [there are two monthl rates for local tele hone service t;no~ce ~ nas a ~ y p base rate of $11.25 for 200 calls plus .0523 for each call over 200. Choice 2 is $24.50 for an unlimited number of calls.
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From page 99... ...
cept (University of Chicago School Mathematics Project, 1989-97; Usiskin, 19911. In a few instances, the content is standard in the curriculum, as with A city charges 8% tax and a restaurant ire the cilly gives a 5% discount for paying cash.
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From page 100... ...
Fo first by
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From page 101... ...
He is a member of the Board of Directors of the National Council of Teachers of ~hathematics7 of the Mathematics/Science Standing Committee of the National Assessment of Educational Progress, and of the United States National Commission on Mathematical Instruction. He has served as a member of the Mathematical Sciences Education Board.
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From page 102... ...
l 1 ~ 1 L 1 :::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::: always feel actually carry oulL, to [Lease out efficienlL ICS AT shall
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From page 104... ...
every ~J 7 ~v, 7 ~J 7 J 7 ~7 J ~J 7 ~ 7 ~.o o .
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From page 105... ...
'~closed forms (multiply by 5 and subtract 1)
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From page 106... ...
. Before coming to EDC, he taught high school mathematics for 24 years to a widle range of students in the Woburn, Massachusetts, public schools, chairing the department for the last decade of his term.
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From page 107... ...
- ~ 1 - -~ J R :::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::: he coals of School O notentla ~· ~O ~Y ~Y O ~
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From page 108... ...
Pbe resented in a practical context r' · ~ W1L oe These
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From page 109... ...
- c~ - - - - - - - - - - - - - - - - - - - ~ - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - ~v · ~to ~· To ~ To ~ of the picture but not the entire spectrum of
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From page 110... ...
the following projects: University oil Minnesota Talented Youth Mathematics Program (UMTYNIP, state and private funding)
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From page 111... ...
For 1 ~J · 1 1 ~ example, students WIll need to creche h ah ah ~ ~1 ~ ~ '1 ·` wileL''er IL''ey can acorn LO buy a car anal, II so, whether it would be better to lease; or do- ~ · 1-~ ~ ~ · Ing llrst. cater In Ille, sound Recisions can come from an understanding of annuities ~1 11 Lo 1 ~ and, more generally, tl to present value Ol which funds need to be saved for future repairs, others will need to consider the pros and cons of renting versus buying.
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From page 112... ...
The discussion above for example can be nhrasecl in more , A, ~ (1~/) ~ - P where f is the annual interest ~ , rate P is the $250 000 annual a ment the , I P Y lottery winner was receiving and ~ is the amount of money still investecl at year n in order to produce the annual payments Then .
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From page 113... ...
known to be far too low Explore the mother ,_ matics behind the binary search method in which the next guess is always the average of the best high ancl low guesses so far. Explore the mathematics behind the linear interpolation search method in which the next guess is determined by fincling the intercept of the line between the best high llf stuclents are impatient with a Usearch~ Prom ceclure ask them to use algebra to find a fort s mula.
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From page 114... ...
and its extensions can provide ities for exploration and discussion of other financial instruments, such as annul ' · · 2 ~ S ~t~es/ pens - - - -- - -I- - - - - - - -~ -- ~- - - -- - - of expected re1:urnl and the liquicli,:y
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From page 115... ...
~ at Mercy claims that if you look at 1:he death rates more carefully, you will see tha1: they are a better facili1:-the sirnpl treat a lot Y Y Y of patients who are more seriously ill Analyze the given data and make a recom ~nendation to our board of directors Y memo in which you clearly justify your decision knowing that the director of the , ~ hospital ou do no1: choose ma appeal Y Y son's paradox it can also occur in other situ I ations involving Weighted averages. Similar most women are employed in low paying Because of the apparent paradox!
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From page 116... ...
LQOKIng at the se~arate cleath rates however the ~ic ~I I ~ tion the death rate is lower at Merc Simi~ I y. ~ ~ ~ · ·~ ~ 1 ~ IJy race, lor Llle univers'Ly as a wilole, anu then separated by college or by department.
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From page 117... ...
By similarly llf one thinks of the death rates as fractions' between the separate death rates and the the case of Mercy hospital, the Uadelitionn looks as follows, where the 63 indicates that this is not the standard aciclition of fractions. r ~7 rat ~_ D/ O~ Notice that this Uaciclition', is perlformecl form the stanclard aciclition of fractions.
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From page 118... ...
Superimposing the data from Excelsior HQS~ pital upon that ~ that the sides of the Excels M_ ercy ~ 3) shows the Mercy parallelogram, but Mercy has a might use dynamic geometry software to .
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From page 119... ...
plane's capacity then with rounding the J J J somewhere between t 95% and 2 05% ~ O ~ Using these exact percentages, the board can conclude that the plane can hold between 48 and 51 machines. One decimal data reduced the uncertain" in the answer y from an machines LO A
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From page 120... ...
If we consider a coordinate lanevvil:h oinl:s (x ) P P fY, these two inequalities determine ~ square of side 1 This square (Figure 3)
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From page 121... ...
that 1 x 1 = 2' This requires calculating the portion of the square that satisfies xy ~ ~ 5 o (Figure 5~0 Is this bigger or smaller than 1/8 calculated as the area of the upper triangle in Figure 4? A comparison of Figures 4 and ~ shows remarkable similarity What is the prep o cise relationship between the line x ~ - 2 ~ ~ yes and the curve xy= 1 o5?
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From page 122... ...
of the curve x - 1 5 the curve must lie Y ~ ., below the line insicle the square. So answer should be a little bigger than 1/~- 12~ ~ U ~ .
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From page 123... ...
question: Are the two rules simply two different ways of saying the same thing or are the offering different advice, As stated the Y ~ · , rules may provide visual images of how far to stay behind another car, but translating that understanding into Practice on the road To The units for the car-length rule are miles Her hour and car lengths and the units for ~lo , Cal sedan is about 14 feet so the car~len~th J 2:1 of interpreting rules of thumb and comparing their results with real data could help students realize that the rules the use have y implications for their actions Also there is ~ · , the 2 · T .
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From page 124... ...
~ u-` ~ · ~ ~f ~ l ~ ~ Lllen II yQUr speeu IS X mpil, IO''OW a~OUL ~ ~ ~ .
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From page 125... ...
estate agents/ rules of thumb may have changed as well. Every subject-from shop create a rule that would work for Dune Chile Y ~ dren Because chilcirents proportions change .
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From page 126... ...
the usability of the ,~ ~ ~ ~ 7 ~ ~ easier LO use In pracLIce L''an Live oL''er. Is IL easier to think in terms of distance measured I· 1 ~ LO ' ^1~ · ~1~ a Wl ~ vary as Lo WIll`::~!
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