# Profit and Loss Formulas for Tenth Students

Document Sample

```					                         Ohio Department of Education

1. Number, Number Sense and Operations: pages 1-5

2. Measurement: pages 5-13

3. Geometry and Spatial Sense: pages 13-21

4. Patterns, Functions, and Algebra: pages 21-27

5. Data Analysis and Probability: pages 27-30

6. References: page 30

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BENCHMARK or STANDARD                            TRANSITION ACTIVITY
Number, Number Sense and       Daily Living Skills     Personal-Social       Occupational
Operations Standard                                     Skills           Preparation
Number and Number Systems
1. Connect physical, verbal and   Find directions to      Find the shortest    Set up delivery
symbolic representations of   Howard, Princeton,      routes that you      service (could be
irrational numbers; e.g.,     Stanford                may have to use      a real student or
construct 2 as a hypotenuse   University, etc.        in emergency         school business:
or on a number line.          using Map Quest.        situations           homework
Print off the map       (applying the        delivery, cards,
that routes your        use of the           foods, flowers,
trip. Is this the       hypotenuse). For     etc.). Students
shortest distance to    example: police      will find the
travel for your         station, hospital,   most efficient
destination? Find       fire department.     routes applying
out by using the        How fast will        rules regarding
formula to              they be able to      triangles and
construct a             respond in an        hypotenuse. .
hypotenuse. If not,     emergency?           Students could
why? What is in                              also do this on
your way? Show                               foot in a
students that reality                        neighborhood
often doesn’t allow                          and try different
them to travel the                           routes. The
hypotenuse/shortest                          students could
distance because of                          also discuss the
land barriers or                             consequences
routes of the                                using the most
highways.                                    direct route to
some places,
Have students drive                          such as walking
a distance close to                          through people’s
their house using                            backyards or on
the hypotenuse                               other private
formula and also                             property (and
using a different                            legal liabilities
route. Time which                            for a ―business).
is faster and have
students explain
why. Have them
list what other
factors apply-

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construction,
barriers (trees,
buildings, etc.),
traffic. Use this
lesson to show
students the need to
allow for extra time
when traveling.

Students can
compare walking to
a destination, once
using the
―hypotenuse‖ and
another time using
―the other two
sides of the
triangle‖ (walking
forward and then
making a 90 degree
turn to walk the
rest of the
distance).
Meaning of Operations
2. Explain the meaning of the nth   Look at the lottery    Have students     Have students
root.                           and how the nth        design            contact insurance
root plays a role in   branching         companies
determining how        programming       regarding
much each person       with n choices    actuarial tables
receives if they       per selection,    for death and
pick the same          and compute nth   accidents. Use
winning number.        root. Have        nth roots to
Students will see      students use      examine the
how a large            spreadsheets to   number of
number can be          verify their      possible
drastically reduced    results.          scenarios, types
if multiple people                       of accidents,
split it equally.                        types of cars,
etc., given a set
Apply skills                             number of
learned to painting                      variables.
or carpeting a
room. If given the                       Use nth roots to
area in an nth root                      examine the
located between                          power of digital
two consecutive                          switching in

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numbers, have                             silicon chips for
students decide                           computers.
between the higher
and lower number.
Computation and Estimation
3. Use factorial notation and       Have students        Using their          How to maintain
computations to represent and   create a password    code, have           professionalism
solve problem situations        needed for an        students list        on a budget (how
involving arrangements.         alarm system.        positive and         to maintain a
Review their work    negative             professional
and use it to        consequences.        wardrobe
explain the          Short codes are      cheaply): Have
difference in using  easy to              students think of
2 digits verses 4    remember but         3 nice shirts, 4
digits. With their   people could         pants, and 2 pairs
password have        guess it. Long       of shoes. Have
them create all      are easy to          students list how
possible             forget, but hard     many outfits they
combinations. Talk   for people to        can form by
about using phone    guess. Again,        changing one or
#’s, birth dates, etc.
specifically         more items.
discuss the          Students could
The students could issues involved        be asked to look
pretend that they    when using           at their wardrobe
are installing an    phone numbers,       at home and pick
alarm system in      birthdays, etc.      out professional
their house in the   Students can         clothes they have
future and need to   discuss how the      at home (shirts,
pick a password      information that     pants/skirts,
(make sure that      is easy for them     shoes, ties, etc).
students do not tell to remember          They will choose
passwords that they such as phone         3 or 4 of these
are currently        numbers or           items and figure
using.) Students     birthdays may        out how many
should not write     be simple to         different
out every possible   remember but         combinations of
combination but      easy for other       clothes they
rather factorial     people to find       have. They will
notation to find out out.                 bring this
how many possible                         information back
combinations there Compute the            to class and
are.                 probability of       discuss how
multiple choice      many possible
Students could       tests (―blind‖       outfits they could
bring locks from     answering‖) for      have. They will
home or look at      getting all of 20,   discuss whether

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safes located at      50 etc. correct.   or not these
their house. They                        outfits actually
will note how                            match and will
many numbers are                         discuss how
on the dial and how                      buying clothes
many numbers are                         that are plain and
needed to open the                       match everything
lock. They will use                      would be helpful
factorial notation to                    if they do not
find out how many                        have a lot of
possible                                 money to spend
combinations there                       on clothes. They
are for this lock.                       will discuss as a
They will discuss                        class how many
as a class which                         shirts,
locks or safes are                       pants/skirts,
the safest.                              shoes, ties they
think it is
necessary to have
if they worked a
full time
professional job.

Consider the
occupation of a
landscaper.
Students must
create different
patterns to
decorate around
a house using a
pre selected
number of
flowers and
trees.
Experiment with
different
mixtures of
colors and
heights to see the
number of
combinations
that can be
created. Have
students remove
one flower from

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the selection and
see how that
impacts the
number of
combinations
that are possible.
4. Approximate the nth root of a      Apply skills            Have students   Have students
given number greater than zero    learned to painting    work together on contact
between consecutive integers      or carpeting a         supplying        mathematicians
when n is an integer; e.g., the   room. If given the     victims of a     or scientists to
4th root of 50 is between 2 and   area in an nth root    tragedy with     collect examples
3.                                located between        basic supplies   of work-related
two consecutive        (hurricanes,     uses of nth roots.
numbers, have          tsunamis, etc.)  What are the
students decide        Have them use    qualifications for
between the higher     nth roots in     their jobs?
and lower number.      estimating
quantities.      Visit a
construction site
(housing,
transportation,
etc.) for use of
nth root in their
calculations.
Bring one
example to the
class you
observed being
used.

Measurement Standard               Daily Living       Personal-Social       Occupational
Skills               Skills           Preparation
Use Measurement Techniques
and Tools
1. Explain how a small error     Have students          Have students      Have students go to a
in measurement may lead       draw diagrams of       examine the        local planetarium and
to a large error in           their dream house      problems that      talk to a scientist.
calculated results.           using a scale 1 in =   arose when         Have them discuss
10 ft. Allow them      countries on the   the importance of
to create every        international      measurement when
room that they         space station      looking at the stars.
would want,            used meters but    The students could
including carpeting    NASA used          focus on how
and furniture. Then    feet.              important it is to be
announce that the                         accurate when
scale was mistaken     Give students a    measuring in

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and 1.25 in. = 10     scenario of         different jobs,
ft. Have students     saving money        because of the
recalculate the       from their          potential problems it
carpeting and         paycheck for a      could cause once
whether or not        vacation            other calculations are
Discuss how such      amount). Have
a small detail        them compute        Have students
affected a lot on a   the number of       examine a type of
larger scale.         paychecks           banking fraud in
needed. Then        which fractions of
Have the class        announce that a     cents (from
bring their           savings             calculations) are
audiograms and        surcharge of        deposited into an
examine their         .025 must be        account. Over
decibel loss. Then    taken from each     millions of
explain that the      deposit.            transactions in a year
measurement of        Compute the         this can add up
sound (bels and       total surcharge     quickly (caught by
decibels) is          and the number      programs logging
logarithmic and an    of additional       number of deposits
increase of 10        paychecks.          rather than size of
decibels is a 100th                       deposits per day).
increase in sound     Have students
pressure levels.      compare the
Present the           total difference
problem of a          that can result
hearing aid           from rounding
amplifying a few      up (to the
decibels too much,    nearest dollar)
but greatly           vs. rounding
increasing            down for a
potential damage      series of school
to their ears.        purchases over
one month.
2. Calculate relative error.   Have students         Perform an          Have students contact
examine the           experiment in       district statisticians
statistical data      which students      regarding school
behind a medical      are tested using    testing data. Have
treatment or drug.    different ways      this person give
Examine the           of                  examples of relative
results including     communication,      error in calculating
relative error in     (ASL, MCE,          and compiling district
measuring dosage      oral and            proficiency data.
effectiveness.        written). Use a     What does a large or
Compare several       list of a hundred   small relative error

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treatments or drugs   words each time      mean in terms of the
and what their        with a different     results of these
relative errors of    form of              testing data. Have
measurement mean      communication.       students find how
for patients.         Have them            their own data
calculate the        compare to school
Have the students     mean, standard       and district results.
track the local       deviations, and
weather from          the relative error
different channels    of each compare
and newspapers for this with their
a month. Then         ―personal
have the students     preference‖ in
figure out the        terms of
relative error of the communication.
weathermen/
newspapers and
decide which is the
most accurate for
the weather.
3. Explain the difference       Have students         Have the             Have the school
between absolute error and   compare product or students do an          district statistician
relative error in            appliance testing     experiment on        (#2 above) explain
measurement.                 data with relative    the effectiveness    the difference
error (i.e., rate of  of speech            between individual
failure) versus       reading, video       errors in student test
receiving an          stories, math        answers in
appliance of          computation,         comparison with
product that          etc. Have each       relative error across
doesn’t work.         student              the population of
participate in       students taking the
several trials       test.
and compute the
class’ statistics
including
relative error.
Interpret the
relative error (in
terms of testing
confidence) vs.
individual
errors.
4. Give examples of how the     Use baking            Have students        Compare and contrast
same absolute error can be      proportions to        compare interest     2 jobs in which
problematic in one situation    show absolute         rates across         precision isn’t
but not in another; e.g.,       error through         savings              extremely important

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compare ―accurate to the          differences in taste.   accounts, CDs,       (retail) to a job in
nearest foot‖ when measuring      Have one group          etc. Have            which precision is
the height of a person versus     complete a recipe       students follow      really important
when measuring the height of      correctly, one          a set amount of      (pharmacist). Discuss
a mountain.                       group complete the      money and            when it doesn’t
recipe in which the     compute              matter to be precise
teaspoons have          possible             in relation to getting a
been changed to         earnings over 10     lot finished (folding
tablespoons, and a      years. Have          clothes) to the
3rd group complete      students use         importance of being
the recipe with         data to make a       precise (prescribing
tablespoons             decision             medication). Create a
changed to cups.        regarding saving     survey for the
preferences.         students to identify
Compare the                                  which type of job
impact of giving 2                           they prefer.
T. of cough syrup
to an adult vs. 2 T
to a 12 mo. baby.

5. Determine the measures of      Have students           Have students        Have students contact
central and inscribed angles   diagram a circular      recreate ―Wheel      Biosphere2 and get a
and their associated major     garden plot that        of Fortune‖ or       plot map: contact at
and minor arcs.                must include at         another game         http://www.bio2.com/
least 5 different       board. Compute        Have students
types of                the relative area    compute the layout
vegetables. Have        of each color vs.    and area for the
them compute the        the probability      various parts of the
area of the various     of the spinner       biosphere.
vegetable layouts       landing in each
using angles and        color (relative to
arcs. Have them         the
compare square          circumference).
footage with a
square and
rectangular plot.

Geometry and Spatial Sense           Daily Living          Personal-Social          Occupational
Standard                      Skills                  Skills              Preparation
Characteristics and Properties
1. Formally define and explain     Students will create    Students will          1. Students will
key aspects of geometric       a floor plan of their   compare the            visit architects and
figures, including:            ―dream home‖.           designs of             compare traditional
a. interior and exterior       They can be very        different shapes       vs. modern design
angles of polygons;        creative but must       of dining room         for variety of

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b. segments related to         include the            tables. Have          geometric shapes
triangles (median,          following:             students compare      in their design. Ask
altitude, midsegment);      - A stained glass      dimensions and        about computing of
c. points of concurrency       window with            area, then cut        area for soliciting
related to triangles        different polygon      cardboard to test     bids from builders.
(centroid, incenter,        shapes inside          user comfort. Try     Visit construction
orthocenter,                - a circular island    numerous              sites and identify
circumcenter);              in the middle of the   geometric shapes      how the
d. circles (radius,            kitchen                and polygons.         geometrical figures
diameter, chord,            - a triangular         Use a survey to       are created from
circumference, major        greenhouse or          compile outcomes      the blueprints and
arc, minor arc, sector,     gazebo in the          to compare            strategies for
segment, inscribed          backyard.              individual and        accurately
angle).                     Have students          group results.        computing area.
compute the            Compare with
dimensions of each     design catalogs.      2. Have students
(needed for                                  include geometric
potential builders’                          design elements in
bids).                                       their wood/metal
shop or other
projects.
Spatial Relationships
2. Recognize and explain the      Have students                                From #1 above,
necessity for certain terms    examine their own                            have students
to remain undefined, such      home for true right                          discuss with
as point, line and plane.      angles, flat                                 architects when
surfaces (planes),                           these terms need to
and congruency,                              be defined (using
etc. Identify                                building or floor
situations in which                          elevation,
these properties                             supporting beam
become important                             angles, etc.) and
(remodeling).                                when they do not
(congruent
elements, etc.).
3. Make, test and establish the   1. From #1 above,      1. Break the          1. Visit architect,
validity of conjectures        have students          students into         engineers, or
about geometric properties     compute the            small groups and      graphic designers
and relationships using        dimensions and         an identical set of   for use of
counterexample, inductive      areas using            tangrams or other     Pythagorean and
and deductive reasoning,       theorems in            manipulatives.        other theorems in
and paragraph or two-          comparison with        Have each group       their work and
column proof, including:       graph paper            create a unique       related
a. prove the Pythagorean       designs.               design and            computations.
Theorem;                                          compute various
b. prove theorems              2. Have student        dimensions. Give      2. Have the school

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involving triangle          measure the least     design to another    shop teachers
similarity and              number of the         group and            describe projects in
congruence;                 dimensions of their   compare              which these
c. prove theorems              bedroom, assuming     calculations.        theorems are
involving properties of     congruency, to        Discuss and          important for
lines, angles, triangles    compute all           resolve any          design and
d. test a conjecture using     Compare numbers
basic constructions         of measurements       2. Examine how
made with a compass         then use theorems     the Inca culture
and straightedge or         to compute.           used geometry:
technology.                 Compare results       http://agutie.home
program.
4. Construct right triangles,     Have students                              Have students
equilateral triangles,         interested in kites                        bring in a variety
parallelograms, trapezoids,    (as a leisure                              of products and
rectangles, rhombuses,         activity) bring in    Hand this            shapes. Experiment
squares and kites, using       examples of kites.    worksheet out to     with the most
compass and straightedge       Or have Japanese      students and ask     efficient ways for
or dynamic geometry            individuals present   them to identify     packing and
software.                      on their kite day     as many triangles    shipping these
celebrations and      and other shapes     items. Visit
types of kites.       as possible,         shipping and
Have the class        within a time        receiving services
discuss the variety   limit. Then have     of local stores to
of shapes used.       them compare         compare with
Have the class        with a partner to    students’ designs.
create their own      find other
designs (and test     examples. Discuss
them!).               how teamwork
helps in these
situations. Then
have teams create
their own designs
to share with
others.
5. Construct congruent figures    Have students         Have students        1. Investigate
and similar figures using      design playground     examine Escher’s     business use of
tools, such as compass,        equipment with        work and use of      CAD-CAM and
straightedge, and protractor   congruent figures;    positive and         other software
or dynamic geometry            use tools or CAD-     negative images.     products for
software.                      CAM programs to       Have students        design,
design.               create similar       engineering, and
images and have      architecture, etc.

11
peers review the
visual effects.      2. Have students
See website with     design a new
lesson plans at      school courtyard,
http://www.dartm     garden, student
outh.edu/~matc/m     lounge, etc.
ath5.pattern/lesso   involving
n7art.html or        congruent features.
artist’s info:
http://www.mcesc
her.com/ .
Transformation and Symmetry
6. Identify the reflection and     Have students find   1. Have students     Have students
rotation symmetries of two-   examples of          visit with a local   interview a dentist
and three-dimensional         product logos from   astronomy club       or dental assistant
figures.                      home, community      and use              regarding visual
or business logos.   telescopes.          image rotation
Examine for          Discuss how          when using mirrors
elements of          images are           to examine and
symmetry and         inverted (upside     clean teeth.
rotation. Also       down) and have
examine 3-D logos    them trace the
and advertising      path of light from
images.              space and into the
eye.

2. Have students
give each other
spatial directions
in ASL involving
right/left and
front/back:
viewers must
reverse these
directions to
interpret
correctly.
7.   Perform reflections and     Students can        Split the class into    Have students pick
rotations using compass and examine Grecian     small groups and        a company logo.
straightedge constructions  floor and wall      provide each            Use reflection and
and dynamic geometry        mosaics, Escher’s   group with a large      rotation to redesign
software.                   tiles, Dream        piece of isometric      the company’s
Catcher mandalas    dot paper. Each         logo. Set up a
etc. (see           group will create       coordinate plane
http://clem.mscd.ed a figure and            around the initial
u/~talmanl/Mandal identify a                logo, then have

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transformation,      students rotate and
and pass it to the   reflect around the x
other group (i.e.,   and y axes. Work
reflection,          by hand at first, but
rotation by 900,     after a draft is
etc.). The group     completed they can
completes the        finish it using the
transformation       computer.
as.html               and (if desired),
Examine using         identifies another   2. Look into the
hand tools and        transformation to    artistic career of
model using           be done by the       M.C Escher and
software. Then        original group,      his work in
design a tile pattern and correct each     interlocking
for a floor or wall   others’ work.        shapes, to examine
mosaic based on                            shape rotation.
mathematical
properties.
8. Derive coordinate rules for     Give each student a Have each student      Have students
translations, reflections and   set of Origami        bring a mirror       identify different
rotations of geometric          directions. Have      into class and       transformations
figures in the coordinate       them identify the     draw a picture of    used in animation
plane.                          views and the         themselves           films and clips.
coordinate rules in through the            Have students use
the directions for    reflection in        clip-art images to
the various steps of which they see.       rotate and
folding their paper Afterwards,            transform images
(e.g., reflecting     compare the          of their own, then
over the y axis).     picture to their     have classmates
Then give students face (have a peer       identify the
paper to follow the give feedback)         rotation points.
directions and        and have the
confirm or change student identify
their previous        coordinate rules
identifications.      they noticed
(reversal). OR
Have students
duplicate each ½
of their faces to
create a full
image; discuss
differences
between full-
image left and
full-image right
versions, and
reversed images.

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9. Show and describe the results    Students must          Create a class        Have class become
of combinations of              create imprints or     competition:          familiar with
translations, reflections and   impressions of         break students        geometry
rotations (compositions);       their footprints and   into groups and       sketchpad
e.g., perform compositions      bring them to class.   show a figure         software. Using
and specify the result of a     Looking at the         with steps of how     reflections and
composition as the outcome      shapes, have           to translate back     rotations of
of a single motion, when        students discover      to the original.      different shapes,
applicable.                     which symmetric        Groups must           students must
transformation is      work together to      create floor plans
taking place (glide    figure out what       of their school, or
reflection –           the original figure   use for activities #5
composition of         was before all the    or 7 above. Print
reflection and         reflections and       results and
translation). Have     rotations. First      compare. Identify
students identify      group to show the     jobs that also use
different real life    correct original      this type of
transformations.       figure wins.          technology.
Visualization and Geometric
Models
10. Solve problems involving        Have students          Have students         Using the PSS
chords, radii and arcs          examine patterns of    examine               (next column’s)
within the same circle.         butterflies using      transmission          wireless activity,
the Butterfly          requirements for      have students
Theorem:               wireless              compare
http://en.wikipedia.   communication         transmission grids.
org/wiki/Butterfly_    devices: what is      Determine which
theorem or             the radius of the     companies have
http://agutie.homes    signal and            more favorable
tead.com/files/Geo     repeater towers?      grids for reception
metryButterfly.htm     Use radii to find     for their locale.
l . Have students      the circumference     Identify users and
identify a butterfly   (reception area)      determine if they
design to use as a     and chords, etc.      agree with results
product logo or        Have them             of the service grid
compute the            spots within their    zones).
amount of color        home or school
needed for 100 of      and explain
these.                 according to the
transmission grid.

Patterns, Functions, and             Daily Living        Personal-Social         Occupational
Algebra Standard                     Skills                Skills             Preparation
Use Patterns, Relations, and
Functions

14
1. Define function formally and   Have students           Have students        Have students work
with f(x) notation.       bring in their          get in pairs and     backwards using the
electricity or gas      compare the          f(x) function to
bills. Have them        benefits of          compare daily or
compute or verify       leasing vs.          weekly earnings for
the unit charge by      owning a car of      various salaried vs.
applying f(x)           their choice; use    hourly job of interest.
function. Compare       f(x) function        Compare equivalent
rates between           and totals to        increases in salary
companies.              compare and          and hourly rates in
Compare several         verify               terms of the function.
months’ bills and       amortization
variable gas rates      rates for loans      Have students
vs. fixed, budget       vs. leasing.         compute Olympic
plans vs. usage         Present              record-holder speeds
payments over a         preferred option     using ―time x rate =
season.                 to class and         distance‖ formulas—
explain why.         what rates do world
When filling their                           record holders need
family car, have        Compare simple       to attain? What
students record and     and compound         careers are available
compute gas             interest rates for   to them later?
mileage using f(x):     deciding
compare to stated       between CDs
gas mileage for         vs. savings
their car.              accounts, etc.

Students compute
between C0 and F0,
metric and English
measurements.
2. Describe and compare          Split class into        Have students        Compare business
characteristics of the        groups and assign       compute              profits and losses, or
following families of         one term to each        population           income and expenses
functions: square roots,      group. Have them        growth over the      using absolute values
cubic, absolute value and     look in everyday        past 200 years.      and numerical signs.
basic trigonometric           life to find            Compare actual
function; e.g., general       applications of this    to ―best fit‖        Compare the
shape, possible number of     function. Each          exponent.            irrigation planes
roots, domain and range.      group must present      Compare overall      when using circular
their function and      population           systems vs.
different examples      growth to that of    rectangular systems:
of how to use it in     the disability       how much arable
the real world (e.g.,   population.          land loss results from
√ : find 1 unknown                           either?
side of right           Use trigono-

15
triangle, perimeter    metric functions
from a cube’s          to design a plate
volume, orbit          or medallion
radius from area or    and compute the
perimeter; absolute    amount of paint
value for              needed for
profit/loss,           1,000.
income/expenses.
Use Algebraic Representations
3.Solve equations and           Have students use      Have students        Have students
formulas for a specific     equations to solve     work in pairs or     calculate the amount
variable: e.g., express     the amount of          small groups to      of salary or wages
the base of a triangle in   laundry detergent      design a hubcap      needed to afford a
terms of the area and       they will need to      using both           house or condo, with
height.                     for different loads.   positive and         ¼ to ⅓ of salary
Also compute           negative (open)      allowed for a
proportions for        space; then use      mortgage. Calculate
using bleach, fabric   trigonometric        gross salary/wage
softener, etc.         functions to         needed to yield
compute amount       appropriate net (with
Have students           of material          taxes, SS, etc.
convert recipes         needed. Have         deducted using
from European or        class develop a      standard rates).
metric cookbooks:       rubric to
solve for amounts       evaluate design
as well as              + cost elements
temperature (F =        to determine
9/5 C + 32). Try        overall ―winner‖
out the results!       and vote.
4. Use algebraic representations Using the algebraic      Have students        Compute how an
and functions to describe     representation for      work in groups       optometrist
and generalize geometric      volume of a cube,       to estimate the      constructs corrective
properties and relationships. rectangular, ½          volume of            lenses. Compute for a
sphere, ½ oval or       various objects      larger model then for
other size              (salt grains and     distances within the
swimming pool           jelly beans used     eye.
and compare.            here):               http://hyperphysics.p
Compute the             http://acept.la.as   hy-
volume of a child’s     u.edu/PiN/act/p      astr.gsu.edu/hbase/ge
pool at ⅓ to ½ of       owers/powers.sh      oopt/foclen.html#c2
the full size.          tml. Set up a
Compare surface         classroom
area to volume of       contest.
the various pools.
5. Solve simple linear and        Have students           Students are on      Have students
nonlinear equations and       identify daily life     a wildlife           compute the three

16
inequalities having square     activities for using   documentation      phase electricity for a
roots as coefficients and      parabolas              trip: they see a   new shopping mall:
solutions                      (basketball,           grizzly bear and   http://www.bced.gov.
volleyball—            Have them          ns/aom13.htm. Then
airborne               compute the        use local power etc.
trajectories). Pick    size of the bear   costs to compute
one activity,          (they can’t get    monthly charges
measure the            close enough to    (heating per
dimensions, and        measure based      volume)—how
determine the          on the angle of    expensive is this mall
parabola and how       sun (time of       to maintain (include
the square root as a   day), length of    janitorial and other
coefficient effects    the shadow and     charges etc. as
the equation.          distance           desired)?
(measured later)
to where the
bear stood:
change time of
day/angle.
6. Solve equations and             Students will solve    Use money          Students are asked to
inequalities having rational   problems dealing       conversion and     minimize the labor
expressions as coefficients    with differences in    add the issue of   costs of hiring
and solutions.                 currency – figure      airport            different numbers of
out currency           conversion fees    workers for different
conversion             vs. automatic      shifts at different
between U.S. and       teller fees.       hourly wages at the
another country        Have students      ―Pizza π‖ at:
U.S. \$100.             contact            http://www.hsor.org/
international      modules.cfm?name=
Students are asked     airports and       Pizza_Pi . then also
to minimize waste      local banks to     check out
for a local            compare: which     McDonald’s
newspaper:             strategy is the    http://www.hsor.org/
http://www.hsor.or     most cost          case_studies.cfm?na
g/modules.cfm?na       effective?         me=mcdonalds or
me=Cutting_Times                          others.
Find out how their
local newspaper                           Students are asked to
minimizes waste.                          maximize profits for
an athletic shoe
company that
produces two kinds
of shoes:
http://www.hsor.org/
modules.cfm?name=

17
High_Step_Shoes
7.   Solve systems of linear         1. Students will      Students will     Students will
inequalities                    compare the cost of debate which        compute the
different forms of    they think are    differences between
power (electric,      fairer: flat or   two difference job
solar, gas, etc.) in  graduated         scenarios: one which
relation to the cost income taxes,      had a lower starting
it costs to start the using systems of wage but a better
power system and      linear            raise each year, or
the annual cost of    inequalities to   one that had a better
operation (e.g., C = justify their      starting wage but less
installation cost +   reasoning. Have of a raise each year.
annual operating      students identify Compute and display
cost X years of       which states do the trend lines and
operation). Tthey     and do not have where they intersect.
can then compare      income taxes.     Have them interpret
total cost based on Have students       this intersection in
life expectancy.      debate whether    terms of average
or not this       turnover and job
2. Have students      would this be a   change figures for
compute gasoline      sufficient reason workers.
prices and compare for relocating.
to their own
family’s choices.
http://www.hsor.or
g/modules.cfm?na
me=Jurassic_Oil
8. Graph the quadratic               Students will graph Have students       Have students
relationship that defines circles.   the impacts of        compute the       contact NASA and
virtual earthquakes orbit of the        compute orbits of
and the intersection moon and when comets; compare
point of two          it would next be with less elliptical
earthquakes in CA: full (or new), or orbits of planets:
http://www.math.m alignment of          http://deepimpact.jpl.
ontana.edu/frankw/ planets. Check nasa.gov/gallery/com
ccp/talks/MathTec their results         et_orbits.html
hExpo/high-           with a calendar. Students use
school.htm            Contact a local   graphing calculators
astronomy club to compute circles &
to find           ellipses for cones.
information       http://www.chevron.c
astronomical      dawards/pdf/ConicSe
events.           ctions.pdf
9. Recognize and explain that       Have students         Have students     Compare slopes
the slopes of parallel lines     compute fetal cell    examine stock     across national,

18
are equal and the slopes of    growth rates (cell     market pages to     regional, state, and
perpendicular lines are        doubling). Model       identify gaining    local metropolitan
negative reciprocals.          accelerated and        and losing          area employment
decelerated rates.     stocks. Use the     data. Interpret in
Compare                applet at           terms of local
cancerous tissue       http://members.s    economic health and
growth rates (can      haw.ca/ron.blon     stability.
use modeling at .      d/perp.APPLET       http://www.bls.gov/b
http://standards.nct   / to compare        ls/blswage.htm,
m.org/document/ee      inverse slopes.
xamples/chap7/7.5/
index.htm)
10. Solve real-world problems     Students explore       Students will       Students will pick
that can be modeled using     how supply and         compare             which they would
exponential or square root    local prices:          over the past       exponential increase
functions.                    http://illuminations   several years       beginning with one
.nctm.org/LessonD      and compute         more penny each day
etail.aspx?ID=L38      relative worth –    (exponential 1,2,4,8,
2                      for example if      etc.) or \$100 each
Students will          annual inflation    day (linear) for a
compare rates of       is 5%, a dollar     month. Have
simple and             would only be       students first predict
compounded             worth \$0.95 in a    and then calculate.
several rates: 3%,     every 14 years,     lanius/pro/rich.html .
5%, 7% etc. and        money is worth
annually).             original value).
http://www.datalife
.com/mall/pages/ex
amples/EXMP_IN
T.HTM
Analyze Change
11. Solve real-world problems     You and your           You’re on your      Have students
that can be modeled, using    spouse are filing      child’s school      choose an
systems of linear equations   your income taxes      PTA meeting         appropriate full-time
and inequalities              together. You get      and in charge of    or part-time job
a notice from the      the tickets for a   (summers, weekends,
an error and owe       game. Student       scenario is that they
\$2716 more             tickets are \$2.50   are saving for a used
dollars. You earn      and adults are      car (choose from
spouse’s income        516 tickets were    many hours will they
so how much            sold and the        have to work (minus

19
would your ―fair       total income         deductions)? If they
share‖ be?             was \$1,950. A        work overtime or
question arose       receive a bonus, how
Students will          about how many       will that change the
compare two cars       adults supported     number of hours
by computing the       the effort: figure   needed?
total monthly costs    out how many
for the loan           of each were         This lesson has
(choose a down-        sold.                students solve supply
payment amount,                             and demand issues
loan terms, and use    Use several          for a business:
amortization           scenarios for        http://illuminations.n
tables) and for the    dividing up          ctm.org/LessonDetail
gas/mileage            costs for a meal     .aspx?ID=L382
(determine distance    with tax and tip
to work). Decide       when sharing
which car would be     with a group of
the better deal.       friends.
12. Describe the relationship    Have students          Calculate            Students will contact
between slope of a line      calculate heights of   shadow planes        or interview city
through the origin and the   trees to be removed    of community         engineers or city
tangent function of the      from a property        buildings at         planners to identify
angle created by the line    without measuring      different times      construction usage.
and the positive x-axis.     the distance.          of the day.
How did buildings in
Compare the          NYC respond to 9/11
slope of             impacts, or New
height/weight        Orleans to Katrina—
between men          what are the slopes
and women.           for stress resistance?

Data Analysis and              Daily Living        Personal-Social         Occupational
Probability Standard               Skills                Skills             Preparation
Data Collection
1. Describe measures of center   Compare utility        Create a             Have students
and the range verbally,       bills over several     scenario where       compare their
graphically and               months to              students are         district’s and state’s
algebraically.                determine a budget     splitting a          grade-level testing
algebraically, to      restaurant bill      results, as well as
display graphically.   with a group.        students with and
Use central            How much will        without disabilities
tendencies vs.         each person pay      (also see
range to decide        (mean)? Is this      Measurement strand
whether they           fair according to    #2: standard error).
should pay             range of
monthly or on          individual           Students can

20
budget.              costs?             compare the
difference in the
Compare items       Compare a           paycheck with
sold in bulk vs.    landline phone      overtime vs. regular
individually at     bill to a cell      pay. How does that
grocery stores to   phone bill over     impact rate of
determine the cost  a period of         deductions vs.
per ounce. Explain  months to see       average deductions?
whether you would   which is more
use results by      efficient—
central tendencies  compare the
or range to make    different
graph the data.     make the best
decision.
2. Represent and analyze           Have students       Have students       Have students
bivariate data using            collect information graph data for      compare company
appropriate graphical           about the number    costs of            expenditures for
displays (scatterplots,         of hours a week     attending a 2- or   supplies vs. sales (to
parallel box-and-whisker        they exercise and   4- year training    determine profit) per
plots, histograms with more     record this         or college          year.
than one set of data, tables,   information into    program of their
charts, spreadsheets) with      graphical displays. choice. Collect     Students can graph
and without technology.         Compare across the data over the        local job market data
class.              past 5 years and    vs. state or national
compare at least    data to compare; or
Compare 2+ years 2 programs on a        can analyze
of any household    chart. Predict      government charts
bill (phone,        future costs then   and graphs to
electric, etc) or   discuss how         compare these data
total mileage on a  important this      and interpret for
car. Or collect     information this    possible trends
utility costs or    is to their         (www.bls.gov).
make & model        decision-
websites.
3. Display bivariate data where    Have students log   Collect survey      Calculate local or
at least one variable is        how much time it    information         state unemployment
categorical.                    takes them to get   about political     by month or season,
morning. They can local or              immigration or
log their daily     community           emigration from the
routine over time   issues, school      state, etc.
etc.
4. Identify outliers on a data      Use previous        Have students       Have students

21
display; e.g., use               activities’ monthly    compare the         examine their own
interquartile range to           bills, exercise, car   impact of a high    standardized testing
identify outliers on a box-      costs, food            outlier on          results and interpret
and-whisker plot.                purchases, etc. to     activity #1         how these compare
plot and determine     (restaurant bill)   with entrance
outliers.              or on a school’s    requirements.
Determine how this     grade level test    Compare scores and
(low cost outlier)                         patterns and outliers.
vs. budgeting                              Or have students
(outlier impact on                         examine industry
means).                                    performance testing
for a career of
interest.
Statistical Methods
5. Provide examples and              Look at national,      Students can        Compare state or
explain how a statistic may       state, regional        design a survey     industry press
or may not be an attribute        statistics (e.g.,      about a             releases with
of the entire population;         voting,                controversial       government data
e.g., intentional or              demographics—          issue (inclusion,   (from Bureau of
unintentional bias may be         age or ethnicity,      assistive           Labor Statistics
present.                          etc.) and analyze      technology,         www.bls.gov, etc.).
whether they           educational         Identify potential for
accurately             methods, etc.):     bias and then analyze
represent local        divide into 2       the type and choice
populations.           opposing groups     of statistics
Identify when          and have each       presented.
groups may choose      generate survey
to use certain         items. Compare  Compare statistics
―more favorable‖       for potential   presented by
groups or              bias. Give the  competing
subgroups of           survey and      perspectives: e.g.,
statistics.            compare results pharmaceutical
for bias.       companies vs.
consumer groups on
costs of medication..
6. Interpret the relationship        Interpret the       Have students      Compare how
between two variables           relationship        examine school different displays
using multiple graphical        between nutrition   outcomes and       emphasize certain
displays and statistical        and healthiness and testing data       factors. Use this to
measures; e.g., scatterplots,   plot changes        (e.g., ETS         compare salary or
parallel box-and-whisker        (amount of sleep    research on drop benefits data from a
plots, and measures of          vs. energy, amount outs and gaps:      workers’ versus
lifestyle).         rg/portal/site/ets perspective.

22
0b5cc7bd0ae70
15d9510c39215
09/?vgnextoid=
05f8e3b5f64f40
10VgnVCM100
00022f95190RC
RD .
Probability
7. Model problems dealing with      Students could                             Use germination
uncertainty with area           throw darts or use a                       rates and planting
models (geometric               spinner to                                 distances of a local
probability).                   determine the                              crop to determine
probability of these                       expected crop yields.
activities How                             Compare this to
does ―skill‖ change                        typical yields.
the probability of
certain events?
8. Differentiate and explain the   Examine how             Collect data       Use local economic
relationship between the        weather is forecast     regarding the      downsizing or
probability of an event and     to compute the          probabilities of   business closures to
the odds of an event, and       probability of rain,    certain events:    compute the odds of
compute one given the           earthquakes,            asteroid           any 1 store closing
other.                          hurricanes, etc.        collision,         or any 1 employee
catching Bird      being laid off.
Compute the             flu, etc.
probabilities of the    Compare the        Discuss the
birth of boys           relative           probability of annual
versus girls; why       probabilities      employment
are there higher        among them.        earnings versus the
rates for boys?                            probability of
Compute also the        Compute the        winning the lottery.
probability of          odds of winning
various disabilities.   at casinos and
how the ―house‖
wins more
overall.

References

Ohio Resource Center for Mathematics, Science, and Reading.
Homepage: http://www.ohiorc.org/
Mathematics Resources: http://www.ohiorc.org/browse/mathematics.aspx

23

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