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Profit and Loss Formulas for Tenth Students

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Profit and Loss Formulas for Tenth Students Powered By Docstoc
					                         Ohio Department of Education
                         Tenth Grade Math Standards


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




                                      1
 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-
                                  speed limits, road



                                            2
                                    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


                                              3
                                    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


                                              4
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



          5
                                                                              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


                                               6
                               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
                               furniture will fit.   (specific           made.
                               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



                                             7
                                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


                                              8
 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


                                                 9
   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


                                              10
      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
      and quadrilaterals;         dimensions.           discrepancies.       congruency.
   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
                                  using a spreadsheet   stead.com/files/in
                                  or CAD-CAM            dex.html
                                  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


                                              12
                                                         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.


                                               13
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
                                    design element;        identify ―dead‖       (and ―dead‖
                                    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.
                                   football,              his/her shadow.    bc.ca/careers/aa/lesso
                                   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
                                                           about upcoming om/about/programs/e
                                                           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
    linear, quadratic,            demand impacts         inflation rates     rather receive, and
    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.
                                  interest; compare      year (about         http://math.rice.edu/~
                                  several rates: 3%,     every 14 years,     lanius/pro/rich.html .
                                  5%, 7% etc. and        money is worth
                                  compounded             about half of its
                                  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,
                                  IRS that you made      basketball          after school). The
                                  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
                                  13/16 of your          $4. Altogether      want-ads). How
                                  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
                                    your choice—        measures to
                                    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-
                                    costs from business making.
                                    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,
                                    ready each          preferences,        worker or business
                                    morning. They can local or              immigration or
                                    log their daily     community           emigration from the
                                    routine over time   issues, school      state, etc.
                                    to collect data.    graduation rates,
                                                        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
                                     impacts purchasing     results.            subscores for
                                     (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
     center and spread.              of money made vs. http://www.ets.o management
                                     lifestyle).         rg/portal/site/ets perspective.
                                                         /menuitem.435c


                                                 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

Ask Dr. Math: http://mathforum.org/library/drmath/mathgrepform.html




                                                 23

				
DOCUMENT INFO
Description: Profit and Loss Formulas for Tenth Students document sample