# Number, Number Sense and Operations Standard

Document Sample

```					                            5th Grade Math Standards

Number, Number Sense and Operation Standards-pages

Measurement Standards-pages

Geometry and Spatial Sense Standards-pages

Patterns, Functions, and Algebra Standards-page

Data Analysis and Probability Standards-page

1
Number, Number Sense and            Daily Living Skills      Personal-Social           Occupational
Operations Standard                                              Skills                 Preparation
Students demonstrate number
sense, including an
understanding of number
systems and operations and
how they relate to one another.
Students compute fluently and
make reasonable estimates
using paper and pencil,
technology-supported and
mental methods.

1. Use models and visual           Discuss the gas        Have student             Use models to
representation to develop the      gauge in a car         research average         represent the grade
concept of ratio as part-to-part   showing the            sizes for parking        or class’ job
and part-to-whole, and the         amount of gas left     spaces and the           interests (number
concept of percent as part-to-     in the tank. Show      minimum number of        who would like to
whole.                             different gas levels   handicapped parking      be nurses, teachers,
on the gauge and       spaces needed and        policemen, etc.).
have students          the size in a lot.       Compute pie charts,
covert that to         (regular parking         compute percents
percent and            spaces are 9'x12' and    and interpret results.
fraction ratios.       handicapped spaces       Identify how these
Have students find     [3% of the total]        groups can be
other situations in    should be 15'x20)        subdivided (by
everyday life that     Using the school         gender, by age, etc.).
shows amounts that     parking lot, create
can be converted to    parking spaces using
percents or ratios.    models and
percentage.

Divide students into
groups (e.g., month
of birthdays, color or
type of car, etc.).
Have students
compute ratios and
percents for each
2. Use various forms of “one”      Have each student      As a class make a        Have students make
to demonstrate the             bring in their         list of all the          a list of all the
equivalence of fractions;      favorite recipe.       different places you     professionals that
e.g., 18 = 9 x 2 = 3 x         Then explain that      see fractions daily.     would with fractions
24    12    2    4       they must make the                              daily in their jobs,
6.
recipe for the entire Have students use         and how frequently
6

2
class, and adjust      baby books to            each does so (higher
the amounts            compare their foot       vs. lower rate of
needed. Have           size to height when      usage) and for what
students discuss       they were born and       purpose.
how, compute the       now. Compare the
ratio for each         ratios (and use other
recipe (total vs.      measures if
class size) – then     available: head size,
reduce to least        etc.).
common
denominator.
3. Identify and generate          Provide the class      Have each student        Class will look into
equivalent forms of fractions,    with both circular     choose their favorite    different careers that
decimals and percents.            and rectangular        sports team and          work nutrition and
foods (pizza,          bring their win-loss     eating correctly.
pie/cake, etc) of      and other statistics     Students will bring
equal area. Have       (basketball:             in nutritional labels
students divide        freethrow and            from their favorite
each into equal        baskets ratios.          foods and calculate
pieces for the class   Compute from raw         these statistics for
and compare using      numbers (when            the product vs. the
percents, decimals,    given) into fractions,   daily recommended
and fractions.         decimals, and            intake. Which of
percentages. Which       these foods most
Have the students      forms are most           closely match the
participate when       commonly reported,       recommended diet
shopping by            and why does the         figures?
figuring out prices    class think so?
of sale items, and
computing
percentage of tax,
etc.
4. Round decimals to a given      Have students          Students measure the     Have students
place value and round fractions   round up figures on    time it takes            research the prices
(including mixed numbers) to      a grocery or other     classmates to run,       of clothes, food,
the nearest half.                 shopping receipt to    walk, or jog             shoes or different
the nearest dollar.    specified numbers of     items related to their
How can this help      laps around a track.     careers. Imagine the
them in real life      They record results      students worked
(estimating            in a table, convert      there and received a
approximate costs      measurements taken       10, 15, or 20%
to know if there       in minutes and           discount on these
was an error).         seconds to tenths of     items. Compute the
a minute, and then       discounted total and
compare speeds           then round to the
across participants      nearest cent.

3
and across numbers
of laps.
5. Recognize and identify          Students are            Class will play         Plan a scenario
perfect squares and their roots.   required to solve a     around the world        where a new
story problem to        with square roots       company increases
choose their house      and perfect squares.    its number of
address number.         Students will draw      customers by its
The space on the        numbers and must        square each day.
mailbox has 5           answer with the         How many
spaces but it must      correct square root     customers would it
combine a 2 digit       or square, and then     have in a week? In a
square number and       move that distance      month?
a 3 digit square        in 100 miles across a
number to form the      world map or globe.
5 digit number.
What are the
different options
that students arrive
at?
http://illuminations.
nctm.org/Lesson
Detail.aspx?ID=
L228
6. Represent and compare           Students will           Create a version of     Examine forms of
numbers less than 0 by             record winter           “Where in the world     owing money, have
extending the number line and      temperatures for a      is Carmen               a banker from the
using familiar applications;       week, or record         Sandiego?” using        community come to
e.g., temperature, owing           temperatures in         latitude and            class and give a
money.                             Alaska or a cold        longitude as + and –    presentation on bank
country. Class will     from 0,0. Draw          accounts and loans,
chart the               cards with              bouncing checks and
temperatures by         positive/negative NS    credit verses debit
day to compare          and EW directions to    cards. Examine
locations and also      see who can return      statements with
Fahrenheit and          the closest in 10       these figures
Celsius. Students       tries.                  indicated.
can compare
summer vs. winter
to compare above
and below 0 for the
different scales.

Give the students a
set “budget” along
with a list of bills.
Have them subtract

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all the bills (a
negative number)
to represent this on
a number line.
7. Use commutative,               Have students total     Show students how         Take salary and
associative, distributive,        living expenses for     to balance a bank         divide by 12
identity and inverse properties   one month. Then         account by using          months, then
to simplify and perform           have students           inverse operations to     subtract out rent,
computations.                     group these items       “check” the bank’s        etc. to find out
accordingly: rent,      results. Have             monthly spending
utilities, food,        students ask parents      and divide for
clothing, etc. and      if they do/do not         weekly, daily. Then
recalculate the total   have these types of       do the inverse
of each group and       accounts and why.         operations to check
then sum the                                      for accuracy.
groups. Have them
explain why the
overall total should
be the same. Use
these group totals
to form a budget.
8. Identify and use relationships Helping PTO or          For Field Day, your       Scenario: You are a
between operations to solve       parent group plan       class is responsible      district
hotdogs and buns        for 1 hour. How           have 174 students
for 357 students,       many games will           with disabilities in
and calculate           you have, and then        4th –5th grade to
according to the        how many supplies         divide among 21
number in each          (bats, balls, ropes,      teachers. Twelve
grade at the school.    streamers, etc.) will     more enroll during
Calculate for those     you need?                 week 1, and then
who may want 1                                    nine withdraw. How
vs. 2 hotdogs, plus                               do you keep these
teachers and staff.                               classes even?
How many extra
should be ordered
to “be safe?”
9. Use order of operations,       Give students a list    Give students a           Have the students
including use of parentheses, to of groceries and         guest list for a party.   examine a pay stub
simplify numerical expressions. their prices. Then        Include who is            and compute the
provide students        coming alone, who         gross vs. net pay.
with a grocery list     is unable to come,        Use order of
and a note to go        and who will bring        operations to
shopping. Have          friends. Have             compute how
students write the      students write an         deductions are
operation for each      equation for the list     calculated.

5
item on the list        using at least three
(especially for         operations to
multiple items—5        compute the total
apples, 2 qts. of       number. Use the
soda, etc.) to figure   same guest list and
out how much            include the types of
money they will         food and drink each
spend. Students         guest prefers
show how the total      (vegetarian, diet
is computed             drink, etc.) in order
according to the        to decide how much
order of operations.    to purchase of each.
10. Justify why fractions need    Log exercise,           Have students            Have students log
common denominators to be         sports training, TV,    convert wireless cell    volunteer time or
added or subtracted.              telephone, or           phone or Blackberry      job visits’ start and
computer time each      minutes to fractions     stop times, then
day using minutes.      and add together,        calculate length of
Then convert into       then calculate           workday. Subtract
fractions of an hour    weekly usage.            out breaks or lunch
to compute weekly                                time. Or have
totals. Have them                                students log their
log other activities                             parents’ work times.
in fractions of
hours and compare
for hobbies, etc.)
11. Explain how place value is    Students can add        Have students log        Have students go to
related to addition and           varying weights of      their results from a     the nurse’s or a
subtraction of decimals; e.g.,    packages they wish      gym class for speed,     medical office and
0.2 + 0.14; the two tenths is     to mail in tenths       distance, etc. using     get their weight
added to the one tenth because    and hundredths, for     measures in the          from a digital scale.
they are both tenths.             a total weight.         tenths and               Then add across the
Compare the price       hundredths. Add up       class. If they wore
of shipping these       the totals across the    shoes or heavy
separately vs.          class).                  clothing, subtract
together (if going                               out a set number for
to the same                                      each.
12. Use physical models, points   Have students           Have students track      How much of a
of reference, and equivalent      redesign the            the amount of time       newspaper is really
forms to add and subtract         storage space in        they spend in            news—or is it
like and unlike denominators      in the classroom.       a week (school,          Have students
and decimals.                     Have them use           sleeping, eating,        measure and
diagrams and            etc.). Have them         estimate the total
compute the             develop a pie chart      area of a newspaper

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fraction or decimal    that represents this. page, excluding the
of how much space      Then have students    margins, used for
is needed for each     develop a “dream      advertising and
major item.            day” use of time that express this as a
they consider         ratio.
“perfect” and         http://www.pbs.org/
represent this.       teachersource/
mathline/lessonplans
/msmp/news/news_
procedure.shtm
13. Estimate the results of      Each student logs      Have students         Have each student
computations involving whole     the number of          compute the changes pick one stock and
numbers, fractions and           hours s/he sleeps      in the population of  chart the increase or
decimals, using a variety of     over a week and        students with         decrease over the
strategies.                      computes a daily       disabilities over the past 6 months. Find
average. Convert       past several years    the average loss or
that into a decimal    (use IDEA’s report    gain (see #6 under
or fraction of a day   to Congress           Probability) and
and estimate how       http://www.ed.gov/    predict the next 6
many “days” they       about/reports/annual/ months’ activity.
sleep each month       osep/index.html).
and year.              Compute the
population change
Have students          between years and
calculate the          predict how much it
distance they walk     is likely to change
or drive to school     next year.
each day and use
that to estimate
their weekly and
monthly mileages.

Measurement Standard                   Daily Living     Personal-Social     Occupational
Skills            Skills           Preparation

Students estimate and measure to a required
degree of accuracy and precision by
selecting and using appropriate units, tools
and technologies.
1. Identify and select appropriate units to  Have students       Take the class     Have students
measure angles; i.e., degrees.               examine their       outside and ask    make a list of
range of            if they know the   careers that
peripheral          degrees            highly involve
vision. Have        between the        the use of
students stand      ground and the     angles and
on X on the         side of the        degrees

7
floor and mark    building (or        (contractor,
the end of        another clear       designer, etc).
vision on the     example). Ask       Bring levels and
both sides of     students to         plumb lines in
them. Measure     prove that it’s     to school and
the angle using   90 degrees          have students
a protractor and  without using a     examine the
compare with      protractor.         school.
the definition    Allow them to
for blindness     work in teams       Have students
and tunnel        and use creative    research one of
vision (200 or    ideas to try to     the careers
less)             measure. Then       including how
http://www.san    have them           they measure
diegoeye.com/o    compare with        angles and
phthalmologygl    using a plumb       degrees, and
ossary.cfm .      line (if they       what tools they
didn’t think of     use to do so.
Examine how in this).
the past people
used the earth’s
angle at
temples:
Stonehenge
(solstice)
temple at
Chicken Itza,
Mexico
(equinox) and
also eclipses
(NASA
http://sunearthd
ay.nasa.gov/200
5/index.htm)
2. Identify paths between points on a grid or    Have students     Pass out maps       Have students
coordinate plane and compare the lengths of      plan a trip to a  of the              write 3
the paths; e.g., shortest path, paths of equal   city in the       community to        interview
length.                                          United States – the class and         questions for
and using a map assign a              their school us
figure out the    different           drivers that
best way to       location to each    involve the
drive (highways of the students.      route they take
and interstates). They must find      to school. Have
Decide which      the shortest path   each student as
way would be      walking,            their bus driver
the fastest but   shortest path       one question

8
some alternate   driving, and        and then report
routes in case ofway most            their answer
construction or  commonly            back to the
accidents.       taken               class.
(by parents or
friends, etc)
from the school
to their assigned
location.
Students must
find the exact
distance from A
to B – but be
able to show
why that isn’t
possible (houses
or buildings in
the way, etc).
3. Demonstrate and describe the differences    Have students    Put students        Invite someone
between covering the faces (surface area)      create different into groups of 2    from the post
and filling the interior (volume) of three-    designs for      and give each a     office or form
dimensional objects.                           backyard         sheet of paper.     of packaging
pools. Which     must work           speak in class.
shape would be together to           Have them
the most         construct a 3       explain linear
effective for a  dimensional         size and volume
backyard (not    figure from this    issues in
too big, but     paper (box,         packaging and
deep enough to cone, etc). After     shipping and
swim in)?        designed the        why they use
Compare the      figure will be      the materials
different shapes filled with         they do.
and the surface popcorn, and
area with the    the group’s
volume to see    shape that can
which one is the hold the most
most efficient.  popcorn wins
the activity.
Afterwards
discuss how the
same area could
produce so
many
4. Demonstrate understanding of the            Students should Students will        Students are
differences among linear units, square units   pick a room in   use volume to       given different

9
and cubic units.                              their house and      examine             dimension
measure the          emergency           options for
dimensions to        health issues:      several office
bring into class.    pints of blood      cubicles and
They will            lost,               students get to
convert the          dehydration,        decide which
linear numbers       etc. Given their    they would
to compute wall      size and weight,    prefer.
or floor size (sq.   how much is         Dimensions
units) and then      their total blood   would be listed
room volume.         volume? How         linear, square
They will pick       does height or      units, and
new dimensions       weight impact       cubical units –
for their dream      computation of      students need to
room and             blood volume?       convert to one
examine how                              to be able to
small linear                             compare.
changes can
result in much
larger change in
volume.
5. a) Make simple unit conversions within a   Look into gas        Student will        Students will
measurement system; e.g., inches to feet,     prices in Europe     measure their       identify
kilograms to grams, quarts to gallons.        or Canada and        height and          occupations for
5. b) Make conversions within the same        the difference       weight and          which
measurement system while performing           compared to the      convert to          measurements
computations.                                 U.S. Students        centimeters and     are very
will report on       kilograms.          important.
that day’s gas       Have students       Discuss the
prices then          make                importance of
convert to liters    conversions         precise detail
to be able to        with their          and the impact
compare prices       family members      of being off by
with overseas.       as well             the smallest
What difference      (immediate          amount.
would it make        family,
to their family’s    grandparents,       Students will
daily activity if    aunt and uncle,     investigate the
gas was that         as many as          Hubble
expensive?           possible) and       Telescope
see if there is a   problem when
Students will        pattern with        U.S. NASA
compare              height and          scientists did
weather reports      weight.             not convert
in Canada and                            from metric to
convert              Students will       inches.

10
temperatures.      emergency trip
Give the           Europe. They
students a copy    will develop a
Explain that it    checklist with
doubled and        temperature
that they must     cautions for hot
figure out and     and cold
convert the        weather.
ingredients to
show the
appropriate
amount (cups to
pints etc.).
6. Use strategies to develop formulas for      Students will      Have students       As a class,
determining perimeter and area of triangles,   measure their      create blue         students will
rectangles and parallelograms, and volume      backyards or a     prints for a tree   work together
of rectangular prisms.                         local park and     house. Measure      to create a blue
figure out the     to find the         print of the
perimeter of all   perimeter and       school building.
the grass.         draw it to scale.   Measure the
Discuss using      Have them           different rooms
the lawnmower      measure and         and find the
to cut the grass   draw in             perimeter and
and how the        windows and         draw to scale on
perimeter will     doors as well as    the blueprint.
affect that.       a roof.             Divide different
Have students      Have them use       parts of the
separate areas     unique window       building to
of the yard and    and door            different groups
find the           shapes, then        of students and
perimeter then     compute wall        allow students
add parts to       area, volume,       to check each
each other to      etc.                others’ work
complete                               before the final
number.                                product is
complete.
7. Use benchmark angles (e.g.; 45º, 90º,       Have students      Have students       Examine houses
120º) to estimate the measure of angles, and   estimate the       build different     and buildings
use a tool to measure and draw angles.         angles between     degree ramps        designed by
clock hands for    and rings for       Frank Lloyd
different times    match box cars      Wright
of the day.        for them to play    (Scottsdale,

11
with.            AZ) Talliesen
Have students                      West, Falling
estimate the      Visit or get     Water (PA)
angles of the     online           Kentuck Knob
perimeters of     information      (PA) and
signs: STOP,      giant            of lines and
YIELD, etc.       rollercoaster.   angles with
Use benchmark    other architects
angles to        (ex. Frank
estimate the     Gehry).
degrees of       Experience
each—vertical    Music Project
and horizontal   (Seattle) or
(turns).         Guggenheim
Museum
(Bilbao, Spain)
www.greatbuild
ings.
com/Frank_Geh
ry.html
www.greatbuild
ings.com/
select by
architect
or
www.greatbuild
ing.com
/architects/Fran
k_Lloyd
_Wright.html

Geometry and Spatial Sense         Daily Living     Personal-Social Skills      Occupational
Standard                              Skills                                     Preparation

Students identify, classify,
compare and analyze
characteristics, properties and
relationships of one-, two- and
three-dimensional geometric
figures and objects. Students
use spatial reasoning,
properties of geometric objects,
and transformations to analyze
mathematical situations and

12
solve problems.
1. Draw circles, and identify      Examine             Draw concentric           Compare why some
and determine relationships        household           circles that represent    farmers use circular
among the radius, diameter,        storage for         levels of social          irrigation systems vs.
center and circumference; e.g.,    canned goods.       relationships, place,     linear systems.
radius is half the diameter, the   How can you fit     family, friends,
ratio of the circumference of a    more in the         acquaintances-explain
circle to its diameter is an       space given the     to others using radius
approximation of π.                size and number     distances.
of each?
Have the class work
together to design a
skateboard park.
Identify the layout and
and arc of ramps.
2. Use standard language to        Identify the best   Students describe to      Examine a diagram
describe line, segment, ray,       seating in          each other different      of your city
angle, skew, parallel and          classrooms,         geometric figures         developed by city
perpendicular.                     auditoriums,        found in their home,      planners. Examine
meeting rooms       school, etc.              for these elements to
for persons with                              maximize traffic
vision loss         Give directions to a      flow, pedestrians,
according to        classmate using           green space, etc.
sightlines (rays,   geometric terms—do
line segments)      they reach the correct
and parallel vs.    destination?
perpendicular
seating.
3. Label vertex, rays, interior    Explain how         Students must draw a    On a diagram, label
and exterior for an angle.         rays and circles    figure (as complex as   how light travels in
are used in         possible) then switch   telescopes for
standard scales     with a partner and      astronomy-compute
for weighing.       have them label the     the angles as the
different geometric     light is refracted
parts.                  through the
telescope.
4. Describe and use properties     Make a class        Design a school so that Have students create
of congruent figures to solve      quilt with each     each class has a view   a pattern to tile the
problems.                          student             into a central          lobby of a new
contributing one    courtyard. Allow        restaurant, shop,
part and            students to use         office, etc. Use
decorating it as    irregular shapes.       rotations and
they wish. Use                              reflections of
each student’s                              congruent figures
preferred shape                             (see Esc her designs

13
to create a class                            http://www.
plan for the                                 etropolis.com/escher/
quilt. (use a
variety of
geometric
shapes).
5. Use physical models to          Go to a store and   Examine the              Fit cubicles into
determine the sum of the           each student find   Biosphere2 (Oracle       office space-whose
interior angles of triangles and   10 examples of      A2) for geometric        design fits the most
quadrilaterals.                    triangles or        shapes and why this      people? Compute
quadrilaterals.     was done.                angles of cubicles.
Explain how         www.bio2.com/            Visit an office at
they are                                     school or in the
packaged, stored                             community and
and displayed.                               compare their
Examine the                                  arrangement.
angles work
together
tangrams-to fit
different shapes.
6. Extend understanding of         Compare X, Y        Play “battleship” or     Choose a local job or
coordinate system to include       coordinates to      other games using        business and get
points whose x or y values may     longitude and       coordinates. Or create   economic
be negative numbers.               latitude on maps    a version of “Where in   information from a
and globes. Have    the world is Carmen      local or state
students find       Sandiego?” and move      website: plot growth
their own city’s    students between         and decline over the
location and        locations using          past several months
those of their      coordinates.             or years on the x and
relatives.                                   y axis.
7. Understand that the measure     Have students Have each student              Compare jobs that
of an angle is determined by                     trace one of their
take pictures of                             use short angles
the degree of rotation of an                     hands on a piece of
trees at home, at                            (laser surgery) with
angle side rather than the                       paper with their
school, or local                             long rays of angles
length of either side.             parks. Computefingers spread apart.          (telescopes).
the angles of Measure the largest            Compare the size of
various tree  and smallest angles            angles.
branches,     between any 2 fingers
regardless of and compare
their length. differences by gender.
Discuss how finger
length does not impact
angle.
8. Predict what three-         Using activity #1 Examine floor plans            Compare 2-D city
dimensional object will result above, develop    and pictures of the            planning maps with
from folding a two-dimensional both 2-D and 3- U.S. Capitol. Divide             3-D CAD-CAM

14
net, then confirm the prediction   D representa-      into small groups and    representations and
by folding the net.                tions of kitchen   choose 1 aspect to       views. Use the 2-D
and food storage. develop as a 3-D          versions to try to
model. Then rate the     predict the 3-D
Have students      U.S. capitol virtual     images—how
imagine they are tour and compare.          accurate is it?
visiting Aruba     www.senate.gov/vtour/
Have them view view your same site,
one area on the    and you view his/hers.
360 degree         Then compare your
virtual tour, then maps and view the site
have each draw a again if needed.
2-D map of that
area. Check the
3-D version to
confirm (or have
a peer check).
www.aruba.com/
pages/vtour.htm

15
Patterns, Functions and Algebra             Daily Living Skills     Personal-Social    Occupational
Standard                                                                Skills          Preparation
Students use patterns, relations and
functions to model, represent and
analyze problem situations that
involve variable quantities. Students
analyze, model and solve problems
using various representations such
as tables, graphs and equations.
1. Justify a general rule for a pattern   Students will           Have students        Have students
or a function by using physical           compare the             examine growth in    choose one
materials, visual representations,        measurement of their    old vs new           career of
words, tables or graphs.                  arm span and their      accommodations,      interest and
height, and compare     or wired vs. cell    then compare
this across the class   phones: compare      employment
http://www.pbs.org/     growth of one with   opportunities
teachersource/          a decline in the     locally,
mathline/lesson         other.               regionally,
plans/atmp/new                               and
heights/newheights    Students are given     nationally:
_procedure.shtm .     list of names of       which would
class members that     be the best
has been               location for
reorganized. They      this career?.
must determine the
pattern of the list
and who might
come next (name
starting with a
particular letter,
male or female,
etc.).
2. Use calculators or computers to        Have students         Have students          Compare two
develop patterns, and generalize          calculate how many    choose a sports        workers, one
them using tables and graphs.             times they can        team or an athlete     working at
bounce a tennis ball  to follow. Collect     minimum
and create a graph:   their performance      wage and one
http://illuminations. scores and graph       working for
nctm.org/Lesson       these. Compare         \$1.00 more.
Detail.aspx?ID=L246 teams and athletes.      Compute how
Have students          many hours it
explain other          would take
qualities that they    each worker
individuals/teams.     \$1,000.

16
3. Use variables as unknown              Have students use     Have students           Have students
quantities in general rules when         formulas to compute   examine Olympic         use formulas
describing patterns and other            unit prices for       athletes and use        to compute
relationships.                           utilities from the    formulas to             net wages
bills. How do the     compute their speed     from gross
rates compare across  using distance =        wages.
classmates?           time x speed.
4. Create and interpret the meaning      Have students         Students will           Students will
of equations and inequalities            compute how long it   compute how to          use a formula
representing problem situations.         would take them to    compile                 to compute
earn money for an     compounded              weekly
object they wish to   savings interest.       earnings
purchase given a      They will then          given a
specific weekly       compare \$500 of         specific
allowance.            money invested at       hourly wage
the current             and an annual
compounded              salary.
interest rate and       Which is
simple interest rate.   larger?
5. Model problems with physical          Students comparison Students compare          Present #4’s
materials and visual representations,    shop for an item they plans for cell          data on salary
and use models, graphs and tables to     wish to purchase      phones using table      vs. hourly
draw conclusions and make                using local and       and graphic data:       wage using
predictions.                             online stores.        which is the better     tables and
on price, model,      http://www.pbs.org/     for peer
features, and other   teachersource/          feedback on
class-determined      mathline/lesson         the preferred
criteria.             plans/atmp/call/call    method.
_procedure.shtm
6. Describe how the quantitative         Have students         Students compare        Students are
change in a variable affects the value   compare rate of       their own height        given a rate of
of a related variable; e.g., describe    growth across their   and weight to           pay increase
how the rate of growth varies over       current lifespan.     standard growth         over time (see
time, based upon data in a table or      Examine rates for     charts to find their    #4). Compare
graph.                                   toddlers vs.          “normative”             a raise of
adolescents and at    positive. Use that      \$1.00 per
other times. Discuss to predict their         hour vs. a
the variables that    future height and       raise of 20%.
affect growth rates,  growth.                 Compare this
including genetic                             with general
patterns.                                     inflation rates.

Data Analysis and                  Daily Living Skills     Personal-Social        Occupational
Probability Standard                                           Skills              Preparation

17
Students pose questions and
collect, organize, represent,
interpret and analyze data to
Students develop and evaluate
inferences, predictions and
arguments that are based on
data.
1. Read, construct and            Have students find     Have students           Have students graph
interpret frequency tables,       data on their          conduct an interview    the frequency of
circle graphs and line graphs.    appliance’s energy     about an issue at       career choice
usage—find on the      school, in their        preferences across
owners’ manuals.       educational or          Compare this with
Compare across         communication           national job
models within the      methods. Collect the    percentages (see
class.                 results and present     Bureau of Labor
as a table or as a      Statistics:
clearer to their
classmates.
2. Select and use a graph that    Have students          Have students           Have students
is appropriate for the type of    compare types of       compare data on         compare local vs.
data to be displayed; e.g.,       graphs to display      racial diversity of     state or regional
numerical vs. categorical data,   utility bill           the school, gender,     salaries for specific
discrete vs. continuous data.     information.           and other issues.       jobs. Compare to
Identify graphs or     Compare with other      local vs. state cost of
tables that are        schools.                living.
presented with some
bills.
3. Read and interpret             Compare voting         Have students           Determine number
increasingly complex displays     results across         examine bar graphs      of jobs available in a
of data, such as double bar       several issues by      of their academic       specific field and
graphs.                           comparing results      testing data across     those that are filled
by Democrats and       several grades and      (e.g., IDEA’s
Republicans.           for several subjects.   teacher and staff
Compare state vs.      How well did their      data:
local results.         school do?              http://www.ed.gov/
osep/index.html.
4. Determine appropriate data     Have students          Identify a problem      Have students
to be collected to answer         determine as a class   on keeping friends,     identify the key
questions posed by students or    something they wish    solving arguments,      criteria they would
teacher, collect and display      to purchase, or an     or improving self-      use to make a
data, and clearly communicate     issue of concern       esteem. Develop a       decision about a

18
findings.                          (high gas prices).      survey to ask others     career. Once these
Have students           how they solve these     are identified for the
identify the            problems or address      class, have students
important criteria to   these issues.            find this information
include in making a     Present the results to   and present it for
decision or coming      others in the school.    each of the careers
to a conclusion.                                 of interest.
Develop a list of
questions as a class
and do the
comparison
shopping or
interview local
shops. Present the
results clearly.
5. Modify initial conclusions,     Use #4 above to         Use #4 above to          Use #4 above to
propose and justify new            justify                 justify                  justify
interpretations and predictions    interpretations.        interpretations.         interpretations.
collected.                         information as          information as           information as
needed.                 needed.                  needed.
6. Determine and use the           Over a period of        For #2 or 3 above,       Compute these
range, mean, median and            three months,           have students            statistics for
mode, and explain what each        compare data for        compute mean,            numerical variables
does and does not indicate         particular utility      median, and mode,        for careers (see #4
about the set of data.             bills, comparing        plus range.              above).
range, mean,
median and mode.
7. List and explain all possible   Have students           Discuss taking           When applying for a
outcomes in a given situation.     examine daily           multiple choice tests    job, have students
weather. Discuss all    or true-false tests      identify the factors
of the possibilities    just be probability      the increase the
in comparison to the    alone. What are the      possibility of
daily weather           possible outcomes        positive outcomes?
forecasts and           for a test with 10
probabilities.          questions?
8. Identify the probability of     Have students flip      Have students roll a     Have students
events within a simple             coins to identify the   dice and graph the       interview
experiment, such as three          probability of          results across the       meteorologists to
chances out of eight.              having 3 girls or 3     class. Compute the       explain how they use
boys in a family.       probabilities and        probabilities in their
compare with class       work, and what these
results.                 predictions mean.
9. Use 0, 1 and ratios between     Have students           Have students            Have students
0 and 1 to represent the           compute the             compute the              compute weather
probability of outcomes for an     probabilities in #8     probabilities in #8 to   predictions using

19
event, and associate the ratio   to a decimal and          a decimal and           ratios and
with the likelihood of the       percentage form.          percentage form.        probabilities.
outcome.
10. Compare what should          Have students             Have students           Have students
happen (theoretical/expected     examine a health          compare the dice        compare weather
results) with what did happen    issue and their           experiment in #8.       predictions with
(experimental/actual results)    likelihood of getting     Try having each         actual weather. How
in a simple experiment.          something (e.g., the      student roll 2 die.     often did the
flu). Track their                                 meteorologists get
health during this                                their predicted
time to compare                                   outcomes?
predicted rates with
actual class rates.
11. Make predictions based on    Have students             From data on the        Have students
experimental and theoretical     examine increases         number of students      discuss the change to
probabilities.                   in gas or utility bills   with disabilities,      an internet and
over the past 2           have students predict   information society.
years, and then use       next year’s number      Have students
these data to predict     of students (use        predict how this has
changes over the          IDEA’s report to        impacted job sector
next year. Or use         Congress                growth and change.
the prior 3 years and     http://www.ed.gov/      Then compare with
predict, using this       about/reports/annual/   national statistics
year’s data to            osep/index.html).       over the past few
confirm or modify                                 years (www.bls.gov)
predictions.

20

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