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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

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Loss Formulas, Loop costs, average cost, Scale Model Aircraft, profit margins, UML models, airliner models, hobby shops, Natural Capitalism, science & Mathematics

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posted: | 7/12/2011 |

language: | English |

pages: | 23 |

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Profit and Loss Formulas for Tenth Students document sample

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