2013  Fall  RESA  Secondary  Mathematics  

   

   

“Putting  the  Practices  Into  Action”      

   

   

       

Stefanie  Buckner,  Med,  NBCT  stefanie.buckner@bcsemail.org  828.231.2889  

Johannah  Maynor,  Med  Johannah.maynor@dpi.nc.gov  919.807.3842  

Crossing  the  RiverCrossing  the  River      Eight  adults  and  two  children  need  to  cross  a  river.    A  small  boat  is  available  that  can  hold  one  adult,  or  one  or  two  children.    Everyone  in  the  group  can  row  the  boat.    How  does  everyone  in  the  group  get  across  the  river?          1. How  many  one-­‐way  trips  does  it  take  for  the  eight  adults  and  two  children  to  

cross  the  river?      2. What  if  there  were  

a. 6  adults  and  2  children?  b. 15  adults  and  2  children?  c. 3  adults  and  2  children?  

 3. Describe  in  words  how  to  determine  the  number  of  one  way  trips  for  100  adults  

and  2  children.        4. Write  a  rule  for  finding  the  number  of  trips  needed  to  get  any  number  of  adults  

(A)  and  two  children  across  the  river.            5. What  happens  to  the  rule  for  finding  the  number  of  trips  if  there  are  different  

numbers  of  children?    For  example:  a. 8  adults  and  3  children?  b. 2  adults  and  5  children?  c. A  adults  and  11  children?  

   6. One  group  of  adults  and  children  took  27  trips.  

a. How  many  adults  and  children  are  in  this  group?  b. Is  there  more  than  one  solution  to  this  question?  c. If  so,  what  rule  fits  each  solution?  

   

Thanks to Karen McPherson Buncombe County, NC

Hexagon  Trains    Below  are  three  trains  with  a  hexagon  pattern.  The  first  train  is  simply  a  regular  hexagon  and  each  train  after  that  one  adds  one  additional  hexagon  to  it's  pattern.  

                             

             train  1                            train    2                          train  3    

1. Compute  the  perimeter  of  each  train.  (Each  side  of  the  hexagon  represents  1  unit.)  

 

2. Determine  the  perimeter  of  a  10th  train.  

 

3. Determine  the  perimeter  of  the  20th  train  without  constructing  it.  Describe  the  strategy  you  used  to  find  the  perimeter  without  constructing  it.  

 

4. Explain  how  to  find  and  compute  the  perimeter  of  any  train  that  uses  this  pattern.  Use  words,  expressions,  and  diagrams  to  support  your  reasoning.  

 

 

 

 

5. Find  as  many  different  strategies  as  possible  to  find  the  perimeter  and  justify  why  the  strategy  works.  

 

 

 

 

Task  Extensions  

6. Terri,  Morgan  and  Bailey  each  came  up  with  a  different  expression  to  find  the  perimeter  of  the        n  th  hexagon  train.  Use  words  and  diagrams  to  explain  what  each  student  was  thinking  to  find  the  perimeter  of  the  n  th  train.  

a. Terri:  1  +  2(2n)  +  1  

 

 

 

b. Morgan:  5  +  4(n  –  2)  +  5    

 

 

 

c. Bailey:  6n  –  2(n-­‐2)  

 

 

 

 

7. Can  your  solution  be  adapted  for  any  polygon  train  pattern?  What  if  the  train  was  in  the  shape  of  octagon?  A  decagon?  Explain  your  answer  using  words,  expressions  and  diagrams  to  thoroughly  answer  the  question.  

                             

Thanks to Karen McPherson Buncombe County, NC

100  trucks  a  day  to  haul  sand  to  Key  Biscayne  beaches  Ivan A. Rodriguez Work to add 44,000 tons of sand to eroded beaches on the eastern boundary of the Village of Key Biscayne is expected to begin the first week of June.   An estimated 100 trucks will be delivering the sand daily to the island during the 30- to 45-day project.   The $1.57 million re-nourishment, designed and permitted by Coastal Systems International on behalf of the village, will require 2,200 truckloads to be brought in weekdays from 7 a.m. to 6:30 p.m.   "This is a challenge because we are only allowed to operate during the village's construction hours," said Village Manager John Gilbert in reference to traffic concerns.   Marine turtle nesting permit requirements will also limit work to daylight hours.   The new sand, which has been permitted through environmental agencies as beach compatible, will come from E R Jahna Industries' Ortona Sand Mine near Moore Haven, FL.   Contractor Eastman Aggregate Enterprises plans to sequence its trucks from the upland mine to maintain efficient placement on the beach and avoid heavier impacts to traffic.   "The trucks will be sequenced to deliver sand at the staging site at an efficient interval, say every 3 to 5 minutes, over an 8- to10-hour work day," said village beach consultant Tim Blankenship from Coastal Systems International.   Due to environmental issues and cost concerns, the contractors won't be barging in the sand, as is generally done in South Florida coastal areas.   "Shallow water and sea grass beds adjacent to the beach on Key Biscayne have to be protected," said Mr. Blankenship, stressing that barging could damage the environmentally delicate communities.   The sea grass beds were previously harmed in a beach nourishment handled by the US Army Corps of Engineers in1987, said Mr. Blankenship. Over time, he said, the sea grass has recovered, bringing the beds very close to the shoreline along the beach.   The beach fill for the nourishment won't be placed on areas where the sea grass grows due to environmental permitting constraints and the high cost of mitigation.   Also, buying enough sand to fill the sea grass areas as well wouldn't be cost effective for the village, Mr. Blankenship said.   The sand is to go through extensive screening, filtering and washing within a five-story structure at the mine in Ortona to produce a high quality sand beach compatible sand product.   The sand's size, texture and color is similar to what is now on Key Biscayne's beaches, and the quality will not impact marine turtle nesting, Mr. Blankenship said.   Key Biscayne will need to add sand to its beaches more frequently due to the smaller quantities of beach fill limited by the upland sourcing.   "We anticipate two or three more events like this in the next 10 years, which we have the permit for," Mr. Gilbert said.   The 6,440 feet of shoreline to be restored will grow 20 to 40 yards wider, depending on the location.   The Miami Seaquarium, which is on the Virginia Key causeway along the road the trucks will use to bring in the sand, hasn't had traffic impacts over the past couple of years from previous restoration projects along the causeway and drilling of the Port of Miami Tunnel and expects the same scenario this time, said President and General Manager Andrew Hertz.   "We are confident that Miami-Dade County Public Works and Waste Management-Causeway Division working with the Village of Key Biscayne and the Rickenbacker Causeway Traffic Control Committee will insure that there will be no impact on the traffic along the causeway as a result of the Key Biscayne Beach re-nourishment project," Mr. Hertz said.   The Village Council of Key Biscayne plans to provide updated information about the project along with pictures and maps on its website. Rodriguez, Ivan. "100 trucks a day to haul sand to Key Biscayne beaches." Miami Today 17 May 2012 <http://www.miamitodaynews.com/news/120517/story7.shtml>

Delivery  Trucks                  A  company  uses  two  different-­‐sized  trucks  to  deliver  sand.  The  first  truck  can  transport  x  cubic  yards,  and  the  second  y  cubic  yards.  The  first  truck  makes  S  trips  to  a  job  site,  while  the  second  makes  T  trips.    1. What  do  the  following  expressions  represent  in  practical  terms?  Use  units  to  justify  your  response.  

a. S  +  T  

b. x  +  y  

c. xS  +  yT  

d. (xS  +  yT)/(S+T)  

e. xS  >  yt  

f. y  >  x  

 2. If  xS  >  yT  and  y  >  x  what  does  this  suggest  about  S  and  T?  Verify  your  answer  using  algebra.  

Thanks to Karen McPherson Buncombe County, NC

Slope,  Rate  of  Change,  and  Steepness:  Do  Students  Understand  These  Concepts?          

               

                                             Let  f(x)  be  a  function  defined  on  the  closed  interval  [0,7].    The  graph  of  f(x),  consisting  of  four  line  segments,  is  shown  above.        1. For  what  interval(s)  of  x  does  f(x)  have  a  rate  of  change  of  2?  Explain  how  you  got  your  answer?  

     2. On  which  interval  of  x  is  the  rate  of  change  of  f(x)  the  greatest?    Justify  your  answer.  

     3. Write  the  piecewise  function  for  f(x).  

     4. Find  the  values  of  x  for  which  f(x)  =  1.    Explain  how  you  got  your  answer.          

f(x)  

Buying  A  Car    

     

     Tony  is  buying  a  car.    He  will  choose  between  two  cars.    The  table  and  the  bullets  below  provide  information  about  each  car.    Calculate  and  explain  which  car  will  cost  Tony  the  least  to  buy  and  use.  

• Tony  estimated  he  will  drive  at  least  200  miles  per  month.  • The  average  cost  of  gasoline  per  gallon  in  his  area  is  $3.70.  • Tony  plans  on  owning  the  car  for  4  years.      

                           

Car   Cost   MPG   Estimated  Repairs  

Car  A   $3200   18   $700  

Car  B   $4700   24   $300  

Shooting  Free  Throws,  Probability,  and  the  Golden  Ratio  

                           Paige  Turner,  the  star  of  the  Bugtussle  High  School  basketball  team,  has  been  fouled  and  now  faces  a  one-­‐and-­‐one  situation.    If  she  makes  the  first  free  throw,  she  gets  to  shoot  a  second  free  throw.    If  she  misses  the  first  free  throw,  she  does  not  get  to  shoot  a  second  one.    For  this  season,  Paige’s  free-­‐throw  shooting  percentage  is  60%.    What  do  you  think  is  the  most  likely  outcome  for  Paige’s  one-­‐and-­‐one  free-­‐throw  situation  –  scoring  0  points,  1  point,  or  2  points  for  her  team?          1. Would  the  same  result  hold  if  Page’s  season  free-­‐throw  shooting  percentage  was  greater  than  or  less  than  60%?  

       2. For  what  range  of  Paige’s  shooting  percentage  would  2  points  be  the  most  likely  outcome?    For  what  range  would  1  point  be  the  most  likely  outcome?    O  points?  

           

         

                                                                                                                                     Consider  the  case  of  Corey  the  Camel  –  the  enterprising  but  eccentric  owner  of  a  small  banana  grove  in  a  remote  desert  oasis.    Corey’s  harvest,  which  is  worth  its  weight  in  gold,  consists  of  3000  bananas.    The  marketplace  where  the  harvest  can  be  sold  is  1000  miles  away.    Corey  must  walk  to  the  market  but  she  can  carry  at  most  1000  bananas  at  a  time.    Furthermore,  being  a  camel,  Corey  eats  one  banana  during  each  an  every  mile  she  walks  (so  Corey  can  never  walk  anywhere  without  bananas)    How  many  bananas  can  Corey  get  to  the  market?                                

Corey  the  Camel  (From  IMP  Year  I)  

 

                                                         There  were  420  students  who  ate  lunch  in  the  cafeteria.    Their  lunch  choices  were  55%  pizza,  20#  salad,  15%  hot  dogs,  and  10%  chicken  nuggets.        

1. Each  plate  of  chicken  nuggets  was  served  with  three  carrot  sticks.    How  many  carrot  sticks  were  needed?    Explain  how  you  got  your  answer.  

     

2. How  many  more  students  ordered  salad  than  hot  dogs?    Explain  how  you  got  your  answer.  

     

3. One-­‐third  of  the  pizza  orders  were  for  pepperoni  pizza  and  2/3  were  for  sausage  pizza.    How  many  orders  were  for  each  kind?    Explain  how  you  got  your  answer.  

     

4. Two-­‐thirds  of  the  students  who  ordered  a  hot  dog  took  a  ketchup  packet,  1/7  took  a  mustard  packet,  and  the  rest  took  one  of  each.    How  many  ketchup  packets  and  how  many  mustard  packets  were  taken  that  day?    Explain  how  you  got  your  answer.  

     

5. The  cafeteria  orders  packages  of  lettuce  to  make  the  salads.    Each  package  holds  2  pounds  of  lettuce.    Each  salad  was  made  with  approximately  10  ounces  of  lettuce.    How  many  packages  of  lettuce  were  needed  that  day?    Explain  how  you  got  your  answer.  

   

What’s For Lunch?