Middle Years Problems - 1999
Vi Maeers, Carlie Brentnell, Kelly Quinney, Kendra Struble, Ruth van Mossel Adema, Helen Molloy, Sherry Sunderland, Joel Christopherson, Shannon Silverthorn, Jodie Wykes, Maria Makris, Donna Frowen, Melanie Mott, Christine Halbgewachs, Stephanie Wurm, Lesley Boulanger, Erica Goode, Lisa Mohr, Shalyn Sitter Andrea Leier, Patrice Klein, Frances Nederhoff, Jenn Mc Ewan Carrie Hopson, Mike Knoll, Lynell Ruecker, Corey Willms, Larry (James) Fuchs, Larry Penner, Jodie Hanson,Shauna Dombowsky
Faculty of Education
University of Regina
During the middle years mathematics methods class (EMTH 215-030) in the of Winter 1999 at the University of Regina, 30 students
worked in small groups gathering data on their group members, and then each group developed a story context that
was meaningful to them. Within this context they creating a problem, which represented a real-world situation
and addressed Saskatchewan middle years mathematics content. Each problem was given to other groups to solve, each
group solving at least two other problems. The "solving" groups provided feedback to the problem creators,
and the "creators" then altered their problem according to the feedback they received.
Each group reflected on the different processes of a) posing a problem, b) solving a problem, c) providing feedback
on a problem, and d) accepting feedback and changing parts of the original problem. All of these different processes
were carried out in the same grouping arrangements. Lastly, each group had to submit to the course instructor the
're-worked' problem, a summary of feedback from others, reflections on the different processes, how their problem
might be used in the middle years curriculum. Below are the eight problems developed by the groups in the class.
In solving the problems created by others, each group was asked to consider the following.
- What type of problem was it? (e.g., process, translation, application, puzzle, . . . )
- Was sufficient information provided to solve the problem?
- Could the problem be solved in more than one way?
- Was there misleading or deliberate irrelevant information provided? What did you do with this information?
- Was this an interesting problem to solve?
- Did you enjoy trying to solve this problem? Why or why not?
- Did you successfully solve the problem? Did you solve it more than one way?
- Comment on the problem's creativity.
- Comment on how well you worked as a group in solving the problem.
- Can you offer suggestions to improve the wording of the problem to make it easier/harder/more interesting,
We ask you the teachers, and, in turn, your students, to work through the following problems and address the
above ten items. We, the students of EMTH 215, section 30, would like your feedback on our problems. We would also
like to provide you with feedback on your strategies and solutions. We will write back to you or we will e-mail
you to give you feedback on how you solved our problems.
You can write to us at the following address:
Students of EMTH 215-030, c/o Dr. M. Maeers, The Faculty of Education, University of Regina, Regina, SK, S4S 0A2.
We will be pleased to communicate with you. If you want to talk about a specific problem given below, then simply
give the students' names, and make sure you write EMTH 215-030 in your communication with Math Central. Also,
be sure to give your names and your teacher's name(s).
MIX-UP AT McDONALD'S
Grade Level: Grades 7-8
Number of Students Who Should Work Together on this Problem: 3 - 5
Carlie, Kelly, and Kendra went to McDonald's. It was lunch hour and they were all hungry and in a hurry. Between
the three of them they ordered: a Big Mac, a cheeseburger, a McChicken, and a Quarter Pounder. They also ordered
a small, large, and super size fries along with two drinks. Can you figure out what each girl had for lunch using
the following clues???
1) Kendra had two burgers.
2) Kelly didn't have a Big Mac.
3) Carlie had a McChicken.
4) The person who had the Diet Coke had the Quarter Pounder.
5) Only two girls ordered drinks.
6) The person who had the McChicken had a strawberry shake.
7) Kendra was short on change so she couldn't afford a drink.
8) The person who had the Quarter Pounder didn't have super size fries.
9) The person who did not have a drink had large fries.
"WE'D LIKE TO ORDER PIZZA, PLEASE"
Ruth van Mossel Adema,
Grade Level: Grades 8, 9 and higher level grade 7
Number of Students Who Should Work Together on this Problem: Individuals or small groups of two or three solvers.
Sherry, Ruth and Helen were getting together over supper to work on their math homework. In order to save time,
they decided to have pizza delivered. They agreed to order a medium size "Canadian" pizza (pepperoni,
back bacon & mushrooms).
The students checked prices listed in the Yellow Pages of their phone directory. They found that Dominators Pizza
sold a medium "Canadian" for $14.55; Pizza Palace sold one for $9.95; Luigis sold a medium for $15.45.
Sherry began to phone Pizza Palace - their pizza looked like the cheapest to her.
"Wait!" called Helen. "Their pizza is only 10 inches. That's too small."
Ruth checked and found that Luigis' medium was 13 inches, while Dominators' medium was 12 inches. Pizza Palace
also had a 12 inch pizza (called large), but at $14.95.
Sherry had $6.50 with her. Ruth had $7.43. Helen had a $10.00 bill.
They live in Regina, Saskatchewan, where the sales tax on food is 7%.
The students ordered the most inexpensive pizza per square inch. Which pizza did they order?
How much money, altogether, did Sherry, Ruth and Helen have left over?
If this was a "Canadian" pizza, why was it measured in inches, eh?
SHOP TILL YOU DROP
Grade Level: Grade 7
Number of Students Who Should Work Together on this Problem: Individuals or pairs
Credit Card balance before shopping spree:
Shannon: 783.00 + 15% (per annum)
Maria: 343.00 + 17% ( per annum)
Jodie: 545.00 + 12% ( per annum)
All 3 girls go to the mall to shop. By the end of the day, each girl has purchased one item. Later in the month,
Shannon guesses that her credit card statement will be $900.00, Maria's is $500.00 and Jodie's is $625.00. A shirt
at $85.00, jeans at $100.00 and shoes at $40.00 were purchased. Shannon loves her new shirt, but what is her actual
balance with interest? Maria looks great in her new jeans, but what is her new total? Jodie is stylish in her
new boots, but what is her new credit card debit? Please remember that interest is not charged on the new purchases.
BACK TO SCHOOL
Grade Level: Grade eight/nine
Number of Students Who Should Work Together on this Problem: Groups of four
Donna, Stephanie, Christine and Melanie went away for the summer of 1998. They all needed to be back in Regina
before their first day of school, on September 7. Each person left her vacation spot on August 5, at 8:00 a.m.
Regina time. With a group of three other friends, ride along with one of the four girls on their way back to school
(in your group of four, one person should do part A, one person part B, one person part C, and one person part
A) Donna left Ottawa in her sporty black family car at a speed of 100 km\h, and drove a total distance of 2781
km. For every 2 hours she drove, she had to stop for 15 minutes to have a potty break with her 3-year-old son.
Being a good mom, Donna also stopped each night for bedtime at 8:00 p.m. and started again at 6 a.m.
B) Stephanie "the speed-demon" left from Calgary at 7:00 a.m. with a distance of 792 km\h to cover.
She was travelling at a speed of 120 km\h, but she did slow down to 100km\h each time she approached a radar zone.
She passed through 4 of them that were each 10 km long.
C) Christine, afraid of heights, decided to fly home from Montreal, which was a distance of 2980 km. The plane
traveled at a speed of 1200km\h. However, the flight crew, in their haste, forgot to fill the plane with enough
gas to make it to Regina, so the pilot had to make an emergency stop in Winnipeg, where they were delayed for 5
D) Melanie left from Dawson City, Yukon, cycling at an average speed of 120 km\day. She had a distance of 3600
km to cover. On one occasion, she had to back track 20 km due to a forest fire. She rested for 72 kh in Whitehorse
and hitched a ride with Monty the truck driver and his one eyed dog Flash, who drove for 48 h averaging a speed
On what day, and at what time would each of the travelers arrive in Regina? Meet back with your friends to talk
about parts A, B, C, and D above. Which girl arrived back in Regina first? Who got back second? Who was the third
to get back and who got back last? Who did you think would be the first to arrive in Regina? Were you surprised?
COME TO OUR RESCUE!
Grade Level: Grades 7-9
Number of Students Who Should Work Together on this Problem: approx. 3 students
Lisa and Lesley are life guarding at Regina Beach one hot summer day. Shalyn and Erica decided to catch some rays
on their rubber raft. Suddenly a wind came up and knocked Shalyn and Erica off their raft into the water. Stranded
in the middle of the lake, Lesley and Lisa must come to their rescue.
The beach is 40 km across. Lisa is on the east side of the beach 2m in shore. Lesley is guarding on the west
side of the beach, 15m in shore. Both are at the boundary of the beach. Shalyn and Erica are 130m off shore and
directly in front of Lesley. Lisa can swim at 70m\min and Lesley can swim 80m\min. Both can run on the beach
at the same speed they swim. Who will get to Shalyn and Erica first and how long will it take them?
Jenn Mc Ewan
Grade Level: 7 or 8
Number of Students Who Should Work Together on this Problem: 1-4
Frances, Andrea, Patrice and Jenn were on a shopping trip in Niagara Falls, Ontario. On the last morning of their
trip, Frances was glancing at the plane tickets and realized that their flight from Toronto was leaving at 11:15
a.m. and not 1:00 p.m. as originally thought.
Is it possible that they could make their flight to Regina, Saskatchewan if it's already 8:30 in the morning?
How fast would they have to drive in order to get to Toronto, and on the plane, if Toronto is 243 km away?
Things to consider:
Leave 10 minutes for packing
Leave 10 minutes to fill the gas tank and use the washroom.
Leave 5 minutes to catch the flight.
Leave 10 minutes for a speeding ticket.
NOT IN THE UNEMPLOYMENT LINE!
Corey, Mike, Carrie and Lynell all want to be teachers. Corey wants to teach Grade 8, Mike wants to teach Grade
6, Lynell wants to teach Grade 7, and Carrie wants to teach Grade 9.
Lo and behold, all of the teachers got jobs but none of the aspiring teachers got jobs in the grade they wanted,
and none ended up teaching the same grade. With the following clues can you figure out which school division each
teaches for, which grade they teach, and which subject they ended up teaching.
1. His Grade 9 math class is currently doing problem solving.
2. One of the teachers ended up teaching in the Yukon, another is teaching in Australia, one is teaching in the
Regina Public School Board, and the last one is teaching in the Regina Catholic School Board.
3. The health teacher does not teach the lowest grade.
4. Carrie meets Lynell every Wednesday at Boston Pizza for supper, right after school. One Wednesday night Carrie
and Lynell discussed the paintings Carrie had created with her students.
5. The social studies teacher had his Grade 7 students study why they had daylight all day in the summer time where
6. Corey is always very concerned about his health and well being.
7. Mike tends to his huskies every day; sometimes they are his only means of transportation.
8. Lynell likes painting.
9. No teacher teaches the same subject as another teacher, the subjects they teach are art, math, health and social.
10. Lynell attends Holy Trinity Catholic Church every Sunday to set a good example for her students.
THE TRAVELING QUARTET
Larry (James) Fuchs,
Grade Level: Grade 8
Number of Students Who Should Work Together on this Problem: 2-3 students
James, Larry, Jodie, and Shauna are planning a trip to Toronto to see the Blue Jays play. They each need to have
$2000 saved in order to go. The difficulty is that they all make various amounts of money, work different amounts
of hours, and have different living expenses.
James works at a Data Center 25 hours a week and earns $14.50/hr. Larry works for the Department of Highways and
earns $15.00/hr., working 40 hours a week. Jodie is proprietor and makes $292.50 before taxes each week. Shauna
works at Sasktel 50 hours a week earning $17.50/hr. After 40 hours she gets paid time and a half. Each person
gives 15% to the government in the form of taxes each month.
Due to their different living arrangements, they each can save different amounts of money. Jodie can put away
35%, James can put away 27%, Larry can put away 20% and Shauna can put away 14% each month after taxes have been
deducted. In what month and week can they all travel together to Toronto if they begin saving on February 14,