Elementary Level Problems - 1999

 Vi Maeers, Chad Parker, Sheldon Rieger, Cheryl Brule, Rhonda Wilmot Stadnick, Leslie Cunnigham, Angela Downs, Kenna Mrygold, Belinda Swehla, Stacey Bradley, Kristy McCall, Brad James, Andrea Wolos, Kendra Slamp, Cheryl Horne, Leisa Neufeld, Cheryl Gero, Tricia Grant, Lisa Schindel, Niki Wasylowich, Kara Leonard, Heather Thomas, Rhonda Tomlinson, Marla Holzer, Kristie Forsyth, Tracy Cowen, Jennifer Mathies, Lynn Stevenson, Danita Goretzky, Doug Dahl Faculty of Education University of Regina

During a recent preservice mathematics methods class (EMTH 215-040) 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 elementary 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 elementary 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.

1. What type of problem was it? (e.g., process, translation, application, puzzle, . . . )
2. Was sufficient information provided to solve the problem?
3. Could the problem be solved in more than one way?
4. Was there misleading or deliberate irrelevant information provided? What did you do with this information?
6. Did you enjoy trying to solve this problem? Why or why not?
7. Did you successfully solve the problem? Did you solve it more than one way?
8. Comment on the problem's creativity.
9. Comment on how well you worked as a group in solving the problem.
10. Can you offer suggestions to improve the wording of the problem to make it easier/harder/more interesting, etc.?

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 40, 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 215-040, 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 215-040 in your communication with Math Central. Also, be sure to give your names and your teacher's name(s).

Number of Students Who Should Work Together on this Problem: approx. 3 students

Problem:

Rhonda, Sheldon, and Cheryl are visiting Chad in Japan. They are now at the bank waiting to change their money into Japanese Yen. Rhonda has \$678, Sheldon has 1/4 of what Cheryl has, and Cheryl has twice as much as Rhonda (all in Canadian Currency). Today, one Canadian dollar will buy 73 yen. How many yen will each person have after the exchange?
Extension: There is a 5% service charge on all currency exchanged. How many yen will each person have after the service charge?

UNIVERSITY CAR POOL

Leslie Cunnigham, Angela Downs, Kenna Mrygold, Belinda Swehla

Number of Students Who Should Work Together on this Problem: 2-4 students

Problem:

Leslie, Kenna, Angela, and Belinda are University students. They car pool every morning to the University of Regina. They have an 8:30 a.m. class. Leslie goes to pick up Angela first. She lives 6.7 km away from Leslie. Leslie is travelling at 100km\h. Next she picks up Kenna who lives 3.3 km away from Angela. The speed limit is 70km\h. After they pick up Kenna they travel 40km\h to Belinda's house which is 2.4 km away. Their final stop is the university. It is 5.2 km away from Belinda's house and they are able to travel 50km\h. What time does Leslie have to leave her house in order to get everyone to class on time?
Time = Distance
Speed

WHAT YOU LOOKIN' AT?

Number of Students Who Should Work Together on this Problem: 2- 3 students

Problem:

Everyday, Brad, Stacey, Kristy and Andrea sit in the food court and stare at people as they walk by. In 1/5 of an hour they see 4 people with red hair, 9 people with blond hair, 7 people with plaid pants, and 2 janitors. If they sat there for 4320 seconds, how many people with red hair would walk by?

MEETING MANIA

Kendra Slamp, Cheryl Horne, Leisa Neufeld, Cheryl Gero

Number of Students Who Should Work Together on this Problem: 3-4 students

Problem:

Kendra, Cheryl H., Leisa, and Cheryl G. Are supposed to meet at the university at 6:00 p.m. to do homework.

Leisa lives 10 minutes away
Cheryl lives 7 minutes away
Kendra lives 14 minutes away
Cheryl G. lives 20 minutes away

Leisa gets to the university at 5:58 p.m. Cheryl H. left home to go to the university 2 minutes after Leisa. Kendra arrived at the university 4 minutes after Cheryl G. arrives. Cheryl G left home at 5:52 p.m. What time did Kendra leave home?

NO TIME FOR BUGS

Tricia Grant, Lisa Schindel, Niki Wasylowich

Number of Students Who Should Work Together on this Problem: groups of 3 or less

Problem:

Niki, Tricia, and Lisa are in grade four and have a huge problem. They are best friends and want to go to see the movie "A Bug's Life." They all have busy schedules and need to find a common day and time to get together. Niki takes a Hip Hop dance class and Tricia is in cross country skiing. Lisa is super busy and is involved in both hockey and singing lessons.

Here is the activity schedule for Niki, Tricia, and Lisa:

Name Activity Day Time
Niki: Hip Hop Dancing Mon., Wed., & Friday 5-8 p.m.
Hip Hop Dancing Sunday 1-3 p.m.
Tricia: Skiing Saturday 10:30-2 p.m.
Skiing Sunday 12-4:30 p.m.
Lisa Hockey Tues. & Thurs. 5:30-7:30 p.m.
Hockey Game Sunday 5-8 p.m.
Singing Saturday 2-3:30 p.m.

The movie schedule is as follows:

Now playing at Rainbow Cinemas: A Bug's Life
Day Time

Monday-Thursday 6:30-8:30 p.m.
Friday 5:30-7:30 p.m. & 9:00 - 11:00 p.m.
Saturday 1:30-3:30 p.m. and 6:30 - 8:30 p.m.
Sunday 1:30-3:30 p.m. and 6:30 - 8:30 p.m.

Remember that the girls go to school from Monday to Friday from 9:00 a.m. until 3:30 p.m. and they need to be asleep by 9 p.m. on nights when they have school the next day.

When can the three girls find a time when they can all go to the movie together?

CRAFT SALE COPYING

Kara Leonard, Heather Thomas, Rhonda Tomlinson

Number of Students Who Should Work Together on this Problem: individually or in pairs

Problem:

Kara, Heather and Rhonda have been busy making crafts after school. They have decided to sell their crafts in a sale next weekend. To advertise the sale they decided to photocopy some flyers. In total they have \$8.40 to spend. How many copies can they make at each store?

Quick Copy: 6 copies for only 36 cents
Copies 'R Us: Super 7 sale! 7 copies for just 49 cents

Which store has the better deal?

SMARTIE CRAVING

Marla Holzer, Kristie Forsyth, Tracy Cowen, Jennifer Mathies

Number of Students Who Should Work Together on this Problem: groups of 2 or 3

Problem:

Tracy and Marla had a craving for Smarties. They decided to go to Safeway to buy Smarties in the bulk section. Kristie and Jen also had a craving for Smarties and decided to go to Shoppers Drug Mart to buy a regular box of Smarties. When Kristie and Jen counted out their Smarties, they discovered they had 97 in their box. Tracy and Marla counted out their Smarties and found that they had three times more Smarties than Kristie and Jen. How many more Smarties did Marla and Tracy have than Kristie and Jen?

SCHEDULING NIGHTMARE

Lynn Stevenson, Danita Goretzky, Doug Dahl

Number of Students Who Should Work Together on this Problem: 2-3 students

Problem:

Lynn, Danita, and Doug are planning a physical education unit on balance. They have to get together for three hours from Monday to Friday to make sure they are on the right track. They have very busy schedules and it is difficult to fit in three hours when they can all get together. They can only meet between the hours of 8:30 a.m. until 10 p.m. each day as they need a good sleep. Here is each person's schedule:

1. They all go to school (university) from 8:30 a.m. until 4 p.m. each day.
2. On Tuesdays and Thursday they all have a lunch break from 12:00 noon until 1 p.m.
3. Doug has meetings during lunch break on Thursdays, he curls on Tuesday evenings from 7:00-10:00, and he plays volleyball on Wednesdays from 8:00 until 10:00 p.m.
4. Lynn works at Saan on Mondays, Tuesdays, and Fridays from 4:00 until 9:00 p.m.
5. Danita works at Office Depot on Wednesdays from 4:00 until 7:00, on Thursdays from 5:00 until 10:00 and she is leaving for Hawaii on Friday evening at 5:00 p.m.

Find the three hours in the week when all of them can get together.

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