1. Problem Solving in Years 7-10
Dr Jack Bana
Student Activities Coordinator
MAWA

2. The horse stud below has a square house surrounded by 8 square paddocks with a total of 22 horses. The four-member family, when looking simultaneously out of the north/west/south/east windows respectively, each see nine horses. How many horses are in each paddock?
Horse Stud

3. George Polya, How to Solve it (1945)
How much should we help the problem solver? Not too little and not too much.
Too little: Student will get bored or frustrated and give up, be turned off
problem solving, and not able to move forward.
Too much: Student will naturally stop thinking and be denied the the opportunity
to continue trying, thus losing a problem-solving opportunity and
not able to move forward.
How much? Enough to keep the student motivated and on task.

4. Competition Dates in 2017 Face-to-Face:- On-Line:-
March 10th Yrs March 17th Yrs 7-8 & Yrs March 18th Years 5-6
On-Line:-
Term Term Term Term 4
Yrs Yrs Yrs Yrs 7-10

5. What is Have Sum Fun (Face to Face)?
A problem-solving competition for teams of six from two year levels. Most problems are NAPLAN-type items. A unique opportunity to engage in cooperative problem solving. Conducted in one evening sitting. Four rounds of 8 items. Time limit of 20 minutes per round. Two or three concurrent venues for each of the 4 competitions.
Years 5-6, Years 7-8, Years 9-10, Years 11-12
Trophies & prizes for the place-getters. All students get a participation certificate.

7. What is Have Sum Fun On Line?
An internet-based problem-solving competition for teams of four. Most problems are NAPLAN-type items. A unique opportunity to engage in cooperative problem solving. Conducted over a three-week period. Three rounds of 10 items, with one round per week. Time limit of one hour per round. Three competitions in 2017 for each of Years 7, 8, 9, & 10 (Terms 2, 3, 4).
Solutions are checked on line with immediate feedback. Results of all participating teams are posted on the website. The competition is now nationwide and is endorsed by AAMT.
Prizes for first three places are $100, $60, $40; and with certificates.
All students get a participation certificate.

8. Year 7 Items

9. Year8 Items Year 8 Items

10. Year 9 items Year 9 Items

11. Year 10 items

12. Feedback from HSFOL Students
ｷ Great opportunity to build problem solving skills
ｷ It is challenging and makes you think
ｷ Learn about other people’s styles of solving problems
ｷ It’s fun working as a team
ｷ Not much opportunity for team-work in school
ｷ Different people are stronger in different aspects of maths
ｷ Working on-line is fast and simple
ｷ Great to have instant feedback
ｷ Good to compete against other teams and schools
ｷ We can have follow-up work on problem solving
ｷ HSFOL is something to look forward to.

13. Feedback from HSFOL Teachers
Lifts the profile of mathematics in the school
Develops students’ enthusiasm for mathematics
The items are comprehensive, so will indicate neglected topics
Students are exposed to a variety of styles of problems
Develops strategies for working in groups
Students like working collaboratively
Students learn much from each other
Students enjoy the competitive aspect
Teachers can observe students working mathematically
Promotes follow-up using the problems in mainstream classes

15. Other Problem Sources
There’s a Problem to Solve. Books 1, 2, 3 by Paula McMahon & Glenys Stade
60 Mathematical Investigations. Book by Barry Bastow, Barry Kissane, Rob Randall et al.
Year 7 Mathematics Activity Tasks. Covers Year 7 Curriculum. Free to DOE schools from the DOE website. Available to purchase from the MAWA website by non-DOE schools
Other Competitions & Websites (see handout)

16. Problem Solving Steps ------- George Polya, How to Solve it (1945)
1. Understand the problem SEE
2. Devise a plan PLAN
3. Carry out the plan DO
4. Look back CHECK

17. Word Problem Solving Research by M Anne Newman (1977)
Read the problem;
Comprehend what is read;
Carry out a mental transformation from the words of the question to the selection of an appropriate mathematical strategy;
Apply the process skills demanded by the selected strategy; and
Encode the answer in an acceptable written form.
Newman: In word problems with Year 6, 70% of errors occurred in steps 1-3
Ellerton & Clements (1996): In Year 8, 80% of errors occurred in steps 1-3

18. Problem Solving Strategies
Check to see if you’ve met a similar problem
Determine the givens and the wanted
Draw a diagram
Make a table or list
Simplify the problem
Look for a pattern
Act it out
Guess and check
Be systematic
Work backwards

19. Problem Solving Strategies
1. If everyone in this room shakes hands with everyone else, how many handshakes would there be?
Which of the previous strategies could be used?
2. How many acute angles of all sizes are shown below? Which strategies could be used?

20. Problem Solving Strategies
3. What number am I thinking of? I multiply it by 5, double it, divide it by 3, add 2, subtract 9, and finish with 3. What was my number?
What strategies could be used?
4. If there are 65 cars and bikes at the school with a total of 180 wheels, how many cars are there?
5. There are 40 points around a circle. How many lines would you need to draw to join every point to every other point?
What strategy could be used?

21. Use Problem Solving in Teaching & Learning To ensure students are moving forward Example: What is the length of the line segment?

22. Need copies of the Years 7-8 and/or the Years problems used in Have Sum Fun 2016? me at Use Problem Solving in Teaching & Learning. Thus, ensure that students are moving forward.