Problem Solving in Years 7-10 Dr Jack Bana Student Activities Coordinator MAWA j.bana@bigpond.net.au

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  

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.

Competition Dates in 2017 Face-to-Face:- On-Line:- March 10th Yrs 11-12 March 17th Yrs 7-8 & Yrs 9-10 March 18th Years 5-6 On-Line:- Term 1 Term 2 Term 3 Term 4 Yrs 5-6 Yrs 5-10 Yrs 3-10 Yrs 7-10

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.

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.

Year 7 Items

Year8 Items Year 8 Items

Year 9 items Year 9 Items

Year 10 items

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.

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

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)

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

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

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

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?

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?

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

Need copies of the Years 7-8 and/or the Years 9-10 problems used in Have Sum Fun 2016? Email me at j.bana@bigpond.net.au Use Problem Solving in Teaching & Learning. Thus, ensure that students are moving forward.