Exploring maths through problem solving


“Providing all students opportunities to engage with challenging mathematical tasks is critical to their development of reasoning and problem solving skills. The problems in this book are designed and sequenced to allow teachers to select optimally challenging problems for students from diverse backgrounds. Importantly, the beautifully illustrated solutions reinforce to students that mathematics can be creative, meaningful and engaging. I love how many problems can be solved using more than one solution strategy. Multiple solution strategies encourage students to look at mathematics from different perspectives and to reflect more deeply on their own strategies.”

Janette Bobis, Professor of Mathematics Education, The University of Sydney

“This is a treasure trove of mathematical puzzles and problems, but much more as we see a selection of different strategies for each problem. I found myself immediately reaching for pen and paper to see whether I could use more than one strategy each time. The layout and colours add to the appeal and add depth to the explanations. I’ll be purchasing many copies for gifts for problem solvers of all ages!”

Associate Professor Mary Coupland, University of Technology Sydney, Past President MANSW and AAMT

“Building Confidence in Maths Problem Solving is an excellent resource for instructors to motivate their students while sharpening their skills in problem solving. A visually pleasing (and colour-coded) volume insofar as each problem and its solutions are limited to a single page, yet thoroughly explained and linked to one or more of the ten strategies used throughout the book. And, if that isn’t good enough, lessons may be constructed to focus on a single method by simply referring to the strategies index.

Everyone who coaches students should have access to this resource guide, whether they participate in math competitions or just want their students to excel at meeting the challenges raised by maths word problems.”

Nicholas J Restivo, Executive Director, Mathematical Olympiads for Elementary & Middle-Schools - MOEMS™

Building Confidence in Maths Problem Solving: A Practical Handbook for Teachers and Parents of Years 5 – 8 Students: Volume 1

By Dr Pauline Kohlhoff

Australian Edition. © 2021.

ISBN : 9780975731659

290 pages

$ 44.95 + postage

About The Book

The resources contained in this new, larger format, APSMO publication are designed specifically to support the teaching of mathematical problem solving to mainstream students in Years 5 to 8.

As teachers and instructors, we know that problems can often be solved in many different ways. With 15 sets of problems and multiple solutions for each problem, this book takes students on a problem solving journey.

Starting with less cognitively demanding problems, the book is sequenced by difficulty and gradually progresses to a more challenging level. The solutions are beautifully presented and illustrated to showcase the application of various problem solving strategies, and a number of unique activity templates are provided throughout the book to assist with teaching.

Importantly, all of the problems are indexed and colour coded according to the problem solving strategy used, which allows teachers and students to practise individual strategies such as:

  • Guess, check and refine
  • Draw a diagram
  • Find a pattern
  • Build a table
  • Work backwards
  • Make an organised list
  • Solve a simpler, related problem
  • Eliminate all but one possibility
  • Convert to a more convenient shape
  • Divide a complex shape

Building Confidence in Maths Problem Solving lays the foundations of effective problem solving, helps to build confidence and provides an opportunity for mainstream students to see mathematics as a fun, creative and engaging activity.


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