Included in this free taster booklet, is one math challenge (a word problem that is typically presented at math competitions or Math Olympiads), with step-by-step explanations for the students.
The math challenge in this booklet is the following:
Show that the sum of 12 consecutive positive integers can never be a perfect square.
I use these math booklets with15 to 18-year-old students, preparing for Math Olympiads or Challenging Tests, such as IB Maths Higher Level.
Where the booklets refer to algebra, calculus or trigonometry concepts, I always include a brief explanation of the concept such that the booklets can be used independently of any curriculum or syllabus the students are using.
The challenges in the booklets can be used as extension homework, practice during term breaks, or as part of an in-class differentiation approach.
The booklets themselves can then be given to the students when they hand in their solutions to the challenges.
In this free booklet, you will only find one (simpler) challenge, with step-by-step explanations and workings. When talented students start working on math problems that go beyond their syllabus, or problems that are presented “out-of-context”, they often think that the solution is some magical formula. They become frustrated when they do not immediately “see” the answer. By grouping challenges around a specific topic, and taking them step-by-step through the problem, the students will experience that by the time they reach the last challenge in the booklet, they will breeze through the explanations and usually do not even need them anymore.
The booklet uses several ways to explain concepts: graphs, diagrams, mathematical notation, plain-language explanations, and examples.