Selective School Maths: Problem-Solving Strategies

## Why Selective Maths Is Different The NSW Selective High School Placement Test is one of the most competitive academic assessments a Year 6 student will sit. Unlike a standard school maths test, the Selective maths section does not simply ask students to apply a known procedure to a familiar problem. It presents novel situations that require flexible thinking, strategic reasoning, and the ability to work efficiently under time pressure. This is why students who perform exceptionally well in school maths sometimes struggle with Selective questions — and why dedicated preparation focused on problem-solving strategies is essential. ## The Four Core Problem-Solving Strategies ### 1. Draw a Diagram This is the single most powerful strategy available to a student in any maths test, and it is consistently underused. When a problem involves shapes, positions, distances, or relationships between quantities, drawing a clear diagram immediately makes the problem more concrete. **Example:** "Four points are placed equally spaced on a circle. How many straight lines can be drawn connecting any two of these points?" Students who try to solve this in their heads often make errors. Students who draw four points on a circle and systematically draw every possible connecting line get the correct answer of 6 almost every time. The habit to build: before reading a problem carefully, check whether a diagram would help. If the problem mentions positions, distances, shapes, or arrangements — draw it. ### 2. Work Backwards Some problems are much easier if you start with the answer and work backwards to the starting point. This strategy is particularly effective for problems involving a sequence of operations applied to an unknown starting number. **Example:** "After doubling a number and then subtracting 7, the result is 19. What was the original number?" Working forwards requires setting up an equation: 2x − 7 = 19. Working backwards is more intuitive: start with 19, add 7 to get 26, divide by 2 to get 13. Both methods work, but working backwards is faster for many students under test conditions. ### 3. Find a Pattern Many Selective questions involve sequences, grids, or arrangements where identifying an underlying pattern leads directly to the answer. The key skill is recognising that a pattern exists and then systematically working out the rule. **Example:** "What is the sum of the first 50 odd numbers?" Calculating 1 + 3 + 5 + 7 + ... + 99 directly would take too long. But listing the first few sums reveals a pattern: 1 = 1², 1+3 = 4 = 2², 1+3+5 = 9 = 3². The sum of the first n odd numbers is always n². So the sum of the first 50 odd numbers is 50² = 2500. Students who have practised identifying patterns solve these questions in under a minute. Students who try to add all 50 numbers either run out of time or make arithmetic errors. ### 4. Guess and Check (Systematically) Guess and check sounds like an admission of failure, but done systematically, it is a highly efficient strategy for many Selective questions — particularly those involving simultaneous conditions. **Example:** "A bag contains 20 coins, all either 10c or 20c, with a total value of $2.90. How many 20c coins are there?" Rather than setting up simultaneous equations, a strategic student might start with 10 of each (total = $3.00 — too high), adjust downward systematically, and find the answer in two or three attempts. Under exam conditions, this is often faster than algebra. The key is to make each guess *informed* — use the result of each attempt to narrow down the next guess. ## Time Management in the Selective Maths Section The Selective maths section requires students to answer 35 questions in 40 minutes — roughly 70 seconds per question. This leaves almost no room for getting stuck. **The Two-Pass Technique:** - **First pass:** answer every question you can solve within 60 seconds - **Second pass:** return to skipped questions with remaining time Students who attempt every question in order, spending several minutes on difficult problems, often run out of time before reaching easier questions near the end of the test. The two-pass technique ensures that marks are never lost simply because of poor time allocation. ## Building Problem-Solving Skills Over Time These strategies cannot be mastered in one or two sessions. They become instinctive through regular practice across a variety of problem types. Effective Selective preparation involves: - **Weekly problem-solving sessions** — structured practice with a variety of question types - **Strategy identification** — after solving each problem, naming which strategy was used - **Mistake review** — understanding every error, not just noting the correct answer - **Increasing time pressure** — beginning with untimed practice, then progressively reducing allowed time ## What Topics Are Covered in Selective Maths? The NSW Selective maths section covers content up to Year 6 level, but applies it in more complex ways than standard classroom questions. Key topic areas include: - Number and place value (including very large and very small numbers) - Fractions, decimals, and percentages - Ratio and proportion - Area, perimeter, and volume - Number patterns and sequences - Probability and combinations - Word problems involving multiple operations No algebra is required — all problems can be solved with Year 6 arithmetic and reasoning skills. ## Preparing With Smart Roots Tutoring At Smart Roots Tutoring in Campbelltown, our Selective School preparation program runs from Term 3 of Year 5 through to the test in July of Year 6. We combine concept teaching with weekly problem-solving practice sessions, full mock tests, and strategy coaching. Every student begins with a free diagnostic session to identify their current level and the specific problem types they find most challenging. We then build a personalised preparation plan around their individual needs. We offer sessions face-to-face in Campbelltown and online across NSW. Find out more on our [Selective School preparation page](/programs) or [book a free consultation](/contact). ## Key Takeaways - Selective maths tests reasoning, not just curriculum knowledge - The four core strategies are: Draw a Diagram, Work Backwards, Find a Pattern, Guess and Check - Time management is critical — use the two-pass technique - Build problem-solving skills through regular, varied practice over at least six months - Review every mistake with the goal of understanding, not just correction