Effective selective entry maths preparation starts by finding out why a question went wrong. A student who misunderstands ratios needs a different next step from a student who understands the mathematics but rushes the final calculation. Treating both problems with another timed paper can leave the underlying difficulty untouched.
This guide offers a practical approach to mathematics and quantitative reasoning for Victoria’s SEHS Year 9 entrance pathway. It includes original examples and a flexible six-week study cycle that families can adapt around school and other commitments.
Use the right starting point
The Victorian Department of Education says required knowledge does not extend beyond the Year 8 curriculum. For the format checked on 15 October 2026, ACER’s exam-day guidance gives Mathematics and Quantitative Reasoning one combined 60-minute block. Calculators are prohibited.
Some families search for “SEHS numerical reasoning”, but the current official label is Quantitative Reasoning. Whatever a resource calls its exercises, examine the skills being practised and the clarity of its explanations. A demanding question can require flexible use of familiar mathematics without introducing advanced school content.
Separate knowledge, interpretation and execution
After a short diagnostic activity, sort errors into three groups. Knowledge gaps occur when the student cannot explain the underlying idea. Interpretation errors happen when the student misunderstands what information means or what the question asks. Execution errors include arithmetic slips, lost units or a correct method applied inconsistently.
Use that diagnosis to choose a response. For a knowledge gap, return to a worked example and explain each step. For an interpretation error, redraw the situation or restate it in plain language. For an execution error, introduce a specific check at the point where the error occurred.
Keep the record small: question topic, cause of error, corrected method and one reminder. A page of useful observations is easier to revisit than a folder full of unexplained crosses.
Use representations before hunting for shortcuts
Here is an original practice example, not an official exam item: a mixture contains red and blue beads in a ratio of 3:5. There are 40 beads altogether. How many are red?
Draw eight equal boxes, representing the total number of ratio parts. Each box contains five beads because 40 divided by eight is five. Three boxes represent red beads, so there are 15 red beads. Check that the remaining 25 blue beads give the original ratio.
Now change the question: if there are 30 red beads, how many beads are there altogether? Three parts now equal 30, so each part is 10 and the total is 80. Comparing these versions shows why identifying the whole matters more than memorising one operation.
Ask the student to create a similar question and explain its answer. Writing a valid problem requires them to understand which quantities are connected and whether the information is sufficient.
Make quantitative reasoning visible
For unfamiliar numerical or spatial problems, encourage a brief description of the structure before calculation. What changes? What stays fixed? Is the relationship additive, multiplicative or dependent on position? Can a diagram, small table or simpler case expose the pattern?
Try another original activity: a row of adjoining squares uses four matchsticks for the first square, then three additional matchsticks for each extra square. How many are needed for seven squares? Draw two or three squares first. The total is four plus six groups of three, giving 22. Ask why seven multiplied by four counts too many sticks.
The explanation is the useful part: neighbouring squares share sides. Then ask the student to express the total for any number of squares in words. Moving between a picture, a calculation and a general description develops flexibility.
A six-week cycle that fits ordinary life
This is a suggested learning cycle, not a promised route to admission. Begin with three sessions of roughly 25 to 35 minutes each week, then adjust for the student’s needs and existing workload. Include review time within those sessions.
- Week 1: Establish a baseline. Use a small mix of familiar topics. Work mostly without time pressure and ask for explanations. Choose two priority gaps.
- Week 2: Repair the first gap. Relearn the concept, complete a few varied examples and revisit it after a day or two.
- Week 3: Repair the second gap. Keep a few questions from the first topic in the mix so the learning remains active.
- Week 4: Mix topics. Practise deciding which method fits before calculating. Include problems with units, diagrams or everyday contexts.
- Week 5: Add controlled timing. Try a short timed set using concepts already understood. Compare accuracy with untimed work.
- Week 6: Review and reset. Retry selected errors without looking at solutions. Choose the next priorities from the evidence.
If the student already attends classes, count that workload before adding independent sessions. A schedule should leave enough energy to think carefully. More practice is useful only when the student can engage with it and learn from the review.
Measure progress beyond the score
Track whether the student chooses a suitable method sooner, explains a solution more clearly and catches errors independently. Record how many corrected questions they can solve again several days later. These observations help distinguish lasting understanding from remembering a recently seen answer.
When adding longer practice, use current official timing information and follow the supplied instructions. Review where time was spent, including questions that were solved correctly but inefficiently. Do not turn one unusually difficult practice result into a prediction about admission.
Families wanting additional guidance can explore Loav’s selective entry preparation programme or enquire about a trial class. A short error record provides a useful starting point for discussing what your child needs next.
