Selective entry made-up symbols questions

The question defines a rule your child has never seen, explains it once, then asks them to use it. ACER says Quantitative Reasoning tests thinking and reasoning with numbers, patterns and shapes, in abstract as well as real-world settings. Made-up symbols are the abstract end.

No child has learned these rules at school, which is the point: can your child follow new instructions exactly? These three are our own, from easier to harder, with the working shown. Ask your child to run the rule aloud on the example, then on a wrong option, and find the step where it goes off track.

Slow down at the rule and speed up after it. Testing the rule on the example first catches a misread before it spoils every step that follows. Quantitative Reasoning shares 60 minutes with Mathematics, so it's worth spending those seconds at the start.

If a rule still makes no sense after a careful reread, ACER suggests your child make an informed guess and come back to it at the end if there is time. This is our method, not ACER's.

The slips here come from rushing the rule: the right step on the wrong number, a step too few, or an undo done backwards. Match each wrong option to a slip below. Then have your child put that option back into the rule, to see where it breaks.

• Using the rule on the wrong number. In the first question, doubling the second number instead of the first gives 11, not 13.
• Stopping one step early. In the second, 16 is the third number out of the machine. The question asks for the fourth, which is 14.
• Undoing a step the wrong way. In the third, halving 16 without adding back the 4 gives 8, and taking the 4 away gives 6. Adding it back gives 10.

Made-up rules make good family games, and inventing rules is a good way to talk about them. ACER says these skills grow over time, through a culture of learning, varied engaging material and talking freely about ideas.

• Invent a symbol together, such as "add the numbers, then double", and take turns setting puzzles with it.
• Play number machine: one person secretly picks a rule, the other feeds in numbers and guesses it.
• After any answer, ask your child to check it by running the rule forwards.

More worked questions are on our quantitative reasoning sample questions page. Three questions show the method; a full sitting shows whether your child still checks the rule with Mathematics on the same clock. Our selective entry practice tests keep the real timing, Practice test 1 is free, and the results by skill show whether new rules cost marks.