Number reasoning questions are puzzles about amounts, such as balances or sharing stickers, solved with thinking more than sums. Children in Year 3 now sit the OC test in Year 4, on 11–12 May 2027.
Number reasoning means working out an amount from a few clues, using thinking more than sums. Liam and Max have 15 stickers altogether, and Liam has 3 more than Max. Put Liam's extra 3 aside: 15 − 3 = 12, shared equally is 6 each, so Max has 6 and Liam has 9.
The sums are small. The skill is choosing a clever first move, such as putting the extra aside, swapping one thing for another, or imagining that every beanbag landed in the same hoop.
How do number problems show up in the OC Thinking Skills test?
Your child reads a short story with numbers in it, such as a classroom balance or a game score, then works out one amount. The Department says Thinking Skills checks critical thinking and problem solving, with no previous knowledge needed, and the section has a range of question types, shown in the practice tests.
The OC Thinking Skills test
What it means for number problems
30 questions in 30 minutes
Look for the clever first move before writing sums
4 options each
Wrong options are often a number from halfway through
No calculator
Keep the numbers small and work on paper
There are no marks lost for incorrect answers
Checking an option in the story is always allowed
The Department doesn't publish a fixed list of question types. Number reasoning is how our lessons group these questions.
Four steps. The last one, checking, is the one children skip, and it's the one that catches a number from the wrong step.
Say what you are finding
Liam's stickers, not Max's. Marbles for two blocks, not one. Underline it.
Choose a first move
Put the extra aside, swap one thing for something equal, or imagine everything is the same kind.
Work in small steps
If all 12 beanbags landed in the 3-point hoop, that's 36 points. Each one in the other hoop adds a little more. Count how many lots you need.
Check in the story
Put the answer back: do the numbers add to the total and fit every clue? Or test an option the same way.
What do OC number problems look like?
Three questions from easier to harder: a classroom balance, sharing stickers and a beanbag score.
Each one shows the answer and the working, so read them with your child. The explanation says why each wrong option is wrong: ask your child which one looked right at first, because that's the habit to fix.
Worked explanation 1
Ben is using a balance in the classroom. All the wooden blocks weigh the same, and all the marbles weigh the same.
3 wooden blocks balance 1 toy truck.
1 toy truck balances 6 marbles.
How many marbles balance 2 wooden blocks?
AA.
4
BB.
2
CC.
12
DD.
6
Answer: A
Answer: A (4)
3 blocks balance 1 truck, and 1 truck balances 6 marbles, so 3 blocks balance 6 marbles.
Share the 6 marbles among the 3 blocks: each block balances 2 marbles.
So 2 blocks balance 4 marbles.
Why the other options are wrong
B (2): 2 marbles balance just 1 block, but the question asks about 2 blocks.
C (12): 12 marbles would balance 2 trucks, not 2 blocks.
D (6): 6 marbles balance a whole truck, which is 3 blocks, not 2.
Worked explanation 2
Liam and Max have 15 stickers altogether. Liam has 3 more stickers than Max.
How many stickers does Liam have?
AA.
18
BB.
9
CC.
6
DD.
12
Answer: B
Answer: B (9)
Put Liam's 3 extra stickers aside: 15 − 3 = 12 stickers are left.
Now the two boys would have the same number, so each has half of 12, which is 6. Max has 6.
Liam has 6 and his 3 extra stickers: 6 + 3 = 9.
Check: 9 + 6 = 15, and 9 is 3 more than 6.
Why the other options are wrong
A (18): This adds the 3 extra stickers on to the total instead of sharing the total between the boys.
C (6): 6 is how many stickers Max has, not Liam.
D (12): 12 is what is left after putting the 3 extra stickers aside; it still has to be shared between the two boys.
Worked explanation 3
In a beanbag game, a beanbag that lands in the blue hoop scores 3 points. A beanbag that lands in the red hoop scores 5 points.
Farah threw 12 beanbags, and every one landed in a hoop. She scored 46 points.
How many of her beanbags landed in the red hoop?
AA.
2
BB.
5
CC.
7
DD.
10
Answer: B
Answer: B (5)
Imagine all 12 beanbags landed in the blue hoop: 12 × 3 = 36 points.
Each beanbag that lands in the red hoop instead scores 2 points more (5 instead of 3).
Farah needs 46 − 36 = 10 more points, and 10 ÷ 2 = 5. So 5 beanbags landed in the red hoop.
Check: 5 × 5 = 25 and 7 × 3 = 21, and 25 + 21 = 46.
Why the other options are wrong
A (2): This shares the 10 extra points by 5, but each red beanbag adds only 2 extra points.
C (7): 7 is the number of beanbags in the blue hoop, not the red hoop.
D (10): 10 is the number of extra points; it still has to be shared by 2.
Which number problem mistakes cost marks?
Most wrong options are a correct number from the wrong step. Each has a quick check your child can run before choosing.
×
Answering for the wrong person or thing: Max's stickers are not Liam's, so reread what the question asks for.
×
Stopping halfway: the extra points still have to be shared out, so ask whether the number you have is the final answer.
×
Skipping the check: put the answer back into the story and make sure every clue still works.
What does the Number Reasoning Without Formulas lesson cover?
Number Reasoning Without Formulas (lesson preview)
A short preview from the SelectiveReady lesson “Number Reasoning Without Formulas”, on number reasoning for the NSW Selective test.
Published:
Read the video transcript
So here's how we crack this case, using our working backwards technique. Let's just grab one of the suspects, say the number 14. First, we test it against clue one. If you divide 14 by three, do you get a remainder of two? Let's see, three goes into 14 four times, which is 12. And yup, there's a remainder of two. Okay, so far so good, now for clue two. If you divide 14 by five, is the remainder four? Well, five goes into 14 two times, which is 10, and you've got four left over. Yes, it works. Since 14 fits both clues, we've found our culprit. Any other number that failed even one of those tests, it would have been eliminated immediately. And boom, there it is, the answer is 14. See, no crazy formulas, no complicated algebra, just a simple logical process of elimination. Case closed.
The preview has English and Chinese captions. It solves a mystery number by working backwards: try a possible answer and test it against each clue.
The full lesson in the SelectiveReady app adds drawing the problem, swapping equal things and the common traps. A free account opens one lesson, How and Why Authors Write; the other lessons need a paid plan.
How can my child practise number problems for free?
Start with Practice test 1, which has Thinking Skills at its real length and time. It's one full practice test with results, with a free account. Every answer is explained, and the results by skill show whether your child loses marks on number problems.
After that, the app has drills by section and topic; a free account drills the free test's questions, and a paid plan opens the rest. At home, use sharing puzzles: two siblings with a few more lollies for one, or coins of two kinds that make a total. Ask your child to explain the first move.
