How to Build 11 Plus Problem-Solving Skills
Most 11+ maths children can do the maths. What they cannot always do is recognise which maths to use, in what order, against an unfamiliar wording. That recognition is what we call problem solving. And it is genuinely teachable.
Here is how I build it with our students.
What problem solving actually means
Problem solving in 11+ usually involves four steps:
- Reading the problem carefully to identify what is given and what is asked
- Selecting the right operation or strategy to address it
- Carrying out calculations accurately in the right order
- Checking the answer makes sense in context
Each step is a separate skill. Children tend to be strong in some and weak in others. Identify which, and teach to it.
Step 1: Reading the problem carefully
Many marks are lost not in calculation but in reading. A child who misses a word or misreads a number cannot recover from there.
Train the habit of:
- Reading the problem twice before starting
- Underlining what is given (the numbers, the conditions)
- Circling what is asked (the question itself)
- Noting any unusual wording or trick (“not,” “except,” “at least”)
Two minutes spent reading carefully saves five minutes of confused calculation later. Always.
Step 2: Choosing the right strategy
Some children panic when they see an unfamiliar question. The fix is exposure to a wide range of problem types, with explicit teaching of strategies.
Strategies worth teaching by name:
- Working backwards. Start from the answer and reverse the steps. Useful when the question gives you the result of several operations and asks for the starting number.
- Drawing a diagram. Many problems become trivial when sketched. Train your child to reach for a pencil drawing as their first response.
- Trial and error. Sometimes the fastest route. Try a guess, check whether it works, refine.
- Looking for patterns. Sequence questions, ratio questions, problems with an underlying structure all reward pattern spotting.
- Breaking into parts. Multi step problems are easier when split into stages: “First I work out X, then I use X to find Y.”
Once a child has these tools by name, they reach for them automatically. The skill of choosing a strategy is not innate; it is taught.
Step 3: Calculating accurately
Strong calculation skills are the bedrock. If your child’s mental arithmetic is shaky, the most carefully chosen strategy will fall apart.
Address calculation accuracy through:
- Daily mental maths drills, short and varied
- Times tables fluency, kept warm even when tables are “learned”
- Showing working out, neatly, every time. Working out is a brain aid, not a chore.
- Avoiding the temptation to do everything in their head. Many wrong answers come from overconfidence.
Step 4: Checking the answer
The most underused skill in 11+ maths. Children rush from one question to the next, never going back to check. Yet a 30 second check at the end of each question would catch many errors.
Train two checks:
1. Sense check
Does the answer make sense in the context of the question? If the question asks how much change someone has from £10 and the answer is £73, something has gone wrong. Children who know to ask this catch dozens of careless errors.
2. Reverse check
Plug the answer back into the question. If a problem says “Tina has three times as many marbles as Sam, and they have 48 between them,” and your child’s answer is Tina has 36 and Sam has 12, check: 36 plus 12 is 48, and 36 is three times 12. The answer is right.
How to practise problem solving
Three principles.
Principle 1: variety beats volume
Twenty different problems beat one hundred similar ones. Children who only practise one type of problem become fluent in that type and helpless outside it.
Principle 2: discuss strategy, not just answers
After your child solves a problem, ask: how did you work that out? What strategy did you use? Could you have done it differently? This conversation is where problem solving builds. Without it, you have only practised arithmetic.
Principle 3: stretch beyond the curriculum
Olympiad-style puzzles, simple logic puzzles, sudoku, even chess, all build the same underlying problem-solving capacity. Children who play with mathematical reasoning beyond the curriculum reach 11+ maths in a stronger position.
Resources for problem solving practice
- Bond 11+ How to Do Word Problems is a sensible starting workbook
- Junior Mathematical Challenge papers (UK Mathematics Trust) for stretch beyond the curriculum
- Murderous Maths books for playful exposure to mathematical thinking
- Logic puzzles like those in Brilliant or in Marcus du Sautoy’s puzzle books
Our weekly maths workshops weave problem solving into every session, building the strategies above through varied practice and structured discussion.
Frequently asked questions
How often should we practise problem solving?
Two to three sessions a week of 20 to 30 minutes, alongside regular maths work. The goal is exposure to a wide range of problem types over time, not intensive cramming.
My child gives up when they cannot see the answer immediately. What do I do?
Teach the habit of trying. "What could you draw? What could you guess?" Make starting a habit even when the path is unclear. The most damaging belief is that maths problems should be solvable instantly, and your child should hold them blameless if they are not. Resilience here is built through encouraged attempts.
Is problem solving genetic or learned?
Almost entirely learned. The children who look like "natural problem solvers" have usually had years of conversation, puzzles and reasoning practice at home. The skill set responds extremely well to teaching.
How do I mark problem solving when my own maths is rusty?
Use the answer key from a reputable workbook. Sit with your child as they work, asking questions about strategy rather than checking arithmetic. Most parents find their role here is conversational rather than mathematical.
