Free SATs Reasoning Practice — Papers 2 & 3

What the Reasoning Papers Cover

There are two reasoning papers — Paper 2 and Paper 3. Each has 35 questions and lasts 40 minutes. Unlike the arithmetic paper, reasoning questions are set in context: word problems, tables, charts, diagrams, and real-life scenarios.

The two papers cover the same range of topics but with different questions. Together, they test the full breadth of the Year 6 maths curriculum. Topics include:

• Number and place value — ordering, rounding, negative numbers
• Four operations in context — multi-step word problems
• Fractions, decimals, and percentages — applied to real situations
• Ratio and proportion — scaling recipes, sharing in ratios
• Algebra — finding missing values, simple equations, sequences
• Measurement — converting units, reading scales, time calculations
• Geometry — angles, coordinates, reflection, translation, properties of shapes
• Statistics — reading tables, bar charts, pie charts, line graphs, calculating mean

How Reasoning Differs from Arithmetic

On the arithmetic paper, every question tells your child exactly what to calculate: 4,567 + 2,389. On the reasoning papers, your child has to figure out which calculation to do.

For example, an arithmetic question might say “Calculate 3/5 of 240”. A reasoning question wraps that same maths in a story: “There are 240 children in a school. 3/5 of them walk to school. How many children walk to school?”

The maths is the same, but the reasoning paper tests whether your child can extract the maths from the words. This is why children who score well on arithmetic sometimes struggle with reasoning — and why specific reasoning practice is so important.

Strategies for Multi-Step Problems

Many reasoning questions require two or three steps. Children lose marks not because they cannot do the maths, but because they miss a step or misread the question. Here are strategies that help:

• Read the question twice. The first read gives the gist. The second read picks up the detail — “how many more”, “how much change”, “what is the difference”. These words tell your child which operation to use.
• Underline key information. Numbers, units, and the actual question being asked. This prevents children from answering a different question to the one that was set.
• Write each step separately. Multi-step problems are much easier when broken into single-step calculations. Encourage your child to label each step clearly.
• Check the units. If the question asks for the answer in metres, make sure the answer is in metres. Converting cm to m (or minutes to hours) is a common source of lost marks.
• Does the answer make sense? A final sanity check catches many errors. If a question asks how many buses are needed for 130 children (32 per bus), the answer is 5 buses, not 4.0625. Real-world context matters.

5 Worked Examples

Common Pitfalls

• Answering the wrong question — the question says “how much change?” and your child writes the total cost instead of the change.
• Forgetting units — writing “36” when the answer should be “36 cm” or “36 m²”.
• Not showing working — if the answer is wrong but the method is correct, clear working earns method marks. No working means no method marks.
• Rounding too early — in multi-step problems, rounding intermediate values can throw off the final answer.

How to Improve at Reasoning

Reasoning improves with exposure to a wide variety of question contexts. The more different types of problems your child sees, the better they become at recognising patterns and choosing the right approach.

SATs Arcade has hundreds of reasoning questions across all topics, each with a worked solution that explains not just the answer but the thinking process. The adaptive system focuses on the topics your child finds most challenging, so practice time is always well spent.

Even 10 minutes a day of reasoning practice makes a measurable difference over a term. The key is variety — don’t let your child only practise what they’re already good at.