# Maths Investigations for KS2: How To Make Mathematical Detectives

**When you think of Maths investigations for KS2, what do you conjure up in your mind? For me it’s about being a great detective, like Sherlock Holmes, and involves lots of consideration, examination, probing, scrutiny and studying.**

The clues are all in the word. Invest + i + gate: I have to go through lots of doors and invest time searching for a solution. For KS2 pupils to work on a Maths investigation, they need to invest time and energy, alongside plenty of reasoning and collaboration with others.

**Maths Investigations at KS2: The Detective Mindset**

Children need to adopt the mindset and persona of a detective (like Sherlock Holmes) when ‘doing’ Maths.

When children do this, they take on board some of the essential characteristics needed to understand a ‘case’: they must have a keen eye for details and strong analytical skills. They need to work with the right strategy.

Sherlock was ruthless at collecting, analysing and deducing information and that’s precisely what children need to integrate into their own ways of working.

Like him, children need to be ruthless in how they look for evidence and gather what data they can to help them solve a problem. The deductions they make need to be backed up with evidence.

Finding an answer is one thing but finding a solution is quite another and that means going through a process. An important intellectual skill is the nurturing of cognitive determination and investigations can support this by giving children contexts to express their thinking out loud.

**The KS2 Maths Investigation Mindset: A Mathematical Detectives**

Mathematicians are nothing special but their styles of thinking can make them appear this way. A key philosophy underpinning ‘mastery’ is the growth mindset and this is also a key ingredient of the detective approach to Maths investigations at KS2.

Maths mindsets have to be ‘open for business’ which means as teachers we need to provide a rich number of opportunities to allow for development. Every child has the potential for developing higher mathematical -logical intelligence.

In her book, Mathematical Mindsets, Jo Boaler argues that in order to promote a detective mindset for Maths, we need to:

- Support all learners to understand that they can learn anything and that struggle is the best time for brain growth
- Teach multidimensional Maths – ask children to represent ideas visually, numerically, graphically, verbally, algorithmically – colour code and make connections between them
- Put the brakes on speed and celebrate depth and creativity
- Encourage and value multiplicity – all the different ways children think
- Help children to realise that they ‘can do’ Maths and that when they believe in themselves then their brains are more active and grow more.

Her suggestions are a great starting point for many schools, but there are more ways in which you can develop good Maths investigation mindset.

Let's Investigate: KS2 Maths Activities

Over 24 Maths investigations designed for Years 5 and 6, including open-ended activities similar to NRich, with many possible ways to complete

**With that in mind, here are 25 ways to help develop a Mathematical detective mindset, that will feed into and support work on Maths investigations at KS2: **

- Inspire awareness of numbers and shapes in the environments and how Maths is all around us.
- Teach and provide a variety of problem-solving strategies (
*this guide to problem solving techniques should help with that*). - Encourage children to work systematically.
- Provide a range of rich tasks so children can ‘get inside’ the mathematics.
- Use low-threshold high ceiling tasks
*like the ones found in this free resource*. - Practise ‘guided Maths’ akin to ‘guided reading’.
- Encourage ‘flow-chart’ thinking and have pupils sequence steps when solving a puzzle.
- Give children opportunities create categories for sorting and classifying.
- Promote the regular use of Venn and Carroll diagrams for ‘graphical thinking’.
- Pour number and strategy games into activities.
- Get children to create and pose their own problems (included open-ended problems).
- Extend knowledge or apply knowledge in new contexts.
- Make brainteasers a daily feature of Maths to train logical thinking.
- Let children work within intriguing contexts.
- Provide ideas for personal learning projects where children can explore, predict and experiment for themselves.
- Devote a part of the classroom to interactive puzzles, problems and posers.
- Push STEAM (Science, Technology, Engineering, Arts and Maths) all the way so that children see and apply Maths across the curriculum.
- Provide opportunities for children to see other people being mathematical or see the role of Maths within different cultural settings .
- Promote a conjecturing atmosphere.
- Set up a range of ‘active assessment’ opportunities for collaborative dialogue rich talking tasks so children can explain, justify, verify, convince and refute.
- Promote a range of questions and prompts to fuel divergent thinking.
- Promote analogy, schematising, defining and deduction.
- Give one or more counterexamples of a given concept.
- Provide challenges to provoke children to clarify differences between related concepts.
- Encourage regular reflective ‘journaling’ so children can transcribe and draw their ideas into a learning log. You can
*find out more about how to embed journaling in the classroom in this free guide to Maths mastery.*

A cerebral culture that develops and places a high value on investigative intelligence must be the starting point for any classroom hoping to cultivate a detective mindset.

Deductive reasoning is one of the most valuable skills a child can have and so this is an essential component of any Maths investigative curriculum.

Mind benders, thoughts and crosses, logic puzzles, riddles all help to support this critical thinking faculty and helps children see patterns, ask questions, learn and discover.

**How to Support Pupils to Succeed at KS2 Maths Investigations**

So many investigations studied at KS2 are pedestrian, and children plod through them with little enthusiasm or little insight. When actually, being ‘mathematically mindful’ is crucial.

One thing we need to do is to help children focus on what’s what and what’s not – in other words, do what Sherlock would do and learn how to recognise vital facts from incidental facts.

Some investigations contain superfluous information in their narratives that can throw children off the trial and it is this extraneous gunk that children should be trained to spot and bin. The power of observation is everything.

Weaning out the incidental facts from those that are relevant helps children crack the case. Knowing how to spot information and what is needed is the first step to becoming a sleuth Maths detective.

Nothing is useless unless you decide it is but identifying the importance of something is what children need to get good at. They need to consider everything and discard with efficiency.

Knowing how to sieve though the information and create a clear connection between numbers and words is the logical way to find a solution.

Children often mess up a question in their SATs because they aren’t paying attention to the finer details. They are trying to get things done quickly and because of that they either miss important information or focus on the smaller details that are ‘distractors’ or redundant and superfluous information. Cultivating new habits of slowing down and paying attention is vital.

A great habit to get children into is simply asking “Why is that there?” when looking at KS2 Maths investigations and SATs style questions.

To build these skills in pupils, try including these investigative Maths questions for KS2 in your next few lessons:

- There are 29 chapters in a book and 45 pages per chapter. The average number of words per page is 500. How many pages in total?
- A packet of Cheesy Wonder crisps weighs 28g. There are 16 crisps in a multipack costing £4.50. Samraaj buys 8 multipacks for his party. How many grams of crisps has he bought?
- A pet food lorry makes a 296 km trip 56 times in 2 months. It’s average speed is 55 km/h. How far does the lorry travel in total?
- Miss Dickens, aged 22, needs to save £846 for her holiday to Menorca. She saves £26 a week. How many weeks will it take to save enough money for her holiday?
- A pack of 32 chocolate rolls weighs 1440g and costs £1.49. How much does one roll weigh?

**Strategies for Approaching KS2 Maths Investigations**

If pupils struggle to know where to begin with investigative questions, you might want to try these techniques. After all, to successfully solve a problem, children need to know exactly what the problem is!

Children could try to:

- Draw a diagram
- Draw a table
- Act it out or use concrete material
- Guess and check
- Create an organised list
- Look for a pattern
- Create a tree diagram
- Work backwards
- Use simpler numbers
- Use logical reasoning
- Analyse and investigate
- Rephrase the question

Defining a problem and investigating a solution provides children with the chance to ‘do’ mathematics, to ‘make sense’ of their world and to ‘be mathematicians’.

When they discover ideas and invent procedures, children have a stronger conceptual understanding of connections between mathematical ideas.

**Remember: Maths Investigations are for Life, not just for Christmas **

When children engage with investigative work they begin to see and appreciate the inner sanctum of and the true beauty of the subject. They can make inferences, get creative, challenge themselves and work with their peers and upgrade their own knowledge, understanding and skills.

(*One easy way to get pupils engaged with Maths investigations is to use these topical Maths activities from Third Space Learning*)

We might assume that investigating, exploring and solving problems are central elements of the Maths lessons in every classroom but this sadly isn’t the case everywhere.

I know of some schools that ‘reserve’ the last week of every half-term to a Maths investigation but this is frankly not enough.

Investigations aren’t booked in like a table for four in a restaurant as a special treat. Investigations need to be a regular feature of Maths work so that the key Sherlock skills are exercised rather than awakened every now and then as some sort of bolt-on to satisfy an ‘added value’ tick-box.

There is always time for a Maths investigation because they can vary in length from just a few minutes to a whole lesson and beyond.

No time? No excuses – there is always time to build in an investigation and the Maths mind palaces need stocking up as ‘empty shelves’ don’t solve problems.

Investigations come in all shapes and sizes and may be framed variously as: a question to be answered, a problem to be solved; a task to be accomplished, or an issue to be explored.

Who says that an investigation has to be a whole lesson? It doesn’t. It could be something you start in the morning and finish in the afternoon – split maths lessons are catching on!

Micro investigations can be some open-ended questions that have no one right answer or it could mean finding the same solution using different routes and pathways.

Small-scale investigations might involve similar open-ended questions but as part of a more complicated context. Macro investigations can involve a range of skills and concepts and be used as an ongoing teaching tool throughout the term that step by step scaffolds understanding.

**Investigations are involving and interesting activities that absorb children. They stimulate holistic thinking, they can be integrated naturally in every part of the curriculum, they promote complex thinking but reinforce basic concepts, and they constitute an essential part of every mathematician’s work. **

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