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Early Years Foundation Stage (EYFS)

Double Trouble

Children often  enjoy matching amounts and spotting things which are the same. Adults could  provide patterns of numbers which are doubles, e.g. on dice, dominoes, egg boxes etc.

Encouraging mathematical thinking and reasoning:

The Mathematical Journey

Same and different:

• describing 'doubles' patterns e.g. "There are five here and five here"
• discussing what is the same and different about domino and array patterns

Counting and cardinality:

• counting to check the same number has been added when doubling

Matching numerals and amounts:

• matching numerals to patterns, or patterns to a number line
• adding on the same number again to double
• 'counting all' to find the total
• 'counting on' from the first number to find the total
• predicting how many there will be before doubling a number

Multiplying:

• talking about six being 'two threes' rather than 'three and three'
• talking about 'doubling three' to get six

• Toy animals for the 'double trouble' story.
• 'Doubles' images: dice, dominoes, Numicon, multilink in two-column arrays, egg boxes.
• Counters and pegboards to make up doubles patterns.
• Stamps or sticky circles to record patterns.
• Large number lines to attach patterns to.

Download a  PDF  of this resource.

How can doubling and halving help me multiply?

Part of Maths and Numeracy Numbers and number processes

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Fin and Snoot are building a rocket. They count and compare the bolts they each have.

Video Transcript Video Transcript

NARRATOR: Hello Snoot. Hello Fin.

BOTH: (ALIEN LANGUAGE)

NARRATOR: You're building a rocket, I see.

You've just got to attach the boosters and you'll be done.

SNOOT: (ALIEN LANGUAGE)

NARRATOR: It looks like you'll need 20 bolts to attach one booster.

Let's see what you've got in your tool box.

So Snoot, you've got 4 packs of 5 bolts.

4 times 5 equals 20.

Just the number we need.

FIN: (ALIEN LANGUAGE)

NARRATOR: Ok Fin, let's see what's in your toolbox.

You've got 2 packs of 10 bolts.

2 times 10 also equals 20!

NARRATOR: I know Snoot, Fin's got exactly the same number of bolts as you just in different packs.

4 packs of 5 bolts equals 20.

And 2 packs of 10 bolts equals 20 as well.

So it doesn't matter if we use your packs or Fin's packs, we'll still have all the bolts we need.

We could even use 2 of your packs and 1 of Fin's packs.

2 times 5 is 10 and adding another 10 equals 20 bolts all together.

NARRATOR: Right then, let's get these boosters bolted on, shall we?

NARRATOR: Ah…

you're going to need more than bolts to fix that.

How can doubling and halving help you multiply?

Everyone finds some numbers easier to work with than others.

If you have to multiply by a number you aren’t too sure about, it can sometimes help to half or double it.

If you have to do 4 X 6 and you’re not sure about the 4 times table, remember that 4 is 2 X 2 .

So you can half the 4 to make 2 . Then you have to double the 6 to make up for this.

So instead of doing 4 X 6 you can do 2 X 12 .

The answer is 24 for both.

How can adding help me multiply? video How can adding help me multiply?

Snoot and Fin add and multiply to find out how many pests are in their kitchen.

How can an array help me multiply? video How can an array help me multiply?

Fin and Snoot count meebs by putting them into equal rows and using multiplication.

Find more 1st Level resources from BBC Bitesize

First Level is a stage of Scotland’s Curriculum for Excellence.

More on Numbers and number processes

Find out more by working through a topic

How can multiples of ten make multiplication easier?

• count 15 of 25

How do I multiply two-digit numbers more easily?

• count 16 of 25

Which way round should I multiply two numbers?

• count 17 of 25

Which order should I multiply numbers in?

• count 18 of 25

• Multiplication and Division

Commutativity (part 2), doubling and halving

• Mastery PD Materials

Spine 2: Multiplication and Division – Topic 2.5

Introduction

Explore how one multiplication equation can have two different grouping interpretations (e.g., an equation from the two times table can be interpreted in terms of groups of two, or two equal groups); make connections between the two times table, doubling and halving.

Teaching points

• Teaching point 1 : The same multiplication equation can have two different grouping interpretations. Problems about two/five/ten equal groups can be solved using facts from the two/five/ten times table. (commutativity)  
• Teaching point 2 : If two is a factor, knowledge of doubling facts can be used to find the product; problems about doubling can be solved using facts from the two times table.  
• Teaching point 3 : Halving is the inverse of doubling; problems about halving can be solved using facts from the two times table and known doubling facts.  
• Teaching point 4 : Products in the ten times table are double the products in the five times table; products in the five times table are half of the products in the ten times table.

Teacher Guide

Representations, all year 2 files, related pages.

• Primary Mastery Professional Development

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Doubling and Halving – Reasoning and Problem Solving

Doubling and Halving - Reasoning and Problem Solving

This worksheet includes a range of reasoning and problem solving questions for pupils to practise the main skill of doubling and halving.

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What's included in the pack?

Doubling and Halving reasoning and problem solving worksheet Answer sheet

National Curriculum Objectives:

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Maths Games and Learning Activties for Fun

Category: doubling and halving, hit the button – topmarks.

Hit the Button Hit the Button is an interactive maths game with quick fire questions on number bonds, times tables, doubling and halving, multiples, division facts and square numbers. The games which are against the clock challenge and develop a Read More …

Daily 10 Covers addition, subtraction, ordering, partitioning, digit values (place value), rounding, multiplication, division, doubles, halves and fractions. Designed for interactive whiteboard. For delivering 10 maths questions for mental maths practise. Can be timed or untimed Ideal for starter and Read More …

Robin Hood Doubles – ICT Games

Click the number on the target that is double the number on the board – see the merry men come out!

Bridge Doubles – ICT Games:

Simple worded doubling. Number line. No objects to support.

Double the Donuts

See how quickly the donuts add up when their number increases by doubling.

Doubling – Mark Weddell

Doubling by partitioning then adding together. Choose two or three digit numbers to double.

Mastery-Aligned Maths Tutoring

“The best thing has been the increase in confidence and tutors being there to deal with any misunderstandings straight away."

FREE daily maths challenges

A new KS2 maths challenge every day. Perfect as lesson starters - no prep required!

Maths Problem Solving At KS2: Strategies and Resources For Primary School Teachers

John Dabell

Maths problem solving KS2 is crucial to succeeding in national assessments. If your Key Stage 2 pupils are still struggling with reasoning and problem solving in Maths, here are some problem solving strategies to try with your classes; all aligned to Ofsted’s suggested primary school teaching strategies.

Reasoning and problem solving are widely understood to be one of the most important activities in school mathematics. As far back as 1982,  The Cockcroft Report , stated:

‘The ability to solve problems is at the heart of mathematics. Mathematics is only “useful” to the extent to which it can be applied to a particular situation and it is the ability to apply mathematics to a variety of situations to which we give the name “problem solving”. […] At each stage […] the teacher needs to help pupils to understand how to apply the concepts and skills which are being learned and how to make use of them to solve problems. These problems should relate both to the application of mathematics to everyday situations within the pupils’ experience, and also to situations which are unfamiliar.’

Thirty plus years later and problem solving is still the beating heart of the Maths curriculum and – along with fluency and reasoning – completes the triad of aims in the 2014 New National Curriculum.

Ofsted’s view on problem solving in the Maths curriculum

Despite its centrality, Ofsted report that ‘ problem solving is not emphasised enough in the Maths curriculum ’. Not surprisingly, problem solving isn’t taught that well either because teachers can lack confidence, or they tend to rely on a smaller range of tried and tested strategies they feel comfortable with but which may not always ‘hit home’. If you’re looking to provide further support to those learners who haven’t yet mastered problem solving, you probably need a range of different strategies, depending on both the problem being attempted and the aptitude of the pupil.

We’ve therefore created a free KS2 resource aimed at Maths Coordinators and KS2 teachers that teaches you when and how to use 9 key problem solving techniques:  The Ultimate Guide to Problem Solving Techniques

The context around KS2 problem solving

According to Jane Jones, former HMI and National Lead for Mathematics, in her presentation at the Jurassic Maths Hub:

• Problems do not have to be set in real-life contexts, beware pseudo contexts.
• Providing a range of puzzles and other problems helps pupils to reason strategically to approach problems, sequence unfolding solutions, and use recording to help their mathematical thinking for next steps.
• It is particularly important that teachers and TAs stress reasoning, rather than just checking whether the final answer is correct.
• Pupils of all ability need to learn how to solve problems – not just the high attainers or fastest workers.

The Ultimate Guide to Problem Solving Techniques

9 ready-to-go problem solving techniques with accompanying tasks to get KS2 reasoning independently

How to approach KS2 maths problems

So what do we do? Well Ofsted advice is pretty clear on what to do when teaching problem solving. Jane Jones says we should:

• Set problems as part of learning in all topics for all pupils.
• Vary the ways in which you pose problems.
• Try to resist prompting pupils too soon and focusing on getting ‘the answer’ – pupils need to build their confidence, skills and resilience in solving problems, so that they can apply them naturally in other situations.
• Make sure you discuss alternative approaches with pupils to help develop their reasoning.
• Ensure that problems for high attainers involve demanding reasoning and problem-solving skills, not just harder numbers.

Perhaps more than most topics in Maths, teaching pupils how to approach problem solving questions effectively requires a systematic approach. Pupils can face any number of multi-step word problems throughout their SATs and they will face them without our help. To truly give pupils the tools they need to approach problem solving in Maths we must ingrain techniques for  approaching  problems.

With this in mind, below are some methods and techniques for you to consider when teaching problem solving in your KS2 Maths lessons. For greater detail and details on how to teach this methods, download the  Ultimate Guide to Problem Solving Techniques

Models for approaching KS2 problem solving

Becoming self-assured and capable as a problem solver is an intricate business that requires a range of skills and experience. Children need something to follow. They can’t just pluck a plan of attack out of thin air which is why models of problem solving are important especially when made memorable. They help establish a pattern within pupils so that, when they see a problem, they feel confident in taking the steps towards solving it.

Find out how we encourage children to approach problem solving independently in our blog: 20 Maths Strategies KS2 That Guarantee Progress for All Pupils.

The most commonly used model is that of George Polya (1973), who proposed 4 stages in problem solving, namely:

• Understand the problem
• Devise a strategy for solving it
• Carry out the strategy
• Check the result

Many models have followed the Polya model and use acronyms to make the stages stick. Which model you use can depend on the age of the children you are teaching and sometimes the types of word problems they are trying to solve. Below are several examples of Polya model acronyms:

C – Circle the question words U – Underline key words B – Box any key numbers E – Evaluate (what steps do I take?) S – Solve and check (does my answer make sense and how can I double check?)

R – Read the problem correctly. I – Identify the relevant information. D – Determine the operation and unit for expressing the answer. E – Enter the correct numbers and calculate

I – Identify the problem D – Define the problem E – Examine the options A – Act on a plan L – Look at the consequences

R – Read and record the problem I – Illustrate your thinking with pictures, models, number lines etc C – Compute, calculate and check E – Explain your thinking

R – Read the question and underline the important bits U – Understand: think about what to do and write the number sentences you will need C –  Choose how you will work it out S – Solve the problem A – Answer C – Check

Q – Question – read it carefully U – Understand – underline or circle key elements A – Approximate – think about the size of your answer C – Calculate K – Know if the answer is sensible or not

T – Think about the problem and ponder E – Explore and get to the root of the problem A – Act by selecting a strategy R – Reassess and scrutinise and evaluate the efficiency of the method

The idea behind these problem solving models is the same: to give children a structure and to build an internal monitor so they have a business-like way of working through a problem. You can choose which is most appropriate for the age group and ability of the children you are teaching.

The model you choose is less important than knowing that pupils can draw upon a model to follow, ensuring they approach problems in a systematic and meaningful way. A far simpler model – that we use in the   Ultimate Guide to KS2 Problem Solving Techniques  – is UCR: Understand the problem, Communicate and Reflect.

You then need to give pupils lots of opportunities to practice this! You can find lots of FREE White Rose Maths aligned maths resources, problem solving activities and printable worksheets for KS1 and KS2 pupils in the Third Space Learning Maths Hub .

You might also be interested in:

• 25 Fun Maths Problems For KS2 And KS3 (From Easy To Very Hard!)
• 30 Problem Solving Maths Questions And Answers For GCSE
• Why SSDD Problems Are Such An Effective Tool To Teach Problem Solving At KS3 & KS4

What’s included in the guide?

After reading the  Ultimate Guide to KS2 Problem Solving Techniques , we guarantee you will have a new problem solving technique to test out in class tomorrow. It provides question prompts and activities to try out, and shows you step by step how to teach these 9 techniques

• Open ended problem solving
• Using logical reasoning

Working backwards

Drawing a diagram

Drawing a table

Creating an organised list

Looking for a pattern

Acting it out

Guessing and checking

Cognitive Activation: getting KS2 pupils in the lightbulb zone

If you need more persuasion, pupils who use strategies that inspire them to think more deeply about maths problems are linked with higher Maths achievement. In 2015 The  National Education Research Foundation  (NFER) published ‘ PISA in Practice: Cognitive Activation in Maths ’. This shrewd report has largely slipped under the Maths radar but it offers considerable food for thought regarding what we can do as teachers to help mathematical literacy and boost higher mathematical achievement.

Cognitive Activation isn’t anything mysterious; just teaching problem solving strategies that pupils can think about and call upon when confronted by a Maths problem they are trying to solve. Cognitive It encourages us as teachers to develop problems that can be solved in more than one way and ‘may require different solutions in different contexts’. For this to work, exposing children to challenging content and encouraging a culture of exploratory talk is key. As is:

• Giving pupils maths problem solving questions that require them to think for an extended time.
• Asking pupils to use their own procedures for solving complex problems.
• Creating a learning community where pupils are able to make mistakes.
• Asking pupils to explain how they solved a problem and why they choose that method.
• Presenting pupils with problems in different contexts and ask them to apply what they have learned to new contexts.
• Giving pupils problems with no immediately obvious method of solution or multiple solutions.
• Encouraging pupils to reflect on problems.

Sparking cognitive activation is the same as sparking a fire – once it is lit it can burn on its own. It does, however, require time, structure, and the use of several techniques for approaching problem solving. Techniques, such as open-ended problem solving, are usually learned by example so we advise you create several models to go through with pupils, as well as challenge questions for independent work. Many examples exist and we encourage you to explore more (e.g. analysing and investigating, creating a tree diagram, and using simpler numbers).

Read these:

• How to develop maths reasoning skills in KS2 pupils
• FREE CPD PowerPoint: Reasoning Problem Solving & Planning for Depth
• KS3 Maths Problem Solving

That time, effort, and planning will – however – be well spent. Equipping pupils with the tools to solve problems they have never seen before is more akin to teaching for life than teaching for Maths. The skills they gain from being taught problem solving successfully will be skills they use and hone for the rest of their life – not just for their SATs.

For a range of problem solving techniques, complete with explanations, contextual uses, example problems and challenge questions – don’t forget to download our free  Ultimate Guide to KS2 problem solving and reasoning techniques  resource here.

KS2 problem Solving FAQs

Here are some techniques to teach problem solving to primary school pupils: Open ended problem solving Using logical reasoning Working backwards Drawing a diagram Drawing a table Creating an organised list Looking for a pattern Acting it out Guessing and checking

Ofsted say that teachers can encourage problem-solving by: Setting problems as part of learning in all topics for all pupils. Varying the ways in which you pose problems. Trying to resist prompting pupils too soon and focusing on getting ‘the answer’ – pupils need to build their confidence, skills and resilience in solving problems, so that they can apply them naturally in other situations. Making sure you discuss alternative approaches with pupils to help develop their reasoning. Ensuring that problems for high attainers involve demanding reasoning and problem-solving skills, not just harder numbers.

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FREE Guide to Maths Mastery

All you need to know to successfully implement a mastery approach to mathematics in your primary school, at whatever stage of your journey.

Ideal for running staff meetings on mastery or sense checking your own approach to mastery.

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Reasoning and Problem Solving Questions Collection - KS1 and KS2

Subject: Mathematics

Age range: 5-7

Resource type: Worksheet/Activity

Last updated

10 March 2023

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These booklets each contain over 40 reasoning and problem solving questions suitable for KS1, KS2 and KS3 classes. These are the questions that we have been putting out each day in March 2016 on Twitter in the run up to SATS.

The answers are provided with some simple notes at the back of the booklet and for some problems supplementary questions and variation has been provided.

As always we welcome any feedback on the work we are doing and the materials that we are releasing. Thank you for taking an interest in our work. The White Rose Maths Hub Team

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graceamfo18

A very good and engaging way to teach mastery of maths. Thank you for sharing

thank you for sharing, this is really good

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Doubling word problems

A lovely problem solving resource for year 2 children to practise their doubling skills.

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