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Problem Solving, Reasoning and Planning for Depth – FREE CPD PowerPoint for Primary School Maths

Anantha Anilkumar

Maths teaching is tough, and teaching Maths teaching is even tougher. Whether you’re a Maths Lead, a member of SLT or a teacher asked to deliver a CPD session on effective teaching of problem solving, the actual delivery can be a daunting prospect. 

At Third Space Learning we’re not just about providing quality maths interventions for pupils – we’re also about easing the considerable burden on teachers, including CPD. Some of you might already be familiar with the CPD videos on our online Maths Hub; to complement and expand on these, we will be releasing a series of CPD Powerpoints covering a wide variety of maths topics.

More details about upcoming PowerPoints can be found below, but we’ve already released our first CPD PowerPoint for free! Focused on ‘Problem Solving, Reasoning and Planning for Depth’, it’s perfect for covering this difficult topic during a staff meeting or INSET day.

A link to the PowerPoint can be found below, but if you’re looking for a breakdown of what it contains before you download, read on!

Problem Solving, Reasoning and Planning for Depth - CPD PowerPoint

A selection of slides to help improve teacher's understanding of how to teach problem solving and reasoning.

Problem Solving, Reasoning and Planning for Depth – Aims of the PowerPoint

While the overall purpose of this CPD PowerPoint is to improve teachers’ understanding of how to teach problem solving and reasoning, this can be split into several distinct aims:

• Establish a clear definition of what we mean by problem solving and reasoning.
• Outline the importance of problem solving and reasoning and the benefits of both.
• Explore some practical strategies.
• Clarify the principles of how to plan for problem solving and reasoning when approaching maths problems .

The order of these aims also reflects the most effective way to approach the topic; we identify exactly what we mean by the terms involved, why their teaching is important, how to go about teaching them, and lastly how to effectively implement them into your long-term planning.

Problem Solving, Reasoning and Planning for Depth – An Overview

With this order in mind, the slides begin with a series of interactive discussions centered on establishing how staff already approach problem solving, and why it’s important to teach pupils the same skills.

Reference is made to the National Curriculum’s key aims regarding pupils’ fluency with the fundamentals of maths and their ability to reason mathematically to solve problems, with example exam questions from both KS1 and KS2 involving a reasoning element.

This is followed by a more in-depth discussion of what exactly reasoning is, including how it may be interpreted and how skills such as metacognition can further enhance our reasoning abilities. This leads into a discussion of how to involve reasoning and maths problem solving in every lesson, with advice and examples of the kinds of questions that may be used.

From here the PowerPoint shifts to looking at how teachers can plan for deep embedding of problem solving and reasoning in their lessons. Initial focus is on how working together can help children develop problem solving skills, with a particular focus on the wealth of research underpinning this notion.

A wider discussion of how to develop group work in maths follows, with examples of strategies teachers may use. Another discussion considers the ‘curse’ of ‘real-life’ problems, and the importance of providing a range of problems to help pupils develop reasoning skills.

The final section of the CPD PowerPoint looks at how staff might practically plan and implement reasoning activities (as well as what should be avoided). Strategies for how a ‘simple’ problem can be adapted to involve reasoning components are covered, and a final activity involves planning out a reasoning activity (of any length) for use in maths lessons next week.

This was just a brief overview of what the PowerPoint contains – download it now to get to get all 52 slides and the guidance attached to each of them!

CPD PowerPoints Coming Soon

We’ll be releasing several more CPD PowerPoints for our Premium Maths Hub users in the near future. Below you’ll find some short summaries of what they’ll be focusing on.

1. Curriculum Design – Blocked Practice Vs Optimal Spacing 

This is about how to plan a curriculum.  By providing children with opportunities to revisit learning has been found to be better.  If learning is revisited too soon after the original learning they don’t need to work hard to retrieve knowledge that they have stored or processed recently.  (Dunlosky et al., 2013). Spacing can be implemented by dedicating part of a lesson to reviewing, re-exposing students to previously learned information or by using cumulative summative assessments.  

2. Mastery in Primary Mathematics

An overview of what mastery is in primary schools.  We look at research into maths mastery and the 7 points the NCETM paper from Oct 14 ‘Confidence and competence’ discusses.  Why we need mastery (ensuring children don’t rush through the curriculum, plugging gaps, making links etc). Also includes tips for planning mastery-based lessons at both Key Stage 1 and Key Stage 2.

3. Variation Theory

A slightly more technical CPD session. Starts with identifying what variation theory is and how it can be used to encourage reasoning in pupils. Comes with lots of examples to work through with the staff!  

4. Maths Talk and Questioning in Maths

Covers mathematical thinking , variation, scaffolding sentence starters to help pupils structure their ideas and more! Provides ideas of how to support memory of mathematical vocabulary (dingbats, etymology of words), ideas on enquiry and elimination and examples of barrier games.  Also discusses top questioning strategies to use (e.g. key problem solving maths questions as learning objectives, if this is the answer… what is the question?, just one more question).

You might also be interested in:

• KS2 Problem Solving
• KS3 Maths Problem Solving
• Why SSDD Problems Are Such An Effective Tool to Teach Problem Solving At KS3 & KS4

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Since 2013 these personalised one to 1 lessons have helped over 150,000 primary and secondary students become more confident, able mathematicians.

Learn how the programmes are aligned to maths mastery teaching or request a personalised quote for your school to speak to us about your school’s needs and how we can help.

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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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I See Problem-Solving - UKS2

The ebook i see problem-solving - uks2 helps all children to learn how to solve multi-step maths questions. questions are broken down step-by-step and represented visually to build understanding, whilst extension tasks and reasoning prompts allow children to explore ideas at greater depth. the ultimate resource for teaching problem-solving in y5/6.

I See Problem-Solving - UKS2 Sample provides 5 free sample tasks. For each task there is a main question , a support prompt and  explain and extend features to deepen the challenge. The  worked examples  model the solutions to the main tasks step-by-step - download below for free. The 58 tasks span all areas of the UKS2 maths curriculum. The purchase price is £30 (£25 + £5 VAT) for the PDF digital download.

I See Problem-Solving - UKS2: Worked Examples (PowerPoint)

I See Problem-Solving - UKS2: Worked Examples (PDF)

In these blogs I explain how the task prompts provide extra scaffold to give children additional help , and how extra layers of challenge can be added. Each task starts with a main question, like the examples below:

Children can use the support prompt if they need some extra help to answer the main question. The support prompt may give a suggested starting point, represent the question visually or address a possible misconception. It helps children to understand and access the task. Here are the support prompts for the above examples:

The explain features then provide an opportunity for children to reason based on the initial task. Prompts may ask children to explain a mistake, spot a pattern or make a link with a similar question. Children have to explain their opinion, deepening their understanding of the main question.

The extend feature gives a more challenging, related question for the children to solve. The mathematical structure of these tasks are similar to the initial prompt, usually with one added layer of complexity. Extend tasks may require children to make a generalisation, think laterally or find all possible answers to a question.

The 58 tasks of I See Problem-Solving - UKS2 cover all areas of the UKS2 curriculum. It corresponds to US grade 4&5 and Australian school years 5&6. The sale price is £30. When ordered, the PDF file is emailed direct to your inbox for your use.

To purchase, click on the link below. If you need assistance ordering, please read the Frequently Asked Questions below or email [email protected].

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Working Systematically at KS2 - Primary Teachers

This page has been superseded by our Working Systematically - Primary Teachers page

Scroll down to see our complete collection of KS2 problems that require children to work systematically, or explore the two sub-collections focusing on important aspects of systematic working.

This collection is one of our Primary Curriculum collections - tasks that are grouped by topic.

Finding All Possibilities Upper Primary

These activities focus on finding all possible solutions so working in a systematic way will ensure none are left out.

Ordered Ways of Working Upper Primary

These activities lend themselves to systematic working in the sense that it helps to have an ordered approach.

Sitting Round the Party Tables

Sweets are given out to party-goers in a particular way. Investigate the total number of sweets received by people sitting in different positions.

Beads and Bags

How could you put these three beads into bags? How many different ways can you do it? How could you record what you've done?

What could the half time scores have been in these Olympic hockey matches?

School Fair Necklaces

How many possible symmetrical necklaces can you find? How do you know you've found them all?

Nine-pin Triangles

How many different triangles can you make on a circular pegboard that has nine pegs?

Five More Coins

Could Ben have any amount of money between 5p and £2 in his pocket if he has five coins?

What Do You Need?

Four of these clues are needed to find the chosen number on this grid and four are true but do nothing to help in finding the number. Can you sort out the clues and find the number?

A Mixed-up Clock

There is a clock-face where the numbers have become all mixed up. Can you find out where all the numbers have got to from these ten statements?

Fifteen Cards

Can you use the information to find out which cards I have used?

Guess the Dominoes

This task depends on learners sharing reasoning, listening to opinions, reflecting and pulling ideas together.

Greater Than or Less Than?

Use the numbers and symbols to make this number sentence correct. How many different ways can you find?

Can you put the numbers 1-5 in the V shape so that both 'arms' have the same total?

Coded Hundred Square

This 100 square jigsaw is written in code. It starts with 1 and ends with 100. Can you build it up?

Multiply Multiples 1

Can you complete this calculation by filling in the missing numbers? In how many different ways can you do it?

Buying a Balloon

Lolla bought a balloon at the circus. She gave the clown six coins to pay for it. What could Lolla have paid for the balloon?

Round the Dice Decimals 1

Use two dice to generate two numbers with one decimal place. What happens when you round these numbers to the nearest whole number?

Can you replace the letters with numbers? Is there only one solution in each case?

A Square of Numbers

Can you put the numbers 1 to 8 into the circles so that the four calculations are correct?

Cubes Here and There

How many shapes can you build from three red and two green cubes? Can you use what you've found out to predict the number for four red and two green?

First Connect Three

Add or subtract the two numbers on the spinners and try to complete a row of three. Are there some numbers that are good to aim for?

Finding Fifteen

Tim had nine cards each with a different number from 1 to 9 on it. How could he have put them into three piles so that the total in each pile was 15?

Four bags contain a large number of 1s, 3s, 5s and 7s. Can you pick any ten numbers from the bags so that their total is 37?

Through the Window

My local DIY shop calculates the price of its windows according to the area of glass and the length of frame used. Can you work out how they arrived at these prices?

All the Digits

This multiplication uses each of the digits 0 - 9 once and once only. Using the information given, can you replace the stars in the calculation with figures?

Choose four different digits from 1-9 and put one in each box so that the resulting four two-digit numbers add to a total of 100.

Light the Lights Again

Each light in this interactivity turns on according to a rule. What happens when you enter different numbers? Can you find the smallest number that lights up all four lights?

This Pied Piper of Hamelin

Investigate the different numbers of people and rats there could have been if you know how many legs there are altogether!

Two Primes Make One Square

Can you make square numbers by adding two prime numbers together?

Sealed Solution

Ten cards are put into five envelopes so that there are two cards in each envelope. The sum of the numbers inside it is written on each envelope. What numbers could be inside the envelopes?

Prison Cells

There are 78 prisoners in a square cell block of twelve cells. The clever prison warder arranged them so there were 25 along each wall of the prison block. How did he do it?

Display Boards

Design an arrangement of display boards in the school hall which fits the requirements of different people.

Button-up Some More Live

How many ways can you find to do up all four buttons on my coat? How about if I had five buttons? Six ...?

The Dice Train

This dice train has been made using specific rules. How many different trains can you make?

Curious Number

Can you order the digits from 1-3 to make a number which is divisible by 3 so when the last digit is removed it becomes a 2-figure number divisible by 2, and so on?

Counting Cards

A magician took a suit of thirteen cards and held them in his hand face down. Every card he revealed had the same value as the one he had just finished spelling. How did this work?

Cover the Tray

These practical challenges are all about making a 'tray' and covering it with paper.

5 on the Clock

On a digital clock showing 24 hour time, over a whole day, how many times does a 5 appear? Is it the same number for a 12 hour clock over a whole day?

Ribbon Squares

What is the largest 'ribbon square' you can make? And the smallest? How many different squares can you make altogether?

The Remainders Game

Play this game and see if you can figure out the computer's chosen number.

Factor Lines

Arrange the four number cards on the grid, according to the rules, to make a diagonal, vertical or horizontal line.

Place the 16 different combinations of cup/saucer in this 4 by 4 arrangement so that no row or column contains more than one cup or saucer of the same colour.

This cube has ink on each face which leaves marks on paper as it is rolled. Can you work out what is on each face and the route it has taken?

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Maths Problem Solving Booklets

Subject: Mathematics

Age range: 11-14

Resource type: Worksheet/Activity

Last updated

23 August 2022

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Maths problem solving booklets covering a wide range of mathematical problems designed to improve problem solving strategies as well as numeracy and mathematical ability.

Designed to be printed as A5 booklets.

Disclaimer: These are free because the problems are from a wide variety of sources, most of which I have forgotten. I am a maths problem magpie and collect maths problems wherever I find them. All I have done is bundled these ones up to make it convienent.

If you find a problem that is yours and you don’t want it used please comment and I’ll remove it - cheers.

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ardglassie1

Very impresses. Ta.

Empty reply does not make any sense for the end user

Excellent resource

Great resource to use at KS3

mummygoth23

Just what I have been looking for. Thanks so much!

Good resources. Thanks you!

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