Ag comhoibriú chun teagasc agus foghlaim a fheabhsú
English Version

What a brilliant two days of maths teaching and learning Maths Counts 2018 proved to be. Close to 500 people attended over the two days to celebrate the work of the hundreds of Irish maths teachers who participated in PDST’s *Lesson-Study* programme throughout 2017-2018. Some highlights of the event included:

- Live lesson by international expert in teaching through problem solving – Prof. Tad Watanabe
- Keynote address by Prof. Watanabe celebrating the success of the Irish
*Lesson-Study*programme and pointing the way to its future growth and development - Three live lessons by Irish maths teachers who participated in
*Lesson Study*2017-2018 - 24 interactive workshops by Irish
*Lesson-Study*teachers - Poster Display comprising the work of 70
*Lesson-Study*research groups - Closing address by JCT Team Leader for Maths – Shane Flanagan
- Live streaming of Prof. Watanabe’s lesson and keynote address
- Exhibits by a variety of Irish Education companies

Thank you to everyone who attended. We will post all resources presented at the conference on this page in the coming days.

Check out all the problem-solving lessons developed by teachers in our *Lesson-Study* Library below including 70 new lesson proposals developed over the course of 2017-2018.

Lesson Title | Description | Strand | Year Group | Level |
---|---|---|---|---|

It’s Show Time | In this lesson, students will … | Number | 1st | OL |

What’s your Angle? | Pupils will be presented with … | Geometry, Trigonometry | 3rd | HL |

Percentage Paradox | Structured problem solving lesson involving … | Number | 1st | Common |

A Pizza of the (Fr)Action | Students are given a problem … | Algebra | 1st | Common |

What about Parallelograms | Exploring properties of parallelograms using … | Geometry | 1st | Common |

Thinking Outside the Triangle | Using a given diagram to … | Geometry | 1st | Common |

The Volume of Money | Through discovery, students derive the … | Number | 2nd | HL |

The X Factor | Exploring different ways to represent … | Algebra | 1st | Common |

The Power that Lies Beneath | Using Assessment for learning techniques … | Number | 2nd | HL |

The Array Model | Using the Array Model to … | Algebra | 2nd | HL |

Straight to the nth Game | Using a problem question to … | Algebra | 1st | Common |

Show Me the Money | Discovering the different measures of … | Statistics | 2nd | OL |

Scrutinizing the Difference between Two Squares | This proposal uses the concepts … | Algebra | TY | Common |

Run Johnny Run, Maths To The Rescue | Using prior knowledge of triangles … | Trigonometry | 2nd | HL |

Point Of Pick-Up | Using prior knowledge of algebra, … | Geometry | 5th | OL |

Place Your Pix | Using the problem of placing … | Algebra | 2nd | OL |

Matchstick Challenge | This lesson is based on … | Number | 1st | Common |

Probability, Statistics | 1st | OL | ||

In The Air | Using a word problem to … | Functions | 5th | Common |

How Big Is Pi? | Using varying circles to discover … | Geometry | 1st | Common |

Getting To The Problem Of The Root | Identifying relationships between quadratic equations, … | Functions | 2nd | HL |

Get Unsnookered | Using a mix of Geometry, … | Geometry, Trigonometry | 5th | HL |

Forthnightly Maths | In a computer game context, … | Functions | 6th | OL |

Express My Point | Students will be introduced to … | Algebra | 1st | Common |

Equating Fortnite-ly | Using word problems in algebra … | Algebra | 1st | Common |

Disco Taxi | Using a word problem to … | Functions | 2nd | Common |

Circling Longitude | A real life scenario of … | Geometry | 5th | OL |

Car Savings Conundrum | Students act as a financial … | Number | 3rd | FL |

Basket Case | Introducing simultaneous equations through word … | Algebra, Functions | 2nd | Common |

All Aboard Quadratic Airlines | This lesson provokes students understanding … | Functions | 3rd | HL |

A Journey in Finance | Modelling a financial problem using … | Number | 6th | HL |

2 or not 2x that is the question | This lesson provides a physical … | Algebra | 2nd | OL |

A Step in the Right Direction | This lesson introduces students to … | Trigonometry | 2nd | HL |

Who is being Irrational? | After calculating some distances using … | Number | 2nd | HL |

When Area is 64 | Students are presented with an … | Functions | 2nd | Common |

What’s your Angle? | Through exploring relationships in triangles, … | Geometry | 1st | Common |

Untangles the Angles | Using various methods students will … | Geometry | 1st | Common |

Unpacking 3D Shapes | Students will examine a square … | Geometry, Trigonometry | 5th | HL |

Transversals are Copycats | Given a diagram with three … | Geometry | 6th | HL |

Top of the Vlogs | Students will present two sets … | Probability, Statistics | 2nd | Common |

Time for Telly | Students will learn to deal … | Number | 3rd | FL |

The Trapezoidal Rule | Students will engage with a … | Geometry, Number, Trigonometry | TY | Common |

The Story of Two Drones | Students will be asked to … | Geometry, Trigonometry | 5th | OL |

The Story of the Gannet | Students will describe the story … | Functions | 2nd | HL |

The Integers Cup | Students will develop understanding of … | Number | 1st | Common |

The Great Wall of Nenagh | Problem solving approach to link … | Algebra, Functions, Number | 2nd | HL |

The Grand Rational | Students are given an algebraic … | Functions | 5th | HL |

The Ex Factor | Through a problem-solving approach, students … | Geometry | 2nd | HL |

The Balancing Act | Introducing Simultaneous Equations through problem … | Algebra | 2nd | OL |

The Formula Speaks Volumes | Students will explore the volume … | Number | 2nd | HL |

The Flow of Money | Students will try to solve … | Number | 2nd | HL |

Takeaway Translation | In this lesson students will … | Algebra | 2nd | Common |

Subway Substitution | Students are presented with a … | Algebra | 1st | Common |

Snowflakes | Students will be challenged to … | Algebra | 3rd | HL |

Simultaneously solving for two variables | Students will be given two … | Algebra | 2nd | Common |

Similar Triangle Wrangle | Students will be using dotted … | Geometry, Trigonometry | 2nd | Common |

Shootin’ Hoops | Students will be provided with … | Algebra, Number | TY | Common |

Sharing the Unknown | Students will understand the need … | Algebra, Number | 2nd | HL |

Run Circles Around Pythagoras | Students will be asked to … | Geometry, Trigonometry | 5th | OL |

Pump Up The Volume | Students will use various strategies … | Geometry, Number | 2nd | OL |

The Power of Algebra | Students will be presented with … | Algebra | 2nd | HL |

Plane Clothes | Students solve a problem on … | Geometry, Number, Trigonometry | 2nd | HL |

Percentages Predicament | Students tackle a percentage increase … | Number | 2nd | Common |

Paving Patterns | Students are encouraged to examine … | Algebra, Functions, Number | 3rd | HL |

Patterns in Polygons | Students use their prior knowledge … | Geometry, Number | 2nd | HL |

Partying with Indices | Through an exponential growth problem … | Number | 2nd | HL |

Paper Ratio | Students will be given A3, … | Number | 2nd | Common |

Murling | Students will work with a … | Algebra, Functions | 2nd | Common |

Multiplying Messi’s Millions | In this lesson students will … | Number | 1st | Common |

Monkey Puzzle | Students develop an understanding of … | Number | 2nd | Common |

Meet You Halfway | Students are given a photograph … | Geometry | 2nd | Common |

Make-Up Money | Students will solve a problem … | Algebra, Functions, Number | 2nd | HL |

M.M.A. Mixed Mathematical Approaches | Students will formulate the area … | Probability, Statistics | TY | Common |

Kevin’s Cash Connundrum | Students will show in many … | Algebra | 1st | Common |

Katie versus Conor – Who will win? | Students explore probability and relative … | Probability, Statistics | 2nd | Common |

Justifying your Thinking | Students are challenged to explain … | Number | 3rd | Common |

It’s Thirsty Work | Students will learn to interpret … | Number | 2nd | HL |

It’s a Matter of Principles | Students investigate the rate of … | Functions | 5th | HL |

It’s Moore of a Process | Students investigate Moore’s Law in … | Functions, Number | 5th | HL |

How much is the special Offer? | Students will be presented with … | Algebra | 2nd | Common |

Heavenly Slopes | Students will engage in structured … | Geometry, Trigonometry | 5th | OL |

Going underground on a Roller Coaster | Students are introduced to quadratic … | Algebra, Functions | 2nd | Common |

Fractions meet Algebra | Students will learn to apply … | Algebra, Number | 2nd | HL |

Elf on the Shelf | Students will use their knowledge … | Geometry, Trigonometry | 3rd | HL |

Diving for Roots | Students are introduced to quadratic … | Algebra, Functions | 2nd | HL |

Dining Out – Who Gets your Money | “In this lesson students will … | Number | 3rd | HL |

Cuir Cruth Air | Trí a bheith ag plé … | Geometry, Number, Trigonometry | 2nd | Common |

Cover the Distance Faster | Students apply their knowledge and … | Geometry, Trigonometry | 2nd | HL |

Count like an Egyptian | Students are given a problem … | Algebra | 2nd | OL |

Box Bonanza | Students work on the problem … | Algebra | 1st | Common |

Baby it’s cold outside | The aim of this lesson … | Algebra, Functions | 5th | HL |

Are we there yet? | Students are encouraged to solve … | Geometry, Trigonometry | 2nd | HL |

Are you up for the Match? | The aim is for the … | Probability | 1st | Common |

Are Circles Pointless | In this lesson students will … | Geometry, Trigonometry | 5th | HL |

Getting Value for Money | Students will try to solve … | Number | 2nd | Common |

Angles to find the Treasure | The students will be given … | Geometry, Trigonometry | 3rd | HL |

2D or not 2D? | The lesson focuses on students … | Geometry, Trigonometry | 2nd | HL |

2D to 3D… That is the Question? | Students will be presented with … | Algebra, Functions, Geometry, Number, Probability, Statistics, Trigonometry | 5th | OL |

Prof. Takahashi’s Lesson Proposal | Through a series of problems, … | Geometry | 1st, 2nd | Common |

Introducing Differential Calculus | Developing an understanding of key … | Functions | 6th | OL |

The Polygon Predicament | Connecting multiple mathematical topics to … | Algebra, Functions, Geometry, Number, Probability | 6th | HL |

The Perfect Selfie | Using geometry and trigonometry to … | Geometry, Trigonometry | 5th | HL |

Developing Frieda’s Field | Developing the formula for the … | Geometry, Trigonometry | 5th | OL |

Enter the Matrix | Solving a multi-variable problem using … | Algebra | 5th | OL |

The General Term of a Quadratic Pattern | Using multiple strategies to develop … | Algebra, Functions | 5th | OL |

Heading for Trouble | Learning how to deal with … | Algebra | 5th | OL |

Navigating an Ash Cloud | Drawing on algebra, geometry and … | Algebra, Geometry, Trigonometry | 5th | HL |

The Water Rocket | Analysing quadratic relationships using multiple … | Algebra, Functions, Number | 5th | HL |

What makes a Parallelogram | Using trigonometry & geometry to … | Geometry, Trigonometry | 5th | OL |

Tick Tock – Area of an Incircle | Use the properties of an … | Geometry, Trigonometry | 5th | HL |

Seeing through the Dab | Applying trigonometry to solve a … | Geometry, Trigonometry | TY | Common |

Decoding De Moivre | Understanding the concepts of rotations … | Algebra, Number, Trigonometry | TY | Common |

How many ways can you prove It? | Understanding the construction of the … | Geometry, Trigonometry | 3rd | HL |

Centre of a Rectangle | Students draw on many topics … | Geometry, Trigonometry | 3rd, 5th | HL, OL |

Comparing Percentages, Decimals & Fractions | Calculate the percentage and fraction … | Number | 3rd | OL |

Coordinate Geometry meets Synthetic Geometry | Using coordinate geometry, theorems, corollaries … | Geometry, Trigonometry | 3rd | HL |

Picture this Quadratic | Modelling images using quadratic functions … | Algebra, Functions | 3rd | HL |

Transformation Trickery | Applying knowledge of transformations for … | Geometry | 3rd | HL |

3D Cubes | Identifying right-angled triangles in 3D … | Geometry, Trigonometry | 3rd | HL |

Anyone for Pizza – Solving Simultaneous Equations | Modelling problems with simultaneous equations … | Algebra | 2nd | HL |

Coffee and Tea Simultaneously | Solving a two-variable problem using … | Algebra, Geometry | 2nd | HL |

An Average Problem | Understand the properties of different … | Statistics | 2nd | HL |

The Cookie Crumbles | Moving from area to volume … | Number | 2nd | OL |

Into the Next Dimension | Understanding the relationship between cross-sectional … | Number | 2nd | OL |

Equivalent Fractions | Students learn to compare fractions … | Number | 2nd | OL |

More Pizza for me | Using scaling to compare different … | Number | 2nd | OL |

Pragmatic Quadratic | Calculating the area of a … | Algebra, Functions | 2nd | HL |

Rich, Happy, Healthy or Famous | Using Census @ School data … | Statistics | 2nd | Common |

Roots and Shoots | Calculating the dimensions of a … | Algebra, Functions | 2nd | HL |

Tri to be Shady | Using many approaches to calculate … | Geometry, Number | 2nd | HL |

The Window Maker | Using two-variable problems to develop … | Algebra | 2nd | HL |

Grazing Gazelles | Discovering Pythagoras’s Theorem. | Geometry, Trigonometry | 2nd | OL |

Tin of Beans | Using the concept of cross-sectional … | Number | 2nd | HL |

Translating Words into Symbols | Using different operations to develop … | Algebra, Number, Probability | 1st | Common |

An Alternative Approach to Alternate Angles | Problem solving to demonstrate that … | Geometry | 1st | Common |

Are you Snookered? | Use axioms and theorems to … | Geometry | 1st | Common |

Perimeter of an Irregular Shape | Calculating perimeter of a shape … | Algebra, Number | 1st | Common |

Home and Away | Understanding distance-time graphs. | Algebra, Number | 1st | Common |

A Tough Climb | Understanding the concept of slope. | Geometry, Trigonometry | 1st | Common |

Mary’s Age | Applying linear equations to problems. | Algebra | 1st | Common |

Perfecting Percentages | Understanding the usefulness of percentages … | Number | 1st | Common |

Count the Sweets | Students apply algebraic reasoning to … | Algebra, Number | 1st | Common |

The Chocolate Challenge | Using equivalent fractions to decide … | Number | 1st | Common |

The Great Hall | Using linear relationships to develop … | Algebra | 1st | Common |

The Problem with Cats & Dogs | Learning to use Venn Diagrams … | Number | 1st | Common |

What’s your Angle? | Applying knowledge of axioms and … | Geometry | 1st | Common |

Working with Fred Pattern-Son | Using a visual pattern to … | Algebra | 1st | Common |

Introducing Algebra & Word Equations | Applying algebraic reasoning to in-context … | Algebra | 1st | Common |

Let’s think about BIDMAS | Applying order of operations to … | Number | 1st | Common |

Dogs do Patterns | Using a real-life problem to … | Algebra, Number | 1st | Common |

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**After breaking new ground in 2017 with live problem-solving lessons by Irish teachers**, Maths Counts 2018 again showcased three live lessons developed through our *Lesson Study* programme. Teachers from Coláiste na Tóirbhirte, Ardee Community School and Coláiste Éamann Rís, Callan taught their research lessons live to groups of students from their own school – all for other teachers to see. It was brilliant to see the huge amount of planning come to fruition in an inspirational hour of teaching and learning. We hope that all teachers present enjoyed the chance to watch somebody else teach.

**Prof. Tad Watanabe wowed students and teachers alike with his problem-solving lessons on fractions. Tad brought the students of Ardee Community College on a fascinating journey, starting with comparing fractions, through to proving that there are an infinite number of fractions between any two fractions. In the course of the journey students grappled with the process of mathematical proof, all the time practising their skills for manipulating algebraic fractions and reasoning as to the properties of different fractions. After finishing his lessons, Tad attended the live lessons and interactive workshops delivered by our Irish Lesson-Study teachers and commented on the high standard of all the work he saw.**

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**We had 23 workshops presented by teachers at Maths Counts 2018, outlining their experience of using ***Lesson Study* for their CPD and of teaching through structured problem solving. The quality of presentation was incredibly high and it was great to see teachers discussing their approaches to teaching each topic and the common problems students present with in the classroom. Every workshop concluded with a question and answer session where teachers got the opportunity to ask the presenter about participating in the *Lesson-Study* programme.

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The huge amount of work undertaken by teachers involved in the 2017-2018 *Lesson-Study* programme was highlighted by the extensively display of posters which outlined the work of each research group. Each group got the chance to take their posters with them back to their schools. Well done to everybody who presented a poster.