| Divide and Conquer | Understanding long division of polynomials | Algebra, Functions | 2nd | OL |
| Step by Step | Students use physical manipulatives to derive and understand the cosine … | Trigonometry | 5th | HL |
| What’s the point? | Students make connections between linear patterns , coordinate geometry and … | Geometry | 1st | Common |
| What’s The Meaning Of Z-scores | Students build on their prior knowledge of mean and standard … | Probability, Statistics | TY | HL |
| Top Dog Area | Students deduce different shapes from a word problem using different … | Algebra, Geometry, Number | 5th | OL |
| Simultaneous Shapes | Students progress from the concrete, to the pictorial, to the … | Algebra, Functions | 2nd | HL |
| Missing In Action | Students use the idea of equality to form, interpret and … | Algebra, Functions | 1st | Common |
| Looks Different, Same Value | Students develop a deeper understanding of equivalent fractions and add … | Algebra, Functions | 2nd | HL |
| Explain that Formula | Students explore properties of 3-dimensional shapes and use nets to … | Number | 5th | OL |
| Across the divide | Students work on real life word problems where the operation … | Number | 2nd | Common |
| It’s Show Time | In this lesson, students will try to solve problems relating … | Number | 1st | OL |
| What’s your Angle? | Pupils will be presented with 2 parallel lines and 5 … | Geometry, Trigonometry | 3rd | HL |
| Percentage Paradox | Structured problem solving lesson involving multiple approaches to a direct … | Number | 1st | Common |
| A Pizza of the (Fr)Action | Students are given a problem to consolidate their learning of … | Algebra | 1st | Common |
| What about Parallelograms | Exploring properties of parallelograms using various approaches and looking for … | Geometry | 1st | Common |
| Thinking Outside the Triangle | Using a given diagram to lead students to the discovery … | Geometry | 1st | Common |
| The Volume of Money | Through discovery, students derive the formula for the volume of … | Number | 2nd | HL |
| The X Factor | Exploring different ways to represent factorisation of a single algebraic … | Algebra | 1st | Common |
| The Power that Lies Beneath | Using Assessment for learning techniques of multiple choice diagnostic testing … | Number | 2nd | HL |
| The Array Model | Using the Array Model to factorise quadratic expressions. This proposal … | Algebra | 2nd | HL |
| Straight to the nth Game | Using a problem question to develop the general formula for … | Algebra | 1st | Common |
| Show Me the Money | Discovering the different measures of central tendency using celebrities as … | Statistics | 2nd | OL |
| Scrutinizing the Difference between Two Squares | This proposal uses the concepts from ‘Algebra through the lens … | Algebra | TY | Common |
| Run Johnny Run, Maths To The Rescue | Using prior knowledge of triangles to explore trigonometric ratios and … | Trigonometry | 2nd | HL |
| Point Of Pick-Up | Using prior knowledge of algebra, coordinate geometry, synthethic geometry and … | Geometry | 5th | OL |
| Place Your Pix | Using the problem of placing a picture in a frame, … | Algebra | 2nd | OL |
| Matchstick Challenge | This lesson is based on first year patterns, introducing students … | Number | 1st | Common |
| It’s Show Time | | Probability, Statistics | 1st | OL |
| In The Air | Using a word problem to graph functions | Functions | 5th | Common |
| How Big Is Pi? | Using varying circles to discover pi and use this discovery … | Geometry | 1st | Common |
| Getting To The Problem Of The Root | Identifying relationships between quadratic equations, roots and graphs | Functions | 2nd | HL |
| Get Unsnookered | Using a mix of Geometry, Trigonometry and Coordinate Geometry to … | Geometry, Trigonometry | 5th | HL |
| Forthnightly Maths | In a computer game context, students will have to identify … | Functions | 6th | OL |
| Express My Point | Students will be introduced to the concept of writing mathematical … | Algebra | 1st | Common |
| Equating Fortnite-ly | Using word problems in algebra to introduce equations | Algebra | 1st | Common |
| Disco Taxi | Using a word problem to introduce transformations of quadratic functions … | Functions | 2nd | Common |
| Circling Longitude | A real life scenario of a drone taking a photo … | Geometry | 5th | OL |
| Car Savings Conundrum | Students act as a financial advisor and must investigate a … | Number | 3rd | FL |
| Basket Case | Introducing simultaneous equations through word problems and solving by graphing | Algebra, Functions | 2nd | Common |
| All Aboard Quadratic Airlines | This lesson provokes students understanding of how quadratic graphs relate … | Functions | 3rd | HL |
| A Journey in Finance | Modelling a financial problem using a geometric series and investigating … | Number | 6th | HL |
| 2 or not 2x that is the question | This lesson provides a physical approach to the understanding of … | Algebra | 2nd | OL |
| A Step in the Right Direction | This lesson introduces students to trigonometric ratios. | Trigonometry | 2nd | HL |
| Who is being Irrational? | After calculating some distances using Pythagoras students will work towards … | Number | 2nd | HL |
| When Area is 64 | Students are presented with an area problem and by exploring … | Functions | 2nd | Common |
| What’s your Angle? | Through exploring relationships in triangles, students will discover that the … | Geometry | 1st | Common |
| Untangles the Angles | Using various methods students will discover different relationships between the … | Geometry | 1st | Common |
| Unpacking 3D Shapes | Students will examine a square based pyramid, identify all 2D … | Geometry, Trigonometry | 5th | HL |
| Transversals are Copycats | Given a diagram with three parallel lines and three transversals, … | Geometry | 6th | HL |
| Top of the Vlogs | Students will present two sets of data in graphic form … | Probability, Statistics | 2nd | Common |
| Time for Telly | Students will learn to deal with problems of time by … | Number | 3rd | FL |
| The Trapezoidal Rule | Students will engage with a problem to find the area … | Geometry, Number, Trigonometry | TY | Common |
| The Story of Two Drones | Students will be asked to apply their knowledge to solve … | Geometry, Trigonometry | 5th | OL |
| The Story of the Gannet | Students will describe the story of a gannet’s dive as … | Functions | 2nd | HL |
| The Integers Cup | Students will develop understanding of integer operations by solving a … | Number | 1st | Common |
| The Great Wall of Nenagh | Problem solving approach to link Patterns, Co-ordinate Geometry and Algebra. | Algebra, Functions, Number | 2nd | HL |
| The Grand Rational | Students are given an algebraic fraction and are asked to … | Functions | 5th | HL |
| The Ex Factor | Through a problem-solving approach, students find the sum of exterior … | Geometry | 2nd | HL |
| The Balancing Act | Introducing Simultaneous Equations through problem solving. | Algebra | 2nd | OL |
| The Formula Speaks Volumes | Students will explore the volume formula for cuboids and develop … | Number | 2nd | HL |
| The Flow of Money | Students will try to solve a tax problem with higher … | Number | 2nd | HL |
| Takeaway Translation | In this lesson students will try to solve a word … | Algebra | 2nd | Common |
| Subway Substitution | Students are presented with a menu and asked to use … | Algebra | 1st | Common |
| Snowflakes | Students will be challenged to express repeating linear patterns algebraically. | Algebra | 3rd | HL |
| Simultaneously solving for two variables | Students will be given two linear equations with two unknown … | Algebra | 2nd | Common |
| Similar Triangle Wrangle | Students will be using dotted paper to produce similar triangles … | Geometry, Trigonometry | 2nd | Common |
| Shootin’ Hoops | Students will be provided with a calculus question that requires … | Algebra, Number | TY | Common |
| Sharing the Unknown | Students will understand the need for algebraic fractions when dealing … | Algebra, Number | 2nd | HL |
| Run Circles Around Pythagoras | Students will be asked to find as many Pythagorean pairs … | Geometry, Trigonometry | 5th | OL |
| Pump Up The Volume | Students will use various strategies to transform different irregular solids … | Geometry, Number | 2nd | OL |
| The Power of Algebra | Students will be presented with a simultaneous linear functions problem … | Algebra | 2nd | HL |
| Plane Clothes | Students solve a problem on the area of a triangle … | Geometry, Number, Trigonometry | 2nd | HL |
| Percentages Predicament | Students tackle a percentage increase problem to understand the concept … | Number | 2nd | Common |
| Paving Patterns | Students are encouraged to examine patterns in various ways to … | Algebra, Functions, Number | 3rd | HL |
| Patterns in Polygons | Students use their prior knowledge of geometry and linear patterns … | Geometry, Number | 2nd | HL |
| Partying with Indices | Through an exponential growth problem it is hoped that students … | Number | 2nd | HL |
| Paper Ratio | Students will be given A3, A4 and A5 sheets of … | Number | 2nd | Common |
| Murling | Students will work with a real world problem involving establishing … | Algebra, Functions | 2nd | Common |
| Multiplying Messi’s Millions | In this lesson students will investigate models and use the … | Number | 1st | Common |
| Monkey Puzzle | Students develop an understanding of the properties of fractions through … | Number | 2nd | Common |
| Meet You Halfway | Students are given a photograph of Sligo town with a … | Geometry | 2nd | Common |
| Make-Up Money | Students will solve a problem based on saving money. By … | Algebra, Functions, Number | 2nd | HL |
| M.M.A. Mixed Mathematical Approaches | Students will formulate the area of the first floor (rectangle) … | Probability, Statistics | TY | Common |
| Kevin’s Cash Connundrum | Students will show in many ways how to represent a … | Algebra | 1st | Common |
| Katie versus Conor – Who will win? | Students explore probability and relative frequency by considering who would … | Probability, Statistics | 2nd | Common |
| Justifying your Thinking | Students are challenged to explain why one Electricity contract is … | Number | 3rd | Common |
| It’s Thirsty Work | Students will learn to interpret graphs by investigating the flow … | Number | 2nd | HL |
| It’s a Matter of Principles | Students investigate the rate of change of a rocket whose … | Functions | 5th | HL |
| It’s Moore of a Process | Students investigate Moore’s Law in order to apply their understanding … | Functions, Number | 5th | HL |
| How much is the special Offer? | Students will be presented with a real life problem verbally … | Algebra | 2nd | Common |
| Heavenly Slopes | Students will engage in structured problem solving to develop their … | Geometry, Trigonometry | 5th | OL |
| Going underground on a Roller Coaster | Students are introduced to quadratic relationships via an in-context problem. | Algebra, Functions | 2nd | Common |
| Fractions meet Algebra | Students will learn to apply their knowledge of fractions and … | Algebra, Number | 2nd | HL |
| Elf on the Shelf | Students will use their knowledge of trigonometry, synthetic geometry and … | Geometry, Trigonometry | 3rd | HL |
| Diving for Roots | Students are introduced to quadratic equations from a functions point … | Algebra, Functions | 2nd | HL |
| Dining Out – Who Gets your Money | “In this lesson students will complete a problem to find … | Number | 3rd | HL |
| Cuir Cruth Air | Trí a bheith ag plé le léaráid ina bhfuil triantáin … | Geometry, Number, Trigonometry | 2nd | Common |
| Cover the Distance Faster | Students apply their knowledge and understanding of coordinates, calculating length … | Geometry, Trigonometry | 2nd | HL |
| Count like an Egyptian | Students are given a problem and asked to explore different … | Algebra | 2nd | OL |
| Box Bonanza | Students work on the problem of calculating the number of … | Algebra | 1st | Common |
| Baby it’s cold outside | The aim of this lesson is consolidate students’ knowledge of … | Algebra, Functions | 5th | HL |
| Are we there yet? | Students are encouraged to solve a problem by finding the … | Geometry, Trigonometry | 2nd | HL |
| Are you up for the Match? | The aim is for the students to discover the Fundamental … | Probability | 1st | Common |
| Are Circles Pointless | In this lesson students will actively participate in solving a … | Geometry, Trigonometry | 5th | HL |
| Getting Value for Money | Students will try to solve a problem involving currency exchange … | Number | 2nd | Common |
| Angles to find the Treasure | The students will be given a map with three different … | Geometry, Trigonometry | 3rd | HL |
| 2D or not 2D? | The lesson focuses on students designing an open rectangular box … | Geometry, Trigonometry | 2nd | HL |
| 2D to 3D… That is the Question? | Students will be presented with a problem in which they … | Algebra, Functions, Geometry, Number, Probability, Statistics, Trigonometry | 5th | OL |
| Prof. Takahashi’s Lesson Proposal | Through a series of problems, students learn about the conditions … | Geometry | 1st, 2nd | Common |
| Introducing Differential Calculus | Developing an understanding of key calculus concepts using rates of … | Functions | 6th | OL |
| The Polygon Predicament | Connecting multiple mathematical topics to solve a geometric problem. | Algebra, Functions, Geometry, Number, Probability | 6th | HL |
| The Perfect Selfie | Using geometry and trigonometry to solve a 3D problem. | Geometry, Trigonometry | 5th | HL |
| Developing Frieda’s Field | Developing the formula for the area of a non-right-angled triangle. | Geometry, Trigonometry | 5th | OL |
| Enter the Matrix | Solving a multi-variable problem using many methods. | Algebra | 5th | OL |
| The General Term of a Quadratic Pattern | Using multiple strategies to develop the formula for a quadratic … | Algebra, Functions | 5th | OL |
| Heading for Trouble | Learning how to deal with a two-variable problem where one … | Algebra | 5th | OL |
| Navigating an Ash Cloud | Drawing on algebra, geometry and trigonometry to solve a problem. | Algebra, Geometry, Trigonometry | 5th | HL |
| The Water Rocket | Analysing quadratic relationships using multiple strategies. | Algebra, Functions, Number | 5th | HL |
| What makes a Parallelogram | Using trigonometry & geometry to calculate the area of a … | Geometry, Trigonometry | 5th | OL |
| Tick Tock – Area of an Incircle | Use the properties of an equilateral triangle to find the … | Geometry, Trigonometry | 5th | HL |
| Seeing through the Dab | Applying trigonometry to solve a 3D problem. | Geometry, Trigonometry | TY | Common |
| Decoding De Moivre | Understanding the concepts of rotations and scales which underpin De … | Algebra, Number, Trigonometry | TY | Common |
| How many ways can you prove It? | Understanding the construction of the bisector of an angle. | Geometry, Trigonometry | 3rd | HL |
| Centre of a Rectangle | Students draw on many topics to find the centroid of … | Geometry, Trigonometry | 3rd, 5th | HL, OL |
| Comparing Percentages, Decimals & Fractions | Calculate the percentage and fraction of a number in many … | Number | 3rd | OL |
| Coordinate Geometry meets Synthetic Geometry | Using coordinate geometry, theorems, corollaries and constructions to show a … | Geometry, Trigonometry | 3rd | HL |
| Picture this Quadratic | Modelling images using quadratic functions and understanding the importance of … | Algebra, Functions | 3rd | HL |
| Transformation Trickery | Applying knowledge of transformations for problem-solving. | Geometry | 3rd | HL |
| 3D Cubes | Identifying right-angled triangles in 3D solids to solve problems. | Geometry, Trigonometry | 3rd | HL |
| Anyone for Pizza – Solving Simultaneous Equations | Modelling problems with simultaneous equations and how elimination can be … | Algebra | 2nd | HL |
| Coffee and Tea Simultaneously | Solving a two-variable problem using different techniques. | Algebra, Geometry | 2nd | HL |
| An Average Problem | Understand the properties of different measures of average. | Statistics | 2nd | HL |
| The Cookie Crumbles | Moving from area to volume in a uniform solid. | Number | 2nd | OL |
| Into the Next Dimension | Understanding the relationship between cross-sectional area and volume for a … | Number | 2nd | OL |
| Equivalent Fractions | Students learn to compare fractions using graphical methods. | Number | 2nd | OL |
| More Pizza for me | Using scaling to compare different quantities fairly. | Number | 2nd | OL |
| Pragmatic Quadratic | Calculating the area of a shape with unknown dimensions. | Algebra, Functions | 2nd | HL |
| Rich, Happy, Healthy or Famous | Using Census @ School data to compare methods for analysing … | Statistics | 2nd | Common |
| Roots and Shoots | Calculating the dimensions of a shape given its area in … | Algebra, Functions | 2nd | HL |
| Tri to be Shady | Using many approaches to calculate an unknown area. | Geometry, Number | 2nd | HL |
| The Window Maker | Using two-variable problems to develop simultaneous equations. | Algebra | 2nd | HL |
| Grazing Gazelles | Discovering Pythagoras’s Theorem. | Geometry, Trigonometry | 2nd | OL |
| Tin of Beans | Using the concept of cross-sectional area to change area of … | Number | 2nd | HL |
| Translating Words into Symbols | Using different operations to develop the same number. | Algebra, Number, Probability | 1st | Common |
| An Alternative Approach to Alternate Angles | Problem solving to demonstrate that alternate angles are equal in … | Geometry | 1st | Common |
| Are you Snookered? | Use axioms and theorems to calculate a pair of missing … | Geometry | 1st | Common |
| Perimeter of an Irregular Shape | Calculating perimeter of a shape with known and unknown lengths. | 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 in understanding proportion. | Number | 1st | Common |
| Count the Sweets | Students apply algebraic reasoning to problem-solve a linear relationship. | Algebra, Number | 1st | Common |
| The Chocolate Challenge | Using equivalent fractions to decide which unit quantity is greatest. | Number | 1st | Common |
| The Great Hall | Using linear relationships to develop algebraic thinking. | Algebra | 1st | Common |
| The Problem with Cats & Dogs | Learning to use Venn Diagrams as a problem-solving tool. | Number | 1st | Common |
| What’s your Angle? | Applying knowledge of axioms and theorems to calculate missing angles. | Geometry | 1st | Common |
| Working with Fred Pattern-Son | Using a visual pattern to introduce linear relationships. | Algebra | 1st | Common |
| Introducing Algebra & Word Equations | Applying algebraic reasoning to in-context problems. | Algebra | 1st | Common |
| Let’s think about BIDMAS | Applying order of operations to generate different numbers. | Number | 1st | Common |
| Dogs do Patterns | Using a real-life problem to develop an understanding of linear … | Algebra, Number | 1st | Common |
Professor Akihiko Takahashi wowed us for the second year running with his open-ended teaching of Geometry using structured problem solving. Professor Takahashi was ably assisted by first-year students from Maynooth Education Campus (incorporating Maynooth Post-Primary School and Maynooth Community College). Professor Takahashi also addressed the conference on the importance of open-ended tasks to maths lessons. You can 
Teachers who participated in Lesson Study 2016-2017 hosted interactive workshops where they gave audience members the chance to try out their problem-solving lesson, discussed their students’ reaction to the lesson and discussed the many ways in which they benefited from being involved in lesson study. All the lesson proposals and problems presented during the workshops are available in our 
The 250+ Maths teachers who participated in Lesson Study 2016-2017 produced a total of 52 lesson proposals. The lesson proposals were summarised by 52 posters which were displayed throughout Maths Counts 2017. All 52 lesson proposals are available for download in our 
Thank you to our sponsors, Microsoft and Build-Up for sponsoring Maths Counts. Thank you to all our exhibitors who provided teachers with lots of useful information about the latest resources for teaching Maths.
