| 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 rule | Trigonometry | 5th | HL |
| What’s the point? | Students make connections between linear patterns , coordinate geometry and real world scenarios | Geometry | 1st | Common |
| What’s The Meaning Of Z-scores | Students build on their prior knowledge of mean and standard deviation to understand and use z scores | Probability, Statistics | TY | HL |
| Top Dog Area | Students deduce different shapes from a word problem using different area and perimeter formulae. Connections are made between trigonometry and generalisation using algebraic notation. | Algebra, Geometry, Number | 5th | OL |
| Simultaneous Shapes | Students progress from the concrete, to the pictorial, to the abstract, solving simultaneous equations using multiple strategies. | Algebra, Functions | 2nd | HL |
| Missing In Action | Students use the idea of equality to form, interpret and solve equations. Students are asked to describe, explain and justify their method for doing this. | Algebra, Functions | 1st | Common |
| Looks Different, Same Value | Students develop a deeper understanding of equivalent fractions and add and subtract algebraic fractions. | Algebra, Functions | 2nd | HL |
| Explain that Formula | Students explore properties of 3-dimensional shapes and use nets to understand where the surface area formula of a cylinder comes from. | Number | 5th | OL |
| Across the divide | Students work on real life word problems where the operation of division is presented in different ways | Number | 2nd | Common |
| It’s Show Time | In this lesson, students will try to solve problems relating to time, and to enhance their understanding and reading of time. | Number | 1st | OL |
| What’s your Angle? | Pupils will be presented with 2 parallel lines and 5 points (A, B, C, D and E). Angle ABC is 110 ̊ and CDE is … | Geometry, Trigonometry | 3rd | HL |
| Percentage Paradox | Structured problem solving lesson involving multiple approaches to a direct proportion percentages problem. Misconceptions around percentage equations are addressed leading to considering an algebraic approach. | Number | 1st | Common |
| A Pizza of the (Fr)Action | Students are given a problem to consolidate their learning of adding fractions and to apply this to the addition of fractions with a variable. | Algebra | 1st | Common |
| What about Parallelograms | Exploring properties of parallelograms using various approaches and looking for connections between these approaches | Geometry | 1st | Common |
| Thinking Outside the Triangle | Using a given diagram to lead students to the discovery of the proof that the exterior angle in a triangle is equal to the sum … | Geometry | 1st | Common |
| The Volume of Money | Through discovery, students derive the formula for the volume of a cylinder. This is achieved through examining the area of a circle (2D) and linking … | Number | 2nd | HL |
| The X Factor | Exploring different ways to represent factorisation of a single algebraic term leading to factorising a two term linear expression. | Algebra | 1st | Common |
| The Power that Lies Beneath | Using Assessment for learning techniques of multiple choice diagnostic testing and effective questioning to explore index rules | Number | 2nd | HL |
| The Array Model | Using the Array Model to factorise quadratic expressions. This proposal includes a unit plan for expanding and factorising in algebra and making important connections. | Algebra | 2nd | HL |
| Straight to the nth Game | Using a problem question to develop the general formula for a pattern | Algebra | 1st | Common |
| Show Me the Money | Discovering the different measures of central tendency using celebrities as examples | Statistics | 2nd | OL |
| Scrutinizing the Difference between Two Squares | This proposal uses the concepts from ‘Algebra through the lens of functions’ to bring students to the discovery of the difference of two squares using … | Algebra | TY | Common |
| Run Johnny Run, Maths To The Rescue | Using prior knowledge of triangles to explore trigonometric ratios and use them to solve problems. | Trigonometry | 2nd | HL |
| Point Of Pick-Up | Using prior knowledge of algebra, coordinate geometry, synthethic geometry and constructions the fairest position for a bus stop is to be located from an aerial … | Geometry | 5th | OL |
| Place Your Pix | Using the problem of placing a picture in a frame, students discover the difference between two squares | Algebra | 2nd | OL |
| Matchstick Challenge | This lesson is based on first year patterns, introducing students to the concept of the general term. | 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 to create the formula for the circumference of a circle using different methods. | 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 solve a real-world problem. | Geometry, Trigonometry | 5th | HL |
| Forthnightly Maths | In a computer game context, students will have to identify intersecting points between a line and a curve using a variety of methodologies. | Functions | 6th | OL |
| Express My Point | Students will be introduced to the concept of writing mathematical expressions and exploring values for a fixed variable in two league tables. | 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 and establishing the algebraic representation of the function. | Functions | 2nd | Common |
| Circling Longitude | A real life scenario of a drone taking a photo at a music festival is presented. Students are tasked with finding the best possible position … | Geometry | 5th | OL |
| Car Savings Conundrum | Students act as a financial advisor and must investigate a number of saving plans to advise their client how long it will take to save … | 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 to their equation and how they can relate to other similar equations | Functions | 3rd | HL |
| A Journey in Finance | Modelling a financial problem using a geometric series and investigating the timeline assosciated with payments | Number | 6th | HL |
| 2 or not 2x that is the question | This lesson provides a physical approach to the understanding of ‘like’ and ‘unlike’ terms. | 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 the discovery and understanding of irrational numbers. | Number | 2nd | HL |
| When Area is 64 | Students are presented with an area problem and by exploring their solutions they will see that all the information pertaining to the problem may be … | Functions | 2nd | Common |
| What’s your Angle? | Through exploring relationships in triangles, students will discover that the exterior angle of a triangle is equal to the sum of the two interior opposite … | Geometry | 1st | Common |
| Untangles the Angles | Using various methods students will discover different relationships between the angles in a diagram based on parallel lines. | Geometry | 1st | Common |
| Unpacking 3D Shapes | Students will examine a square based pyramid, identify all 2D shapes possible using the points given and find the areas of these shapes. | Geometry, Trigonometry | 5th | HL |
| Transversals are Copycats | Given a diagram with three parallel lines and three transversals, students will use their knowledge of geometry to identify existing relationships between pairs of angles, … | Geometry | 6th | HL |
| Top of the Vlogs | Students will present two sets of data in graphic form and will learn that there are more than one way to represent data. | Probability, Statistics | 2nd | Common |
| Time for Telly | Students will learn to deal with problems of time by solving a problem based on when a film of given duration will end if advertisements … | Number | 3rd | FL |
| The Trapezoidal Rule | Students will engage with a problem to find the area of an irregular shape and by doing so will find a formal method for dealing … | Geometry, Number, Trigonometry | TY | Common |
| The Story of Two Drones | Students will be asked to apply their knowledge to solve a real life scenario of two drones on a collision course. | Geometry, Trigonometry | 5th | OL |
| The Story of the Gannet | Students will describe the story of a gannet’s dive as represented by a quadratic graph using words, the parameters of height and time and mathematical … | Functions | 2nd | HL |
| The Integers Cup | Students will develop understanding of integer operations by solving a problem based on a game of golf. | 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 uncover as many properties of the fraction as they can using algebraic procedures, tables and … | Functions | 5th | HL |
| The Ex Factor | Through a problem-solving approach, students find the sum of exterior angles of a triangle in as many ways as possible. | 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 a formula for volume of all prisms leading to the discovery of the formula for … | Number | 2nd | HL |
| The Flow of Money | Students will try to solve a tax problem with higher and standard rate of tax, to enhance their understanding of how tax works. | Number | 2nd | HL |
| Takeaway Translation | In this lesson students will try to solve a word problem using a variety of methods and will discover that such problems can be solved … | Algebra | 2nd | Common |
| Subway Substitution | Students are presented with a menu and asked to use an algebraic expression to describe the bill. | 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 variables and will be required to solve for the two unknown variables using as many … | Algebra | 2nd | Common |
| Similar Triangle Wrangle | Students will be using dotted paper to produce similar triangles and understand that a line parallel to a side produces similar triangles. | Geometry, Trigonometry | 2nd | Common |
| Shootin’ Hoops | Students will be provided with a calculus question that requires them to utilize their algebraic knowledge of roots to construct the pathway of a basketball. | Algebra, Number | TY | Common |
| Sharing the Unknown | Students will understand the need for algebraic fractions when dealing with basic real-world problems. | Algebra, Number | 2nd | HL |
| Run Circles Around Pythagoras | Students will be asked to find as many Pythagorean pairs when c is 5 leading to the discovery of the equation of a circle. | Geometry, Trigonometry | 5th | OL |
| Pump Up The Volume | Students will use various strategies to transform different irregular solids into familiar cuboids and thus calculate the volume. | Geometry, Number | 2nd | OL |
| The Power of Algebra | Students will be presented with a simultaneous linear functions problem and encouraged to solve the problem in a variety of ways. | Algebra | 2nd | HL |
| Plane Clothes | Students solve a problem on the area of a triangle in as many ways as possible. The solutions help form connections between geometry and coordinate … | Geometry, Number, Trigonometry | 2nd | HL |
| Percentages Predicament | Students tackle a percentage increase problem to understand the concept of ‘more than 100%’. | Number | 2nd | Common |
| Paving Patterns | Students are encouraged to examine patterns in various ways to derive connections between linear patterns, equations and graphs. | Algebra, Functions, Number | 3rd | HL |
| Patterns in Polygons | Students use their prior knowledge of geometry and linear patterns to write a mathematical statement describing the relationship between the sum of the angles and … | Geometry, Number | 2nd | HL |
| Partying with Indices | Through an exponential growth problem it is hoped that students will recognise the usefulness of indices in such situations and discover the first law of … | Number | 2nd | HL |
| Paper Ratio | Students will be given A3, A4 and A5 sheets of paper and asked to investigate any relationships between them in as many ways as possible. | Number | 2nd | Common |
| Murling | Students will work with a real world problem involving establishing the distance from the origin and roots of a quadratic function. | Algebra, Functions | 2nd | Common |
| Multiplying Messi’s Millions | In this lesson students will investigate models and use the concept of a “thought experiment” in a real life context to illustrate the operation of … | Number | 1st | Common |
| Monkey Puzzle | Students develop an understanding of the properties of fractions through a real-life problem. | Number | 2nd | Common |
| Meet You Halfway | Students are given a photograph of Sligo town with a coordinate grid superimposed on it. They are asked to find the location which is halfway … | Geometry | 2nd | Common |
| Make-Up Money | Students will solve a problem based on saving money. By discussing the various approaches used it is hoped that students will identify connections between several … | Algebra, Functions, Number | 2nd | HL |
| M.M.A. Mixed Mathematical Approaches | Students will formulate the area of the first floor (rectangle) of Conor Mc Gregor’s holiday home in Las Vegas. | Probability, Statistics | TY | Common |
| Kevin’s Cash Connundrum | Students will show in many ways how to represent a word problem which will lead to an algebraic equation. Following this they will solve an … | Algebra | 1st | Common |
| Katie versus Conor – Who will win? | Students explore probability and relative frequency by considering who would win in a fight between Katie Taylor or Conor McGregor. | Probability, Statistics | 2nd | Common |
| Justifying your Thinking | Students are challenged to explain why one Electricity contract is better value than another by describing a graph of their pricing structures. | Number | 3rd | Common |
| It’s Thirsty Work | Students will learn to interpret graphs by investigating the flow of liquid into three different containers. | Number | 2nd | HL |
| It’s a Matter of Principles | Students investigate the rate of change of a rocket whose path is modelled by a quadratic function. | Functions | 5th | HL |
| It’s Moore of a Process | Students investigate Moore’s Law in order to apply their understanding of Logarithms and Exponential Functions andhow they are related to each other. | Functions, Number | 5th | HL |
| How much is the special Offer? | Students will be presented with a real life problem verbally and visually and will learn to recognise how to solve a simultaneous equation using elimination. | Algebra | 2nd | Common |
| Heavenly Slopes | Students will engage in structured problem solving to develop their understanding of the “slope” of a line, and of the relationships between the slopes of … | 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 equations to the solving of equations involving algebraic fractions. | Algebra, Number | 2nd | HL |
| Elf on the Shelf | Students will use their knowledge of trigonometry, synthetic geometry and their problem solving skills to find the angle of depression from a point. | Geometry, Trigonometry | 3rd | HL |
| Diving for Roots | Students are introduced to quadratic equations from a functions point of view and will use this to make connections to the algebraic method(s) for factorising … | Algebra, Functions | 2nd | HL |
| Dining Out – Who Gets your Money | “In this lesson students will complete a problem to find out how much a meal costs before tax is added by finishing this question they … | Number | 3rd | HL |
| Cuir Cruth Air | Trí a bheith ag plé le léaráid ina bhfuil triantáin agus cearnóga, tiocfaidh na daltaí ar ghaol idir a n-achair. Tabharfaidh an gaol seo dóibh … | Geometry, Number, Trigonometry | 2nd | Common |
| Cover the Distance Faster | Students apply their knowledge and understanding of coordinates, calculating length and Pythagoras’ Theorem to calculate the distance between two points, with the intention they will … | Geometry, Trigonometry | 2nd | HL |
| Count like an Egyptian | Students are given a problem and asked to explore different approaches leading them to query the difference between multiplication and addition. | Algebra | 2nd | OL |
| Box Bonanza | Students work on the problem of calculating the number of matchsticks in a structure which leads to developing linear expressions. | Algebra | 1st | Common |
| Baby it’s cold outside | The aim of this lesson is consolidate students’ knowledge of how to solve a quadratic equation algebraically and graphically whilst also drawing on students’ prior … | Algebra, Functions | 5th | HL |
| Are we there yet? | Students are encouraged to solve a problem by finding the midpoint between two points. This can be achieved in many ways. Through Ceardaíocht students will … | Geometry, Trigonometry | 2nd | HL |
| Are you up for the Match? | The aim is for the students to discover the Fundamental Principal of Counting through problem solving using all previous knowledge to extend their learning into … | Probability | 1st | Common |
| Are Circles Pointless | In this lesson students will actively participate in solving a problem that will progress towards understanding, recognising and applying the equation of the circle | Geometry, Trigonometry | 5th | HL |
| Getting Value for Money | Students will try to solve a problem involving currency exchange set in a real life situation. | Number | 2nd | Common |
| Angles to find the Treasure | The students will be given a map with three different routes to treasure for three pirates. Students must identify the routes and calculate the distances … | Geometry, Trigonometry | 3rd | HL |
| 2D or not 2D? | The lesson focuses on students designing an open rectangular box when given the area of its base and total surface area of the box. | Geometry, Trigonometry | 2nd | HL |
| 2D to 3D… That is the Question? | Students will be presented with a problem in which they need to select and use appropriate knowledge from the different strands in maths, and decipher … | Algebra, Functions, Geometry, Number, Probability, Statistics, Trigonometry | 5th | OL |
| Prof. Takahashi’s Lesson Proposal | Through a series of problems, students learn about the conditions required for congruency (includes student worksheets). | Geometry | 1st, 2nd | Common |
| Introducing Differential Calculus | Developing an understanding of key calculus concepts using rates of change. | 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 relationship. | Algebra, Functions | 5th | OL |
| Heading for Trouble | Learning how to deal with a two-variable problem where one relationship is noon-linear. | 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 parallelogram. | Geometry, Trigonometry | 5th | OL |
| Tick Tock – Area of an Incircle | Use the properties of an equilateral triangle to find the area of its incircle. | 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 Moivre’s Theorem. | 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 a rectangle. | Geometry, Trigonometry | 3rd, 5th | HL, OL |
| Comparing Percentages, Decimals & Fractions | Calculate the percentage and fraction of a number in many ways. | Number | 3rd | OL |
| Coordinate Geometry meets Synthetic Geometry | Using coordinate geometry, theorems, corollaries and constructions to show a quadrilateral is a rectangle. | Geometry, Trigonometry | 3rd | HL |
| Picture this Quadratic | Modelling images using quadratic functions and understanding the importance of roots. | 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 used to solve them. | 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 uniform solid. | 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 data. | Statistics | 2nd | Common |
| Roots and Shoots | Calculating the dimensions of a shape given its area in general terms. | 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 a circle into volume of a cylinder. | 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 measure. | Geometry | 1st | Common |
| Are you Snookered? | Use axioms and theorems to calculate a pair of missing angles. | 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 relationships. | Algebra, Number | 1st | Common |
