Activities
Geometry and Measure
Constructing QuadrilateralsAge 10+ Time 12 hrs: This activity is about understanding the properties of quadrilaterals. A far deeper understanding is gained if we can use them to construct the shapes themselves. This is a real challenge, but the scaffolding provided in this activity enables the students to do it. Computer required. 

Transformation GameAge 13+ Time 30 mins to 1 hr: This is a fun board game to be played in groups of 24. Students use cards to transform a shape and gain points according to where they land on the board. This can be used as a consolidation activity for reflections, rotations and translations. Lots of fun guaranteed! 

Giant Congruent TrianglesAge 13+ Time 2  3 hrs: Students explore the conditions for congruency of triangles by constructing giant triangles with playground chalk and testing conjectures. The activity is then backed up with a thought provoking paper based challenge. Great practical lesson with rich possibilities. 

Parking RotationsAge 12+ Time 12 hrs: This activity gets students to investigate the effect of changing the centre of rotation. It starts with a series of fun games in which the students have to park a car in a garage by giving the correct rotations. 

Impossible DiagramsAge 10+ Time 1hr: A simple activity designed to get students to reach for their knowledge of properties of angles and shapes. Students are given a number of diagrams and asked to debate and conclude about whether or not they can actually exist. Great exercise in using reasoning and applying knowledge. 

Rotation Reflections & ProofAge 14+ Time 12hrs: A really nice investigation that requires students to apply and make links between a range of topics. Can students find a single rotation that has the same effect as two reflections? Can they formulate a general theory that works given any two reflections? Can they prove it! 

Impossible TrianglesAge 14+ Time 1hr: A simple activity designed to get students to reach for their knowledge of triangle geometry. Pythagoras's theorem, SOHCAHTOA, Sine rule and Cosine rule. The activity provides an excellent opportunity for giving meaning to and practicing these concepts. 

Festive SnowflakesAge 9+ Time 30m: This is a lovely Christmas activity! Students are asked to make some beautiful snowflake images using dynamic software. They can then share their work with the world by adding their snowflake to collaborative presentation. Why not run a competition in your school for the best image? 

Sine Rule  Using a TheodoliteAge 15+ Time 1h: This practical activity gets students to make a simple theodolite and use it to make measurements around the school grounds. It’s a great application of the Sine Rule. If students have thought and questioned you about why learning trigonometry is useful then this is the activity for them! They will have no doubt seen surveyors on building sites using digital theodolites on tripods and perhaps wondered what they were doing. This activity gets them to act as surveyors to find the distances between different positions. 

Brand SymmetryAge 12+ Time 12h: Students use their knowledge of equations of lines to rebuild well known, symmetrical logos from a small fragment of the image. They then find and/or make their own logos, providing for their partner only a small fragment (using FREE photo editors such as paint.net, gimp or others) from which to rebuild the original. 

Proof  Pythagoras' TheoremAge 14+ Time: 12hrs Proof is a hugely significant part of mathematics. This activity is an ideal first experience of proof for students since scaffolding is provided: a cutup activity first allows them to get the feeling for a demonstration of Pythagoras’ Theorem; this is followed by 3 different proofs. The only requirement is that students can find the areas of simple shapes and expand and simplify double brackets. A great introduction to the beauty of proof! 

Prism VolumesAge 13+ Time: 12hrs This is a very practical activity to help students develop a sense of volume/capacity and how to calculate it for prisms. Through pouring sand or water into and between a range of millimetre precise relational prisms, students discover that the volumes of prisms are proportional to the areas of their crosssections! Plenty of handson challenge for all abilities. 

Similar TrianglesAge 14+ Time: 1 hr+ A great triangle mystery! These 24 triangles can be split in to 8 groups of 3 similar triangles by matching the angles. Students can use proportional reasoning to work out the missing lengths on the similar triangles. Present the triangles and say 'Find out the missing lengths' or add some structure depending on the class. The activity can be extended in to Pythagoras's theorem and trigonometry. 

Olympic Rings LogoAge 14+ Time: 12hr In this activity students are set the task of producing their own logo for the Olympic Games. The initial challenge is to create four beautiful dynamic images using dynamic geometry. Students are led through each construction with individual help videos to get to grips with the equation of circles, controlling the centre, radius and path of the circles. Opportunities for a class competition. 

Renaissance MathematicsAge: 12+ Time: 1h What changed during the Renaissance? This activity looks at the revolution in using algebra to describe geometries, graphs, 3D perspective and the introduction of decimal notation. It can be used as part of a Renaissance School Day where students make links between subjects and then present their findings in a whole school assembly. Overview of this day, lead by History department, available here. 

Vector TranslationsAge 11+ Time: 1hr An introduction to the concept of vectors or for teaching translation. Students use arrow diagram vectors to reconstruct a picture and also record the vector in column format. They can then use Autograph or Geogebra to make their own challenge for a partner to reconstruct. The activity closes with a freekick, vector shootout applet. 

Indestructible QuadrilateralsAge 11+ Time: 13hr This activity is all about establishing and working with the defining properties of quadrilaterals. Students work with dynamic constructions and move them around to try and establish what is always, sometimes and never true about them so that they can identify wich shape it is. Students are then invited to construct their own before working on problems about the sets and subsets. 

Quadrilateral PropertiesAge 11+ Time: 12hr By copying and pasting multiple triangles students experiment with what quadrilaterals, and polygons, can and can’t be made with different triangles. They then classify triangles using a flowchart, before creating their own flowchart to identify the special quadrilaterals. The activity closes with a triangular jigsaw puzzle that students have to fit into a sheet of quadrilaterals then, a work of art! 

Interior AnglesAge 13+ Time: 2hr This activity gets students to discover the formula for the sum of interior angles in polygons. The investigation can be completed using dynamic geometry software and is followed by an opportunity to justify the results geometrically in two different ways. Finally, it is completed with a lovely application using knowledge of interior angles to create semitessellations. A very complete resource. 

Rearranging SOHCAHTOAAge: 15+ Time 1hr This activity is all about helping students to understand how to solve rightangled trigonometry problems. The activity encourages students to make 'correct statements' about the situations/diagrams given and become fluent in rearranging them to make unkowns the subject and ths solve the problem. Students can do this on their own computers or it can be done from a central computer as a whole class activity. 

Which Rule?Age: 15+ Time 1hr This activity is designed to help students solve trigonometry problems by encouraging them to 'Speculate' about what might be possible. Students are asked to state different truths or complete different equations for a given diagram without being told what to solve for. Having completed the equations they are asked to think about which of them is most useful for solving for a particular variable. 

Making a Trig CalculatorAge: 14+ Time 1hr Use dynamic geometry and the fundamental principles of trigonometry to construct and program a trig ratio calculator. The essence of this acitivity is in students constructing their own. The logical steps required to do so involve real enquiry in to the nature of trig ratios. The result is really pleasing! 

Paper BaublesAge: 12+ Time 12hrs Ideal for Christmas celebrations, this activity gets students to design and create Platonic and Archimedean polyhedra and make them into decorations. No messy glue is required, as tabs are folded and stapled on the outside, making them easy and quick to make, as well as attractive and decoratively original. 

3D PerceptionAge: 12+ Time 1h The aim of this resource is to develop student’s association of nets, hence surface area, with 3D solids, hence volume. The activity starts with a matching activity, nets and solids, some of which work, some don’t, students can cut and fold to check. Two virtual manipulative websites are then used, one aimed at inspiring them with a wide, and unusual range of 3D shapes. 

Rectangular RelationsAge: 11+ Time 12 hrs Students are given A3 templates of parallelograms and trapeziums to cut out, fold, rotate, reflect, paste in an attempt to fit them inside a template rectangle. No dimensions are given. Students have to decide what dimensions of the original parallelogram and trapezium correspond to the length and width of the rectangle  the activity's emphasis is on mathematical process. 

Sine Cosine: Model WavesAge: 15+ Time: 30mins1h. Students use geometry software to model wave pictures from reallife objects and situations. In doing so, students will investigate the effects of the coefficients for sine and cosine waves e.g. y = a cos[b(xc)]+d asking themselves: “What Changes?”, “What Stays the Same?”. No software is required 

Sine Cosine TransformationsAge: 15+ Time 12 hrs Using Autograph or the free Geogebra or Microsoft Maths 4.0, students investigate the functions of the sine and cosine graph. Students record the key, defining points in a preprepared table: coordinates of the maximum and minimum and xintercepts, as they change different parameters using the constant controller or sliders. Without technology, students then have to predict these key points for different functions. 

Sine and Cosine: Triangle, Circle, Wave!Age: 15+ Time 1h This activity introduces sine and cosine graphs using the video of the construction of a Ferris wheel that demonstrates the link with triangles. Students then sketch the graph of their movement on the Big Wheel. The aim is to link the sine and cosine ratios to a circle. Students use calculators to plot the graphs exactly (spotting symmetries to save them calculation time!). VM also available. 

Circle CircumferenceAge 11+ :Time 40mins+ This investigation enables students to discover pi for themselves through a practical activity. The classic method of measuring the circumference of a circle with string is enhanced with a lovely applet and a chance to use dynamic geometry to make very accurate measurements. This activity is best attempted before the students have any knowledge of pi. It is an alternative to the Discovering Pi 

Pyramid ModelAge: 13+ Time 2 hrs This is a lovely practical activity to help students visualise and derive the formula for the volume of a pyramid. By constructing square based pyramids (10cm by 10cm) with height 5cm then fitting six of them together to make a cube of edge 10cm they realise the volume of the pyramid is 1000/6cm². The activity is supported with videos and practice questions. 

Prism PeopleAge: 13+ Time 2 hrs Exploring prisms by making them! Students are asked to build model robots from different types of prisms. The practical element of building a prism is used to help students discover the related features of these shapes. Following this, students areasked to look in more detail at the structure and surface area of prisms and test out what they have learned on some examples and challenges. 

Body Surface AreaAge: 13+ Time 40mn  1 hr. Working in small groups students are asked to find an approximation for the surface area of their bodies. This is a great practical investigation using surface area of prisms and spheres, etc. with real life applications. It encourages students to think critically about area. Which 3D shapes will best approximate the shapes of the different parts of the body? 

Dancing VectorsAge: 15+ Time 2 hrs. Introduce vectors through dancing! This is a great fun and effective activity where students imagine displacement vectors as dance moves! The vectors are combined to make a dance routine. Get the whole class up and dancing this routine to Donna Summer's hotstuff! It is a memorable experience and really helps students get to grips with this concept. 

3D UncoveredAge: 15+ Time 12 hrs. This activity uses technology to help students with the notoriously difficult idea of working with 2D planes within 3D situations and thus solve problems with trigonometry in 3 dimensions.Google Sketchup is a simple and clear visual aid that encourages students to literally look at the problem from a different angle. 

Escher SymmetryAge: 13+ Time: 2h. Observing symmetrical objects comes quite naturally to students because we are surrounded with symmetry. Here’s an activity that takes that skill a giant step further. A great example of how the use of computer software can create a whole new type of activity, this investigation gets students to analyse the symmetry in Escher tiling patterns by reflecting, rotating and translating them using Geogebra. 

Rotation NavigationAge: 11+ Time: 1h. When describing rotations, students often forget that coordinates define a centre of rotation. Through the designing and playing of the “Around the World” and “Jungle Obstacle” games students get lots of experience of defining rotations in a fun and creative environment. The software forces students to consider angle and direction and displays the coordinates of the centre of rotation. Lots of scope for extension challenging able 1415yr olds as a starter activity. 

Nature's SymmetryAge: 11+ Time: 12hrs Students explore the rotational and reflective symmetry occurring in nature and have fun producing their own flower symmetry patterns. This instantly engaging activity makes use of dynamic geometry software geogebra which is freely available requiring no software installing at geogebra.org 

Measuring the WorldAge: 13+Time: 1 to 1.5 hr This activity provides an interesting context to make some proportion and ratio calculations. Google Earth is used to make measurements about distance and angles of longitude and latitude. These are then combined to make calculations about the circumference of the Earth. No previous knowledge of Google Earth is required. 

Equation ReflectionsAge: 11+ Time: 12hrs Students often think reflection is easy, but the big change at this level is the need to define, using equations, the position of the mirror line. This activity uses Geogebra and/or Autograph to explore points on different lines to remind students why lines can be defined using equations. Three furtheractivities oblige students to use equations to perform reflections and create a reflective, art masterpiece!


Modelling MusicAge: 15+ Time: 1h. This activity helps students see the connection between mathematics and music. Students see the shape of music (pure tone sound appears as trig functions) thanks to sound recording software (Audacity). No need to install the software, as short videos and images are ready to use. Students would be expected to have seen the graph of a sine curve before, and have some understanding of transforming graphs. 

Dr WhoAge: 13+ Time: 1 hr+. This is a really absorbing and engaging puzzle that is rich with interesting mathematical behaviour. The essential learning objective for this activity is about scale factors of enlargement and repeated enlargement. The medium for the challenge really appeals and this type of dynamic question represents a whole new genre of questions that are offered by technology... 

KaleidoscopeAge: 13+ Time: 1 hr+ Explore the concept of rotation with this dynamic problem. Students are shown an animation created from a construction in dynamic geometry and asked to recreate it by examining its properties. The construction is all based on repeated rotation. This is an absorbing problem combining some critical thinking with creativity. 

Plans and ElevationsAge: 11/12+ Time: 1h This activity uses the excellent Freudenthal Institute's Wisweb interactive "Rotating and Building Houses" to help students develop their ability to visualise 2D representations of 3D shapes. The activities on this page are carefully designed to get the most out of the virtual manipulative, with students using it to test their 2D written representations (digitally in word) in a 3D environment and to set challenges for their partner to solve. 

Piece of CakeAge: 14+ Time: 1 hr Which is the biggest piece? Give students this selection of parts of circles and ask them to put them in order of size. The result is an intuitive need to work out the area of sectors of circles! 

321 Blast off!Age: 14+ Time: 40mins This short activity asks students to calculate the height of a water powered rocket. This practical lesson gets students out of the classroom and gives them a genuine application of rightangled triangle trigonometry. It is also a great oppportunity to explore error bounds. You may even wish to embark upon a joint project with the science department at your school. 

Spherical CylindersAge: 14+ Time: 1h This activity uses a useful interactive website animation to help students work out for themselves the relationship between the volume of a sphere and the volume of a surrounding cylinder of equal height and diameter to that of the sphere's. Once they understand where the formula comes from, they then apply it, in pairs or small groups, to a series of interesting, if unusual, problems! 

Human LociAge: 14+ Time: 2 hrs A chance to get your class outside, Human Loci is a fun and revealing activity that gets students representing various loci by positioning themselves according to the rules given. Best played in teams! 

Discovering SOHCAHTOAAge: 13+ Time: 1.5  2 hrs This investigation gets students to discover the three trigonometric ratios for rightangled triangles. Dynamic geometry software replaces a classic pencil and paper method for constructing and measuring sides in triangles. Conjectures about ratios are quickly made and tested. 