Geometry and measures

Maths

Secondary

Students learn about 3D maths, outside of the classroom

A boys' school in south London improves their students' 3D awareness by visiting local buildings, making paper shapes, using student mentors, and looking at the algebra of origami. Woolwich Polytechnic school in London goes on a trip to the Gherkin and Greater London Authority City Hall in central London, both buildings with unique structures. Back at the school, fired up after their excursion, the students create their own structures and in the process find out a lot more about algebra and geometry.

3D Awareness

An imaginative way of thinking about the accuracy of measurements

An unusual and active lesson planning idea for teaching Key Stage 3 pupils about making accurate measurements, in this secondary mathematics resource. Maths teacher Mark Dawes, at Comberton Village College, gets his Year 8 students to choose some non-standard units to measure things in and around their classroom. After measuring the height of the door in pencil cases, the width of the whiteboard in shoes and the length of the corridor in 'Bens', the class comes to some conclusions about the bounds of accuracy that can realistically be claimed for different units of measurement. Mark trusts his pupils to behave responsibly while they slide their classmates along the corridor to measure how long it is, and he feels this is a memorable and enjoyable lesson which tackles a difficult mathematical concept.

Accuracy of Measurements

Formulae for the areas of different shapes for KS4 maths

Fran and Dave explain areas and the formulae for different shapes in this video aimed at Key Stage 4 maths classes. Fran's friend wants to know how much it will cost to re-tile her bathroom and Dave is promised a homemade cookie if he is able cost it. Dave wants the largest cookie, but to work out which cookie is the biggest, he needs to work out their surface areas. As Dave arrives at the house his first task is to work out the area of the walls to be covered by tiles, a job that is complicated by a mirror and windows. Separately Fran works out the area of the walls, and then changes the figure when her friend decides she wants a circular and then arched mirror. Meanwhile Dave works out the cost of re-tiling the bathroom, and is rewarded with the circular cookie, which he worked out was largest. When the cookie arrives it is considerably smaller than he expected, does this mean he got the formula for the area of a circle wrong?

Areas of Circles and Composite Shapes

Eleven mathematic sequences filmed around Gaudi's church in Spain

These 11 short sequences, shot in and around Gaudi's La Sagrada Familia church in Barcelona, each display a different aspect of mathematics for pupils to explore, investigate and discuss. Each sequence poses a question intended to stimulate mathematical discussion rather than to elicit a correct answer to a computation. The programme is intended to be used in sections, stopping and replaying the video to analyse the information. It can be shown to pupils on a whiteboard where the pictures can be annotated, or worked on by pupils individually, or in groups on PCs or laptops. The mathematical content rewards repeated viewing and provides a rich source of mathematical imagery.

Barcelona's Big Church

Ten maths sequences filmed during a cricket match

Cricket is a game based on numbers and maths, offering questions about how fast a ball travels, how high, what the score is, and why cricket pitches are often oval. These ten short sequences, shot during a Saturday cricket match, each display a different aspect of mathematics for pupils to explore, investigate and discuss. Each sequence poses a question intended to stimulate mathematical discussion rather than to elicit a correct answer to a computation. The programme can be shown to pupils on a whiteboard where the pictures can be annotated, or worked on by pupils individually, or in groups on PCs or laptops.

Cricket Match

How a maths department has incorporated APP in the KS3 curriculum

How a maths department transformed KS3 teaching by incorporating Assessing Pupils' Progress (APP) throughout the new curriculum. Through two lessons on angles, the maths department at Plantsbrook School, headed by Tom Pole, shows how its redesigned KS3 curriculum delivers APP evidence. Tom uses personally designed assessment diagrams to record observations made during the lessons, and shows how peer assessment can help with evidence collection. Finally, teacher Stuart McAusland shows how his Year 7 class peer assesses homework about sequences.

Designing APP Assessment for Maths

Using scale factor and enlarging shapes for KS4 maths pupils

How to use a scale factor to work out new dimensions and enlarge different shapes is explained through real-life scenarios in this video for use in KS4 maths lessons. Dave has cut two pieces of cake for himself and Fran, but cannot work out why Fran says his is eight times larger when all the sides are only twice the length of hers. Dave then tries to help a dance school enlarge a logo and paint it on some t-shirts. He successfully enlarges the logo using a scale factor of three, but can't work out why, when he comes to paint the design on the t-shirt, he quickly runs out of ink. Back in the studio, Fran demonstrates the relationship between length and area scale factors and suggests that maybe that was why Dave may not have had enough ink. Finally, the t-shirts are painted and the dance group are happy, and so is Dave, when he finally works out why his cake is eight times bigger than Fran's.

Enlargement

Games and number puzzles are used in maths lessons

The staff at Comberton Village College in Cambridgeshire motivate students by using games and number puzzles in their lessons. Teaching a range of abilities, the school's use of games enables students to interact with one another and the subject more. Two Year 8 groups create quadrilaterals by joining points on a circle. The higher set see come up with a rule involving the number of points available. While the lower set class make quadrilaterals with a piece of rope before using the same activity to consolidate the names and properties of shapes they make. Meanwhile, Year 7s try a number puzzle which encourages accurate calculations and supports a whole class investigation and Year 9s, use a number game to think about generalisations and proof.

Enrichment Tasks

Finding out about the Golden Ratio for KS3 maths

Maths teacher, Steve Humble, uncovers the golden ratio in the architecture at Durham Cathedral. Ideal for Key Stage 3 maths students. Steve Humble examines how a cathedral like Durham was designed by following the master mason's use of practical geometry, symmetry, pattern and proportions. Here, Steve investigates the proportions in Durham Cathedral and discovers ratios that are very similar to the golden ratio. He encourages teachers and students to find examples of the golden ratio in their school buildings and local churches.The video uses Northern Architecture's Making Architecture Count project for schools.

Finding the Golden Ratio in Durham Cathedral

A group of Year 9s study geometry in Hampshire

A group of Year 9 students in Hampshire study geometry by gathering and analysing information from their local children's playground. Wildern School in Hampshire has adopted a rather different approach to help engage students and interact with maths. By taking photos of playground equipment, the Year 9s then upload these images onto special computer software, in order to calculate gradients, angles and learn about trigonometry. Later, we hear students and teachers reflect upon this effective and motivating method.

Professional Development for Quality Teaching

Subjects

> Secondary Maths

> Geometry and measures