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INforM – Interactive Notebooks for Mathematics Alison Clark-Wilson, Carol Knights and Adrian Oldknow The Mathematical Association (MA), UK. This is a collection of 18 SMART Notebooks, and associated files, illustrating a range of interactive approaches to teaching mathematics in 11-16 age range. These are linked to the English National Curriculum for Key Stages 3 (11-14) and 4 (14-16). They contain web links, teachers’ notes and a variety of files for use with software such as Cabri, Excel, Geogebra, Geometer’s Sketchpad, TI SmartView and the Mathematical Toolkit. Book 1 – Tilings and Tesselations Starting with an activity based on hexagon patterns, the main exploration is to find another shape to complete a tiling based on regular pentagons. Tilings with arbitrary triangles are explored, and links made with transformation geometry and actual tiling patterns found in architecture. Keywords: geometry, hexagon, pentagon, photograph, rotation, tessellation, transformation. Book 2 – Gradients Starting with photographs of playground slides, pupils use rulers and protractors to estimate angles of slope and to find gradients in a variety of forms such as fractions, ratios and percentages found on real road signs. Keywords: angle, gradient, horizontal, percentage, photograph, protractor, slope, vertical. Book 3 – Enlargements Similar shapes are drawn on a grid and pupils have to locate the centre of enlargement and the ratios of corresponding lengths, leading to the definition of `scale factor’. Files are included in Cabri, Sketchpad and Geogebra to support investigations with enlargements, as well as in a web-page. Keywords: Cabri, centre, Geogebra, geometry, enlargement, scale factor, Sketchpad, transformation. Book 4 – T shapes on a number grid The starter activity encourages pupils to define different positions on a number grid in terms of a number n. The main task uses a “10 grid” and a pile of T shapes to provide a context for pupils to generate some algebraic expressions and create an equation that connects a number inside the T shape, n with the sum of the numbers inside the T shape. Keywords: algebra, formula, grid, number, template. Book 5 – Areas on a geoboard The activity uses a computer representation of a 5-by-5 array of nails on a plywood base called a `geoboard’. Shapes are made by connecting any of the 25 dots, and areas measured – with the aim of developing the formula for the area of a triangle. Links are made to NCTM Standards materials. Keywords: area, base, geometry, grid, height, point, segment, triangle. Book 6 – Medians Starting with a set of cards showing single digits, pupils drag the cards into numerical order and identify the middle one, for an odd number of cards, and the middle pair for an even number – leading to the definition of median. Activities are then developed around an interactive dice simulation, Keywords: average, data handling, dice, median, order, set, statistics. Book 7 – The Answer is 36 This activity illustrates the use of the SMART Ideas software to show links between mathematical topics, in this case mental calculations, and resources to support their teaching and learning. Keywords: calculations, equivalent, links, mental, mind map, SMART Ideas. Book 8 – Straight line graphs through the origin The materials support the development of the algebraic representation of straight-line graphs in coordinates in the form y = mx + c and the relationship between m and the gradient (slope) of the line. Resources used included the Mathematical Toolkit from the SMART Gallery. Keywords: algebra, coordinates, equation, gradient, intercept, line, Mathematical Toolkit, slope. Book 9 – Transforming triangles The first activity is exploring horizontal and vertical lines of symmetry in capital letters. The main task is classifying quadrilaterals by their symmetries, and there are files in Cabri and Sketchpad to help with this, as well as ideas for use with the Mathematical Toolkit. Keywords: axis, diagonal, geometry, horizontal, mirror, reflect, symmetry, transformation, vertical. Book 10 – Generating sequences Starting with a photograph of a hair drier, pupils build up sequences to fit patterns and to generate algebraic rules. The main activity uses Excel spreadsheets as “Ink aware” applications to build up term-to-term sequences. Keywords: algebra, ink aware, number, pattern, sequences, spreadsheet, term. Book 11 – Wrist and neck sizes The first activity explores the range and mean of a data set. Data is gathered for the wrist (cuff) and neck (collar) size of pupils in order to compare spreads of results for boys and girls using Excel spreadsheets. Scattergraphs are explored with Excel, TI InterActive!, TI SmartView and the Mathematical Toolkit – and straight line graphs are fitted “by eye”. Keywords: best-fit, data handling, data set, line graph, mean, range, scattergram, statistics. Book 12 - Powers and Standard Form The first activity ‘Work out the size of Jupiter’ serves as an introduction to the notation and leads to a comparison between sizes of planets. The main activity is based on a video of cell division, and leads to discussion of both positive and negative indices. Keywords: number, exponential, index, power, relative, scale, size, standard form, video. Book 13 - Probability Students compare experimental data and theoretical probabilities to gain understand that if they repeat an experiment, they may - and usually will - get different outcomes, and that increasing sample size generally leads to better estimates of probability and population parameters. Keywords: coin, data handling, dice, experiment, outcome, probability, proportion, spinner, statistics, success, table. Book 14 – Ratio Pupils explore simplifying ratios by dragging stars and ‘smileys’ to arrange them in rows. Using a variety of extracts from the same photograph of a balloon, students identify the similar ones and find their linear ratios. They have to rescale a photograph to fit a given frame. Finally they explore the ratio of diameter to circumference in a circle. Keywords: circle, circumference, dimension, enlarge, geometry, height, length, number, photograph, ratio, rectangle, similar, transformation. Book 15 – Working in Three Dimensions The activities are related to work in Design & Technology and Art & Design. The mathematics covers 2D representations of 3D objects, nets, elevations and perspective. Resources use include animations from the SMART Gallery, files for Cabri 3D and photographs of bridges, buildings etc. Keywords: art, Cabri 3D, design, dimension, elevation, geometry, net, perspective, photograph, plane, projection, solid, space, technology. Book 16 – Bearings and distances The activities are related to work in Geography. The mathematics covers estimation of angle and length, use of bearings, reading and using scales. Using excerpts from maps, together with ruler and protractor, students find bearings and distances and take part in a power-boat race! Keywords: angle, bearing, compass, direction, distance, geography, protractor, scale. Book 17 – Radioactive Dating The activities are related to work in History and Science. The mathematics covers sequences, linear functions, quadratic functions and logarithms – so different pages may be omitted and the resulting Notebook saved for a particular year group. The main activity is the Carbon 14 dating of the wooden round table from Winchester castle alleged to have been that of King Arthur. Keywords: carbon, decay, exponential, history, interpolation, inverse, linear, logarithm, radiation, science. Book 18 – Video analysis The activities are related to work in Art & Design, PE, Sports and Science. The mathematics covers symmetry, shapes, linear functions, quadratic functions and transformation of function. A range of techniques are used to extract coordinate data from digital photographs and video clips. Keywords: algebra, art, coordinates, design, functions, graph, linear, Mathematical Toolkit, photograph, physical education, quadratic, science, sports, Tracker, transformations video, Vidshell.