Download INforM – Interactive Notebooks for Mathematics

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.