100 IDEAS FOR TEACHING MATHEMATICS

Transcription

1 100 IDEAS FOR TEACHING MATHEMATICS Mike Ollerton SUB Gottingen A continuum L O N D O N N E W Y O R K

2 CONTENTS ACKNOWLEDGEMENTS INTRODUCTION xii xiii SECTION I A number of number puzzles SQUARE 1 2 Observing patterns on a 100 grid, summing sequences 100 SQUARE 2 4 Coding moves on a 100 grid, arithmetic CARD TRICKERY 1 5 The arithmetic behind a card trick CARD TRICKERY 2 6 Another card trick and more arithmetic FIVES AND THREES 8 Dominoes and arithmetic DIVISORS 1 10 Deciding on divisors DIVISORS 2 11 Developing divisors DIVISORS 3 12 Exploring divisors DIVISORS 4 13 Lowest Common Multiples and divisors DOUBLING AND DOUBLING AND Arithmetic by continually doubling (ABCD) DOUBLING IN MODULAR ARITHMETIC 15 Exploring modular arithmetic EXPLORING UNIT DIGITS 16 Exploring unit digits, sequences FIVE DICE/FIVE CARDS TO A HUNDRED 17 Arithmetic from dice NETWORKS 18 Coding and analysing a line pattern, generalizing, formula PALINDROMES 19 Exploring numbers, generalizing, arithmetic

3 PARTITIONS AND PRODUCTS Addition, multiplication, indices, formulae SCALE FACTORS Enlargements, ratio STORIES Here's the answer, what's the question? TAKE THREE DICE Arithmetic, properties of numbers TAKE THREE NUMBERS A right good number puzzle TAKE A STRIP OF PAPER From number to algebra DOMINO DELIGHT Number patterns, algebra and fractions FRACTION WALLS AS NUMBER LINES Fraction walls, fraction number lines, decimals, percentages FRACTIONAL FROGS Addition and subtraction of fractions, infinity TWO MORE FRACTION PROBLEMS Patterns in fractions, generalizing A COUPLE OF PERCENTAGE PROBLEMS Making sense of percent, compound interest SECTION 2 Puzzles to NAG (Number, Algebra and Graphs) your students with FIBONACCI 1 Sequence generators, golden ratio, graphing data FIBONACCI 2 Properties of the Fibonacci sequence, algebra FIVE NUMBERS IN A RING 1 Differencing, generalizing FIVE NUMBERS IN A RING 2 Summing products, summing quotients, coordinate pictures JOINING DOTS Exploring structures, generalizing SPROUTS A strategy game using nodes, arcs and regions

4 SQUARE MEETING POINT PROBLEM 39 Number patterns, generalizing, writing formulae TURNING INSIDE-OUT ' 40 'People math', a bit of fun, generalizing X+ Y = Partitioning, algebra, graphing 100 SQUARE 3 42 Algebrizing on a 100 square TAKE TWO NUMBERS 43 Addition, number patterns, generalizing DIAGONAL DIVERSIONS 1 44 Practising Pythagoras and trigonometry in a problem-solving context CARD TRICKERY 3 45 Puzzling out a card trick, constructing a formula LONGEST PATH THROUGH A RECTANGLE 46 Number pattern leading to a quadratic NUMBER ROUTE PROBLEMS 47 Number problems and algebra 3 'MULTIPLIED' BY 2 IS 8 48 Number patterns, generalizing, writing a formula SECTION 3 Puzzles to cause your students to shape up SQUARE 9-PIN GEOBOARD 1 50 Shapes, properties, areas, perimeters, collecting like terms SQUARE 9-PIN GEOBOARD 2 51 Vectors, generalizing, equations of straight lines UNFOLDING AND LINE SYMMETRY 52 Shapes, properties, symmetry TRIANGLES WITH CONSTANT PERIMETER 1 53 Coding and constructing triangles, exploring perimeters TRIANGLES WITH CONSTANT PERIMETER 2 54 Classifying triangles, area, practising Pythagoras and trigonometry TANGRAMS 1 55 Instructions for producing tangrams TANGRAMS 2 56 Extension ideas with tangrams TAKE A SQUARE PIECE OF PAPER 57 Visualization, shape, properties, angle

5 A CLOSED PROBLEM TO INVOKE 'STUCKNESS' A 'closed' problem to invoke 'stuckness' SHAPES IN SHAPES Perhaps even more 'stuckness', shape, generalizing to a formula PASSOLA Passing a ball of string around a circle of people, shape, angle LOCI Geometric construction, determining loci SQUARE CUT Dissecting and reconstructing a square, people maths DIAGONAL DIVERSIONS 2 Pentagon triangles, Fibonacci FINDING SOME CENTRES OF TRIANGLES 1 Constructions through paper folding FINDING SOME CENTRES OF TRIANGLES 2 From constructions to Cabri to circle/angle theorems ENLARGEMENTS ON A COORDINATE GRID Coordinates, enlargements, scale factors and area MORE COORDINATE PROBLEMS Calculations with coordinates EXPLORING COORDINATES AND VECTORS Coordinates, vectors and Pythagoras JOINING TRIANGLES Shapes, symmetry, angle CIRCULAR GEOBOARD 1 Shapes, coding, classifying, proving CIRCULAR GEOBOARD 2 Calculating angles CIRCULAR GEOBOARD 3 Circle/angle theorems CIRCULAR GEOBOARD 4. Using and applying trigonometry SECTION 4 Puzzles to see how your students measure up SQUARE 9-PIN GEOBOARD 3 76 Exploring squares on geoboards, generalizing AREA OF 20CM 2 Areas of rectangles on a square grid

6 AREAS OF TRIANGLES ON SQUARE-DQT GRID PAPER 78 Areas of triangles on a square grid AREAS OF SQUARES ON THE SIDES OF TRIANGLES 79 An exploration of Pythagoras' theorem CIRCLES 1 80 Strips of paper, sellotape and 71, writing formulae CIRCLES 2 81 Area of circles on a square grid, writing formulae A SURFACE AREA PROBLEM 82 Cuboids, surface area and a number pattern with a 'hole' TANGENTS 83 Exploring tangents SECTION 5 A few beer MATs, some glue and a lot of imagination USING ATM MATS 1 86 Making 3D solids, Euler USING ATM MATS 2 87 Making more 3D solids (deltahedra) USING ATM MATS 3 88 Truncating Platonic solids USING ATM MATS 4 89 Exploring Archimedean solids TAKE AN A4 PIECE OF PAPER 91 Making cuboids, calculating volumes, surface area, writing formulae SYMMETRY IN 3D 92 Plane and rotational symmetry in 3D SHAPES FROM FOUR LINKING CUBES 93 Making shapes, exploring properties, proof AN ALTERNATIVE 'NET' OF A CUBE 94 A 2D shape, a pairs of scissors and a puzzle to follow CUBE DISSECTION 1 95 Inside every cube there's a tetrahedron just waiting to come out CUBE DISSECTION 2 96 Cubes, tetrahedron, octahedrons and formulae

7 SECTION 6 SFGs, not perhaps as interesting as The BFG but nevertheless some giant-sized ideas for the classroom EXTENDING SEQUENCES BACKWARDS Just as the title says! EXPLORING LINEAR SEQUENCES 99 Forming linear sequences, graphs GRAPHING FACTOR PAIRS 100 Factors, coordinates, graphs, square roots EXPANDING AND FACTORIZING QUADRATICS 101 Factorized and expanded forms of quadratic expressions GRAPHING QUADRATICS An extensive exploration of graphs of quadratic functions (1) GRAPHING QUADRATICS An extensive exploration of graphs of quadratic functions (2) GRAPHING QUADRATICS An extensive exploration of graphs of quadratic functions (3) GRAPHING QUADRATICS An extensive exploration of r graphs of quadratic functions (4) SECTION 7 Ideas for budding data handlers WEATHER PAGE 108 Means, medians modes, charts, scattergraphs, cross-curricular, conventions PROBABILITY FAIRGROUND Dealing with data from simple experiments (1) PROBABILITY FAIRGROUND Dealing with data from simple experiments (2) QUIZ SHOW 111 A puzzle about logic and possibly tree diagrams GUESS THE COLOUR 112 A simple probability experiment, experimental v. theoretical outcomes CAN YOU 'REACH'YOUR HEIGHT? 114 The whole of the KS1-KS4 statistics curriculum in a few measures CUBES IN AN ENVELOPE 116 A sampling experiment, predicting outcomes TESTING, TESTING 117 Testing with a twist and ceding control: students writing the questions