| About the author |
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xii | |
| Online resources |
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xiii | |
| Introduction |
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1 | (19) |
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What does this book contain? |
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1 | (1) |
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What's new in this edition? |
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2 | (1) |
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What equipment will I need? |
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3 | (1) |
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Why is there such a strong emphasis on games? |
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3 | (1) |
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4 | (1) |
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5 | (1) |
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What are the indicators for dyscalculia? |
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6 | (1) |
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What about learners with other specific learning difficulties? |
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7 | (1) |
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What kind of teaching do dyscalculic learners need? |
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7 | (2) |
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What's next, after working through this book? |
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9 | (1) |
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Table: Summary of the main teaching points addressed by the games in The Dyscalculia Toolkit |
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10 | (2) |
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Table: All the activities and games in The Dyscalculia Toolkit listed according to their numeracy topic or main teaching points |
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12 | (8) |
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Section 1 Early Number Work with Numbers Up to 10 |
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20 | (55) |
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20 | (1) |
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What are the main problems? |
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21 | (1) |
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21 | (2) |
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23 | (1) |
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Activity -- Make dot patterns for the numbers 1 to 10 |
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23 | (1) |
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Activity -- Focus on key component facts |
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24 | (2) |
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Activity -- Make transparent dot pattern cards for the numbers 1 to 5 |
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26 | (1) |
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27 | (1) |
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Activity -- Explore smaller numbers inside larger numbers |
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28 | (1) |
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29 | (1) |
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Activity -- Change one dot pattern into another |
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30 | (1) |
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Activity -- Change dot patterns by adding or subtracting |
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31 | (1) |
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Activity -- Use dot patterns to explore the idea of odd and even |
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31 | (1) |
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32 | (1) |
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Game -- Key Components Guessing Game |
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33 | (1) |
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Activity -- Sort and re-sort a set of dominoes |
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34 | (1) |
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Activity -- Connect subtraction to addition |
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35 | (1) |
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Activity -- Regroup: Apply logic to find new component facts from given facts |
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36 | (1) |
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Activities -- Become familiar with Cuisenaire rods |
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37 | (2) |
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Activity -- Explore odd and even with Cuisenaire rods and with money |
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39 | (1) |
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Game -- Odd and Even Collectors |
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40 | (1) |
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Game -- Draw Your Race on a Number Line |
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41 | (1) |
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Activities -- Use Cuisenaire rods to learn all components of the numbers 1 to 10 |
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42 | (1) |
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Activity -- Make a `Story' of a number |
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43 | (1) |
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Game -- Race to Tell a Story |
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44 | (1) |
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Activity -- Make and read equations with Cuisenaire rods |
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45 | (1) |
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Activities -- Draw and record equations informally |
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46 | (1) |
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Game -- Key Facts Triad Game |
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47 | (1) |
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Game -- Post-It Note Subtraction |
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48 | (2) |
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Activities -- Record equations in writing |
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50 | (1) |
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Activity -- Make up word problems to match a given number fact |
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51 | (1) |
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Game -- Cover the Numbers (or Shut the Box) |
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52 | (1) |
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53 | (1) |
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Activity -- Make a bead string, in two colours, of 10 beads |
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54 | (1) |
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Activities -- Learn complements of 10 with the bead string |
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55 | (1) |
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Game -- How Many Beads? How Many Are Hidden? |
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55 | (1) |
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Activity -- Find complements of 10 with Cuisenaire rods |
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56 | (1) |
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Game -- Complements Number Search |
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57 | (1) |
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Game -- Complements Ping-Pong |
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58 | (1) |
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58 | (1) |
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Activities -- Explore and learn the doubles up to 5 + 5 |
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59 | (2) |
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Activities -- Estimate and measure using Cuisenaire rods |
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61 | (2) |
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Activities -- Focus on plus/minus 1 and plus/minus 2 |
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63 | (2) |
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Game -- Who Has the Most Equations? |
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65 | (1) |
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66 | (1) |
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Activity -- Compare the difference and equalise |
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67 | (1) |
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Activities -- Hidden quantity subtraction |
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68 | (1) |
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Activity -- Teach complementary addition |
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69 | (1) |
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Activity -- Complementary addition on a number line |
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70 | (1) |
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Activity -- Make up word problems about missing numbers |
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71 | (1) |
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Activity -- Use reasoning to find near-complements and near-doubles |
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72 | (1) |
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Activity -- Identify the best strategy for different situations |
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72 | (1) |
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Activities -- Use money for component work |
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73 | (2) |
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Section 2 Basic Calculation with Numbers Above 10 |
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75 | (51) |
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75 | (1) |
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What are the main problems? |
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76 | (1) |
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76 | (3) |
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79 | (1) |
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Activity -- Connect the numbers 10 to 20 with the numbers below 10 |
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79 | (1) |
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80 | (1) |
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81 | (1) |
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Activities -- Focus on the `teen' numbers |
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82 | (2) |
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Activities -- Explore the numbers between 10 and 20 with Cuisenaire rods |
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84 | (3) |
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Activities -- Learn the doubles up to 10 + 10 |
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87 | (1) |
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88 | (1) |
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89 | (1) |
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Activities -- Locate 2-digit numbers and put them in context |
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90 | (3) |
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Activities -- Complements to 20 |
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93 | (2) |
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Activity -- Complements to larger multiples of 10 |
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95 | (1) |
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Activity -- Complements on a number line |
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96 | (1) |
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Activity -- Introduce bridging through 10 with Cuisenaire rods |
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96 | (2) |
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Game -- Five and What's Left |
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98 | (1) |
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Activity -- Bridge through 10 on a number line |
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99 | (1) |
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Activity -- Practise bridging and reinforce the commutativity of addition |
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100 | (1) |
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Game -- Frame an Addition |
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100 | (2) |
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Activity -- Bridge through multiples of 10 on a number line |
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102 | (1) |
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Game -- Race Along a Number Line and Bridge |
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102 | (1) |
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Game -- Race to the End of the Number Line |
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103 | (1) |
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Activity -- Complementary addition, or subtraction by adding |
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104 | (1) |
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Game -- Frame a Subtraction |
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105 | (2) |
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Activity -- Complementary addition for subtracting round numbers |
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107 | (1) |
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Activity -- Harder complementary addition on a number line |
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108 | (2) |
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Activities -- Complements to 100 |
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110 | (3) |
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113 | (1) |
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Activities -- Practise and extend the doubles facts |
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114 | (1) |
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Activity -- Halving is the opposite of doubling |
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115 | (1) |
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Activity -- Find half of round numbers |
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116 | (1) |
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Activity -- Function machines for doubling and halving |
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117 | (1) |
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Activity -- Use reasoning to find near-complements and near-doubles |
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117 | (1) |
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Activity -- 9 is almost 10 |
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118 | (1) |
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Activity -- The Basic 8 strategies |
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119 | (1) |
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Activity -- Identify the best strategy for different situations |
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120 | (1) |
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Game -- Subtraction Equations |
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120 | (2) |
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Activity -- A flexible approach to partitioning |
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122 | (1) |
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Activities -- Explore partitioning methods for 2-digit mental additions |
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122 | (2) |
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Activity -- Teach an expanded written method for column addition |
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124 | (1) |
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Activity -- Avoid decomposition in subtraction |
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124 | (2) |
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126 | (40) |
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126 | (1) |
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A note about the threefold nature of the column labelling system |
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126 | (1) |
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What are the main problems? |
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127 | (1) |
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127 | (2) |
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129 | (1) |
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Activities -- Exchange units into tens |
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129 | (1) |
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Activities -- Concrete counting on place value mats |
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130 | (1) |
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131 | (1) |
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Activities -- Make a 20-step staircase and explore the `teen' number names |
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132 | (1) |
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133 | (1) |
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Game -- Race to Cover 100 |
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133 | (1) |
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Game -- Four Throws to Reach 100 |
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134 | (1) |
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Activities -- Make and read numbers made of Cuisenaire rods or base-10 materials |
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135 | (1) |
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Games -- Dice and Spinner Games |
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136 | (1) |
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Activities -- Practise subtraction and decomposition with concrete materials |
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137 | (1) |
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Game -- Spot the Decomposition |
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138 | (1) |
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Activities -- Use a spike abacus |
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138 | (1) |
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Game -- Win Counters on a 100-Square |
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139 | (1) |
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Game -- Race Through a 100-Square |
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140 | (1) |
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Activities -- Practise adding and subtracting 10 and 100 |
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141 | (1) |
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142 | (1) |
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Activity -- Transform a 2-digit number in two steps |
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143 | (1) |
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Activity -- Teach the threefold repeating pattern: units, tens and hundreds |
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144 | (1) |
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Activities -- Explore place value as a shorthand |
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145 | (1) |
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Activities -- Read and write multi-digit numbers |
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146 | (1) |
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Activities -- Build up large numbers, one column at a time |
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147 | (1) |
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Activity -- What is the value of ...? |
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148 | (1) |
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Game -- Two-Digit Sequences |
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149 | (1) |
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Game -- Three-Digit Sequences (Focus on Tens) |
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150 | (1) |
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Game -- Place Value Boxes |
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151 | (2) |
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Game -- Calculator Skittles |
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153 | (1) |
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Activity -- Partition numbers into tens and units in various ways |
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154 | (1) |
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Activity -- Split off the `teen' numbers |
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154 | (1) |
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155 | (1) |
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Activities -- Locate any number on a number line |
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156 | (1) |
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Activity -- Round up or down |
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157 | (1) |
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Game -- The Six-Card Rounding Game |
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158 | (1) |
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Game -- The Rounding Challenge |
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159 | (1) |
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Activity -- Teach × 10 and + 10 as a shift between columns |
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160 | (1) |
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Activity -- Extend place value thinking to decimals |
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161 | (2) |
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Activity -- Connect decimal place value notation to money |
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163 | (1) |
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164 | (2) |
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Section 4 Times Tables, Multiplication and Division |
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166 | (58) |
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166 | (1) |
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What are the main problems? |
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167 | (1) |
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168 | (2) |
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170 | (1) |
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Activities -- Build small numbers out of equal-sized groups |
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170 | (1) |
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Activity -- Connect division to multiplication from the very beginning |
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171 | (1) |
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Activity -- Illustrate simple word problems |
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172 | (1) |
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Activity -- Use Cuisenaire rods to show that multiplication is commutative |
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172 | (2) |
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Activities -- Use Cuisenaire rods to connect multiplication and division |
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174 | (2) |
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Activity -- Diagrammatic recording of multiplication and division |
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176 | (1) |
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Activity -- Connect step-counting and repeated addition with times tables |
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177 | (2) |
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Activity -- Practise mental step-counting from given tables facts |
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179 | (1) |
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Activities -- Make times tables patterns on a 100-square |
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180 | (2) |
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Activities -- Make times tables patterns on number lines |
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182 | (1) |
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Activities -- Key fact: Double means `multiply by 2' |
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183 | (1) |
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Activity -- Key fact: ×5 is half of ×10 |
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184 | (1) |
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Activity -- How many 10s? So, twice as many 5s |
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185 | (1) |
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Activity -- Key facts division practice |
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186 | (1) |
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Activity -- ×9 is almost ×10 |
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187 | (1) |
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Game -- Don't Walk If You Can Take the Bus |
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188 | (2) |
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Activity -- Find all the steps of any times table by reasoning from key facts |
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190 | (4) |
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Activity -- Practise all the steps of any times table by reasoning from key facts |
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194 | (2) |
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Activity -- Find division facts by reasoning from key facts |
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196 | (1) |
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197 | (3) |
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Activity -- Construct a multiplication grid |
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200 | (2) |
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Activity -- Complete a partially filled multiplication grid |
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202 | (1) |
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Games -- Using self-correcting cards to practise individual times tables |
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203 | (1) |
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Game -- Multiples from the 1--6 Times Tables |
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204 | (1) |
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Activity -- Harder mixed tables practice |
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205 | (1) |
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Game -- Products in a Row |
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206 | (1) |
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207 | (2) |
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Activities -- Change the shape of the multiplication rectangle |
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209 | (2) |
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211 | (2) |
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Activity -- Use rectangle sketches to help derive new multiplication facts |
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213 | (1) |
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Activity -- Use rods to explore short division |
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214 | (2) |
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Activity -- Teach an expanded written notation for short division |
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216 | (1) |
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Activity -- Use rectangle sketches to support short division |
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217 | (2) |
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Activity -- Compare division sketches to multiplication sketches |
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219 | (1) |
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Activity -- Teach the divisibility rules |
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220 | (1) |
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Game -- Divisibility Rules |
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221 | (1) |
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Activity -- Boxes for long multiplication |
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222 | (2) |
| Recommended Books and Resources |
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224 | (2) |
| Appendix: Introduction to Concrete Manipulative Materials |
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226 | (5) |
| Index |
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231 | |
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