Designed for all teachers, this book provides a wealth of materials and resources to support the needs of learners, aged 6 to 14 years, who have difficulty with maths and number.

IntroductionSection I: Early Number Work with Numbers Up to 10 Overview What are the main problems? Activity - Make dot patterns for the numbers 1 to 10 Activity - Focus on key component facts Activity - Make transparent dot pattern cards for the numbers 1 to 5 Game - Make 5 Activity - Explore smaller numbers inside larger numbers Game - Numbers Inside Activity - Change one dot pattern into another Activity - Change dot patterns by adding or subtracting Activity - Use dot patterns to explore the idea of odd and even Game - Collect 5s Game - Key Components Guessing Game Activity - Sort and re-sort a set of dominoes Activity - Connect subtraction to addition Activity - Regroup: Apply logic to find new component facts from given facts Activities - Become familiar with Cuisenaire rods Activity - Explore odd and even with Cuisenaire rods and with money Game - Odd and Even Collectors Game - Draw Your Race on a Number Line Activities - Use Cuisenaire rods to learn all components of the numbers 1-10 Activity - Make a 'Story' of a number Game - Race to Tell a Story Activity - Make and read equations with Cuisenaire rods Activity - Draw and record equations informally Game - Key Facts Triad Game Game - Post-It Note Subtraction Activities - Record equations in writing Activity - Make up word problems to match a given number fact Game - Cover the Numbers, or Shut the Box Game - Clear the Deck Activity - Make a bead string, in two colours, of 10 beads Activities - Learn complements of 10 with the bead string Game - How Many Beads? How Many Are Hidden? Activity - Find complements of 10 with Cuisenaire rods Game - Complements Number Search Game - Complements Ping-Pong Game - Ten in a Bed Activities - Explore and learn the doubles up to 5 plus 5 Activities - Estimate and measure using Cuisenaire rods Activities - Focus on plus/minus 1 and plus/minus 2 Game - Who Has the Most Equations? Game - Domino Tens Activity - Compare the difference and equalise Activities - Hidden quantity subtraction Activity - Teach complementary addition Activity - Complementary addition on a number line Activity - Make up word problems about missing numbers Activity - Use reasoning to find near-complements and near-doubles Activity - Identify the best strategy for different situations Activities - Use money for component workSECTION 2: Basic Calculation with Numbers Above 10 Overview What are the main problems? How to help Activity - Connect the numbers 10-20 with the numbers below 10 Game - Polka Dots Game - Regroup Activities - Focus on the 'teen' numbers Activities - Explore the numbers between 10 and 20 with Cuisenaire rods Activity - Learn the doubles up to 10 plus 10 Game - Double Take Game - It All Adds Up Activities - Locate 2-digit numbers and put them in context Activities - Complements to 20 Activity - Complements to larger multiples of 10 Activity - Complements on a number line Activity - Introduce bridging through 10 with Cuisenaire rods Game - Five and What's Left Activity - Bridge through 10 on a number line Activity - Practise bridging and reinforce the commutativity of addition Game - Frame an Addition Activity - Bridge through multiples of 10 on a number line Game - Race Along a Number Line and Bridge Game - Race to the End of the Number Line Activity - Complementary addition, or subtraction by adding Game - Frame a Subtraction Activity - Complementary addition for subtracting round numbers Activity - Harder complementary addition on a number line Activities - Complements to 100 Game - Keep the Change! Activities - Practise and extend the doubles facts Activity - Halving is the opposite of doubling Activity - Find half of round numbers Activity - Function machines for doubling and halving Activity - Use reasoning to find near-complements and near-doubles Activity - 9 is almost 10 Activity - The Basic 8 strategies Activity - Identify which strategy works best in different situations Game - Subtraction Equations Activity - A flexible approach to partitioning Activities - Explore partitioning methods for 2-digit mental additions Activity - Teach an expanded written method for column addition Activity - Avoid decomposition in subtractionSECTION 3: Place Value Overview A note about the threefold nature of the column labelling system What are the main problems? How to help Activities - Exchange units into tens Activities - Concrete counting on place value mats Game - Magic 10s Activities - Make a 20-step staircase and explore the 'teen' number names Activity - Cover 20 Game - Race to Cover 100 Game - Four Throws to Reach 100 Activities - Make and read numbers made of Cuisenaire rods or base-10 materials Games - Dice and spinner games Activities - Practise subtraction and decomposition with concrete materials Game - Spot the Decomposition Activities - Use a spike abacus Game - Win Counters on a 100-Square Game - Race through a 100-Square Activities - Practise adding and subtracting 10 and 100 Game - Steer the Number Activity - Transform a 2-digit number in two steps Activity - Teach the threefold repeating pattern: units, tens and hundreds Activities - Explore place value as a shorthand Activities - Read and write multi-digit numbers Activities - Build up large numbers, one column at a time Activity - What is the value of ...? Game - Two-Digit Sequences Game - Three-Digit Sequences (Focus on Tens) Game - Place Value Boxes Game - Calculator Skittles Activity - Partition numbers into tens and units in various ways Activity - Split off the 'teen' numbers Game - Jump 10 Activities - Locate any number on a number line Activity - Round up or down Game - The Six-Card Rounding Game Game - The Rounding Challenge Activity - Teach x 10 and divded by 10 as a shift between columns Activity - Extend place value thinking to decimals Activity - Connect decimal place value notation to money Game - Rounding RacesSECTION 4: Times Tables, Multiplication and Division Overview What are the main problems? How to help Activities - Build small numbers out of equal-sized groups Activity - Connect division to multiplication from the very beginning Activity - Illustrate simple word problems Activity - Use Cuisenaire rods to show that multiplication is commutative Activities - Use Cuisenaire rods to connect multiplication and division Activity - Diagrammatic recording of multiplication and division Activity - Connect step-counting and repeated addition with times tables Activity - Practise mental step-counting from given tables facts Activities - Make times tables patterns on a 100-square Activities - Make times tables patterns on number lines Activities - Key fact: Double means 'multiply by 2' Activity - Key facts: x5 is half of x10 Activity - How many 10s? So, twice as many 5s Activity - Key facts division practice Activity - x9 is almost x10 Game - Don't Walk if You Can Take the Bus Activity - Find all the steps of any times table by reasoning from key facts Activity - Practise all the steps of any times table by reasoning from key facts Activity - Find division facts by reasoning from key facts Game - Mouse Tables Activity - Construct a multiplication grid Activity - Complete a partially filled multiplication grid Games using self-correcting cards to practise individual times tables Game - Multiples from the 1-6 Times Tables Activity - Harder mixed tables practice Game - Products in a Row Game - Factors Activities - Change the shape of the multiplication rectangle Game - Areas on a Grid Activity - Use rectangle sketches to help derive new multiplication facts Activity - Use rods to explore short division Activity - Teach an expanded written notation for short division Activity - Use rectangle sketches to support short division Activity - Compare division sketches to multiplication sketches Activity - Teach the divisibility rules Game - Divisibility Rules Activity - Boxes for long multiplicationRecommended Books and ResourcesAppendix: Introduction to Concrete Manipulative Materials