The Dyscalculia Toolkit

Ronit Bird is a teacher whose interest in pupils with specific learning difficulties began with a focus on dyslexia. She qualified as a teacher at London University and subsequently gained a further qualification as a specialist teacher of learners with SpLD. While working with dyslexic pupils in a mainstream school, Ronit started to develop strategies and teaching activities to help support the learning of pupils who were experiencing difficulties in maths.Ronit has taught in both primary and secondary settings, and has worked as a SENCO in both the independent and state sectors. As part of the Harrow Dyscalculia Project in 2006–2010, Ronit ran training courses on dyscalculia for subject leaders, teachers and teaching assistants, later working in an advisory capacity with participating schools across the Harrow LEA.Ronit currently works as a teacher and continues to create and deliver professional development courses for teachers. Over the past few years Ronit has developed a growing interest in making demonstration videos for teachers and parents.

• IntroductionSection I: Early Number Work with Numbers Up to 10OverviewWhat are the main problems?Activity – Make dot patterns for the numbers 1 to 10Activity – Focus on key component factsActivity – Make transparent dot pattern cards for the numbers 1 to 5Game – Make 5Activity – Explore smaller numbers inside larger numbersGame – Numbers InsideActivity – Change one dot pattern into anotherActivity – Change dot patterns by adding or subtractingActivity – Use dot patterns to explore the idea of odd and evenGame – Collect 5sGame – Key Components Guessing GameActivity – Sort and re-sort a set of dominoesActivity – Connect subtraction to additionActivity – Regroup: Apply logic to find new component facts from given factsActivities – Become familiar with Cuisenaire rodsActivity – Explore odd and even with Cuisenaire rods and with moneyGame – Odd and Even CollectorsGame – Draw Your Race on a Number LineActivities – Use Cuisenaire rods to learn all components of the numbers 1–10Activity – Make a ‘Story’ of a numberGame – Race to Tell a StoryActivity – Make and read equations with Cuisenaire rodsActivity – Draw and record equations informallyGame – Key Facts Triad GameGame – Post-It Note SubtractionActivities – Record equations in writingActivity – Make up word problems to match a given number factGame – Cover the Numbers, or Shut the BoxGame – Clear the DeckActivity – Make a bead string, in two colours, of 10 beadsActivities – Learn complements of 10 with the bead stringGame – How Many Beads? How Many Are Hidden?Activity – Find complements of 10 with Cuisenaire rodsGame – Complements Number SearchGame – Complements Ping-PongGame – Ten in a BedActivities – Explore and learn the doubles up to 5 plus 5Activities – Estimate and measure using Cuisenaire rodsActivities – Focus on plus/minus 1 and plus/minus 2Game – Who Has the Most Equations?Game – Domino TensActivity – Compare the difference and equaliseActivities – Hidden quantity subtractionActivity – Teach complementary additionActivity – Complementary addition on a number lineActivity – Make up word problems about missing numbersActivity – Use reasoning to find near-complements and near-doublesActivity – Identify the best strategy for different situationsActivities – Use money for component workSECTION 2: Basic Calculation with Numbers Above 10OverviewWhat are the main problems?How to helpActivity – Connect the numbers 10–20 with the numbers below 10Game – Polka DotsGame – RegroupActivities – Focus on the ‘teen’ numbersActivities – Explore the numbers between 10 and 20 with Cuisenaire rodsActivity – Learn the doubles up to 10 plus 10Game – Double TakeGame – It All Adds UpActivities – Locate 2-digit numbers and put them in contextActivities – Complements to 20Activity – Complements to larger multiples of 10Activity – Complements on a number lineActivity – Introduce bridging through 10 with Cuisenaire rodsGame – Five and What’s LeftActivity – Bridge through 10 on a number lineActivity – Practise bridging and reinforce the commutativity of additionGame – Frame an AdditionActivity – Bridge through multiples of 10 on a number lineGame – Race Along a Number Line and BridgeGame – Race to the End of the Number LineActivity – Complementary addition, or subtraction by addingGame – Frame a SubtractionActivity – Complementary addition for subtracting round numbersActivity – Harder complementary addition on a number lineActivities – Complements to 100Game – Keep the Change!Activities – Practise and extend the doubles factsActivity – Halving is the opposite of doublingActivity – Find half of round numbersActivity – Function machines for doubling and halvingActivity – Use reasoning to find near-complements and near-doublesActivity – 9 is almost 10Activity – The Basic 8 strategiesActivity – Identify which strategy works best in different situationsGame – Subtraction EquationsActivity – A flexible approach to partitioningActivities – Explore partitioning methods for 2-digit mental additionsActivity – Teach an expanded written method for column additionActivity – Avoid decomposition in subtractionSECTION 3: Place ValueOverviewA note about the threefold nature of the column labelling systemWhat are the main problems?How to helpActivities – Exchange units into tensActivities – Concrete counting on place value matsGame – Magic 10sActivities – Make a 20-step staircase and explore the ‘teen’ number namesActivity – Cover 20Game – Race to Cover 100Game – Four Throws to Reach 100Activities – Make and read numbers made of Cuisenaire rods or base-10 materialsGames – Dice and spinner gamesActivities – Practise subtraction and decomposition with concrete materialsGame – Spot the DecompositionActivities – Use a spike abacusGame – Win Counters on a 100-SquareGame – Race through a 100-SquareActivities – Practise adding and subtracting 10 and 100Game – Steer the NumberActivity – Transform a 2-digit number in two stepsActivity – Teach the threefold repeating pattern: units, tens and hundredsActivities – Explore place value as a shorthandActivities – Read and write multi-digit numbersActivities – Build up large numbers, one column at a timeActivity – What is the value of …?Game – Two-Digit SequencesGame – Three-Digit Sequences (Focus on Tens)Game – Place Value BoxesGame – Calculator SkittlesActivity – Partition numbers into tens and units in various waysActivity – Split off the ‘teen’ numbersGame – Jump 10Activities – Locate any number on a number lineActivity – Round up or downGame – The Six-Card Rounding GameGame – The Rounding ChallengeActivity – Teach x 10 and divded by 10 as a shift between columnsActivity – Extend place value thinking to decimalsActivity – Connect decimal place value notation to moneyGame – Rounding RacesSECTION 4: Times Tables, Multiplication and DivisionOverviewWhat are the main problems?How to helpActivities – Build small numbers out of equal-sized groupsActivity – Connect division to multiplication from the very beginningActivity – Illustrate simple word problemsActivity – Use Cuisenaire rods to show that multiplication is commutativeActivities – Use Cuisenaire rods to connect multiplication and divisionActivity – Diagrammatic recording of multiplication and divisionActivity – Connect step-counting and repeated addition with times tablesActivity – Practise mental step-counting from given tables factsActivities – Make times tables patterns on a 100-squareActivities – Make times tables patterns on number linesActivities – Key fact: Double means ‘multiply by 2’Activity – Key facts: x5 is half of x10Activity – How many 10s? So, twice as many 5sActivity – Key facts division practiceActivity – x9 is almost x10Game – Don’t Walk if You Can Take the BusActivity – Find all the steps of any times table by reasoning from key factsActivity – Practise all the steps of any times table by reasoning from key factsActivity – Find division facts by reasoning from key factsGame – Mouse TablesActivity – Construct a multiplication gridActivity – Complete a partially filled multiplication gridGames using self-correcting cards to practise individual times tablesGame – Multiples from the 1–6 Times TablesActivity – Harder mixed tables practiceGame – Products in a RowGame – FactorsActivities – Change the shape of the multiplication rectangleGame – Areas on a GridActivity – Use rectangle sketches to help derive new multiplication factsActivity – Use rods to explore short divisionActivity – Teach an expanded written notation for short divisionActivity – Use rectangle sketches to support short divisionActivity – Compare division sketches to multiplication sketchesActivity – Teach the divisibility rulesGame – Divisibility RulesActivity – Boxes for long multiplicationRecommended Books and ResourcesAppendix: Introduction to Concrete Manipulative Materials