The Dyscalculia Toolkit: Supporting Learning Difficulties in Maths

The new edition of the bestselling Dyscalculia Toolkit continues to meet the needs of specialist and non-specialist teachers working with learners aged 6 to 14 years, who have difficulty with maths and number.

Now with over 220 activities and 55 games, new and improved illustrations, and an expanded list of recommended readings, useful websites & resources, the new edition also includes:

• more on dice and board games, multiplication and division;
• new downloadable and printable teaching materials (including tracking sheets, activity sheets, game boards and teaching resources);
• updated videos.

Packed full of practical, creative and innovative ideas and strategies this is the complete toolkit to help teachers and parents support learners with dyscalculia or those struggling with mathematics.

Table of Contents

Introduction

SECTION 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 work

SECTION 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 subtraction

SECTION 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 Races

SECTION 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 multiplication

Recommended Books and Resources

Appendix: Introduction to Concrete Manipulative Materials

"The new dyscalculia toolkit has a great introduction that is broken down into manageable chunks, brilliant explanations and interesting reading. The new tables explain what each game entails at the start of the book, making planning and using the toolkit much easier and effective especially if short on time! Very enjoyable to read, and highly recommended."
- Karen Jones, Chartered Educational Psychologist, The Educational Guidance Service