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The Dyscalculia Toolkit
Supporting Learning Difficulties in Maths

Third Edition
Additional resources:


April 2017 | 224 pages | SAGE Publications Ltd
The new edition of the best-selling 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 math and numbers. With over 200 activities, 50 games, and new and improved illustrations, the updated Third Edition also includes exclusive access to a new companion website. Featuring 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.

Available with Perusall—an eBook that makes it easier to prepare for class
Perusall is an award-winning eBook platform featuring social annotation tools that allow students and instructors to collaboratively mark up and discuss their SAGE textbook. Backed by research and supported by technological innovations developed at Harvard University, this process of learning through collaborative annotation keeps your students engaged and makes teaching easier and more effective. Learn more.
 
About the Author
 
About the Companion Website
 
How to Access the Companion Website
 
Introduction
What's New in this edition?

 
What does this book contain?

 
Why is there such a strong emphasis on games?

 
How to use this book

 
What is dyscalculia?

 
What are the indicators for dyscalculia?

 
What about learners with other specific learning difficulties?

 
What's next, after working through this book?

 
Table: Summary of the main teaching points addressed by the games in The Dyscalculia Toolkit

 
Table: All the activities and games in The Dyscalculia Toolkit listed according to their numeracy topic or main teaching points

 
 
Section 1: EARLY NUMBER WORK WITH NUMBERS UP TO 10
Overview

 
What are the main problems?

 
How to help

 
Activities and Games:

 
Activity - Make dot patterns for the numbers 1 to 10

 
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 pattern 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

 
What about learners with other specific learning difficulties?

 
What's next, after working through this book?

 
Table: Summary of the main teaching points addressed by the games in The Dyscalculia Toolkit

 
Table: All the activities and games in The Dyscalculia Toolkit listed according to their numeracy topic or main teaching points

 
 
Section 1: EARLY NUMBER WORK WITH NUMBERS UP TO 10
Overview

 
What are the main problems?

 
How to help

 
Activities and Games:

 
Activity - Make dot patterns for the numbers 1 to 10

 
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 pattern 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

 
Activity - 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 and read equations with Cuisenaire rods

 
Activity – Make a ‘Story’ of a number

 
Game – Race To Tell a Story

 
Game – Post-It Note Subtraction

 
Activities – Draw and 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 + 5

 
Activities – Estimate and measure using Cuisenaire rods

 
Activities – Focus on plus/minus 1 and plus/minus 2

 
Game – Who Has the Most Equations?

 
Activity – Compare the difference and equalise

 
Activities – Hidden quantity subtraction

 
Activity – Teach complementary addition

 
Activity – Complementary addition on a number line

 
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

 
Activities and games:

 
Game – Polka Dots

 
Game – Regroup

 
Activity – Connect the numbers 10–20 with the numbers below 10

 
Activities – Focus on the ‘teen’ numbers

 
Activities – Explore the numbers between 10 and 20 with Cuisenaire rods

 
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

 
Activity – A flexible approach to partitioning

 
Activities – Explore partitioning methods for 2–digit mental additions

 
Activity – Teach an alternative written method for column addition

 
Activity – Avoid decomposition in subtraction

 
Activities – Complements to 100

 
Game – Keep the Change!

 
Activity – Learn the doubles up to 10 + 10

 
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

 
Game – Double Take

 
Activity – 9 is almost 10

 
Activity – The Basic 8 strategies

 
Activity – Identify which strategy works best in different situations

 
 
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 and games:

 
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 – 2-Digit Sequences

 
Game – 3-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

 
Game – The Six-Card Rounding Game

 
Game – The Rounding Challenge

 
Activity – Teach × 10 and ÷ 10 as a shift between columns

 
Activity – Extend place value thinking to decimals

 
Activity – Connect decimal place value notation to money

 
 
Section 4: TIMES TABLES, MULTIPLICATION AND DIVISION
Overview

 
What are the main problems?

 
How to help

 
Activities and games:

 
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 (repeated addition) with multiplication

 
Activity – Step–count one or two steps from various tables facts

 
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: × 5 is half of × 10

 
Activity – How many 10s? So, twice as many 5s

 
Activity – × 9 is almost × 10

 
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 – Don’t Walk if You Can Take the Bus

 
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

 
Activity – Diagrammatic practice of the area model of multiplication

 
Activity – Use rectangle sketches to help derive new multiplication facts

 
Activities – Change the shape of the multiplication rectangle

 
Game – Areas on a Grid

 
Activity – Boxes for long multiplication

 
 
Suggestions for further reading
 
Appendix: Introduction to concrete manipulative materials
 
Index

Sample Materials & Chapters

Bird - The Dyscalculia Toolkit - Introduction


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