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