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