3. Exploring Numbers
3.1 Introduction
One of the most important aims of adult numeracy education is to build students' confidence with numbers and their associated language. This means first acknowledging students' existing knowledge, then building on this to expand their understanding of the number system and how it works. Understanding of the patterns of tens within our number system provides the basis for a range of 'in the head' calculation strategies described in other sections of this resource.
The intention of this section, Exploring Numbers, is to bring together a collection of favourite activities which encourage students to become more familiar with the properties of numbers, the operations used with them, and their associated language.
3.2 Number Patterns
This activity uses sequences of numbers, called number patterns, to provide practice with basic operations.
It also provides an opportunity for you to assess the existing number skills and knowledge of your students.
Number patterns can be used with a range of students as they can be made easy or quite challenging.
3.3 Capital Cities of Australia
This activity uses a map of Australia and the populations of Capital cities as a source of large numbers for students to practise ordering, verbalising, and approximating, whilst raising their awareness about Australia. It is an ideal activity for integrating with literacy or language learning.
3.4 Back to Back Numbers
This pair activity is designed to encourage reading, writing, speaking and listening in relation to numbers. It will enhance learners' capacity to:

Interpret the value of numbers written in symbols (place value)

Articulate the value of numbers using words

Translate between numbers written in figures and spoken English.
3.5 Key Words for Calculations
Words to do with arithmetic such as add, multiply, subtract, divide are not often used in ordinary conversation. As a result many people, especially those from other language backgrounds, have not acquired this vocabulary and are confused in mathematical learning situations. This activity promotes discussion of the arithmetic related words, practice at hearing and speaking them and relating them to the appropriate symbols and calculator keys.
3.6 What’s the Secret Number?
This activity is designed to reinforce students' knowledge and use of the language of numbers and operations (+  x) as they perform simple arithmetic calculations. It comprises a selection of 'cooperative logic' problems related to numbers and their properties. To solve the problems students interpret conceptual language such as odd, even, greater/less than, as well as the language of the operations. Ideally students work together in small groups to solve the problems cooperatively, thereby reading, listening to and interpreting the relevant language as well as doing the calculations.
3.7 Talking About Numbers
This activity is a game in which players practise listening to and understanding mathematical language. Although competitive, winning is based purely on chance, not on mathematical skills.
3.8 Estimate or Accurate
Estimation skills are extremely important in an era when students are tempted to trust any result displayed on a calculator or spread sheet. These skills are also powerful tools in budgeting or planning situations when exact calculations are not necessary. This activity is designed to develop students' awareness of the idea of estimation, the language associated with it and the use of sensible or friendly numbers to approximate simple calculations.
3.9 Multiplication Tables – Grids
Many students feel really bad because they still don’t know their tables 'after all these years'. Sometimes only a few shaky facts will lead to students becoming anxious about all tables, and so a small investment of effort will give a large return in confidence. Certainty with multiplication and addition facts will go a long way towards overcoming maths anxiety.
3.10 Multiplication Tables – Flashcards
Certainty with multiplication and addition facts will go a long way towards overcoming students' maths anxiety. Sometimes only a few shaky facts will lead to students becoming anxious about all tables, and so a small investment of effort will give a large return in confidence.
3.11 Multiplication – Bingo
Learning multiplication facts (tables), and being able to recall them when needed, not only assists students with in the head calculations, it also boosts their confidence with numeracy enormously. This activity is a game, modelled on the traditional Bingo, which provides practice at recall of multiplication facts. The element of luck and competition keep students' attention and interest more than multiple practice examples on paper could ever do.