The 64 Building science concepts books have been listed here with links to selections of related assessment resources.

# Conceptual maps

**Alex Neill**

Probability is all around us. There are the weekly Lotto and Big Wednesday draws, poker machines proliferate, and many games are ruled by the roll of a dice, a coin toss, or the random numbers that computer games use. All of these are driven by chance (probability).

**Alex Neill and Jonathan Fisher**

Addition is typically the first and the simplest mathematical operation that students meet. It has a very close cousin in subtraction, which is generally somewhat harder for students.

This concept map includes addition and subtraction of whole numbers and decimal fractions, as well as negative numbers.

This concept map includes addition and subtraction of whole numbers and decimal fractions, as well as negative numbers.

**Jonathan Fisher**

Geometry can be described as the study of spatial relationships involving properties of shape, space, and position. Geometry is an area of mathematics that can provide opportunities to develop accessible creative problem solving and reasoning skills for students.

This map reflects the thinking described in Effective Literacy Practice in Years 1 to 4 and Effective Literacy Practice in Years 5 to 8. While each comprehension strategy is unpacked individually in this map and in the supporting ARB resources, as readers progress, they use the strategies in combination with each other and in increasingly complex ways with more complex texts. The aim is to assist students to develop multiple comprehension strategies and to use them purposefully.

**Alex Neill**

When we think of basic facts, possibly the first thing that springs to mind are our “times tables”. But there is far more to them than this. Just about anything in mathematics can be a basic fact. The main ones encountered are the whole-number basic facts, and in particular addition and multiplication, and their close cousins subtraction and division. However, we should memorise simpler facts, like our addition and subtraction facts. Often these have been ignored. Just maybe 7 × 8 may pop into mind just a tad more automatically than 7 + 8.

**Alex Neill**

Computational estimation is being able to quickly and easily get a number that is close enough to the exact answer of a mathematical problem to be useful. Usually it involves some simplified mental calculation.

**Teresa Maguire and Alex Neill**

Algebraic thinking is about generalising arithmetic operations and operating on unknown quantities. It involves recognising and analysing patterns and developing generalisations about these patterns.

**Jonathan Fisher and Teresa Maguire**

The study of patterns is a key part of algebraic thinking. It is important that students are able to recognise and analyse patterns and make generalisations about them. Algebraic patterns can be created from shapes, sounds, colours or numbers. Patterns can be visual or spatial. They can be repeating or they can be growing.

**Jonathan Fisher**

Underlying the development of fractional thinking is a number system that is different from the whole numbers that students have already had experience with. Fractions have different rules for naming, quantifying, ordering, adding, subtracting, multiplying, dividing, etc. Students will need to develop an understanding of these rules and be able to apply them when working with fractions. Using a variety of visual and numerical representations for fractions can support students to build up experiences with the different areas of fractions (fractional constructs).