Understand place value, order integers, decimals and fractions, and calculate with the four operations and directed numbers using the correct order of operations (BIDMAS).

What this dot point is asking

WJEC opens its number content with the structure of the number system: place value, ordering positive and negative integers, decimals and fractions, and calculating with the four operations using the correct order of operations. This is the most basic and the most heavily used skill in the whole qualification, because every later topic, from compound measures to probability, leans on accurate arithmetic. On Unit 1 you must do all of this without a calculator, so fluent written and mental methods are essential, and a sign slip or an order-of-operations error in the first line of working ruins everything that follows.

Place value and ordering

Place value gives each digit its worth: in $4\,508$ the $5$ means five hundreds, and in $0.029$ the $9$ means nine thousandths. Reading place value correctly is what lets you multiply or divide by powers of ten just by shifting digits: $\times 10$ moves every digit one place to the left, $\div 100$ moves them two places to the right.

To order a mixed list of fractions, decimals and negatives, convert them all to the same form, normally decimals, and compare digit by digit from the left.

The four operations with directed numbers

Adding and subtracting directed numbers is easiest on a number line: $+$ moves right, $-$ moves left. Two signs together combine: $-(-4)$ becomes $+4$, so $6 - (-4) = 10$, while $+(-4)$ becomes $-4$, so $6 + (-4) = 2$.

So $-6 \times -7 = 42$, $-20 \div 4 = -5$, and $(-3)^2 = 9$ but $-3^2 = -9$, because without brackets the power applies only to the $3$.

The order of operations: BIDMAS

When a calculation mixes operations, the order matters.

A fraction bar acts as a hidden bracket, grouping its whole top and whole bottom, so $\dfrac{8 + 4}{3} = \dfrac{12}{3} = 4$, not $8 + \tfrac{4}{3}$.

Written methods without a calculator

Unit 1 expects fluent column methods. For long multiplication, multiply by each digit and add the partial products, keeping place value with zeros as placeholders. For long division, work through the dividend digit by digit. For decimals, line up the points when adding or subtracting; to multiply decimals, multiply as whole numbers and then place the point so the answer has as many decimal places as the two factors combined ($0.4 \times 0.3 = 0.12$, two decimal places).

Why this matters

These skills are assessed in their own right at the start of papers but, more importantly, they sit inside every other question on both components. A percentage, a Pythagoras calculation or a probability tree all collapse if the underlying arithmetic or the order of operations is wrong. Because WJEC awards method marks generously, setting out clear, ordered working protects marks even when a final answer slips, and on the non-calculator Unit 1 it is the difference between a secure grade and a scattered one.