Number — Integers and Decimals — Self-Assessment

Place Value (1a.1)

Each digit in a number has a value based on its position — thousands, hundreds, tens, ones, tenths, hundredths, thousandths.

Understanding place value is essential for ordering decimals correctly — 0.8 is bigger than 0.45 because 8 tenths > 4 tenths.

Place Value (1a.1) — Key Knowledge

Place value the value of a digit depending on its position in a number
Decimal places positions after the decimal point — tenths, hundredths, thousandths

Ordering Decimals (1a.1)

To compare decimals, line up the decimal points and compare digit by digit from left to right.

A common mistake is thinking 0.45 > 0.8 because 45 > 8 — always compare place by place.

Ordering Decimals (1a.1) — Key Knowledge

Ordering arranging numbers from smallest to largest or largest to smallest
Number line a visual tool for comparing and ordering numbers

Rounding (1a.1)

Rounding means replacing a number with an approximate value. Look at the digit after the one you're rounding to — if it's 5 or more, round up.

Rounding to significant figures starts counting from the first non-zero digit — so 0.00347 to 2 s.f. is 0.0035.

Rounding (1a.1) — Key Knowledge

Decimal places rounding to 1 d.p., 2 d.p. etc.
Significant figures rounding to 1 s.f., 2 s.f. etc. — count from the first non-zero digit
Estimation rounding numbers before calculating to get an approximate answer

Adding and Subtracting Integers (1a.2)

Addition and subtraction of whole numbers using column methods — line up the digits by place value.

The foundation for all number work — secure methods here prevent errors in harder topics.

Adding and Subtracting Integers (1a.2) — Key Knowledge

Column addition carry digits when a column totals 10 or more
Column subtraction borrow from the next column when you can't subtract

Multiplying and Dividing Integers (1a.2)

Long multiplication and short/long division — breaking calculations into manageable steps.

These written methods must be fluent before tackling algebra and fractions.

Multiplying and Dividing Integers (1a.2) — Key Knowledge

Long multiplication multiply by each digit separately, then add the results
Short division bus stop method — divide digit by digit
Long division used when dividing by a two-digit number

Operations with Decimals (1a.2)

Adding/subtracting decimals — line up the decimal points. Multiplying/dividing — use powers of 10.

When multiplying decimals, you can ignore the points, multiply as integers, then put the point back in.

Operations with Decimals (1a.2) — Key Knowledge

Decimal point alignment line up decimal points for addition and subtraction
Powers of 10 multiplying by 10 moves digits one place left; dividing by 10 moves digits one place right

Negative Numbers (1a.2)

Negative numbers sit below zero on the number line. Adding a negative moves left; subtracting a negative moves right.

The key trap: subtracting a negative makes the answer bigger, not smaller. Think of it as removing a debt.

Negative Numbers (1a.2) — Key Knowledge

Subtracting a negative same as adding — 5 − (−3) = 8
Sign rules for multiplication and division positive × positive = positive; negative × negative = positive; positive × negative = negative

Factors and Multiples (1a.3)

Factors divide exactly into a number. Multiples are the times table of a number.

Factors go into the number (they're smaller or equal). Multiples come out of the number (they're bigger or equal).

Factors and Multiples (1a.3) — Key Knowledge

Factor a number that divides exactly into another — factors of 12 are 1, 2, 3, 4, 6, 12
Multiple a number in the times table of another — multiples of 3 are 3, 6, 9, 12...

Prime Numbers (1a.3)

A prime number has exactly two factors: 1 and itself. 1 is NOT a prime number.

2 is the only even prime number. 1 is not prime because it has only one factor.

Prime Numbers (1a.3) — Key Knowledge

Prime number a number with exactly two factors — 2, 3, 5, 7, 11, 13...
Prime factorisation writing a number as a product of its prime factors using a factor tree

HCF and LCM (1a.3)

HCF is the largest factor shared by two numbers. LCM is the smallest multiple shared by two numbers.

HCF is always smaller than or equal to both numbers. LCM is always bigger than or equal to both numbers. Don't mix them up.

HCF and LCM (1a.3) — Key Knowledge

HCF — Highest Common Factor the biggest number that divides into both — HCF of 12 and 18 is 6
LCM — Lowest Common Multiple the smallest number in both times tables — LCM of 12 and 18 is 36
Venn diagram method use prime factorisation to find HCF and LCM systematically

Squares, Cubes and Roots (1a.4)

Squaring means multiplying a number by itself. Cubing means multiplying it by itself three times. Roots reverse these operations.

√ undoes ² and ∛ undoes ³. So √49 = 7 because 7² = 49, and ∛27 = 3 because 3³ = 27.

Squares, Cubes and Roots (1a.4) — Key Knowledge

Square n² = n × n
Square root √n — the number that squares to give n
Cube n³ = n × n × n
Cube root ∛n — the number that cubes to give n

Index Notation and Laws of Indices (1a.4)

Index notation is a shorthand for repeated multiplication. The laws of indices give shortcuts for combining powers.

The most common mistake: thinking 2³ means 2 × 3 = 6 instead of 2 × 2 × 2 = 8.

Index Notation and Laws of Indices (1a.4) — Key Knowledge

Index notation 2⁵ means 2 × 2 × 2 × 2 × 2 = 32 — NOT 2 × 5
Multiplying powers aᵐ × aⁿ = aᵐ⁺ⁿ — add the indices
Dividing powers aᵐ ÷ aⁿ = aᵐ⁻ⁿ — subtract the indices
Power of a power (aᵐ)ⁿ = aᵐⁿ — multiply the indices
Zero power a⁰ = 1 — anything to the power of 0 is 1

Number — Integers and Decimals

Self-Assessment

Session Complete

Number — Integers and Decimals