Pearson Edexcel International GCSE in Mathematics (Specification A) · 4MA1 · Free · no account needed

Integers, Place Value & Ordering

In one sentence. Negative numbers, the order of operations, and putting any mix of numbers in order — the arithmetic everything else stands on.

Number — one of 8 modules in this strand, and one of 53 in Pearson Edexcel International GCSE Mathematics. Both tiers.

This module ends with Brahmagupta. Learn Integers, Place Value & Ordering, teach it, then defend it against Brahmagupta.

Where this sits in the specification

Specification 4MA1, 1.1 Integers · 1.3 Decimals. Incandio is aligned to this specification; it is not published by, endorsed by or affiliated with Pearson, and the sub-topic numbers are given so you can check every module against your own copy.

  • 1.1 — Integers
  • 1.3 — Decimals

1 · Understand it

What it is

Place value says every digit's worth depends on WHERE it sits: in 3.596 the 9 means nine hundredths. Integers extend the number line below zero, and the order of operations (brackets, indices, division/multiplication, addition/subtraction) fixes the one agreed reading of any calculation.

Why it works

Without an agreed order, 2 + 3 × 4 would honestly be both 20 and 14, and no two calculators would agree. The rules aren't decoration — they are what makes an expression mean one thing. Negatives work because subtraction and 'owing' behave identically: falling 9° from 8° must land at −1° for temperature differences to stay consistent.

When a question is asking for it

Every time you touch a calculation. Specifically: temperature and money problems (negatives), any expression mixing operations (BIDMAS), and 'order these' questions — where the winning move is always to convert everything into ONE form (usually decimals) before comparing.

How to hold it in your head

Hold the number line in your head, not 'rules about signs'. Adding moves right, subtracting moves left, and multiplying by a negative flips you to the mirror side. −6 + 14 is just: start 6 below zero, walk 14 to the right.

2 · The mistakes that cost marks

  • "0.45 is bigger than 0.5 because 45 > 5." Length of digits is not size — line up place values: 0.50 vs 0.45.
  • "−7 is bigger than −2 because 7 > 2." On the number line −7 sits further LEFT: colder, deeper in debt, smaller.
  • "Two minuses always make a plus." Only for multiplying/dividing. −3 − 4 is −7, not +7 — you walked left twice.
  • Working left-to-right through 3 + 4 × 2 to get 14. Multiplication binds first: it is 3 + 8 = 11.

3 · Worked examples

Laid out the way an examiner wants working shown — every step is a mark.

Work out 20 − 12 ÷ (−4) + 2³.

  1. Indices first: 2³ = 8, so the expression is 20 − 12 ÷ (−4) + 8.
  2. Division next: 12 ÷ (−4) = −3.
  3. Now only + and −, left to right: 20 − (−3) + 8 = 20 + 3 + 8.

Answer: 31

Order from smallest to largest: 0.7, 2/3, 68%, 0.665.

  1. Convert everything to decimals: 2/3 = 0.667 (3 dp), 68% = 0.68.
  2. Line them up to the same number of places: 0.700, 0.667, 0.680, 0.665.
  3. Read them off the number line.

Answer: 0.665, 2/3, 68%, 0.7

4 · Prove it — the five questions

The five questions climb Grade 6 → 9+ and are marked inside Incandio on your own device, against authored accepted forms, with a diagnosis of the wrong answer you actually gave. The answers stay in the app so that the practice is worth doing; the questions themselves are here.

  1. Grade 6 — At midnight the temperature is −6 °C. By noon it has risen by 14 °C, and by the next midnight it has fallen 9 °C from the noon temperature. What is the temperature at the second midnight? (answer in °C)
  2. Grade 7 — Find the difference between 7/10 and 71.5%, giving your answer as a decimal.
  3. Grade 8 — Work out (2 − 5)² × 4 − 10 ÷ (−2).
  4. Grade 9 — Work out (0.2)³ ÷ 0.04.
  5. 9+ — n is an integer with −3 ≤ n < 2. Work out the sum of all possible values of n.

Think you understand it?

Reading is the start. On Incandio a topic counts as mastered only once you have taught it and defended it — the two things a revision guide cannot ask of you.

Incandio this topic → Prove it. Teach it. Defend it. What does “Incandio it” mean?

  1. Prove it — five questions on Integers, Place Value & Ordering, marked on the spot, that tell you what was missing rather than just what was wrong.
  2. Teach it — Explain how Integers, Place Value & Ordering works — and why — to Ember, an AI pupil who does not have it yet. The method matters more than the vocabulary.
  3. Defend it — Argue Integers, Place Value & Ordering against Brahmagupta — three rounds, marked against descriptors you can read before you begin.
  4. Then the exam — read all 11 authored exam-style questions on this unit, each with its command word and its tariff, then have them marked on Incandio with the mistake you actually made named.

Completely free. No subscriptions, no paywalls, no account needed to start.

Carry on through the course