PAss Functional Skills

Four operations

Four operations for GCSE Environmental Science OCR: what it means, how to set the working out, and the questions it is asked in.
  • GCSE
  • OCR
  • Environmental Science
  • Spec S1
  • 8 min read
  • 10 revision boxes

Introduction

2 boxes
4 min read

What is four operations?

Listen to this box

Transcript

A short spoken summary of four operations and where it is used.

A spoken walk-through of four operations before you read the notes.
Check the answer against an estimate before you move on, so a place-value slip is caught here.
Worth knowing: ×10\times 10 moves every digit one column left.
4 rows

The four operations reference table

Work through the method one line at a time and write down what changes at each step.
The layout below is the one the mark scheme expects.

Diagram showing four operations laid out step by step

The same idea drawn out, so the method is visible.
Term
Meaning
Example
Common slip
Marks
Row 1 column 1
Row 1 column 2
×10\times 10 moves every digit one column left
Row 1 column 4
Row 1 column 5
Row 2 column 1
Row 2 column 2
x2+5x+6=0x^2 + 5x + 6 = 0
Row 2 column 4
Row 2 column 5
Row 3 column 1
Row 3 column 2
x2+5x+6=0x^2 + 5x + 6 = 0
Row 3 column 4
Row 3 column 5

Learning

6 boxes
3 steps

How to work with four operations

The specification wording is precise here, and the mark scheme follows that wording exactly.
The layout below is the one the mark scheme expects.

Diagram showing four operations laid out step by step

The same idea drawn out, so the method is visible.
Worth knowing: 49=7\sqrt{49} = 7.
  1. Read the question and write down what is being asked for.
  2. Set out the working for four operations in the order the method gives.
  3. Substitute the values and simplify.
Start from the definition and substitute the numbers the question gives you.
Simplify one line at a time: ×10\times 10 moves every digit one column left.
Answer: x2+5x+6=0x^2 + 5x + 6 = 0
2 rules

Key facts: Four operations

Read the units in the question before you start; a converted unit is the most common slip.
The layout below is the one the mark scheme expects.

Diagram showing four operations laid out step by step

The same idea drawn out, so the method is visible.

  • Rule 1

    How four operations behaves in the 1st of the cases the specification names.
    34×25\frac{3}{4} \times \frac{2}{5}

  • Rule 2

    How four operations behaves in the 2nd of the cases the specification names.
    34×25\frac{3}{4} \times \frac{2}{5}

  • Rule 3

    How four operations behaves in the 3rd of the cases the specification names.
    a2+b2=c2a^2 + b^2 = c^2
5 steps

How to work with four operations

Check the answer against an estimate before you move on, so a place-value slip is caught here.
Worth knowing: x2+5x+6=0x^2 + 5x + 6 = 0.
  1. Read the question and write down what is being asked for.
  2. Set out the working for four operations in the order the method gives.
  3. Substitute the values and simplify.
  4. Check the answer against an estimate before writing it down.
Start from the definition and substitute the numbers the question gives you.
Simplify one line at a time: 34×25\frac{3}{4} \times \frac{2}{5}.
Answer: 49=7\sqrt{49} = 7
3 rules

Key facts: Four operations

Work through the method one line at a time and write down what changes at each step.
Worth knowing: ≈160\approx 160.

  • Rule 1

    How four operations behaves in the 1st of the cases the specification names.
    49=7\sqrt{49} = 7

  • Rule 2

    How four operations behaves in the 2nd of the cases the specification names.
    a2+b2=c2a^2 + b^2 = c^2

  • Rule 3

    How four operations behaves in the 3rd of the cases the specification names.
    ×10\times 10 moves every digit one column left
3 steps

How to work with four operations

The specification wording is precise here, and the mark scheme follows that wording exactly.
  1. Read the question and write down what is being asked for.
  2. Set out the working for four operations in the order the method gives.
  3. Substitute the values and simplify.
Start from the definition and substitute the numbers the question gives you.
Simplify one line at a time: ×10\times 10 moves every digit one column left.
Answer: 49=7\sqrt{49} = 7
2 rules

Key facts: Four operations

Read the units in the question before you start; a converted unit is the most common slip.

  • Rule 1

    How four operations behaves in the 1st of the cases the specification names.
    49=7\sqrt{49} = 7

  • Rule 2

    How four operations behaves in the 2nd of the cases the specification names.
    34×25\frac{3}{4} \times \frac{2}{5}

  • Rule 3

    How four operations behaves in the 3rd of the cases the specification names.
    x2+5x+6=0x^2 + 5x + 6 = 0

20 minutes

Get your predicted grade

Twenty questions gives you a predicted grade, your target, and the gap between them — plus the topics that close it fastest.
Get my predicted grade

Examples

2 boxes
4 marks · worked

Worked example: four operations

Read the units in the question before you start; a converted unit is the most common slip.
Worth knowing: ×10\times 10 moves every digit one column left.
1 marks · worked

Practice question 10: ≈160\approx 160

The specification wording is precise here, and the mark scheme follows that wording exactly.
Worth knowing: ×10\times 10 moves every digit one column left.

Practice bank

Thousands of revision questions

Every topic is backed by graded practice with instant marking and full solutions.
Try it now
Practice questions
5,000+
Topics
10
Marking and solutions
Instant

Common questions

How many marks is four operations usually worth?
Between one and four, depending on how many steps the question asks for.
Is this on the GCSE Environmental Science OCR paper?
Yes — it sits in the Algebra strand.