PAss Functional Skills

Tree diagrams

Tree diagrams for ESOL English Language: what it means, how to set the working out, and the questions it is asked in.
  • ESOL
  • English Language
  • Spec S12 · S7
  • 13 min read
  • 9 revision boxes

Introduction

2 boxes
1 min read

What is tree diagrams?

Listen to this box

Transcript

A short spoken summary of tree diagrams and where it is used.

A spoken walk-through of tree diagrams before you read the notes.
Sketch the shape even when the question does not ask for one — it makes the next step obvious.
Worth knowing: ×10\times 10 moves every digit one column left.
6 rows

The tree diagrams reference table

Practise the routine version until it is automatic, then move to the multi-step questions.
Worth knowing: ≈160\approx 160.
Term
Meaning
Example
Row 1 column 1
Row 1 column 2
a2+b2=c2a^2 + b^2 = c^2
Row 2 column 1
Row 2 column 2
x2+5x+6=0x^2 + 5x + 6 = 0

Learning

5 boxes
5 steps

How to work with tree diagrams

The examiner marks the working, so a correct answer with no method still drops marks.
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 tree diagrams 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: 34×25\frac{3}{4} \times \frac{2}{5}
3 rules

Key facts: Tree diagrams

This idea appears again in the higher-mark questions, so it is worth over-learning.
The layout below is the one the mark scheme expects.

Diagram showing tree diagrams laid out step by step

The same idea drawn out, so the method is visible.
Worth knowing: ≈160\approx 160.

  • Rule 1

    How tree diagrams behaves in the 1st of the cases the specification names.
    a2+b2=c2a^2 + b^2 = c^2

  • Rule 2

    How tree diagrams behaves in the 2nd of the cases the specification names.
    x2+5x+6=0x^2 + 5x + 6 = 0

  • Rule 3

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

How to work with tree diagrams

Sketch the shape even when the question does not ask for one — it makes the next step obvious.
  1. Read the question and write down what is being asked for.
  2. Set out the working for tree diagrams 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: ≈160\approx 160
2 rules

Key facts: Tree diagrams

Practise the routine version until it is automatic, then move to the multi-step questions.

  • Rule 1

    How tree diagrams behaves in the 1st of the cases the specification names.
    ≈160\approx 160

  • Rule 2

    How tree diagrams behaves in the 2nd of the cases the specification names.
    49=7\sqrt{49} = 7

  • Rule 3

    How tree diagrams behaves in the 3rd of the cases the specification names.
    x2+5x+6=0x^2 + 5x + 6 = 0
4 steps

How to work with tree diagrams

The examiner marks the working, so a correct answer with no method still drops marks.
The layout below is the one the mark scheme expects.

Diagram showing tree diagrams laid out step by step

The same idea drawn out, so the method is visible.
  1. Read the question and write down what is being asked for.
  2. Set out the working for tree diagrams 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

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Examples

2 boxes
4 marks · worked

Worked example: tree diagrams

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.
4 marks · worked

Practice question 9: x2+5x+6=0x^2 + 5x + 6 = 0

Sketch the shape even when the question does not ask for one — it makes the next step obvious.
The layout below is the one the mark scheme expects.

Diagram showing tree diagrams laid out step by step

The same idea drawn out, so the method is visible.
Worth knowing: a2+b2=c2a^2 + b^2 = c^2.

Practice bank

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Common questions

How many marks is tree diagrams usually worth?
Between one and four, depending on how many steps the question asks for.
Is this on the ESOL English Language paper?
Yes — it sits in the Markets and demand strand.