⚖️ Ratio Province · Proportion

Constant of proportionality

Model constant of proportionality with a constant relationship and use it to find missing values. In this lesson, focus on direct proportion uses a constant relationship.

← Back to Region Back to Dashboard
🏅
Constant of proportionality Pathfinder Earned through mastery, boss success and strong scores — not by clicking through locks.

Player progress

Level 1 · Apprentice

0 / 100 XP

0 day streak 0% topic learning 0 completed topics 0 badges 0 boss wins 10 open sections4 practice levels

Learn · open now

Understand Constant of proportionality

Model constant of proportionality with a constant relationship and use it to find missing values. In this lesson, focus on direct proportion uses a constant relationship.

Direct proportion uses a constant relationship. The ratio y ÷ x stays constant and the graph passes through the origin. For constant of proportionality, the final written answer should make that exact relationship visible rather than hiding it inside an unexplained result.

Start here

Constant of proportionality: Direct proportion uses a constant relationship. Recalculate the constant ratio y ÷ x from the final pair. Keep the constant of proportionality representation visible until the final line.

Picture the idea

Move one coordinate on a proportion graph and inspect the constant ratio or product at every point. Use the model to explain one change you notice while working on constant of proportionality.

Check as you go

Recalculate the constant ratio y ÷ x from the final pair. Write that check beside the final constant of proportionality answer.

Key vocabulary

proportionconstantscale factordirect proportioninverse proportionproportionality

Rules and key facts

Given information: Constant of proportionality — y is directly proportional to x. When x = 3, y = 6. Find y when x = 5. Method choice: Write each labelled part against its own total before comparing or scaling. Keep ratio parts in the stated order and scale every part by the same factor. Calculation or reasoning: k = 6 ÷ 3 = 2. Then y = 2 × 5 = 10. Final answer: 10. Check: Keep ratio parts in the stated order and scale every part by the same factor.

  • Identify whether the relationship is direct or inverse.
  • Use a known pair to calculate the constant.
  • Write the matching relationship.
  • Substitute the new value and check the constant remains unchanged. Record the check explicitly for constant of proportionality.

Step-by-step method

  1. Identify whether the relationship is direct or inverse.
  2. Use a known pair to calculate the constant.
  3. Write the matching relationship.
  4. Substitute the new value and check the constant remains unchanged. Record the check explicitly for constant of proportionality.

What you need first

  • Recognise the vocabulary: proportion, constant, scale factor.
  • Be able to explain the purpose of constant of proportionality before calculating.
  • Keep the relevant values, units and representation visible while you work.

Real-world use

  • Unit pricing
  • Journey time and speed

Visual / interactive

See the idea, then move it around

Skip to Practice

Move one coordinate on a proportion graph and inspect the constant ratio or product at every point. Use the model to explain one change you notice while working on constant of proportionality.

Interactive maths model Connected to this topic; move controls, check outputs, then earn XP only from verified actions.
Responsive · validated · topic linked

Worked examples

Examples, methods and exam thinking

Level 1 · Foundation

Understand the idea with small numbers, one representation and one clear step.

Level 2 · Secure

Use the standard Year 8 method with mixed examples and normal wording.

Level 3 · Challenge

Handle multi-step or less familiar questions and explain choices.

Level 4 · Exam-style

Solve a worded question, show reasoning, check accuracy and write a final sentence.

Foundation example

Build confidence

Given information: Constant of proportionality — y is directly proportional to x. When x = 3, y = 6. Find y when x = 5. Method choice: use the constant of proportionality method and show each step with the stated values. Calculation or reasoning: k = 6 ÷ 3 = 2. Then y = 2 × 5 = 10. Final answer: 10. Check: substitute or compare with the original information to confirm the result fits the question.

  1. Identify whether the relationship is direct or inverse.
  2. Use a known pair to calculate the constant.
  3. Write the matching relationship.
Secure example

Use the normal method

Given information: Constant of proportionality — y is directly proportional to x. When x = 3, y = 9. Find y when x = 17. Method choice: use the constant of proportionality method and show each step with the stated values. Calculation or reasoning: k = 9 ÷ 3 = 3. Then y = 3 × 17 = 51. Final answer: 51. Check: substitute or compare with the original information to confirm the result fits the question.

Check: Check the constant of proportionality result against the original information.

Challenge example

Stretch the idea

Given information: Constant of proportionality — y is directly proportional to x. When x = 3, y = 12. Find y when x = 16. Method choice: use the constant of proportionality method and show each step with the stated values. Calculation or reasoning: k = 12 ÷ 3 = 4. Then y = 4 × 16 = 64. Final answer: 64. Check: substitute or compare with the original information to confirm the result fits the question.

Try explaining why each step works before checking the answer.

Exam-style example

Show your reasoning

Given information: Constant of proportionality — y is directly proportional to x. When x = 3, y = 15. Find y when x = 15. Method choice: use the constant of proportionality method and show each step with the stated values. Calculation or reasoning: k = 15 ÷ 3 = 5. Then y = 5 × 15 = 75. Final answer: 75. Check: substitute or compare with the original information to confirm the result fits the question.

Exam tip: Underline the units and command word. Show the key calculation and write the answer in context.

Common mistakes

  • Assuming every increasing relationship is direct proportion. This is a key trap when answering constant of proportionality questions.
  • Using y ÷ x for an inverse relationship.

How to check your answer

Recalculate the constant ratio y ÷ x from the final pair. Write that check beside the final constant of proportionality answer.

Extension challenge

Create a constant of proportionality problem with a tempting incorrect answer. Solve it, apply the check, and explain exactly where the incorrect method breaks down.

Practice · always open

Question practice with hints and full solutions

Choose a difficulty, answer questions, ask for hints, see the method, retry, or generate a similar question. XP rewards accurate work and improved scores.

I’m Stuck

Year 8 practice studio

Practice Studio

Foundation, secure, challenge and exam-style questions are available immediately with instant feedback.

Progress 0/0 Score 0 Streak 0
I’m Stuck

Answer the questions, then check your score.

Score tracking: Answer questions to start tracking your score.

Games · always open

Constant of proportionality challenge

Use proportion quest controls to solve three checked constant of proportionality rounds. Solve at least two of three marked rounds and use feedback to correct any error.

Press Start Game to enter a topic-specific maths arena.

Boss challenge

Challenge Constant of proportionality Guardian

The boss is available when you feel ready. Boss victory badges and legendary status still require a strong pass.

Constant of proportionality Guardian

Timed mixed-difficulty battle. Practice first if you want, or jump in and learn from feedback.

12 mixed questions5:00 timer×2 XP multiplier
Timer readyAwaiting battle

Study cards and flashcards · always open

Study the essentials quickly

Study cards

Core idea

Constant of proportionality: Direct proportion uses a constant relationship. Recalculate the constant ratio y ÷ x from the final pair. Keep the constant of proportionality representation visible until the final line.

Tap to mark reviewed
Key vocabulary

proportion · constant · scale factor · direct proportion · inverse proportion · proportionality

Tap to mark reviewed
Rules

Identify whether the relationship is direct or inverse. Use a known pair to calculate the constant. Write the matching relationship. Substitute the new value and check the constant remains unchanged. Record the check explicitly for constant of proportionality.

Tap to mark reviewed
Formula / fact

Given information: Constant of proportionality — y is directly proportional to x. When x = 3, y = 6. Find y when x = 5. Method choice: Write each labelled part against its own total before comparing or scaling. Keep ratio parts in the stated order and scale every part by the same factor. Calculation or reasoning: k = 6 ÷ 3 = 2. Then y = 2 × 5 = 10. Final answer: 10. Check: Keep ratio parts in the stated order and scale every part by the same factor.

Tap to mark reviewed
Foundation example

Given information: Constant of proportionality — y is directly proportional to x. When x = 3, y = 6. Find y when x = 5. Method choice: use the constant of proportionality method and show each step with the stated values. Calculation or reasoning: k = 6 ÷ 3 = 2. Then y = 2 × 5 = 10. Final answer: 10. Check: substitute or compare with the original information to confirm the result fits the question.

Tap to mark reviewed
Secure example

Given information: Constant of proportionality — y is directly proportional to x. When x = 3, y = 9. Find y when x = 17. Method choice: use the constant of proportionality method and show each step with the stated values. Calculation or reasoning: k = 9 ÷ 3 = 3. Then y = 3 × 17 = 51. Final answer: 51. Check: substitute or compare with the original information to confirm the result fits the question.

Tap to mark reviewed
Challenge example

Given information: Constant of proportionality — y is directly proportional to x. When x = 3, y = 12. Find y when x = 16. Method choice: use the constant of proportionality method and show each step with the stated values. Calculation or reasoning: k = 12 ÷ 3 = 4. Then y = 4 × 16 = 64. Final answer: 64. Check: substitute or compare with the original information to confirm the result fits the question.

Tap to mark reviewed
Exam-style example

Given information: Constant of proportionality — y is directly proportional to x. When x = 3, y = 15. Find y when x = 15. Method choice: use the constant of proportionality method and show each step with the stated values. Calculation or reasoning: k = 15 ÷ 3 = 5. Then y = 5 × 15 = 75. Final answer: 75. Check: substitute or compare with the original information to confirm the result fits the question.

Tap to mark reviewed
Common mistake

Assuming every increasing relationship is direct proportion. This is a key trap when answering constant of proportionality questions.

Tap to mark reviewed
Exam tip

For constant of proportionality, show the key representation before the final calculation. Use this final check: Recalculate the constant ratio y ÷ x from the final pair.

Tap to mark reviewed
Real-world use

Unit pricing, Journey time and speed

Tap to mark reviewed
Checklist

I can explain constant of proportionality, use the method, check for mistakes, and answer an exam-style question.

Tap to mark reviewed

Flashcards

I’m Stuck

Help for Constant of proportionality

Use this whenever a question feels confusing. Nothing here is locked.

Simple explanation

Constant of proportionality: Direct proportion uses a constant relationship. Recalculate the constant ratio y ÷ x from the final pair. Keep the constant of proportionality representation visible until the final line.

Think of constant of proportionality as a careful model: make the important values visible, change one thing at a time, and use the check to prove the answer fits.

Step-by-step breakdown

  1. Identify whether the relationship is direct or inverse.
  2. Use a known pair to calculate the constant.
  3. Write the matching relationship.
  4. Substitute the new value and check the constant remains unchanged. Record the check explicitly for constant of proportionality.

Hint 1

Start by naming the given information and the exact result required for constant of proportionality.

Hint 2

Identify whether the relationship is direct or inverse.

Full worked solution

Given information: Constant of proportionality — y is directly proportional to x. When x = 3, y = 6. Find y when x = 5. Method choice: use the constant of proportionality method and show each step with the stated values. Calculation or reasoning: k = 6 ÷ 3 = 2. Then y = 2 × 5 = 10. Final answer: 10. Check: substitute or compare with the original information to confirm the result fits the question.

Method: Identify whether the relationship is direct or inverse. → Use a known pair to calculate the constant. → Write the matching relationship. → Substitute the new value and check the constant remains unchanged. Record the check explicitly for constant of proportionality.

Common mistake warning

Assuming every increasing relationship is direct proportion. This is a key trap when answering constant of proportionality questions.

Choose a support button above when you need a nudge.

Mastery milestones

Badges reward learning, not locked clicking

  • I can explain constant of proportionality in my own words.
  • I can use these words accurately: proportion, constant, scale factor.
  • I can follow the 4-step method without guessing.
  • I can avoid this mistake: Assuming every increasing relationship is direct proportion.
  • I can apply this check: Recalculate the constant ratio y ÷ x from the final pair.
🥉 Bronze Badge Foundation completed
🥈 Silver Badge Guide completed
🥇 Gold Badge Practice completed
💎 Platinum Badge Mastery passed
🐉 Legendary Badge Boss defeated