3.2.1 Understanding and using direct and inverse proportion

• What is the key characteristic of inverse proportion illustrated in the example?

  Opposite directions
• Why does the time taken to complete the job decrease as the number of workers increases?

  Work is distributed
• What happens to one quantity in direct proportion when another quantity increases?

  It increases at the same rate
• If one quantity in an inverse proportion increases, the other quantity also increases.

  False
• Arrange the following pairs of workers and time in descending order of time taken:

  1️⃣ 2 workers, 12 hours

  2️⃣ 4 workers, 6 hours

  3️⃣ 6 workers, 4 hours

  4️⃣ 8 workers, 3 hours
• In the scenario of travelling a set distance, what increases as the distance covered increases?

  Fuel consumed
• What is the constant product in the example of workers and time to complete a job?

  12 worker-hours
• How much money is earned for working 3 hours in the example of direct proportion?

  £15
• What is the first step in solving problems with direct proportion?

  Identify the quantities
• What is direct proportion?

  Things increase at same rate
• What happens to one quantity in an inverse proportion as the other quantity increases?

  It decreases
• What do you use the constant of proportionality to find?

  Missing quantity
• In the example provided, what is the value of the constant product (k)?

  24
• If 2 people take 12 hours to paint a room, how long would it take 6 people?

  4 hours
• Arrange the speeds and travel times in the example from slowest to fastest:

  1️⃣ Speed: 30 miles/hour, Time: 4 hours

  2️⃣ Speed: 40 miles/hour, Time: 3 hours

  3️⃣ Speed: 60 miles/hour, Time: 2 hours

  4️⃣ Speed: 120 miles/hour, Time: 1 hour
• If 3 pencils cost £1.50, how much will 10 pencils cost?

  £5.00
• What is the general equation for inverse proportion?

  A * B = k
• Arrange the scenarios in order of increasing complexity based on the type of quantities involved.

  1️⃣ Baking cakes

  2️⃣ Making juice

  3️⃣ Buying items

  4️⃣ Travelling a set distance

  5️⃣ Earning money