Starter of the Week 16: Stairway to Heaven

Screen Shot 2023-08-27 at 7.01.56 AM

Starter of the Week 16: Stairway to Heaven

Starting with the numbers: 2,4,6,8 fill in the bottom grid in any order. Work out the box above by adding the two numbers below.

Here are some possible questions to explore:

  1. What is the biggest possible total you can make in the top row?
  2. Create a hypothesis for a strategy that always gives the biggest possible total.
  3. Prove your result by considering integer numbers π‘Ž, 𝑏, 𝑐, 𝑑
  4. When the ladder is now 5 blocks high, what is the biggest possible total for the numbers 2,4,6,8,10?
  5. Using letters π‘Ž, 𝑏, 𝑐, 𝑑, 𝑒 explain how you know you have found the largest total.
  6. Explore different heights of ladders. What is the pattern that would help you predict in terms of π‘Ž, 𝑏, 𝑐, 𝑑 … a ladder 8 blocks high?

Teacher notes:

Level of difficulty: Accessible for all students

Syllabus knowledge required: None – but would fit well with a lesson just before or just after introducing the binomial expansion and Pascal’s triangle.

You can download the pdf of the problem and the solution here.

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Maths teacher

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