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