Why 8?
Choose any four consecutive even numbers. Multiply the two middle numbers together. Multiply the first and last numbers. Now subtract your second answer from the first. Try it with your own numbers. Why is the answer always 8?
Age
11 to 14
Challenge level
Problem
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Choose any four consecutive even numbers. (For example: 6, 8, 10, 12). Multiply the two middle numbers together. (e.g. 8 × 10 = 80) Multiply the first and last numbers. (e.g. 6 × 12 = 72) Now subtract your second answer from the first. (e.g. 80 - 72 = 8)
Try it with your own numbers. Why is the answer always 8?
Student Solutions
Peter Hopkinson
from Tithe Barn School, Stockport (Year 5) has carefully explained his thinking.
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Teachers' Resources
Here are some suggestions on the possibilities offered by the problem.