median
don steward
mathematics teaching 10 ~ 16

## Saturday, 1 December 2018

### equal tops pyramids

the purpose is for students to practice simplifying expressions, within a context
a powerpoint is here

all of the equal top block numbers can be found by trial and improvement and that is the intention, especially for the harder tasks

other techniques can be used

sheet 1 leads to a simple linear equation
sheet 2 leads to a linear relationship that generalises to c = 2n, d = 3n - 4 with top numbers: 6n - 5
sheet 3 can be solved with simultaneous equations, with one solution
sheet 4 leads to a relationship that generalises to a = 2n + 1, b = 3n - 1 with top numbers: 12n - 5
sheet 5 with 3 variables can be generalised to a = 4n - 2, b = 7n - 2, c = 14n - 6
sheet 6 has 4 variables, the smallest equal top number is a triangular number (and you can also make 81 and ...?)
sheet 7 is one that Martin used with his students
they found the smallest possible equal number by finding common terms in the four sequences (which is less than 50) you can also make 209 and ...?