Visual patterns in grade 10

In grade 10 we are working on quadratics.  We looked at visualpatterns.org and modelled some patterns by drawing terms 4 and 5 and 0 to extend the pattern in both directions.

We made tables, and looked at differences (it’s quadratic if the 2nd difference is constant).  We also looked for groups of “n” and squares of “n”.

We notice the constant, and colour it so we can see it’s always there.  It is also in the equation at the end (the term with no variable).

We also made our own patterns from a given expression.

We noticed by the end of the class that the “a” value (the coefficient of the squared term) is HALF of the 2nd difference.