“Show me the math”

It’s amazing what math grade 9s can show with a bucket of polygon tiles and the instruction to “show me the math”

We saw rotational symmetry

Parallel lines, and symmetry about an axis.

We saw hexagonal based prisms…

Proved that hexagons can be made up of trapezoids (red) rhombuses(blue) or equilateral triangles (green)

Some showed fractions….that 2 rhombuses are 2/3 of a hexagon….but so are a trapezoid and a triangle (which happen to represent 1/2 and 1/6 respectively) so we know that 1/2+1/6=2/3

We saw that honeycomb pattern made up of hexagons…and trapezoid combos

And when we ran out of those they were made of rhombuses and triangles too

Some made pictures…here’s a very symmetrical owl 

Some patterns filled the space perfectly

Others were showing patterns in rings.

And some patterns looked like they were missing something.  This one below caused some concern.  Many people wanted to fill the gap beside the square.  We wondered if a thin rhombus would fit.

We examined the rhombuses to see if we could figure out about the angles inside.  We saw that 12 of them fill the whole way around the central point.  We know that a full circle is 360 degrees, so each acute angle is 360/12 which is 30 degrees.

We know that a quadrilateral has 360 degrees, and if you remove two 30 degree angles, there are 300 degrees left for the other two congruent obtuse angles.  Each obtuse angle must be 150 degrees.

We could go on and on about more angle discoveries…and we will be looking to do more this coming week.