Use coordinates to compute perimeters of polygons and areas of triangles and rectangles, e.g., using the distance formula. *(Modeling Standard)
INTERPRETATION OF OBJECTIVE - G.GPE.B.7
This objective is connects perimeter and area to the coordinate plane. We use the distance formula, the coordinate grid and Heron's Formula to determine areas of various shapes.
(1) The student will be able to determine the perimeter and area of various shapes on the coordinate grid.
(2) The student will be able to use a variety of techniques to determine the area of a shape.
THE BIG IDEA
Area is a concept that is found everywhere and so this is just another context for it. When shapes are placed on a grid we gain a number of new techniques in discovering their areas.
TRAPS & PITFALLS
Not a lot of issues here.... Area is a very familiar concept and apply those concepts to the coordinate grid don't make it much harder. As I have said on almost every objective in this unit... the only thing to trip students up will be their algebra skills using things like the distance formula.
Area is everywhere!! We connect it to an earlier unit where we introduced many area formulas and relationships to calculate volumes.
Area continues from here as well for example in calculus we calculate the area under a curve to help us determine lots of different things. Volume is always connected to area.
MY REFLECTIONS (over line l)
This is quite an easy concept to teach especially because we already handled in earlier in the year. The only thing that slows them down again is the errors found in the distance formula or in Heron's Formula.
The truth is once you learn the 'Box' technique .... why would you use any of the others. It is just too simple.