What Does it Mean to Do Math?

Gurps1.jpgThe GURPS Basic Set which contains rules for the paper and pencil roleplaying game designed by Steve Jackson describes an ability that you can bestow on a character you are creating.

Lightning Calculator – You have the ability to do math in your head, instantly. If you have this talent, then you (the player) may use a calculator at any time, to figure anything you want – even if your character is fleeing for his life at the time!

This description seems to imply that doing math and calculating are the same thing. Do you agree or disagree? Make your case.

No Squares Here

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Recognize and Categorize Shapes – Grade 4

Everyone wants to count triangles in this figure but what about rhombi, parallelograms and trapezoids? Hexagons and pentagons? Dodecagons anyone? The abundance of parallel lines make this a good figure for 4th graders to study, both as a review of some of the shapes addressed in previous grades and as an opportunity to classify quadrilaterals based on the presence of one or two sets of parallel lines.

2.G.A.1 – recognize triangles, quadrilaterals, pentagons and hexagons

3.G.A.1 – recognize rhombi as examples of quadrilaterals

4.G.A.2 – recognize parallelograms and trapezoids* by their attributes

Investigate

Q1:  What shapes do you see?

Q2:  How many of each shape are there? Count all same sized shapes as one shape. [For example, there are 4 different sized triangles, all equilateral.]

Q3:  How would you organize each of these shapes into categories?

Q4:  How many categories do the rhombi belong to? Make your case.

*Although students are composing trapezoids as early as grade 1, it’s not until grade 4 that students are expected to consider its defining attributes. Use the inclusive definition of the trapezoid, a quadrilateral with at least one set of parallel sides.