Tag Archives: class

Geometry with Geoboards

Last Sunday we also played with geoboards.

We first asked the kids to make a triangle, and it turned out that they come in many varieties:

ImageImageWe then had them build quadrilaterals.  Here’s a sample:

ImageWe briefly discussed some terminology such as square, rectangle, parallelogram, trapezoid, convex…  The first two were of course familiar terms, and a few kids had heard of a trapezoid but many would struggle to define them if asked to describe the difference.  Some kids would also make comments such as “I made the largest quadrilateral possible” or “I made the smallest one”.  We did not yet discuss the concept of area with them, but I think that we will in the near future.

We then moved on to slightly more challenging assignments.  We would tell the kids to make a figure with exactly one interior point, or exactly five points on the boundary.  For the older kids we eventually would put conditions on both interior and boundary points.

Not surprisingly, geoboards are a great tool for introducing and exploring basic geometry concepts.  In the future, we also hope to use them to continue with the theme of geometry of numbers.

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Multiplication before addition?

There are ten people in the room.  How many eyes are there?  How many legs?  What about arms and legs combined?  Fingers?  Our older group didn’t have much trouble with this – they were pretty good at counting by 10’s to get to the answer.

It was next established that out of the 10 people, 7 are kids.  How many kids’ eyes are there?  In theory, this question shouldn’t be much harder than the previous ones, but all of a sudden some kids were trying to count the eyes by 1’s, others by 2’s, and both were making mistakes (probably because everyone was sitting in a circle and the adults are interspersed among the kids).  Finally, someone attempted to add 7+7, and after a mistake or two, the right answer was pronounced.

The actual goal of the lesson was to start informally introducing multiplication and division (for division, the kids worked in small groups and divided various amounts of glass beads amongst themselves).  And, on one hand, it is not necessary to be stellar at addition and subtraction to understand these ideas on a conceptual level.  However, in order to actually do many interesting things with the concepts, it helps when the kids are comfortable with counting at least by every number up to ten.  So does it make sense to introduce multiplication before the kids have mastered addition?

You could go either way on this one.  It turns out that mental math, even within the realm of 20, is a weakness across the board in our groups. And while doing addition drills isn’t exactly in line with our approach to making math fun, getting comfortable with mental math is a critical skill that will enable deeper exploration of many concepts (and will be really impressive to teachers and peers alike). And thus, we’re looking for ideas on how to get comfortable with addition and subtraction for 5-7 year olds in a fun way.  But it’s unclear that we should wait until they do indeed master this skill before introducing more complicated and interesting concepts.  Introducing notions like multiplication and division on a conceptual level may help them better understand the ideas behind these concepts instead of simply memorizing the times tables.  So for now, we’re putting up with counting on fingers and really entertaining mistakes.  Stay tuned for our progress.