Geometry
&
Measurem
ent
SEAMEO QITEP in MATHEMATICS Yogyakarta, October 5th & 7th 2013
ILHAM RIZKIANTO
Kanisza Figure
A central feature of geometry is
learning to ‘see’, that is, to discern,
geometrical objects and relationships, and to become aware of relationships as properties that objects may or may not satisy.
Imagine Considering moving a bookcase from one room to
another, but not being sure if it would fit
through the doorway. If you did not have a ruler, how might you find out without
actually moving it?
The key aspect of any measuring is to
make a comparisons. One way to do
this is to decide on a unit and to have some way of replicating the unit (or breaking it up into smaller sub units) and juxtaposing this with the thing to be measured.
Mathematics is not only connected to the world of numbers.
In Geometry, the issue is to understand the space
around us. It is related to the two- & three- dimensional world and the related shapes & figures.
Measurement is aimed at quantifying our physical environment. The emphasize in this process makes
measurement the connecting link between arithmetic and geometry.
The connection
arithmetic
measurement
Lay the first sheet down on the table. Lay the second one partly on the top of the first, so that the top-left corner of the upper piece coincides with the top-right corner of the
lower piece and the bottom-left corner of the upper piece coincides with the left edge of the lower piece.
Repeat this with several more pieces. What do you notice?
You may discover that some pieces
coincide. You may be surprised at the shape you see emerging. This shape will tell you about angles involved.
Now, try to find at least 4
questions that could be used as follow up questions for this
activity.
Activity 1: Live up the paper
Every teacher should have his/her own special collection of geometric tidbits – short little puzzles, problems, and
curiosities in geometry to warm up the class, to gain attention, to involve, to challenge, to maintain interest, or
Move just three dots to form an arrow pointing down instead of up.
A solid has this for both its top and front view. Draw its side view.
How many rectangles are in this figure?
Take two pieces of the paper. Take the first piece and curl it in potrait orientation so it forms a tall, thin cylindrical shape. Take the other one, do the same but in landscape orientation so it forms a shorter and fatter cylindrical shape.
If you were to fill each of these cylinders with popcorn, which one do you think would hold more? Or, do you think they would hold the same amount?
This activity is intended to explore the volume of cylinders with the same
lateral areas and to see the connection between volume and area.
Now, try to find at least 4
questions that could be used as follow up questions for this
activity.
Activity 2: Popcorn Holder
The core teaching principles of RME
Activity
Reality
Level
Intertwinment
Interactivity
Activity 3: Tangram
Mark points at the following
coordinates: (0,0), (0,2), (1,1), (1,3), (2,2), (2,4), (3,1), (3,3), (4,0), (4,4)
Connect the following points with a line segment to create a tangram set: (0,0) and (4,4), (0,2) and (2,4), (1,1) and
(1,3), (1,3) and (4,0), (2,4) and (3,3)
Cut out the tangram pieces and create an animal or object using all seven
There are 13 possible tangrams altogether that are in the form of
polygon. Of these 13 tangrams, one is a triangle, six are quadrilaterals,
two are pentagons, and four are
hexagons.
BIG IDEA: How a shape can be
composed and decomposed, or its
relationship to other shapes, provides insights into the properties of the shape
The geometric thinking involved has to do with the invariance of area under
moving of the pieces, as well as trying to imagine a silhouette shape as
decomposed into the puzzle pieces.
Construct your own measurement system “from scratch” according to following outline:
1. Choose some commonly available object to define the basic measurement unit. Measure your height with this unit.
2. Define related units of linear measure that are more convenient for dealing with much bigger and much smaller things. Use them to specify the distance from Yogyakarta to your home town, the length of
football field, the width of A4 paper,and the thickness of the RME book.
3. Define related units to measure area and volume. Use them to
specify the area of A4 paper and one much larger object of your choice, and the volume of a bottle for dispenser and one much smaller object of your choice.
4. Make conversion tables that relate your system to the metric system.
5. Compare your system to the metric system. In what ways is it better? In what ways is it not as good?
Activity 4: Make your own system
Please send the written result of this activity in word ducument to
What have
you learned
?
One quote for you
“Everybody is a genius. But if you judge a fish by its ability to climb a tree, it will live its whole life believing that it is
