Geometry 2D

Today’s problem (Mar 27):

To activate our brains we asked students to define symmetry.

Then we looked at today’s problem:

Here is what it looked like:

Once all the drawings were up, we searched for some mis-conceptions.  Here’s what they identified:

Consolidation:  Our discussion focused on why these drawings had lines through them that created two halves that were not symmetrical.  The students noticed that in order for symmetry to happen, all points on one side had to be equal distance from the line of symmetry on the other side (using a perpendicular line).  It would be the same as folding the paper and having both halves line up exactly.  If they don’t line up exactly, then it is not a line of symmetry.

Some students noticed that if you draw a line across a rectangle from corner to corner, the two shapes are the same, but not symmetrical along the line of symmetry (you would have to flip one side over).  We then looked at the work “congruent” as meaning a shape that is the same size and same shape.

Today’s problem (Mar 29):

Today’s problem was to use a Venn Diagram to sort the alphabet (capital letter only).  The students were asked to think about angles. 

Here are some of the results:

Consolidation:  We focused on types of angles (big, small, and square).  Some students knew that angles greater than 90 degrees are called OBTUSE, angles smaller than 90 degrees are called ACUTE, and angles exactly 90 degrees are called RIGHT (or SQUARE) angles.

We also had a discussion about what makes up an angle (can it have a curved line?)  We decided that angles have to be made of line segments.  When 2 line segments meet, the figure it makes is called an angle.

March 30:

Today we worked on identifying and naming angles.  The students worked on math sheets (to be finished for homework)

April 3:

We have been working on equal angles using pattern blocks.  This lead to measuring angles using a single pattern block (beige rhombus) as one unit to compare all the other angles to.  We also learned about acute, right, obtuse, line, reflex, and a full rotation.  We are now beginning to look at protractors.

Equal angles:

Measureing angles (using a beige rhombus as a single unit):

Some groups realized that the beige rhombus (acute) angle measured 30 degrees (because 3 fit into a right angle) and were therefore able to figure out the angles in degrees:

Good work!

April 4:

Having practiced with our “unit” protractor, we turned our sites on real protractor.  Together we came up with three steps to guarantee a correct answer:

We practiced on the Smart board:

Then we got to work on some individual sheets.

Today’s problem (April 5):

The students were asked to  draw shapes (grade 4’s = quadrilaterals, grade 5’s = triangles and irregular polygons).  Then they were to measure all the angles in the shape, and add them together.  Here are some of the results:

Consolidation:  The students were asked to see if they could find some patterns.

One conclusion we came up with was that all the angles of a quadrilateral should add up to 360 degrees, and that all the angles of a triangle should add up to 180 degrees. 

We then took all the angles of a square (and a triangle) and put them together in a different way, to show how a square and a circle (or a triangle and a straight line) have something in common:

Today’s problem (April 10):

Today students were asked to sort a variety of shapes (grade 4’s quadrilaterals only):

Some students sorted by colour:

Some sorted by the number of sides:

Some students sorted by angles:

Some students sorted using lines of symetry:

Consolidation:

We focused our discussion on what makes a shape, a shape.  How do we define one shape from another.  We focused on the attributes of quadrilaterals.  Here is what they came up with:

Today’s problem (April 12):

First we reviewed our math language:

We focused on attributes of shapes (such as opposite parallel sides, opposite equal sides, opposite equal angles, etc…).  We looked at how mathematicians show this information,

for example, opposite equal sides:

opposite parallel sides:

and opposite equal angles:

Then the students were given some riddles using attributes of shapes:

They were then asked to come up with their own:

Consolidation:  We will consolidate tomorrow when the students try to solve the riddles.

Today’s problem (April 16th):

Today we solved the riddles done last class.

Consolidation: We focused on a few riddles.  We looked at riddles that could be answered with more than one shape.  We discussed attributes that make up shapes and how many shapes fit into the definition of other shapes (for example a square could also be considered a parallelogram because it fits into the definition – a square has opposite equal angles, opposite equal sides, and opposite sides are parallel.  But a parallelogram cannot be considered a square because it does not always fit into the definition of a square, it does not necessarily have four right angles or four equal sides).

Here are some examples of what we looked at:

 

Only a rhombus and square HAVE TO have four equal sides:

Although a trapezoid has ONLY one pair of parallel sides, many shapes also have a pair of parallel sides (squares, rectangles, parallelograms, rhombuses, etc…)

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