Geometry 2D - Student examples (Bansho – 3 part math lesson)

We have been starting our unit on 2D geometry.We had a discussion about what they already know, and what they think geometry means.  This is what they came up with:

Today we focused on "congruent", "similar" and "lines of symmetry". 

Today's question (April 12):

Today the students were asked to explore lines of symmetry.  We had a discussion about what they think that means and then they were asked to draw 10 or more shapes, and include all the lines of symmetry within those shapes.

Here is what it looked like on the board:

Here were some of their answers:

Consolidation:  The students were then asked to look at the answers on the board and see if they could find any mis-conceptions.  This is

what they found:

This opened a discussion about what a line of symmetry is.  Does it need to break the shape into 2 congruent pieces, or is there more.  The answer was that a line of symetry also has to create a mirror image.  This line makes two congruent shapes, but they are not mirror images, so it is not a line of symmetry.

This shape also drew some attention.  The students decided that it did fit into the definition of a line of symmetry:

The last question they were asked was, is there a common shape that does not have a line of symmetry.  The students thought that a parallelogram does not have a line of symmetry.

They were given one question to think about:  Since shapes are defined by their properties or attributes, can a shape be defined (in part) by its lines of symmetry?

There were homework sheets:

symmetrysymmetry-2symmetry-drawlinessymmetry-sketching

Today's question (Apr 13):

Today we discussed what criteria we think are used in order to define shapes.  We came up with these ideas:

Then the students were asked to use a Venn diagram and classify all the letters of the alphabet (capitals only) in as many different ways as

they could.  Here's what they came up with:

Consolidation: We focused our discussion around the last example.  We discussed the meaning of "right angle" (90 degrees), "acute angle" (smaller than 90 degrees), and "obtuse angle" (larger than 90 degrees). 

Today's (and yesterday's) question (April 15):

Yesterday the children were asked to use pattern blocks and explore angles.  They were asked to use the shapes to find equal angles.

Pattern blocks:

Here are some of the results:

Consolidation: We looked at how people made equal angles (for example, two green triangles together make an angle equal to an angle on a yellow hexagon.Then we talked about how students showed which angle they were focusing on, and how mathematicians show the angle they are focusing on. 

Today they were given the following information. The angles of the orange square are all 90 degrees.The angles of the green (equilateral) triangle are all 60 degrees.From these two pieces of information they were asked to figure out all they angles of each different shape found in the pattern box (beige rhombus, blue rhombus, yellow hexagon, orange square, green triangle, red trapezoid). 

Here is what the students came up with:

Consolidation:  We focused on how the students used equal angles (two triangles = one hexagon angle) to figure out the answers (60 degrees + 60 degrees = 120 degrees, therefore the angles of the hexagon are all 120 degrees).

Today's question (April 20):

We have been learning about angles and how to measure angles using protractors.

We applied those skills to today's question.  Grade 4's were asked to draw a number of quadrilaterals, measure each angle, and then add the angles together.  Grade 5's were asked to do the same with triangles.

Here is what the students came up with:

Consolidation:  We focused on two things today.  Number one, a common error that occurs when using a protractor is reading the wrong number (there is an inside set of numbers and an outside set of numbers on the protractor). 

The students came up with 2 solutions to this common mistake.  First, they if the angle is an acute angle, then the number must be less than 90 degrees.  Second, they came up with a little saying: "Either you're RIGHT-IN, or your LEFT-OUT".  This means when you measure an angle that faces right, you use the inside numbers on the protractor, and when you measure an angle facing left, you use the outside numbers.

Number two, we looked at the numbers that came up most often in the totals (total of all the angles in a polygon added up together).  We notices that the 4 angles of a quadrilateral should always add up to 360 degrees, and that the three angles of a triangle should always add up to 180 degrees.

Today's question (April 21):

Today we focused on the attributes of triangles (grade 4's) and quadrilaterals (grade 5).

The grade 4's work is displayed:

Together we had a discussion to brainstorm what attributes or properties of a shape (4 sided) could be used to define it.  Here is the list the students came up with:

Using these ideas, the students were asked to come up with definitions of various quadrilaterals.  Here's what they came up with:

Next class we will continue to explore how polygons are identified by their attributes.

Today's question (April 27th):

Today the students created riddles using the properties of various shapes.  Then they did a gallery walk and tried to answer each other's questions.  Here are some examples:

The students had a lot of fun!