Tiling

Tiling

You can use 2 shapes, but you can't have any overlap or gap.

Think about what you know for tessellations:

I know a shape tessellates if it's angles are factors of 360.

 

Observations

*When I look at their vertices (where the shapes come together) it equals 360. 

*Angle measure is always 360 (with no overlaps or gaps)

*Can draw triangles in hexagon. 60+60=120

*I can tell they tile if the angle measures added together equal 360. 

*The shapes make the angle for the other shape.

Tessellations

After watching the bee video, the hexagons in the honeycomb tessellate. What does that mean?

Which shapes tessellate?

What do we notice about the shapes that tessellate?

Observations:

*All the angles are the same

*Single angle measures are factors of 360

(90 degrees goes into 360 4x)

(60 degrees goes into 360 6x)

(120 degrees goes into 360 3x)

Class rule: I will know a shape tessellates if...

I know a shape tessellates if it's angles are factors of 360.

Making a Rule for Irregular Polygons

In your group, choose three strong observations. Then, make a rule that can be used for all irregular polygons to find the sum of all the angles. 

Are regular polygons the same or different from irregular polygons? 




Casey:


Any polygon will have the circle in the middle subtract out the value of the circle which is 360.


The reason for the # of triangles is to count the # of sides.


The 360 is already include in the whole shape and we don't need it so we subtract.


Rule for regular polygons works for irregular polygons.


Look back to R-43.

What is a rule for finding the sum all angles? What about a single angle measure?

Homework: 
Comp Corrections Due Wed

Due Tuesday 
L-40 pg. 53 #3-10
pg. 58 #23 



R-43 Write a Rule: If I know the sum of all the angles how can I figure out the single angle measure?

Sum of all angles Divided by # of sides = single angle measure



1. Devon's work: I created some irregular polygons and ripped off the sides. Is there a relationship between the # of sides and the angle of degree?

2. Trevor's work: I took some polygons, some are regular and some are irregular. Cut them in thirds, halves, fourths. Trying to make other shapes or triangles. (Angle measure for a triangle is always 180)

3. Casey's work: I made each side the base of a triangle. I also made the same number of triangles to match sides.

R-44 Write as many observations as you can. Can you find the relationship between the # of sides and degree angle?

Polygon chart

This week we were given 6 polygons and were asked to count the sides, find the angle measure, and the sum of all the angles. We also had a discussion about precise measuring and how measuring is not perfectly accurate. 

We also looked for patterns on this chart and used what we knew about the patterns to determine the degree of a Decagon (10 sides) and a nonagon (9 sides). 

R-43 write a rule that you could use to find the sum of all the angles for any number of sides polygon. 

For example: 112 sided polygon 

What is a Polygon?

What Observations can you make? 


Based on the information above, what do you think is a Polygon?