City Map - Parallel Lines Cut by A Transversal

I found this idea a long time ago.  It's on Wikispaces.


I really liked it and have had my students do it two years now.  I altered it a little. 



They are more creative than I am, so I try not to restrict them too much.


I give this a little after they learn about parallel lines cut by a transversal.  It's not completely new to them, but some do struggle a little with where each of the buildings should go.  I tell them to make a fake map on a smaller paper before they draw it on the big one.




I do not require them to make large, good-looking buildings.  I know that many of them have much better maps if they're allowed to make simple figures.  If I was the student, that's the position I would be in.



I also hang the prettiest ones on the wall in the hallway, as long as most of their locations are correct!




One map had Mike Wazowski Rd and other animated street names.  Some of them like to have themes, but many of them are pretty standard.

One maps had This Street, That Street, Which Street, Where Street, and There Street, etc.  That may be my favorite!

The two intersecting lines don't have to be parallel, but it's easier if they are!

Your Name Here - Midpoints

Just like the "Thankful" words and the "Character" words activities, I have a Name-Activity where students calculate midpoints.



Actually, I think for the College Algebra class, they calculate distance, but it makes no difference.


When I do the Name, Character, and Thankful activities, one of them is for slope, one is for distance, and one is for midpoint.  I usually do the name first, and I do them in the order of Lesson number.
That's all with my Geometry students.
With the College Algebra students, I 'have' to cover the distance formula.  It's probably something I should just skip, but I don't like skipping things, so we do this instead.





With the Thankful and Character activities, I usually don't hang up each word.  I try to not get too many repeats and I only pick the ones that are neat, colored, and look good.

With the Names activity,  I hang every single one up.


I keep the same requirements for each of these assignments:


*Every letter must have only straight line segments.  No curves!
*Every segment must have a slope that is not zero or undefined.  (No horizontal or vertical lines.)
*Every word must be drawn in something other than pencil.


Sometimes, this may be a challenge.  

That is a "U."

Some students decide they don't like the way the name looks, so they redo several letters just to improve one.


**Generally, this activity is easier to do with all-capital letters.
**Sometimes letters can be a little tricky to make w/o vertical or horizontal lines.  These can be done by placing the letters at an angle and/or drawing them 'artistically.'



For these projects, the kids have to show work.  
That work must include calculations with the ordered pairs.  (That is the entire point of this project.)  
It has to be organized!


The name has to be at least 4 letters long.

King Frostine Wages War

 

I'm very proud of this.  I wrote it  a couple years ago during finals.  Finals are boring!  I had only done one lesson of this 3-lesson unit.  I was getting ready to do the rest when we came back from break in January.
I made up the story, but not the names or 'races.'  Don't sue me.  I'm not making money off of this!

Geometry, "Center" of a Triangle, a Task from King Frostine

You live in the land of Sunderedcounter in Intermedio Tierra where King Frostine rules over all of the Lilliputians.  You are the king's head mathematician.

John Hurt's voice

 

There is some disarray in the land.  King Frostine is ready to wage war with three nearby cities Crystalgarth, Sunderfen, and Sharpetide.  His plan is to use catapults to continuously launch water balloons at each city until they surrender.

The assault will go fine as long as the liliputians have access to a camp nearby.

King Frostine only has enough resources to set up only one camp as a refilling station.

 
King Frostine must pick the location of his camp very carefully.  The camp must be exactly the same distance away from each Crystalgarth, Sunderfen, and Sharpetide.


The reasons for this are political.  King Frostine's biggest supporters, Lemel Hailglow, Hazel Flameshimmer, and Bracken Goldtree, each prefer he focus on a different city. 


Lemel wants to attack Crystalgarth.  The mermaids from Crystalgarth are always singing limericks about the liliputians right outside Lemel's house.

Hazel wants to attack Sunderfen.  The dragons of Sunderfen are always dropping jello-filled water balloons onto Hazel's daisies.

Bracken wants to attack Sharpetide.  The centaurs of Sharpetide are always stealilng Bracken's pumpkins.

King Frostine must pick a location that is equidistant to each so he isn't showing any favoritism.





He needs your help.  You have taken a map of Intermedio Tierra and connected Crystalgarth, Sunderfen, and Sharpetide.  This has created a triangle.

 



King Frostine set each of your apprentices Brelynd, Jarthan, Tolbain, and Camnar the task to determine where the camp should be located.


 

Brelynd thinks we should locate it at the centroid.
Jarthan thinks we should locate it at the orthocenter.
Tolbain thinks we should locate it at the incenter.
Camnar thinks we should locate it at the circumcenter.

Which place should we locate the camp of water balloon refills?

Use geometry vocabulary to explain this.


If you're not a math teacher, then you can stop reading here!



The following pages contain a map of Intermedio Tierra.

Calculate the distance from the camp to each of the cities.

Brelynd thinks we should put the camp at the centroid.  Use this graph to locate the location (ordered pair) of the centroid.  Be sure to label the midpoint of each side of the triangle.  Use a ruler to draw the medians.  Graph the centroid on the map.

Jarthan thinks we should put the camp at the orthocenter.  Use this graph to locate the location (ordered pair) of the orthocenter.  Use a ruler to make a (GOOD) sketch of each altitude.  Remember altitudes are perpendicular, and should be labeled as such.  Make a (GOOD) estimate of where the orthocenter is located. Label the orthocenter on the map.

Tolbain thinks we should put the camp at the incenter.  Use this graph to locate the location (ordered pair) of the incenter.  Use a compass and a straight-edge to construct each angle bisector.  Remember to label the angles as bisected.  Make a (GOOD) estimate of where the incenter is located. Label the incenter on the map.

Camnar thinks we should put the camp at the circumcenter.  Use this graph to locate the location (ordered pair) of the circumcenter.  Use a straight-edge to sketch each perpendicular bisector.  Remember to label the sides as bisected.  Determine where the circumcenter is located. Label the circumcenter on the map.

I put the same graph paper map on each page.
It's easiest if you use a right triangle.

Chutes & Ladders and Candy Land

Once, long ago, we played Chutes and Ladders in my class.  I found a C&L pic online, and then I proceeded to edit the pic by adding a question into EACH box!   CRAZY!!!!  Since then I have grown much wiser.

*We played Chutes & Ladders.  It was not the first time in my (teaching career) life that I thought Spongebob was taking over.  Many of the kids knew the game because of Eels and Escalators.
!!!
 = |

You just have to provide them the game board.  The cards are the questions.  Duh!



I found them online and printed them on my color printer.  I put them in a plastic sheet protector.  and then let them use random things as game pieces.  I have some pegs for a 'block game,' or erasers or paper clips.  I was a few pieces short, and told the kids they could provide their own pieces if they wanted.  They came up with a few pieces and it all worked out.

The came cards were various questions that the students had just been learning, just about to be tested over, or something in between.

I split the class into groups of 2-5, depending on how many supplies I have and how mature the students are.

The kid answers the question, and if s/he gets it right, then rolls the dice to figure out how many to move forward.  If s/he lands at the bottom of the ladder then s/he climbs it.  If s/he lands at the top of the chute, then s/he falls down it.
In Candy Land, you can play with the color cards, but I doubt you have enough.  It's just easier to roll the dice.


During a pedagogical epiphany, I decided that absent students should not 'get out' of doing the work for this.
I mostly just copied the same questions into worksheet form.  I didn't do them all because the game cards had several versions of each topic.

The kids got points for participating in the game.  The absent ones had to fill out the paper to receive the points.



Geometry Questions

 

College Algebra Questions



Calculus Questions



We played this game the last day of class before Thanksgiving!

Math Jenga

After seeing something like this online, I decided to make my own version of Jenga.

I have questions for Geometry, Advanced Algebra & Trigonometry, College Algebra, and Calculus.

For Calculus, I have implicit differentiation and slope of tangent line questions.
For College Algebra, I have horizontal, vertical, and oblique asymptote questions.
For Adv Alg & Trig, I have right triangle trig and inverse trig questions.
For Geometry, I have slope of parallel and perpendicular line questions.



I told the kids the tape and paper on the blocks were just part of the game, like referees in a football game.  If the tape or paper were to blame for the tower crashing, then whoever was 'up' then was responsible for losing.

Each question also had a point on it.  Answering it correctly would earn the student 1, 2, or 3 points.

Knocking the tower over earns the student -20 points.

Then they start over and continue playing.

You have to monitor them.  Some of them like to play Jenga w/o doing the math problems.
Some of them like to let only certain students pull out the blocks, not allowing everybody to have a turn.




I should have just done a more generic thing where the students pull out a block, and answer the 'next' question in a stack of 'cards.'  This way I can do it for one unit, and then again for any other unit I would like.  That is what I have been doing for Chutes & Ladders and Candy Land.

With the way it is, sometimes students try one block, and if it's only 1 point, then they decide to put it back and try another (maybe trickier) 3-point block.

This is for review.  With anything like this I always tell the students, "Between the 3 of you, you should be able to determine whether you're correct.  If not, let me know if you have questions."

Also, these things can be competitive, but they usually help each other out.  It's a better review session that way.

Hexaflexagons

I actually found a copy of my old post on Hexaflexagons!


So... the 'dates' are a little off.


Last spring I attended the NCTM national conference in Denver.  I attended some really great sessions.  The last one was the finale with George and Vi Hart.  They are what I like to call “recreational mathematicians.”  You know… because that’s a thing!  After seeing some of Vi’s videos, I was interested.   
 


Later, I decided I wanted to do the hexaflexagons in school.  It was her idea, really.  We had a hexaflexagon party on Martin Gardner’s birthday.  He was the ‘original recreational mathematician.’    His birthday is October 21, so I put it on iCal, and waited for the day to come.  I showed Vi’s videos Hexaflexagons, Hexaflexagons 2, Hexaflexagon Safety Guide, and Hexaflexamexagon- I think that’s the one that hooked me originally!  I printed off the hexaflexagon template.  I told the kids to be sure to make good creases!  They created their tri-hexaflexagons, decorated them, and a few even tried the hexa-hexaflexagon.

 

Truthfully, I have not figured out the hexa-hexaflexagon.  In due time.  …  I’m getting better at the tri-hexaflexagon.  One class (out of 6) I had a tough time with the tri-hexaflexagon.  I finally got it to fold the correct way and it was the very end of class.  I decided to go ahead and let them finish it the next day, but we didn’t need to spend an entire class on it.  So I came up with a little research worksheet.  To ensure they didn’t use Wikipedia, I made them ‘cite’ their sources.

 

I thought it was pretty cool and the kids liked it.  It makes math fun again- at least a little!

I made them color some design to show that when you 'flex' it, the design changes.

This year, I made my own template.  It wasn't too difficult, but it worked the best.  It was not perfect, but if you made the creases well, then you could make a hexaflexagon.

Christmas Decorations!

When I was in the middle of my early years of teaching, I was at a Hobby Lobby almost 150 miles from my high school.  I found a blue and gold Christmas tree that was 2-3 feet tall.  It was really blue and yellow, so that's why I was a little surprised to see it.  I, of course, purchased it and loved to decorate my classroom with it.
When I changed schools, I left the blue and gold tree in the office of my English teacher friend.  She only stayed at that school for another year or two.  I assume she left it there for one of her friends.

Next, I could not find a purple and/or purple and gold tree.  I looked and looked, but they never did have one.  After looking at many things on Pinterest, I had an idea.  I decided to make my tree out of PVC pipe and I hung it on my door.

My dad helped a lot with sawing the pipes and gluing them together.  It was a little more difficult than I expected.
I spray painted it purple.

Here is a picture with Christmas lights.  Each light has the name of one of my students.  I tried to make the colors random, and then I put them in order by class and then alphabetically.  It was a PAIN!  In the middle of doing it, I told myself to never do that again!!!
It did look cool.



This year I found the shiny purple wrapping paper.  Then I did something that no good person should do.  I bought Christmas-things in October.



For the inside part of my classroom, I use my old 2-3 ft tall fiber optic tree.
 

One kid said, "Well that's a redneck Christmas tree."  : /
Well, can I blame him?
This picture is actually two years old.  This year, I used a different book on the chair.  This time I used a thin, red book.  It was for my Modern Geometry class during my junior year in college.

Eventually, I did find a purple tree.  It's 1-2 ft tall and  I put it on the corner of my desk that is previously occupied by my painted pumpkin.

Broncs are... Broncs Value... Broncs Have...

I like to use half- sheets of 8.5X11 grid paper.

It's usually large enough to fit one word.  (When it's not, then the kids add another paper, or part of another paper to the end.)


The student draws his or her name on the paper.  Then he or she calculates the midpoint of each segment.
The student draws a (pre-approved) word on the paper.  Then he or she calculates the slope of each segment.
The student draws a (pre-approved) word on the paper.  Then he or she calculates the distance of each segment.
The student draws a (pre-approved) word on the paper in block letters.  Then he or she calculates the perimeter and area of each composite figure.




The pre-approved word usually has a theme.  
This time the theme was positive characteristics.

I made a sign for each category.  They said:
Broncs are...
Broncs Value...
Broncs Have...


then I split up the words so they would sound correct grammatically.

I used purple for the backgrounds of my signs because it's one of our school colors.


For this to work, the kids had to follow these guidelines:
*Every letter must have only straight line segments.  No curves!
*Every segment must have a slope that is not zero or undefined.  (No horizontal or vertical lines.)
*Every word must be drawn in something other than pencil.


**Generally, this activity is easier to do with all-capital letters.
**Sometimes letters can be a little tricky to make w/o vertical or horizontal lines.  These can be done by placing the letters at an angle and/or drawing them 'artistically.'

For these projects, the kids have to show work.  
That work must include calculations with the ordered pairs.  (That is the entire point of this project.)  
It has to be organized!

I tried to come up with several, various, long words.  If the kids come up with an alternative, they can use it as long as I approve of it.  I usually go for at least 6 or 7 letters:
For the Characteristics Activity, the list I gave them was:

	ACCURATE		CHARACTER		CREDIBLE		ENDURANCE
	ATTENTIVE		CIVILITY		DARING		ETHICAL
	AUTHENTIC		COURAGE		DECORUM		ETIQUETTE
	BRAVERY		COURTESY		DIGNITY		FAITHFUL
					DISCIPLINE		GENUINE
		GOODNESS
				KINDNESS		RIGHTEOUS
		GRACIOUS
				OBJECTIVE		SINCERE
		HONESTY
				PATIENT		STAMINA
		HONORABLE
				PERSEVERE		TOLERANT
		INTEGRITY
				POLITENESS		VIRTUOUS

I would put Sincere, Credible, or Accurate
 in the Broncs are...  category
I would put Kindness
in the Broncs Value...  category

I could put
Integrity or Decorum
in both the Broncs Have... or Broncs Value...  categories

with several repeat words, that was a good way to decorate



Check out my Thankful Activity.  It's similar, but this time they calculate distance.
Check out my Name Activity.  It's similar, but this time they calculate midpoints. 

We are Thankful for...

I like to use half- sheets of 8.5X11 grid paper.

It's usually large enough to fit one word.  (When it's not, then the kids add another paper, or part of another paper to the end.)



The student draws his or her name on the paper.  Then he or she calculates the midpoint of each segment.
The student draws a (pre-approved) word on the paper.  Then he or she calculates the slope of each segment.
The student draws a (pre-approved) word on the paper.  Then he or she calculates the distance of each segment.
The student draws a (pre-approved) word on the paper in block letters.  Then he or she calculates the perimeter and area of each composite figure.



The pre-approved word usually has a theme.  
This time the theme was things we are thankful for.  
The composite figures happen around January/February, so the theme is things we love.

To help fit the theme, I offer extra credit when certain colors are used.  For the things we love, I recommended that they use red, pink, orange, or purple.  Then I taped them on the wall in a heart design.
I didn't think I would be able to succeed again with a pumpkin shape, so I cheated.  I used my projector to draw a pumpkin shape, and then just put the words in the color-appropriate place.
For the thankful theme, I recommended they use orange, brown, or green.



Some kids used a mixture, but that didn't really help my wall-picture.  Next time I will need to emphasize: orange OR brown OR green!
I did use those words, off to the side.  I didn't get a clear picture of them though.

Last year when I did the Things We Love, there were some repeats, and I left them off. 


I used purple because it's one of our school colors.


For this to work, the kids had to follow these guidelines:
*Every letter must have only straight line segments.  No curves!
*Every segment must have a slope that is not zero or undefined.  (No horizontal or vertical lines.)

**Generally, this activity is easier to do with all-capital letters.
**Sometimes letters can be a little tricky to make w/o vertical or horizontal lines.  These can be done by placing the letters at an angle and/or drawing them 'artistically.'


For these projects, the kids have to show work.  
That work must include calculations with the ordered pairs.  (That is the entire point of this project.)  
It has to be organized!

I tried to come up with several, various, long words.  If the kids come up with an alternative, they can use it as long as I approve of it.  I usually go for at least 6 or 7 letters:
For the Thankful activity, the list I gave them was:

BREATHING				CAMPFIRES				CELLULAR
		ABILITY				FRIENDS
CLOTHING				CHILDREN				EDUCATION
		CHALLENGES				HOLIDAYS
EYESIGHT				FREEDOM				ELECTRICITY
		LEARNING				MOUNTAINS
GROCERIES				OPPORTUNITY				EMPLOYMENT
		READING				SUNSETS
HEARING				RAINBOWS				INTERNET
		SECURITY				SUNSHINE
MEDICINE				AFFECTION				PLUMBING
		SLEEPING				VACATIONS
MILITARY				DEVOTION				SAVINGS
		WISDOM				WEEKENDS
VACCINES				KINDNESS				VEHICLE
		DIVERSITY				LAUGHTER

Check out my Characteristics Activity.  It's similar, but here they calculate slope.
Check out my Name Activity.  It's similar, but here they calculate midpoints.