GEO - Middle School Geometry Game

All this month I'll be posting games from the Fall 2023 GAMES seminar at GVSU. This senior capstone was begun by Char Beckmann. See many of the games in this YouTube playlist. Many of the games completed in my seminar are in this playlist. In the seminar, we play lots of games and math games, the future teachers make a first video to promote a class math game that already exists, we develop a group game (a monster-themed middle school Desmos escape room and Math Heads, a number mystery game), and they develop a game of their own.

Leah Barber selected Greater Than for her first video, an integer multiplication game. (Handout)

Leah's original math game is a great spin on Uno called Geo. Cards & Handout. What follows is Leah's explanation of the game and thoughts on why play games in math class.

How Geo Came To Be

My idea of Geo came from Professor Golden mentioning Uno during one of our classes. I thought that Uno already included a lot of good components of a math game. This included number recognition, being able to categorize and identify different elements of a category, problem solving, catch-up factor, surprise elements,  etc. Since Uno already had strong components of a math game I decided to create a game that was based on it. At the start I was thinking about doing a game that had to do with geometry so I began thinking of ways students could categorize shapes. Initially I didn’t know if I wanted students to create their own connections between different shapes, so I considered doing a Guess Who style game. However, after trying out a draft version of it I thought Geo would not only be less complicated but it would still offer students the opportunity to practice identifying shapes based on properties and computing area. From here I decided that instead of colors and numbers, like regular Uno, the two categories would be shape and area. Then I went through and made a rough draft of the game that iterated through many revisions until I was happy with its final form. Throughout these iterations I changed things like what the special action cards would be, what shapes would be included, how many cards would be included, what the shapes looked like, and what information I would include on the individual shape cards. 

Why Teachers Should Play GEO:

There are many reasons why teachers should play Geo with their students. Geo covers different Michigan Math Standards such as: CCSM. 6G.1: Find the area of right triangles, other triangles, special quadrilaterals, and polygons and CCSM. 5G: Classify two-dimensional figures into categories based on their properties. Beyond letting students practice finding the area of different polygons and identifying shapes by their properties, Geo helps students practice integer multiplication, reason mathematically, and build problem solving skills. Due to Geo being a competitive game, students often become engaged doing math, checking the work of other students, and reasoning mathematically in order to win. This is another reason why teachers should play Geo with their students. Geo allows students to engage in math in a fun, interactive way. Many learners have anxiety around math or think that it is boring, hard, irrelevant, etc. Geo is a way to get learners engaged and have fun while doing math. 

Other Uses: 

The materials of Geo could be used outside of playing the game. Teachers could use the cards to create a memory style game where students try to match different areas or shapes. Other uses include going through the cards as examples of computing areas with students. Teachers could also play a Polygon Capture style game where students identify all the shapes they can that fit under the different command cards. Following playing Geo teachers could have a discussion with students about what they noticed or wondered when playing the game. This could start a good dialogue about different shape properties, how different shapes are related or different, definitions of shapes, etc. They could also have students discuss strategies and problem solving skills they used to try to win. 

Why Play Math Games? 

There are many reasons to play games in the math classroom. To start, math games allow students to engage in mathematics in a fun, interactive way. Students often think that math is boring, too analytical, irrelevant, etc. By playing games in the classroom students can experience math in a way that it often isn't presented to them. This can also dispel anxieties many students experience with math. Due to previous bad experiences with math, whether it be a harsh teacher, tough material, or overwhelming course load, students can develop anxiety surrounding math. This can also affect how students think of themselves. Bad experiences with math that cause students to do poorly can lead to them thinking they are dumb or not a “math person”. By involving games into lessons students can create positive experiences with math and start to dispel any anxiety or negative thoughts surrounding math.

Math games also allow students multiple entry points to engage in math. Oftentimes this idea of not being a “math person” is due to inaccessible lessons. By including a math game in a lesson you can create many opportunities for students to participate in math. A good math game includes some aspect of luck, strategy, catch up, or surprise that allow students who are struggling to still succeed. By creating accessible activities for students they can start to think of themselves as someone who is capable of doing math. 

Getting students to reason and express themselves mathematically can be challenging. Often students don’t want to participate in discussions in math class due to a multitude of reasons. Including a math game however is a great way to get students talking about math. Due to the competitive nature of games students are more likely to reason, argue, make conjectures, and express mathematical ideas in order to win. This creates a great dialogue where students can think through material covered in class together and come to conclusions on their own. By doing this students will continue to grow their self concept as a mathematician and be able to better communicate mathematical ideas. Math games also help students build problem solving skills. A good math game has players interacting with each other and constantly trying to figure out their next move. As stated before a good math game also includes strategy. These elements allow students to build their problem solving skills as they identify what they need to do to win, how they are going to do that, executing their plan, assessing how it worked, and what they will do next time. 

Lastly, including math games in the classroom is a great idea because it is a great way to introduce, explore, or practice mathematical concepts. Teachers or parents may feel that including a game in a lesson will distract students from their learning. This however is not the case. Math games are not something that is just filler. Instead math games are great ways to introduce new concepts by allowing students to get familiar or explore with new ideas in a low stakes, fun environment. Math games can also be used to help students review a concept they already learned by applying their knowledge in a new way. 

Angle of Coincidence

Quick idea for a math game on angles, hopefully I get to try it this week.

Materials: deck of angle vocabulary cards, blank paper, ruler, pens, protractor.

Set up: (make if necessary and) shuffle angle vocabulary cards.

Draw phase: teams take turns

• add a point, and 
• connect to one, two or three other points from your new point.
• each team adds right angle mark or congruent length if that's their intent
• both teams make 5 points.

An example:

Play phase: on your team's turn

• roll a die (that's this turn's points)
• flip a card. Claim an angle or a set of angles that fit the condition. You can only claim unused angles.
• score that many points for each angle you claimed that fits the condition.
• check: if you can't find one or find one mistakenly, the other team can catch you for 2 points per angle.
• game is to 20 points, run out of cards, or all angles are claimed.

 Example: red scored an acute, a right and a pair of vertical angles. Green scored a pair of congruent angles and a set of supplementary angles.

Design reflection:
Could use a context, but the only thing that comes to mind is shooting metaphors. Maybe bird watching? You know how the kids love bird watching!

Foxtrot, of course, has angle games covered.
They even get triggy with it.

Lots of nice bits here, I hope. Constructing the board, using notation, eventually even making the cards. Some classic interaction (catch the opponents out in a mistake), but could be more. The thing I like the best is how the game will change in between playing. What angles were you unable to find, what combinations can you make, etc.

Possible starting card set:

• an acute angle
• a right angle
• an obtuse angle
• a pair of congruent angles
• a set of congruent angles that are not right angles
• a pair of complementary angles
• a pair of adjacent angles
• a pair of cute adjacent angles
• a pair of acute obtuse angles
• a pair of vertical angles 
• a set of angles that add to 180 degrees
• a set of angles that 
• a pair of corresponding angles
• a set of interior angles
• a pair of congruent exterior angles
• a pair of angles that add to 180 degrees
• a straight angle

What else would you add? I'd want a set of cards a playing field to start, then introduce the making aspects when the students know how to play. Warning: only roughing out playtesting so far.

What do you think?

Geometric Landscape

I got shifted from my usual (of late) secondary student teacher supervision to elementary preservice teacher prep this fall. (We have an unusually low number of student teachers this fall.) I love this teaching, too, so it will be a treat. Pam Wells, David Coffey and Jon Hasenbank were already coplanning a revision to the course, so it gave me a chance to dive in and collaborate. And gave me my first chance to look in detail at the K-5 Geometry common core. So I thought I'd share what I saw:

First I collated them, then tried to look for a way to organize them more sensibly. They are pretty unevenly written. From vague generalities to hyper-specifics. The best common threads I saw were the action verbs about what the students were supposed to be able to do.

Our assignment was to sort them into a concept map or landscape of learning.  I'm very fond of the landscape of learning model for teachers. I first saw the idea in Fosnot and Dolk.  In addition to those Young Mathematicians at Work books, they are involved in the great Mathematics in the City project and the excellent curriculum Contexts for Learning Mathematics. Here's a sample chapter from the YMAW: Algebra book. This sample chapter from Contexts for Learning has a Multiplication Landscape of Learning (page 16).

A landscape emphasizes the many paths through understanding that students might take, and are loosely organized from bottom to top in terms of students development. (Read also Christopher Danielson on landscapes. Here's a landscape from years ago I developed with novice teachers for teaching money.)

Here's what I came up with. I'd love feedback on ordering from top to bottom, what you would add, and classification into strategies, concepts and models.

(Here it is as a PDF.)

There's things that are quite sophisticated present (hierarchical structuring, Van Hiele level 2 and level 3 reasoning) and very accessible things missing (motions, congruence and similarity). Even though they are not included, of course, you can still teach them; use those ideas to help students access the ideas that are required.

As I develop and revise activities for the course I'll be sure to share them. Again, if you have feedback about the landscape, shout it out!

Angle Acquisition

Quick game idea. I've had a few bustling around, and I've got to get started writing them down.

Observing student teachers is a great job. I get to see and have in depth teaching discussions with lots of hard-working, talented teachers.  And see a broad range of content. We use a coaching model, which helps these be positive exchanges and ratchet up the interest level of the dialogue.

I was observing Terry Austen (the class he writes about here) and realized that once students knew the terminology well for parallel lines they were correctly identifying and applying the relevant properties.

That gave me the idea for a game. I thought it would be neat if students used the terminology to capture points. My first idea was to have a parallel line puzzle - I like those as practice, too - and have the players build it and then take the pieces. That's a lot of set up, though, so I decided on cards to make for less preparation. There's name cards to cut out, still.



Let me know what you think. I'll try it out with the PSTs this semester and post an update.

Watermelon: any questions?

Dan Meyer, purveyor of pedagogical principles and master of mathematical memes, has popularized or coined the idea of #anyqs on twitter.  A math teacher will post a photo (or video) and ask, "Any Questions?"

Here's my photos:

Post questions in the comments or I'll record any twitter questions I see.

Who Are the New Teachers?

Guest post today from one of our student teachers from this past semester.  Sarah Cavazos will be student teaching in Fennville, MI this fall and is - to steal a phrase from Sir Ken Robinson - exceptional but not an exception.  She is bright, dedicated and passionate about teaching.  I find that many of our novice teachers have much in common with her.  This past semester I got to see her try a game of her own design in a classroom that had not done much of that, and adjust it on the fly to improve both gameplay and better address learning outcomes.  Then she gave a terrific Little Big at the end of the semester about teaching all students.



Triangle Rummy

Object of Game: Obtain a set containing the picture, the name and the definition of the same triangle.

Triangle Rummy is a game made for two to four players that contains 24 cards (7 pictures, 7 names, 7 definitions and 3 Free cards). There are 7 different triangles in the deck of cards, each demonstrated by a picture, a name and a definition. There are also three Free cards (Free Picture, Free Name and Free Definition).

To start the game, the dealer deals out three cards to each player and places the rest of the deck face down between the tables. The youngest play starts by taking the top card from the deck. In order to keep three cards in their deck, the player must discard one of the cards in their hand face up next to the facedown pile. The player to the left can chose to take the face up card in the discard pile or choose to take a chance and take the next card in the discard pile. In order to win, a player must obtain the same triangle demonstrated by three different cards.

If any player obtains a Free card, they can choose to use that card in place of a triangle name, picture or definition depending on the name of the card. For example, say a player had the picture of an isosceles right triangle and the name of the isosceles right triangle and then obtained the Free Definition card. In order to win the game, the player must say the definition of an isosceles right triangle. If the Free Picture card was played, the player must draw the correct picture as well as have the matching name and definition cards. If the Free Name card was drawn, the player must name the correct triangle and have the matching definition and picture cards.


The Unreachables






Photocredit: qthomasbower @ Flickr

Change the Channel

Yeah! The K-8 geometry video is ready for release! The students did a great job getting footage, and had lots of creative ideas that used their talents. I hope you enjoy it!  (The students would love it if you share the link.)

The video started back at the midsemester when students at our school were making a lipdub.  During my class.  "Can we go?" (GVSU lipdub - came out pretty well.)

"Not now - you had to be involved before."

"What's a lipdub?"

So I showed them what I consider the classic of the genre, Shorewood High School's reverse lipdub.  We were just starting our unit on teaching (following doing, preceding learning).  So we talked about how many teachers find it hard to get students to do any work, and yet here's a whole school working their butts off to make a video.  They had a great discussion about it, bringing up choice, student interest, engagement and other factors.  Then... "can we make one?"

Any reasonably bright teacher would have seen that coming, but not me.  "I'll think about it."

Starting our last unit, I brought it up.  If we're going to do it, it's time.  Discussion led them to believe that the reverse lipdub was right out, followed shortly by a lipdub.  Some students were really into the idea, most were in favor, and a few were dead against it.  There's a fair number of choice workshops in my courses, and I said most of the prep work would be choice.  They wouldn't be graded on the success or not.  The class voted on it with most in favor.  I started freaking out.  It was worth doing to me because:

• Student interest was high, 
• The idea of how to capture and communicate math is relevant to a math ed class,
• By the end of the semester it could be connected to review, and
• The preservice teachers wanted to be able to show it to their students to answer why they should be engaged.

But as the last couple weeks went by, only a few students were contributing.  (We had a google doc for students to add their ideas and development to.) My freak out got freakier.  Was it even going to be worth trying?  Part of this was also I wanted them to see a teacher giving something a go, taking a risk.  That's better if I'm uncomfortable, right?

We used our last class period to do the filming.  One of the cameras failed completely.  I just wheeled in all the manipulatives with which they had had the most fun.  Objective: get some good footage.

One student had written the Math, Math, Baby rap, and found someone to rap, so they started choreographing it.  Other students got building and drawing.  One student had come up with an I Love Charts style demonstration (on Jeggings, which you can buy but she proves do not exist), and another was ready to demonstrate our amazing rubber band enlarger.  The atmosphere got charged and they really got into the spirit.  In hindsight, we should have gotten this footage earlier, and then students could film and add to it.  Ultimately I had to do the first pass editing, but it was inspiring to do it because they got such good footage.  The Geometry song came from me noticing that it would fit to Adam Sandler's Hanukkah song, the guitarist learning it in 5 minutes from youtube, and the singer coming up with the lyrics (with some crowdsourcing) on the spot.

Even if there was no video result, I would have been happy to see the students so engaged in making math visible and engaging.  But it's better with the video!

Resources: Jamendo was a great place to find cc 3.0 music, and I think the songs from Antony Raijekov (jazz) and Josh Woodward (pop/folk) really help make it. They're not math songs, but nobody's perfect.

Glide Reflection

That's my attempt at a Glide Reflection Frieze.

This week my K-8 students were working on motions again.  Using the Geogebra activities at Motion Sketches and More Motion Sketches.  For K-8, there's really not a need for glide reflections because they're usually not a part of the curriculum.

This doesn't fit with Euclid's vision of motions, which was strongly tied to congruence.  Any two objects are congruent if and only if there is a motion from one on to the other.  (Aka rigid motion or isometry or Euclidean transformation...)  This requires four motions, not just three.  But a glide reflection is just a slide and a flip, you may say, we don't need it.  Well all the motions can be made from just reflections, but we still teach turns and slides.

But I've been stumped as to a good way to present these glide reflections.  Students can recognize them by a process of elimination and students can make a motion that is a glide reflection.  The next level of knowing a motion is to be able to specify it.  Students are good at finding lines of reflection, and can specify direction and distance for a translation.  It is difficult for many/most to find the center of a rotation, without being told.  They can do it in a dynamic environment (cf. MotionControl, a geogebra webpage) but it is difficult for them to construct.  The first guess seems to be connecting corresponding points and trying where the lines cross.  (Which doesn't work.)  So it's really hard to get students to know how to specify a glide reflection.  Mathematicians usually describe a glide reflection with a vector and a point or position of that vector.  The vector indicates the direction and distance of the slide, and the line containing the vector is the line of reflection.

This sketch is my attempt at a glide reflection sketch - the goal was to create an environment where students might be able to notice things that would lead them to construct the idea.  I would love it, if you try it out, to get feedback about ways to make the sketch more supportive.  Thanks!

As a webpage or geogebra sketch.

Preassessment, Part II

So I asked my teacher assistants about their dispositions towards growth, because that makes an even bigger difference now that they're trying to help others learn.  My geometry students I asked about... geometry.  It has a benefit of starting to communicate what is in K-8 geometry and it familiarized them with Michigan's standards. (Which were all important up until the common core.  They're still close since we were an Achieve state.)

But instead of quizzing them on content that they've mostly had at some point, I want to know more about how they experience the problems.  (I do peek at their answers, of course.  Data is good.)  In particular, if the answer was available by recall, by one or two steps,  required more thought than that, or if they do not know how to begin the problem, or cannot answer.  I feel like that moves it away from feeling like a quiz, and the results have felt more honest since I started polling for this kind of information.

Here's the assessment and results.  The questions are mostly mild modifications of released items and sample practice items for the big state assessment.



322 Pre Assessment

The lack of comfort with unit conversion and the metric system is quite typical, as is the challenge of recalling and applying formulas.  All of these students have had our course for all elementary teachers, and are typically quite sound on most of the content.  It's quite striking for me that even math majors have these issues.  What chance does a typical student have?  A challenged student?

At the end of the content, I ask them what questions this raised for them about teaching.  Bold and italics are my categorization of their responses.

Questions on teaching K-8 Geometry
Big Teaching Questions:

• What should the teacher be doing?  How do we find ways of teaching that creative, engaging and instructive? Where do we find the best ideas for lesson plans? How can we use the standards to help plan a fun lesson?
• What should students be learning? What exercises lead to deeper understanding?  How can we be sure our students understand vs performing procedures?
• How much time do you spend on a topic? How do you teach everything in a year? What do I do when one or two students don’t understand – do I continue or stop for them? How do you teach so everyone is on the same level?
• How much work should be shown on each problem by students? (Different at different grade levels?) Should it be shown or mandatory?
• How to introduce a brand new topic?
• Are students allowed to use calculators? What tools can they use on assessments?

Students:

• How do teachers organize material to make it easier for students?
• What is their vocabulary? How do we take that into consideration? How do we teach the language?
• How will I teach to students with different learning styles?  How do we explain well enough for all students to understand?
• What do students find most engaging?
• What variety of solutions do students come up with?

Content Specific:

• How can I apply this stuff to life?
• How does it [all this content?] all fit together?
• What geometry concept is the most difficult for students?  What strategies do we teach to solve geometry problems? How do children do these when I used later knowledge?
• How much geometry is there in the younger grades?
• Is measurement hard for students?
• How to teach formulas without just memorizing? Are there other techniques besides formulas for volume, etc? How do you break formulas down? How do you help kids memorize them?
• How do you teach conversions so students can remember?
• Quite Specific:  How do you teach to estimate? How do you teach congruence?  Do students use pi=3.14 or do they need to know more?  How do you find areas of arced shapes?

I'd be interested in ways you can think of making the assessment better, other data I could collect, or what you noticed about the results.

Pi in June

In honor of 2pi day (June 28th)...

From the awesome Dinosaur Comics, of course.

Why celebrate half the holiday?  Get the whole circle!  That old pi day is for squares.  Er, semicircles, at least.

Seriously, we did this activity in the preservice elementary class and I thought I'd share.  It culminates in the usual measure a bunch of circles activity, but tries to motivate it.  Sure it's amazing that all those ratios are close, but why would you do it in the first place?  And why are they all the same anyway?  For me the answer is similarity.  This activity was motivated by my students wanting to know more about pi, as it came up when doing volume of solids (someone remembered a formula), and that got people wondering.  In addition, our geometry class comes before our number class, and lots of students had said that fractions were what was most confusing.  And pi practically lives in ratio city.

Similarity

Two objects are similar in geometry if one is an enlargement of the other.  Mathematicians often use ratios to investigate them.

Consider a 2x3 rectangle.  A 4x6 rectangle is an enlargement.  But a 4x5 rectangle is not.  Can you tell by looking?  Describe what you see.


People discussed how the 4x5 should be similar because its 2 wider and 2 longer, but in the 4x6, which looks the same, you can see 4 or the original rectangle.


What ratios can you make with the two similar rectangles that are the same?

Students made both 2/3 to 4/6 and 2/4 to 3/6.


If you wanted to make a rectangle that was similar and 5 squares wide, how long should it be?  Can you prove your answer is right?

Some students set up a proportion and solved with cross multiplying... although they confessed that they didn't know why cross multiplication worked.  One student saw 5 as 2 + 2 + half a 2, and calculated 3 times 2.5.  We talked about how that was excellent proportional thinking because instead of 2+2+1, she relatedit back to the original as half of 2.  I showed how in the picture you could see the 7 as 2.5 of the 3's, or 3+3+half of 3.

A 24x36 poster is supposed to be an enlargement of an 18 x 27 poster.  Is that possible or not?  Explain?

Saw quickly with ratios.

Find the lengths of the diagonal of each poster using the Pythagorean Theorem. 

Refresh, connect question.

Sum up what you see about ratios and enlargements/similarity:

Jotted down and discussed at their tables.  Enlargement and proportional were heard in a lot of the conversations.

Common photograph sizes are 3x5, 4x6, 5x7, 8x10, 11x14 and 16x20 and 20x30.  Sketch, outline or shade in the ones you can on graph paper.  Which are similar?  Which are closest to similar?


The sketched them separately, so I did a nested version on the board to show another way.  (Often a student will have done it that way.)


Most cameras record in a ratio of 3:2, movie camcorders in 4:3 and hi-def in 16:9.  How do these compare to common print sizes?  What sizes would you use for your regular prints and for an enlargement?

General agreement on the 4x6.



Circular Arguments

Looking at these circles, they look pretty similar in the usual English sense.  Are they similar in the mathematical sense?  How do you know?



This was an unexpectedly interesting discussion.  Most people thought yes, they are all similar,  and then one student made them hesitate.  That led to proportional talk and someone brought ovals into it.  I asked if people knoew what made a circle a circle and they didn't.  They discussed how the only things you could measure are the radius/diameter or the circumference.


Give three different pairs of similar rectangles.  Compute the ratios of their perimeter to their longest side.  What do you notice?

Students saw the constant ratios quickly when they shared examples.  One student made the jump to the idea of scale.  Pretty cool.

What might that mean about circles?  Give your reasons.  (This is basically asking for an educated guess.)

Time was tight, so I was a bit leading here.  What ratio would the rectangle example be like for circles?  "Circumference to radius."  So if circles are all similar... "Then the ratios should be the same."


Divide and Conquer

•    Data collection:  in your group measure the circumference and diameter of at least 10 different circles. (details to follow)
•    Add your data to the class stem and leaf.
•    Which is the best choice for typical (mean, median, mode) and why?

 We discussed how to measure diameter and circumference, and agreed on precision.  (Two decimal places for the ratio.)  We got over 50 data points, and it made a pretty nice bell curve between 2.8 and 3.8.  There were two measurements of 6.00, but she realized she had divided by the radius.


The mode was 3.20 (5) followed by 3.18 (4).  The median was 3.19.  The mean about 3.22.  Curiously, the majority of students felt that the spread was too big to be explained by measurement error, so circles must not all be similar!  I did let them know that they were, but it would take a more theoretical argument to prove it to them.

All in all it felt much more contextual to start with similarity, and students made a lot of sense about why pi might have been discovered.

The activity sheets are below.  But also be sure to check the comments, where Alexander Bogomolny has a couple of very relevant links about the idea of measuring one circle as accurately as possible.
Similar to Circles

More Motion Sketches

These sketches are to investigate the composition of motions, starting with reflections.  For a schema activation, I asked my preservice teachers to think about compositions.

Schema Activation:  What happens when you do two of a motion?  (Same type, not necessarily the same motion.)  Please guess if you don’t know.

Motions	Result-type	Know/Guess?
Translation then a translation		K/G
Rotation then a rotation		K/G
Reflection then a reflection		K/G
Glide reflection then a glide reflection		K/G

This brings up the idea of orientation both in terms of turning and in terms of face-up/face-down.

For a focus we have the following:
Focus:  Today we’re just going to concentrate on reflections and their compositions.  We have three different sketches to consider, and will also consider the questions that could be asked about each.  A composition of motions is when you make one movement and then another.  The combination is still a motion, as the original and image are still congruent.

We're also going to consider using questions to move us forward.  The types of questions described by literacy instructors are:

1. Literal - factual answer available or quickly available by recall, or can be found directly in the text.
2. Application - answer found by applying known method or looking up with slight modification.  The method of getting the answer is known.
3. Inference - answer requires prediction or extension from known information.  Can be an outright prediction or come from reading between the lines.
4. Analysis/synthesis - answer requires combination or deduction from other known information, possibly requiring a method not currently known by the respondent.

In the three sketches, the students are asked to take more and more responsibility for the questions they are answering.

Activity:

  Two Reflecting Lines:  webpage or geogebra file 

  Two Skew Lines:  webpage or geogebra file

   Two Parallel Lines:  webpage or geogebra file

We discussed these sketches together.  They asked about finding the center of rotation and saw a neat connection with the reflecting lines.  They also saw a neat connection between finding the center of a rotation and finding the center of a circle, but couldn't remember or figure out how.  They found a cool relationship between the direction and distance between parallel lines and the resulting direction and distance of the translation. 

Reflection:  What did you do during this workshop?  So what did you learn?  Now what would you want to consider next about motions or questioning?

Bonus: (or... extension)

Two Glide Reflections: webpage or geogebra file







Coming Soon:

• a tale of two lessons - why can't everything work?
• Sue's MathMama Dialogue:  what's wrong with math education?

Math in Action 2010

Grand Valley State University sponsors a terrific little math conference each year called Math in Action.  I think started by Jan Shroyer back in the whereupon.  It has 30ish workshops for K-12 math teachers, mostly very practical.

I'm hosting 6 wonderful preservice teachers presenting geometry games for K-8 teachers, so I'm posting the electronic versions here for people to be able to download.  If you were a participant and wanted a Word file to edit instead of a pdf, just email me.  The address is available on my workpage, linked on the right.

Anne Harkema: Rope Charades
Lauren McKee: Quadrilateral Concentration and the required Quadrilateral Cards
Emily Trybus: Area Block (link to a previous post)  
Rebecca Sochacki and Brynne O’Connell: Polygon Capture
Jill Dzierwa: Triangle Detective (link to a previous post)

As a bonus, here are the two bonus games from the Quadrilateral Concentration sheet.  Both are other uses of the Quadrilateral Cards.  Not included here is Quadrilateral Euchre, which is Euchre for a partially ordered card set.  Verrrry geeky in a midwest sort of way.

Quadrilateral Go Fish

Materials:  Deck of Quadrilateral cards. Best with 3-5 players.

Setup:  Deal 5 cards to each player.  Put the rest face down in the middle, either in a neat stack, or mixed up in a big pond.

Gameplay:  Start to the left of the dealer.  On a player’s turn they can ask a particular player for a specific property.  For example:  “Do you have a shape with opposite angles congruent?”  You can not ask for a shape by name.  (“Do you have a rectangle?”)  If the player has a card like that, they have to give it over.  If they have more than one, they get to choose which card to give away.  If you have a matched pair of the same type, you can play them down. 

Winner:  First winner is the first player to go out.  Second winner is the player with the most pairs.

Variations:
•    Instead of asking by properties, ask by name.
•    Start with 7 cards.
•    Allow players to play cards on other people’s pairs.  (If you have a pair of rectangles I can play a rectangle.)

Quadrilateral Guess Who

Materials:  Quadrilateral card deck.  2 players.

Setup:  Sort the quads by type.  Each player puts one quadrilateral of each type face up in front of them, and the others go face down in the middle.  Each player draws a card from the middle and keeps it hidden from the other player.

Gameplay:  On your turn you can ask one question about the other player’s hidden quadrilateral.  That player answers yes or no.  Turn face down the quads you have that don’t match.

Winner:  first player to guess the other player’s card.