An Electronic Scavenger Hunt on the Evergreen Curriculum
and Other Sites to Explore Rich Mathematical Experiences for K-5 Students
Designed by Vi Maeers
This scavenger hunt is intended to do three things: introduce you--very quickly--to the Evergreen Online Curriculum (EC); take you through problems solving at the grade 3 and 5 levels and show you how to use the various components of the EC for problem solving; enable you to explore website resources that can help you select a topic for your next assignment for this class.
Part A: A quick walk-through the EC
Part B: Problem Solving
Go to the "Scope and Sequence" area on Problem Solving. You'll
see it follows much the same format as in the printed guide. Return to "Mathematics: A Curriculum Guide for
the Elementary Level" and click on Grade Three Mathematics and then on #2, Strand: Problem Solving-Understanding.
You'll see arrows at the top of the page and a pull-down menu. What is the purpose of the arrows and the pull-down
menu-check it out? Click on "Bibliography" on the pull-down menu and then click again on the letter "p"-that
will take you to some problem solving resources. Quickly read through the summaries of the 6 titles under "p."
Click on the "Recommended URL Database." Under the search criteria enter mathematics, K to 5 and problems
and click on search. Two links appear. If you enter K-12 how many links appear? _______ Click on the link for "Grade
Five Math Problems." There are some good ideas here for problems for the classroom. Do one of these problems
by yourself or with a friend and share your strategies.
Go to the media link under indexes and see the different media that can be used in conjunction with problem solving.
Find the Grade Five Mathematics Curriculum and go to the problem solving section and again click on "understanding."
The Grade Five section on problem solving-understanding is different in two immediately obvious ways from the Grade
Three. What are these two ways? ________________________________________
In the pull-down menu box click on "problem sets and rubrics." Click on "problem description sheets"
and then on "Dimes and Quarters," "Making Change," and Talking About Shapes" (I'm taking
you to these three problems because at this point these are the only problems with printed rubrics). Check out
these 3 problems. Try to do one of these problems and then compare your answers with those on the rubric (found
at the link: "Grade 5: general rubric for determining achievement levels in problem solving." You need
to scroll down past the general rubric to find specific ones for each of the above 3 problems). Also check out
the "problem solving checklist" which gives students an opportunity for self-assessment. Each problem
has a box asking students to check off their level, if they have completed a self-assessment, if they want this
problem to be placed in their portfolio, and if they want it to go towards their marks. These problems were part
of the 1997 Provincial Learning Assessment in Mathematics (PLAM). These problems, and other performance-based tasks,
are a departure from the traditional pencil and paper tests.
Now let's leave the Sasked site and hunt for problems on-line at other sites. We did leave the Sasked site above
when we visited a link from the URL database. Let's find another way to find good links.
Over the summer we had a summer student evaluate and organize a bunch of math websites that previous groups of
students had discovered. We have some of these sites in an access database at Sasked. Return to the first page
of "Mathematics: A Curriculum Guide for the Elementary Level" and you'll see a flashing "New"
sign beside Math Website Search. You'll notice the U of R logo and you'll find 15 (not 2 sites) if you enter K-5,
problem solving, and all. These are sites that have been evaluated and approved by us, but have not gone through the rigourous Sasked evaluation by three teachers and
approval by the Western Protocol Committee. You may want to visit the evaluation link and read our website evaluation
criteria.
There are some great sites listed here and I would suggest you visit them and get some ideas for problems and/or
puzzles. There is one site that is NOT listed as one of the problem solving links, mainly because it is a mega-link.
Go now to:
http://mathforum.org/~steve/steve/mathpuzzles.html
At the above site you'll find hundreds of websites, some of which may be really good. But remember, many of these
sites will NOT have been evaluated by us or by Sasked, so critically evaluate them before you use them.
You may want to take a few minutes now to look at some of these sites. Please also visit http://mathforum.org/pow/ as it has
problems of the week at all levels.
There is another site to go to now for assistance in finding resources and information about problem solving: http://mathcentral.uregina.ca Click on "Resource Room," then on "Browse our Database," then
click on "elementary," and then click the radio button beside problem solving. [Note: you could have
entered "Problem Solving" in the search box on the home page of Math Central-in the Resource Room, but
you would have got ALL the problem solving resources, not only the elementary ones. Actually, I believe the # of
elementary resources is the same as ALL the resources-for problem solving; this is not true for other strands.]
Please read problem # 3 as it deals with networks-a possible choice of a rich mathematical experience for students.
Part C: Other web resources for your next assignment
You can return to the Elementary Resource Room database and click on any
of the other radio buttons to view our resources for the other strands.
Let's go to the bank of geometry resources. I would like you to check out # 3 and 4 as they are resources submitted
by previous pre-interns. Entry #6 "the 4-Color theorem" is another example of a rich mathematical experience.
There are lots of websites that address the mathematics of maps and map coloring. Try entering "mathematics
and maps" into Google. You get 316 listings. Some of them are excellent resources if you want to do map coloring
and/or the mathematics of maps for your project. I really like the Most Colorful Math of All at http://www.c3.lanl.gov/mega-math/workbk/map/mpbkgd.html It comes with links to map coloring photomasters and a link to the Mega-Math home page. I
also really like Cynthia Lanius' Mathematics of Cartography which can be found at http://math.rice.edu/~lanius/pres/map/
Much of this site's information is perhaps geared to a more advanced audience than K-5 students, but the link to
"Fun Mathematics Lessons" at the bottom of the page will take you to some very different sorts of mathematical
activity, some rich ideas for the classroom. Let's Do Math, Pizza Fractions, Pattern Block Fractions, The Million
Dollar Mission, Power Cards, and Online Geometry all seem to me to be appropriate activities for K-5 students.
Return to the Resource Room, search by keyword area,and enter tessellations in the search box. Entry # 2 was submitted
by a group of pre-interns a few years ago. This resource has been "hit" more times than any of our other
resources and has awarded Math Central the Illuminations Award -see the Site Information link on our home page.
This tessellations resource is truly an outstanding resource and a very popular area of study in elementary mathematics.
Back at the Sasked Math Website database (that we made) at http://www.sasked.gov.sk.ca/~uofred/ try
searching for tessellations under K-5 and geometry.
Now let's see if we can find some other websites that can help you decide on a rich experience that will provide
an interactive environment for your students. Whatever experience you decide on, design, create etc. it really
must involve some aspect of real mathematics that will engage our young learners in some of the mathematical discoveries
in the history of mathematics, it must have a substantive mathematical element and you need to know the mathematics
that your experience is dealing with. The children need to have an interactive experience with this element of
real mathematics; they need to be doing something mathematical-perhaps engaged in mathematical activity similar
to that of our mathematical "ancestors." The websites above and below are links to some of the "big
ideas" in mathematics, but you need to "grasp" the essence of these ideas, make them your own, and
imbed them in an activity that young learners can deal with.
Specific Sites Addressing the Topics Suggested
in Class (but please do not feel limited by these topics).
1. Go to http://camel.math.ca/Education/MallMath/
and you will see our very own Academic Vice President-Katherine
Heinrich and a colleague engaged in a Math in the Mall experience. Read some of the activities and you will find
out about kaleidocycles and hexaflexagons. Also, you may want to visit http://kancrn.kckps.k12.ks.us/rosedale/duncan/Kaleidocycles.html for a mpg and a visual outline of how to make a kaleidocycle. Another site worth
visiting is http://members.tripod.de/jkoeller/kaleidocycles.htm
2. To find out more about Star Balls you should revisit Math Central and enter Star Balls in the search box in
the Resource Room or go to http://mathcentral.uregina.ca/RR/database/RR.09.98/wagner1/starry.html There may be other websites for Star Ball information but so far I have not searched
the web for them.
3. There are many sites that provide information about, pictures of, models of, and activities on the Platonic
Solids. Rather than repeat these sites here please go to http://education.uregina.ca/mathed/elementary/Fall%202001/DevgeomthSS.html and scroll to the last part of this link to find the web resources that I have listed.
If you go nowhere else, please visit this site http://www.korthalsaltes.com/index.html If
you decide to work on the Platonic Solids for your project you should ask yourself and your students why there
are only 5 Platonic Solids, what are the 5 solids; have them assemble them from the nets and have information (at
least in your head) about Plato and about the meaning he attributed to these 5 solids. You could have students
make a Platonic Solid mobile, with the solid names and information about each solid attached to the mobile.
4. For some information about Pentagonal Stars please revisit http://camel.math.ca/Education/MallMath/ and
go to # 4. I was unable to find any other links that elaborated on Pentagonal Stars, but perhaps a library would
be a good source of information. You need to know what they are, how to make them, the mathematics of Pentagonal
Stars, and their importance in the world (I saw some reference to religion, to earth crystals, to Chaos theory,
to wheat field designs, etc.) The questions I would ask are "do they exist in nature, and, if so, under what
conditions or how, where and why do they exist. What are they and (how) are they useful to life on this planet?"
5. Mobius Strips or bands can also be found at the above site, but you'll also find lots of other sites that can
provide you with additional information. You may want to visit a 3-D java viewer site at http://www.frontiernet.net/~imaging/java3dviewer.html and
see an animated mobius strip, or an animated teapot or torus etc-all in framed or solid views.
6. Math problems-I think we dealt sufficiently with problems earlier-see above. I have an additional link for word
problems for all grade levels at http://www.stfx.ca/special/mathproblems/welcome.html
and a link for Famous Problems in the History of Mathematics at http://mathforum.org/isaac/mathhist.html
7. Mathemagic-you'll find hundreds of sites. Start with this one-it sort of sets the stage for further exploration
http://members.aol.com/loosetooth/pi.html
It's about Pi and I know that's a bit above the K-5 level, but it's
a fun site for us to visit. Try this site http://personal.cfw.com/~clayford/index.html
there are a few good ideas here. You may want to explore Chisenbop!!
8. I'm a bit uncertain about letting you work with any form of commercial game in its "off the shelf"
format. You need to think about your game more deeply than simply playing it in the traditional way. For example,
if Abalone if the game of choice, I would expect that you work through several "play to win" strategies
and try to have the children do the same. Is there a "winning formula" and what is the mathematics of
this winning formula?
9. Ideas and information about knots and knot theory can be found at http://www.earlham.edu/~peters/knotlink.htm If
you would like to work on the mathematics of knots and the history and development of knot theory the above site
and this next one http://www.c3.lanl.gov/mega-math/workbk/knot/knot.html have just about everything you need.
10. Network theory, found in the Bridges of Konigsburg can be found at http://faculty.ssu.edu/~kmshanno/math210/kbridge.htm
11. Problems in other bases-do a search for yourself and see what you can come up with.
12. Traditional games-the ones you worked with in class-can be found at Math Central. Enter "Aboriginal"
in the Resource Room search box. You can also go to Karen Arnason's website for other games. I would suggest that
you make a new Traditional game (NOT one in our collection). Maybe you could explore one of the Inuit Games. See
http://www.ahs.uwaterloo.ca/~museum/vexhibit/inuit/english/inuit.html
for some information about Inuit Games.
13. There are many sites that deal with Origami. One that you might find useful is the following http://www.origami.vancouver.bc.ca/ Have
fun.
14. Maybe Fibonacci and the Golden Section are interesting to you. Find out more about the wonderful world of Fibonacci
by visiting the links at this site http://www.mcs.surrey.ac.uk/Personal/R.Knott/Fibonacci/fib.html
15. For information about Tessellations-go to http://mathforum.org/sum95/suzanne/links.html There
are also many many other tessellation sites.
16. The Tower of Hanoi is a very old and very famous puzzle. I will show it to you in class, but see if you can
solve it online. This website will give you that opportunity http://www.sci-ctr.edu.sg/interexh/java/Hanoi/index.html
17. There are some interesting interactive problems at this site http://www.sci-ctr.edu.sg/interexh/interexh.html
(the above one--the Tower of Hanoi-- was one of them). Try some of the others.