Frieze Designs

In my research into lessons involving FNMI content, I came across Frieze patterns from information in:

http://mathcentral.uregina.ca/RR/database/RR.09.01/mcdonald1/

This article describes Frieze patterns as "patterns or border patterns....commonly found in wallpaper borders, designs on pottery, decorative designs on buildings, needlepoint stitches, ironwork railings and in many other places" and that they're used "in the textiles and clothing of the indigenous peoples of North America."

Upon viewing some of the examples Judy McDonald and Harley Weston included in their article, my eyes drifted to this colourful Frieze pattern:

(Image from McDonald and Weston "Frieze Designs in Indigenous Art")

The pattern is gorgeous and at first I thought to keep it in the back of my mind for our patterning unit.  However, when studying the pattern I found that it would be useful for our multiplication unit too.  In this unit, we ask students to write word problems from a given picture.  Since the concept of multiplication is "equal groups" I figured this pattern would work out well.

So I presented this pattern and background information on what a Frieze pattern was to my students.  Next, the students talked about what was repeating and we made a list of the patterns they found.  Then we discussed various ways we could write multiplication problems from it.  They were quite creative and came up with the following:

Question #1

There are 4 circles.  They are 4 pie shaped pieces in each circle.  How many pie shaped pieces are there altogether?

Question #2

There are 4 circles.  There are 2 yellow pie shaped pieces in each circle.  How many yellow pie shaped pieces are there altogether?

Question #3

There are 5 groups of triangles.  There are 2 triangles in each group.  How many triangles are there altogether?

They also solved the problems they wrote.  What I found interesting was they started extending multiplication word problem writing to other patterns they found - in books, their own clothing, in the school, at home.  It was great to see them take this skill and apply it in other real world settings.

Cree Numbers

One resource that my math coach turned me to in order to help me work towards my goal of incorporating FNMI content in my classroom was Tammy Taypotat, an Educational Psychologist with the Good Spirit School Division No. 204.  Ms. Taypotat has taught in our division for a number of years and had a plethora of great ideas to share.

One idea I gravitated quickly towards is having Cree number words displayed in the classroom.  I already had a traditional number line (numeral, tally mark representation, number word) and thought that this was an easy idea to implement as all I needed to do was add to what I currently had.

When I started researching Cree number words I quickly found it to be a daunting task as there are many different dialects - Plains Cree, Woodland Cree, Swampy Cree.  Since the area in which my students reside is Plains Cree, I decided to adhere to that dialect.  Therefore, I did much cross checking between various resources and came up with a document with Plains Cree number words and symbols for the numerals 1-20.  It is my hope that all the words, spellings, symbols, phonetic symbols are accurate and truly reflect the language of the Plains Cree (to the best of my ability).  If there are any discrepancies, please let me know so I can make the correct amendments.

I have attached the document for those who'd like to use it in their classroom as well.

Plains Cree Numbers

When the students came in and saw the additions to our number line they were very excited and wanted to know how the words are pronounced.  In my research, I found a website where the words are said orally which I knew would be a great resource.

Numbers in Plains Cree #1-49

Every day we're going to count in Plains Cree, starting with 1-5 and building on from there, and will use the above website to guide us towards correct pronunciation.  The symbols in addition to the words are a great example of another way numbers and words can be represented.  I also found it interesting how there are patterns in the Plains Cree numeral words and their corresponding symbols.  I'm looking forward to having students compare these patterns with those of the English language number words.

Factor Fishing

When in Saskatoon a few weeks ago, I picked up a copy of the Saskatoon Star Phoenix and found an article that inspired me.

"Add some culture, subtract the boredom"

 http://www.thestarphoenix.com/life/some+culture+subtract+boredom/9111029/story.html

In this article, math teacher and statistician Stavros Stavrou teaches a concept in the context of fishing.  This made me think that fishing could be used in a variety of ways in the classroom. According to Aboriginal Affairs and Northern Development Canada (http://www.aadnc-aandc.gc.ca/eng/1307460755710/1307460872523#chp1) fishing was an important food resource for First Nation groups in Canada.  So to build upon these two ideas, I figured my students could fish for factors in their multiplication unit.

Prior to starting the activity, we discussed how First Nations hunted, gathered and fished as a way to sustain a living.  Also, that they used all parts of an animal, nothing was wasted.

To make the fish, I used salmon fish clipart and (as grade 3 in Saskatchewan looks at multiplication up to 5x5), assembled packages where there were one 0 and two each of the numerals 1 through 5 labelled on salmon fish cards.

(Salmon is also the symbol of Persistence).

On the backs of each card I fastened a magnet which could then be picked up (reeled in) with natural made fishing rods (wooden dowel, string, magnet).

We start our multiplication unit (focusing on equal groups) with the picture strategy.  So for our activity, students fished for two factors.  They then had to represent their factors with the picture multiplication strategy accurately.  We did this in partners with one person fishing for the factors, and the other using the strategy to find the product. The fisher then checked their partner's work for accuracy.  They then switched who was fishing and repeated the activity.

The students really enjoyed this activity.  It was a great way to meld First Nation cultural awareness, multiplication and fun into one!  We will be using this activity again in the future with other multiplication strategies.  I'd also like to create "product" fish to be used for our division unit.

Counting Sticks

In our math class, I try to incorporate a variety of games where students can use their skills and critical thinking abilities.  In combining this with including FNIM (First Nation, Inuit, Metis) content, my math coach found the following game:

Ahkitaskoomnahmahtowinah - Counting Sticks

This activity lends nicely to the concepts of even/odd numbers, addends to compose a sum, and the overall concept that odd plus even is odd.

For information on the game and how it's played please click on the link above (title of activity).

In my classroom I have a variety of learning needs (which I'm sure is like most classrooms all over the world).  One of the reasons I really liked this activity is that it allows for a change of the amount of sticks you use.  In the original game it suggests 25.  In grade 3 we work on missing addends in sums to 20 so I used 17.  However, I could easily differentiate this for a developing group and we used a sum of 11.  By being able to differentiate, I was able to include all students through a pod setting with success and feelings of accomplishment and understanding on their part.

When we did this activity in each pod, we worked as a whole group.  In the original game it states that students play in two parties but I found that for my purpose it worked better when the students could talk with one another and work together.  Before beginning the game, I also had students tell what an odd/even number is and how they know.  We then made an anchor chart with odd numbers to 20 so they had a visual reference during the activity.

During the activity, when we made various bundles and guessed the missing addends we noted the different combinations on chart paper.   We did this a few times before I asked students what they noticed (what patterns they saw).  Having the visual in front of them was much easier for them to draw conclusions and make a rule (rule: an odd plus an even makes an odd sum).  For those students who needed further prompting, we added (e) and (o) beside numbers to help them find the rule.

It was exciting to see students draw conclusions and note patterns in the addends to compose an odd sum.  With the combinations on chart paper, it also allowed me to add visuals to help in prompting those students who required more (ex. I would add an 'e' over the even numbers and an 'o' over the odd numbers to help in the identification process).

The students quite enjoyed this activity and I found that it lends to many extension activities to further prove the rule, such as:
     1) Do the same activity with an even sum and see if the rule holds true
     2) Do the same activity with a different odd sum to see if the rule holds true for all odd sums

I love activities that have students think critically and draw conclusions but then allow for further studies to prove and reason.  I look forward to trying many more activities along these lines that also bring FNIM content into our classroom.

Talking Stick

Incorporating FNIM content, ideas, methods accurately and appropriately is something I'm working very hard to do in my grade 3 mathematics classroom this year.  One of the first things I've done to work towards achieving this goal is to use a talking stick.

This stick we used was natural and came from a willow tree.

The stick is plain in nature but I know that various talking sticks are available and used in classrooms.  They can have carvings and representations along with feathers, beads, etc.  I learned more about talking sticks and the use of them from speaking with my math coach, our FN coordinator and resourcing http://www.firstpeople.us/FP-Html-Legends/TraditionalTalkingStick-Unknown.html.  A talking stick must be passed in a clockwise manner and only the person holding the stick may speak.  The rest of the members in the circle listen actively and respectfully to the ideas presented.

I used a talking stick at the beginning of each math pod (during a 1 hr lesson - 3 pods at 20 min each) and had students share what they knew about even and odd numbers.  The students were very good at showing respect to the talking circle and use of the stick.  Upon reflection, I don't believe I would use a talking stick for this purpose in a lesson of similarity in the future.  As the students spoke, it occurred to me that the topic didn't necessarily foster participation from each student since the topic was narrow and after one idea was presented, it was difficult for many to build on with other/new ideas.  Also, there were times when I wanted to interject and further prompt students but couldn't.  I will continue to find other ways to use a talking stick in math class along with other subject topics.  Perhaps a whole class situation as opposed to pod work in order to give more time to the activity.  

For more information on Talking Circles: http://firstnationspedagogy.com/talkingcircles.html