Berry Mass Extension

So to extend on our berry mass findings from yesterday's lesson, today we compared our berries at a 1:1 ratio.

Again, we made predictions as to what we figured would be the heavier of the two and then we started to compare using our balances.

What we found was quite interesting! On a 1:1 comparison, our FRESH berries were the heavier ones this time. The class continues to speculate on why this could be, ie. bigger size of the item being weighed, size of berries within their own group (ie. some strawberries were bigger than others).

We had a lot of fun with these lessons and I loved how the students found ways to extend their learning.  They also enjoyed being able to snack on the rest of the berries (untouched ones of course).

Berry Mass Comparison

We are currently studying mass and all it encompasses. Students have learned to find the mass of various objects and have been comparing items using terms lighter than or heavier than. Upon considering ideas of how to incorprate FNMI content into this unit, I recalled a conversation I'd had with Tammy Taypotat earlier in the school year. When discussing various ideas she has done in the classroom and brainstorming different lesson ideas, she had mentioned finding the mass of berries.

Berries were a food staple for many FNMI groups. They grew in the wild throughout the country and could be harvested for sustenance.  

To incorporate this into the classroom, I decided to have students find the mass of dried berries and their fresh counterparts and then compare them (using terms heavier and lighter).  I was able to find certain dried fruits at Bulk Barn and then hunted down their fresh counterparts at Superstore and Wal-Mart. I was able to find the following berries:

Raspberries

Blueberries

Strawberries

Cranberries

(Warning: dried fruit can be VERY pricey).

To start, students made predictions as to which they thought was heavier for each type of berry: dried or fresh.  Next, we took a 1/2 cup of one type of fresh berry and found its mass using a balance and weights. Once the balance was even, I orally noted the various gram measures we used as students wrote them down on scrap paper and added them together to find the mass.  This was a great way to practice counting on, mental math and counting by 25s (we made math connections to money).

We noted this mass in our chart on the board (see pic below). Next, we found the mass of its dried counterpart and recorded it next to its fresh form.  We then made comparisons based on the masses - ie. Which one was heavier? Lighter?  What was the difference between the masses? 

Overall, students noted from the data collected that the dried forms of fruits weighed more than the fresh.  They further took the lesson to infer why this may be.  Some suggestions were: the fresh fruit didn't fill in the measuring cup (there were some gaps between the berries), there is water and air filling up the fresh berries which may make them lighter, etc.

At the end, students found ways to further extend this lesson:

1) Compare one fresh berry to one dried berry (of the same kind)

2) Soak the dried berries in water to see if they retain the water

3) Weigh dried berries soaked in water to dried berries in regular form (of the same kind) to see if there is a difference in mass

The students really enjoyed this lesson and with their inquiry have managed to extend it into tomorrow's dayplan. :)

Perimeter and Area

I found this neat activity the other day in my hunt for FNMI math material.  In our grade 3 math curriculum linear measurement unit we look at perimeter but not necessarily area.  However, this could be adapted for perimeter and the area portion could be used as an extension activity or for those grades/other curricula that encompass this concept.  Also, the use of the term "Kokum" lends nicely into cultural dialogue of terms for grandmothers and grandfathers worldwide (and can include the various cultures found in our own classrooms).

Again, this activity is from the Saskatchewan Government (alas, the document in whole which I can not seem to find online).  If any of my readers come across such document or know of it's online whereabouts, please let me know as I'd love to direct link it to my website for further acknowledgements.

Host Drum Problem Solving Task

I return to concepts taught in math as the year progresses to ensure student understanding and since math concepts continue even after a unit is "completed".  This ensures that students continually use the skills learned and apply them to various situations so that they become understood.

Last week, students worked on a Host Drum problem solving task that incorporated their knowledge of time and addition.   Each student received a sheet as follows:

(Taken from a unit from Saskatchewan Education)

To prep for the task, we read about host drums and talked about pow-wows.  I never showed a video of one, or even of a portion of pow-wow dancing, which I wish I would have and will definitely do next time. Then we looked at the examples of the host drum programs (group 1 and two) and made observations.  The students observed that there were only 5 different songs but they could be used repeatedly.  So we listed the 5 songs that were used (on the bottom of their sheet).

Next, I gave the students their task: to create a pow-wow program for the host drum for 1 hour.  Considering the information on the sheet was in minutes, they needed to use their knowledge that an hour is 60 minutes to help them (the idea of conversions to similar units).  Then we talked about starting with the grand entry and working from there.  Here are a few examples of the students' work:

 

When they finished one, they were challenged to come up with another program.

We talked about proving that the total was 60 minutes and how to show this.  This student showed it through addition equations with ongoing calculations.  We also noted how groups of 10 were made.  When asked why, this student said it was the easiest way to add and group the numbers.

The students really enjoyed this task and took on the challenge eagerly.  It was also easy to modify for those students who needed by changing the time of the program.  For these students, they made a program for 1/2 hour (30 minutes).

Time & Moons

Within our time unit in math, students study the months of the year, days per month, create their own calendars, answer questions, make comparisons, and more.  We talk about how we use the traditional Gregorian calendar - 12 months in a year with specific days per month.  When looking to incorporate FNMI content into this area of math, I chose to do so with using moon cycles.

Students and I talked about how FNMI groups did not use the calendar we are currently familiar with to tell time as per months, days of the week, etc.  Instead, they used their own methods of time measurement.  One of these was using the moons (new, full, quarter).  Sometimes FNMI would refer to "the next full moon" or "two moons away", etc.  As we discussed this concept, students looked at how moons are represented on the Gregorian calendar and for this we each had our own calendar page (I'm a stickler for keeping old calendars for art and found that they came in super handy for this unit in math as well).

First, we looked at how the moons are represented on a calendar.  Then we noted when a new or full moon was and how this didn't always coincide with the first day of the Gregorian calendar.  Next, we compared how long it was from one moon to the next (ie. full moon to full moon).  For this, we used calendars copied onto legal paper with four months so they could compare and see that moon to moon differed from our traditional "month to month".

Students found that there are 28 or 29 days in between moons.  We then talked about how this was different from the calendar we use today.  It was great to see students make various observations such as it's a shorter time span between moons than months, they start in different places (part of the month, day of the week).  When we discussed why there would be 28 or 29 days in between moons, and not a consistent number, students were quick to note it was because some months had 30 days and others had 31.

We concluded the lesson by reading a tale from Keepers of the Earth, Native Stories and Environmental Activities for Children by Caduto, Michael J. and Bruchac, Joseph.  The tale "How Coyote Was the Moon" talked about how the people needed a moon, because it was so dark, and someone had stolen the previous moon so they were looking for a new one.  Coyote volunteered however his nosiness resulted in him not continuing to be the moon, and another one eventually chosen.   This tale was a great way to bridge the concepts while including literacy into mathematics.  This book also has other tales that work well with various math units.

Resources

I continue to update the Resource List on the side of the blog with digital and online links to information and resources I use in and to create my lessons.  However, I've also found some great print resources that I'd like to share which have ideas for not only math but ELA, science, social studies and arts ed too.

Bentwood Boxes

As I continue on this journey of incorporating FNMI content into my grade 3 math classroom, I find I do a lot of searching and locating information regarding various FN groups in Canada.  Along with my research, I try to find connections between what I am learning and the outcomes my students need to achieve in math.

As we finish up our 3-D object unit, I wanted to find a FNMI lesson that would be beneficial to my students.  To my excitement, I found out about Bentwood Boxes which connected nicely.

Bentwood boxes were cedar boxes made by West Coast FN (ie. such as, but not limited to, Haida and Salish).  They were used for various purposes such as storing food and clothing, as well as ceremonial items.  These boxes were used both in the home and on trips. More information about Bentwood boxes can be found at:

Canadian Museum of History

Working Effectively With Aboriginal Peoples.com

Aboriginal Mathematics K-12 Network

To begin the lesson, I showed students various images of Bentwood boxes and asked them what 3-D object they resembled.  The students quickly showed their knowledge by connecting these to cubes and rectangular prisms.

    

We then discussed what these boxes are, where they originate from and I showed them a map of the West Coast of Canada so they could understand the location.  Geography plays a great understanding in the different FNMI groups in Canada.  Next we brainstormed different uses for these boxes and students elicited wonderful ideas that matched the information I had found, along with many more.

One of the neat things about Bentwood boxes is that the sides are made from one plank of cedar wood.  This was cool as we discussed how the wood was bent after it is steamed, not cut and adhered in a manner we're more accustomed to thinking about.  The students also made connections to other materials used to create structures (science unit) that are able to bend.

I was able to show the students an example of the steps used to create a Bentwood box (see above links) and a quick video via youtube highlighting the steaming and bending process: Making Bentwood Boxes

As we proceeded in the lesson, I then showed the students a net of a cube and some were quickly able to tell me it was a cube.



However, I told them that I did not understand how this was a cube since it was flat (at which point I grabbed a cube and held it to the SmartBoard to show that they were very different).  Using a cube solid (manipulative) students then proved to me how the net and the cube were the same.  Some of their responses / proofs were:
1) the flat squares on the net were the faces of the cube
2) the lines were the edges - and even the ones not touching a face (since an edge is where two faces meet), when we fold the net the edges will meet faces
3) the net needs to be folded to also create vertices

At this point I was completely thrilled at the connections and proofs my students were making.  They were readily using math language and using definitions of terms to show their meaning.  So, when I told them they were making their own version of a Bentwood box (ie. cube) the class response was "Yay!".

Just prior to beginning we noted the carvings on the boxes and discussed how these were special and important to each FN group.  The carvings were representative of their group, culture and things that were important to them.  Therefore, the students needed to draw images (one per face) on their cube net / bentwood box that were important to them.

Needless to say, students learned about Bentwood boxes, made great mathematical connections, communicated ideas, made proofs and incorporated elements of science and arts ed in this lesson.  They did a great job of making some very personal boxes to share with their families.

You can use any printable cube net to make a Bentwood box.  Some great websites I found were:

Wacky Kids

Scholastic

FNMI Structures & 3-D Objects

We've been delving into the world of 2-D shapes and 3-D objects in math as of late.  While it's fun and educational to use our shapes to create various patterns (many lessons based on FNMI culture can derive from patterns), there are also ways to incorporate FNMI content into 3-D objects.

As students have learned the names of objects, they've also begun studying the objects in their world and how they relate or imitate these objects.  For example: a tent is a rectangular prism, dice are cubes, boxes can be cubes and rectangular prisms, a birthday hat is a cone.

Using our knowledge of 3-D objects, students studied various pictures of FNMI structures (which tied in nicely to our science unit on structures) and found 3-D objects within these.

The pictures students looked at were:

 Image courtesy: http://www.fortmcphersontent.com/products/tipis/canvas-tipis/

Image courtesy: http://www.scrapbookoftruth.com/2014/02/10/random-thoughts-igloo/

Image courtesy: http://commons.wikimedia.org/wiki/File:Inukshuk,_Whistler.jpg

The images were all placed in a SmartBoard file (to allow us to write on the images).

At first, students studied the images and discussed with a partner what 3-D objects they found within each structure.  Then as a class, students shared their findings.

Here is what they discovered about FNMI structures and 3-D objects.

What I really loved about this lesson is that students started to really look at different structures and the 3-D objects related in their own worlds.  They then were automatically making comparisons to the FNMI structures.  Many students further questioned other FNMI structures which would lead nicely into an inquiry study.

Small Number, the Salmon Harvest & Division

As we moved from learning about multiplication to division, I wanted to keep as many ties to that unit as possible.  When students make connections between their learning, concepts and ideas it makes it more concrete for them and they're able to create their own understanding with a base schema.

In our multiplication unit, we talked about how salmon is a symbol of persistence and a staple for many First Nations groups (as hunting, fishing and gathering were traditional ways of life for FNMI groups).  As we move into division, I wanted to connect the ideas and theme together as we discuss how division is the opposite of multiplication and related to fact families.  To continue with this theme, from my resources (print and person) I came across this video:

Small Number and the Salmon Harvest:

http://mathcatcher.irmacs.sfu.ca/story/small-number-and-salmon-harvest

In this video, Small Number (a young boy) helps out with the salmon harvest.  He learns many skills and the video shares with the audience how they fish (using nets). In our division unit, we're currently looking at the division strategy sharing.  In using this strategy, students need to understand that they're sharing with a set number of groups and need to find the amount in each group.  The video lends well to this concept as during it, there is reference to sharing fishing (dividing) among the families.

To extend using this video into division concepts, I came up with the following questions for students to work through:

If they caught 25 fish and there were 5 families, how many fish would each family get?

If there were 20 fish caught to be shared with 4 families, how many fish would each family get?

If 14 fish were caught and only 2 families were sharing, how many would each family get?

These problems offered critical thinking skills and offered realistic, FN connected ideas.

Here are a couple of students performing the task:

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