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