Saturday, February 11, 2017

Constructing 3 Dimensional Figures

 
In geometry, 3 dimensional figures is one of those areas of math that is a lot of fun to teach, but can be tricky for kids who are usually great at math!  Instead of mathematical reasoning, it involves more spatial awareness, and the ability to mentally turn shapes around.  As a result, you may find some kids who are not used to coping with frustration in math class suddenly feeling overwhelmed.  The upside is that some kids who feel like they are not good at math are suddenly your helpers.  Use this as an opportunity to teach that no one is good at everything, but everyone is good at something! 

Folding up nets for 3 dimensional figures

To foster cooperation and appreciation for others' unique talents, I like to partner students up to complete sets of 3D models.  There are two activities that help kids with different objectives for 3 dimensional figures.

The first activity involves nets.  These are great for helping kids see all the faces in a model at a glance.  Students can count the faces more easily on a flattened net than on the drawing in their workbook or test. 

 

Tips for folding and taping our 3 dimensional figures

Models of 3 dimensional figures including prisms and pyramids
When preparing materials for this activity, consider the needs of your class.  The thicker the paper, (cardstock, coverstock, 32 pound paper, or copy paper) the harder it is for some students to cut and fold clean creases.  I find it's more difficult than it used to be, since younger kids have more screen time and less color/cutting/fine motor time.  On the other hand, once the creases are in place, it's easier to tape the thicker the paper.  If you spread this project over two days (one cutting/folding and the other taping/counting) consider if and when you will have extra hands in the class to help out.   

Also consider whether or not your shapes will have "flaps" for taping.  For some kids, it's an extra folding step, which is a disadvantage.  But again, when it comes to taping, it can be helpful.  My advice is to use nets with flaps because you can always cut them off to differentiate for some kids.  
 
Once the folding and taping is complete, further students learning by counting the faces AGAIN.  This can be challenging for students because there's no obvious starting or stopping point, so it's easy to lose count.  Model the strategy of drawing a dot on each face to help keep track of what's been counted.

Another activity that is always a hit is building models with toothpicks and gum drops (or marshmallows).  This activity helps students count the edges and points in 3 dimensional figures.  I would NOT have students count the faces on these models, since they are "empty." 

 

Tips for building our 3 dimensional figures


Before tackling this challenge, I teach students the difference between prisms and pyramids. 
A prism can start with any 2D shape for a base.  Next, build up with vertical toothpicks.  Put gumdrops on the top of each, and connect the top gumdrops so there is a face with an identical shape and size as the base.  The resulting sides are squares.  Explain to students that if they had longer toothpicks for the sides, those faces would have been rectangles instead of squares, and it's a prism either way.

A pyramid, like prisms, can start with any 2D shape for a base.  However, instead of building up with vertical toothpicks, tilt them slightly toward the center.  Those toothpicks need to come together in the center to be joined by a single gumdrop (or marshmallow).  The top center vertex is the defining quality of a pyramid.  Notice that the sides are all triangles.   

The kids will have a blast "playing with gumdrops" during this math lesson and get a better grasp of them at the same time.  Then, once your structures are complete, if you need homework pages or written assessments, check out my 3D figures pages

As an enrichment activity, students can try creating shapes with all triangle or all pentagon faces, similar to the nets for dodecahedrons or octahedrons, tetrahedrons.  Just be aware these will require an abundance of materials! 


 



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Saturday, January 28, 2017

Southeast Region Landforms Art


I've already talked about how I introduce students to the history, natural resources, and products of a region. Today I'm going to talk about our fourth concept: Landforms.

We start discussing Southwest region landforms the same way as we did with our other concepts, with a concept map.

 

Concept Maps

 

Then just as before, we read the text with our "lens" of finding landforms.

However this time, I urge students to spend more time looking at the text features rather than reading every single paragraph over again.

For one thing, the maps are going to give a lot of information.  Additionally, the headings are going to help us remember what the sections are about.  A heading that reads, "A proud people" is probably not going to have as much information about Southwest region landforms as a heading that reads, "A lay of the land."

We do play our "Beat the Teacher" review game that I described in an earlier post to emphasize the key terms I want students to know for the test.  And when it comes to the region we're familiar with, here in the Northeast, this is as far as I go.  But today I want to skip ahead a few months to talk about what happens when we cover terrain that is unfamiliar to students.  Growing up in a city in Massachusetts, my students are not familiar with Southwest region landforms like canyons, mesas, or plateaus.  So to help these terms stick and give students the "other worldly-ness" feeling of a new landscape, we make art!

 

Southwest Region Landforms Art

 

This art project is one of the highlights of our Southeast Region Unit. I've tried a variety of media to create this project, but the key is always holding the page lengthwise, hand drawing a straight line, drawing the shapes, then cutting along that single, jagged line.  This produces TWO "jigsaws" and helps students see the inverse relationship between the canyons and plateaus, valleys and mountains.  This will tie in with our science unit on weathering later on, but that's a blog post for another time.

Southwest region landforms art with limited materialsOne method for creating our landscapes with the Southwest region landforms is to prepare the page BEFORE drawing out the shapes.  I provide thinly cut strips of paper (think 1/8 inch) for students to glue in rows.  They draw on the back and once cut, they glue it onto blue paper for a sky color.


The advantages of this method are easily accessible materials as well as opening the door to discussions of visible layers of sedimentary rock (and more science connections).


The major disadvantage to this project is that for some students, cutting through two layers of construction paper and glue is an arduous task, especially when they have to cut along that whole line with no natural breaks.


Southwest region landforms art with pastelsAnother method is to use pastels.  First, rub the lightest color on the jigsaw.  Hold it firmly against the background and rub UPWARDS.


What happens is the colored pastel dust you brushed up becomes the sky, and the area that the jigsaw was covering stays the original color of the paper (so brown is a good choice).  Next, choose a second color that is lighter than the first.Rub it on the jigsaw, then hold it firmly a little higher up than the first.  Rub upwards again, and you get another layer of Southwest region landforms in the distance.


As you can guess, this project requires a steady hand when it comes to rubbing the color upwards, because you can't erase (but you can save the jigsaw for a second attempt).


The final method is my personal favorite because it seems to have the highest success rate, and it looks really dramatic.


Southwest Region Landforms Displays

 


The medium is oil pastels on black paper.I demonstrate how to create a sunset, with concentric circles and colors.  If you think of the order of colors in a rainbow, ROYGBIV, reverse the letters in ROY's first name to YOR.  Then reverse the rest of the letters of his last name to VIB.  Finally, omit that middle initial.  There's no green in this sunset.  I allow students to include pink as well.  Depending on the hue (peachy or fushia), it looks best either between the orange and red or red and violet.

Southwest region landforms art with pastelsNotice that it's not necessary to complete the underside of the circle, but more than halfway ensures there's no missing coverage later on.


After the colors are on the page, use a tissue to rub along the edge of each circle.  This will help them blend.  Do NOT use fingers for this step!  Not only do the pigments stain, but the oils from your fingers can cause black/grey discoloration on the artwork.


Southwest region landforms art displaysFinish by laying a black jigsaw of the landscape over the top.  The result looks like a landscape with the Southwest region landforms in silhouette.

Could you use crayons for this project to avoid mess? Absolutely! If you notice on my filing cabinet (top, middle) there was one absent student who completed the project using crayons. The materials are up to you. But I find this project in my Southeast Region Unit get kids much more excited about learning about a new region than the note-taking alone.









Saturday, January 21, 2017

United States Geographic Regions Empty Box Project

 
In my last blog post in this series on United States geographic Regions, I talked about integrating social studies content with ELA objectives as we take notes on natural resources and products of each region.  Today I want to share an activity that is so easy to set up, and it helps make the social studies content feel more relevant to our everyday lives.  I call it the "Empty Food Box Geography Project."

United States geographic Regions Empty Package ProjectFirst, I send home a letter about a "volunteer homework assignment." Students are encouraged to bring in empty, DRY containers of food.  I emphasize that cans are not desirable, although the paper labels from cans are fine.  

Label Boxes with United States Geographic Regions

I set up an area with 5 boxes, one for each of the United States geographic regions.  Then, as the boxes come in, students read out what state the food came from.  We determine which region that state is in and place it in the correct box.   
As time goes on, we look for patterns.  Where does our produce come from?  (Hint:  It's not all local).  What about our grains?  By the time we start learning about the Midwest region, I get to hear a lot of, "That makes sense!" when we see crackers from Illinois, since this is our nation's "breadbasket."  
This activity takes just a couple minutes at the start of each social studies period, and can be done year round.  Some years I launch it at the beginning of the year so the kids get a preview of how to categorize the states into each of the United States geographic regions.  Other times, if I know it's a group of kids with high participation rates from home, I launch it during my Midwest Region unit (around midyear).  This way I don't end up with more food boxes than space to store them!  And the Midwest always "wins" with the most boxes, so it's a perfect time to highlight the importance of our food production.

United States Geographic Regions and Consumer Education


The kids love this project because it's food related and an easy way to participate.  I love it because not only does it reinforce what they're learning about American products and provide practice for categorizing states by United States geographic regions, it also starts getting them to read food labels.  Looking beyond the front packaging is an unrelated, but very important life skill!  



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Wednesday, January 18, 2017

Measuring Angles Art

 
Geometry is my favorite thing to teach in math and that's probably because I can turn anything geometry related into an art project!

To help kids understand measuring angles, we start with quarter turns.  Since I teach it after a unit on time measurement, I make the connection to starting at 12:00, and the minute hand stopping at 15, 30, 45, and back to 1.  I explain that one difference between the angles and the clock is the hour hand moves slightly, while the angles stay at multiples of 90 degrees.

The first art project happens once we make the connection that two right angles, each 90 degrees, add up to 180.  And the result is a straight line.  We use drawing triangles to draw right angles and straight lines.  But to get a feel for the movement and amount of space from one position to the next, we trace circles.  Teaching tip:  use yellow paper and at least half your students will be psyched to be making Pac Man during math class.

Measuring Angles Art

 
Measuring angles art projects
Paper or plastic cups are good options for tracers.  I tend to have plenty of plastic takeout containers on hand so we can reuse them for painting from year to year and those work great for this project as well.  By filling in the arcs, kids can see that even though the arcs can vary in size, they have a defined start and end point if it is 90, 180, 270, or 360 degrees.


For our second art project, I give students two "lines" (strips of paper) and we practice rotating one of them around in a clockwise direction.  Once they are glued we trace the the arcs again, and this time we label the degrees after measuring angles.


By introducing these 4 angle sizes, students were able to make pretty good initial estimates about angles that were "near 90," "near 180," "near 270" and "near 360."  Before I even started teaching them how to line up and read a protractor, they were getting a sense of reasonable measurements of angles.



 

Measuring Angles Task Cards for Additional Practice


Measuring angles task cardsThese art activities get kids excited before the hard work of using protractors for measuring angles to the nearest 5 degrees.  My class used to struggle with this skill for one silly reason:  laying a protractor across the spine of the workbook.  It just didn't work!  And since tearing out pages was another fine motor challenge they weren't prepared for, I realized in needed an alternative.  So I made my own task cards!

These cards are great for measuring angles in isolation as well as within polygons.  I even threw in a bonus for students to "discover" when it comes to adding up all the angles of like colors (hint:  each set of like colored angles form a complete circle).  I've had great success with these task cards since there are lots of examples for kids who need repeated practice, and adding up to 360 degrees is engaging enrichment for students who need more stimulation.






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Sunday, January 1, 2017

Find Balance as a Healthy Teacher

 
A while back I posted about reducing my blogging rate, but I didn't elaborate why.  Back then I thought my reasons weren't teaching related so they didn't belong on this blog.  But now I realize that prioritizing one's time is one of the most important things a healthy teacher does, so it is absolutely something I should share with you here.

A couple years after getting married, my husband and I were getting comfortable (read:  overweight).  I was comfortable in my grade level, making resources that worked great for my own class and were also publishable quality.  I had insights to write about here on this blog and a collaborative blog a few times per week.  I had so much I wanted to share with others, feeling so productive, that I was getting to sleep around 1 am every night.  

Then one of my former colleagues passed away at the age of 52.  

The last conversation I had with her, she had been talking about how she NEEDED to lose weight.  Her doctor told her to get serious about it.  She sounded serious about it.  But before she did anything about it, her health took a turn.  She had to leave teaching.  And although things were up and down for a while, she never got the chance to improve her health the way she wanted to.  She never found her balance as a healthy teacher.  

After mourning her, I started thinking about what I should learn from her life and tragic death.  I decided that I needed to make my health a priority.  I bought a Fit Bit, and although it took me a year, I cut some of my bad eating habits, exercised regularly, and lost 20 pounds.  My arthritic knee stopped bothering me.  Although it took me 2 years, I started going to bed closer to 11 than 12.  I went to physical therapy for a 10 year old shoulder problem that had gradually escalated from occasional ache to actual pain, and actually got strong enough to change the way my arm moves.  The pain is pretty much gone.  

 

How do you become a healthy teacher?



How did I take back control and become a healthy teacher?  

After receiving that initial wake up call that drove me to action, in order to turn intention into a plan, I made time.  Yes, I had to give up some things I enjoyed, like some blogging time and some resource creating time.  

 If you're struggling with the question of, "How do I make time when I'm so busy," I read a quote on Instagram a few weeks ago that was very poignant:

Instead of saying, "I don't have time,"
Try saying "It's not a priority for me."

I think about this in the context of exercise and food preparation. 
Once I had a plan, I had to stick with it.  Dwelling on fear was a good initial "kick in the pants" but in the long term it's not a healthy way to stay motivated.  So in order to keep going, I looked for healthy teacher role models who I could relate to.  To do the same, ask yourself:

 

Who is my healthy teacher competition?  

 

Healthy teacher ideal competition a.  Someone 15 years younger than you
b.  Someone the same age as you, who has been training for 15 years
c.  Someone 15 years older than you who has been training for 15 years
d.  Someone who is in their 80s who can run a marathon

I have answered c and d.  Because the fact is, (a) I can't turn back the clock.  No matter how hard I exercise, I won't look like I'm in my 20s because I've already been there, done that.  To set a long term future goal, I need to look for healthy teacher role models who are older than me and fitter than I currently am right now.  

Even my friend who is (b) exactly the same age as me and running marathons is not useful for me when looking for workout inspiration, because she's got too much of a head start.  Unless she slows down, which I don't wish on her, I won't catch her.  And THAT'S OKAY.  We all have our unique assets and flaws.  

Instead, I look at my colleague (c) who eats right, works out regularly, and in spite of a hip replacement and being 15 years older than me, is in better physical shape than me.  SHE is my healthy teacher role model.  I know that if I keep up the work I started 3 years ago, I can reach her level of fitness.  I bet if I work hard, I could do it in LESS than 15, but if I want to do that, I need to get on it!  And who knows, maybe someday if I work hard enough I'll be (d) and 80 year old marathon runner.  I just enjoy knowing that as a human being, I may have the potential within me, even if I don't choose to take my fitness quite that far.   

And finally, I would be remiss if I didn't mention my workout partner, who I am married to.  He was at a similar fitness level as me to start with, and we have been holding each other accountable with our exercise regimen. I'm lucky and grateful!

It's not easy to start and stick with a healthy lifestyle.  Not every decision I make is the best one for my health.  But I start every day with a plan, inspiration, role models, accountability, and a mindset that my health is a priority.

 



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