Tag Archives: geometry

Sharing our Shape Art

During 2nd quarter of first grade one of our units (which I think is one of the most fun to teach and learn about!) is geometry.  A few years ago, it was also a time when we were visited by a fabulous artist who taught us about watercolors and a new geometry/art project was born.  The topic has been different every year (for example last year kiddos had to make their house), but the focus every time has been on using what they know about 2D shapes to create a picture, then paint it.

We used shapes we had already learned about and used in math (pattern blocks that were squares, trapezoids, rhombuses, hexagons and triangles) and traced them to create a design.  It was pretty tricky for some of us, as we’re still working on fine-motor skills and the tracing part can be hard!  No worries, though, because in Rm. 111 we have a boatload of grit and we just kept trying!

After we had a pencil drawing that covered the whole page (which is an expectation we have whenever we do a painting or drawing project on big paper), we were ready to paint it.  Kiddos were asked to paint it to match the colors of the actual blocks.

As with most watercolor projects we do, the last step is to trace our pencil marks with Sharpie.  This makes the shapes crisp and clear.

Our last step is to analyze the creation, showing what we know about the shapes we’ve been working on.  Kiddos completed a sheet called Shape Talk, that went along with their mathematical design.

 

 

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Often, depending on the time year this unit happens, mathematicians may be asked to write equations to show how many of two shapes they have altogether, for example: triangles + hexagons =

Once these were finished, they hung on our hallway bulletin board for a while and they were BEAUTIFUL to look at every day!  Check out our hard work!

 

Lions, Rectangles and Triangles–Oh My!

We have been on a bit of a geometrical journey as of late.  We’ve studied sides, corners (which we know are called angles), diamonds (which of course are really called rhombuses!), square corners, trapezoids and loads of other things.  We’ve taken pictures, manipulated blocks, read books and even drawn pictures.  Pictures of shapes, and now pictures of lions, too.  Let me explain. 🙂

Well, actually, let me let a guest author explain. 🙂

Hi parents, guardians and friends of Room 202 1st graders! My name is Kate, or Ms. Holzmueller, and I work as a TA at Robinson. I’m one of the TA’s assigned to the 1st grade recess (where I often referee kickball) and lunch (where I help maintain order and pass out napkins and embellish hamburgers with ketchup smiley faces!) I’ve been spending time in Mrs. Bearden’s classroom the past few months, supporting some of the fantastic kiddos and doing a few read alouds, too! 🙂
Last week I spent time during math rotations having discussions with kids about squares and triangles and other shapes. (One of the benchmarks for first grade learners is that they, say, recognize that a square is a square because it has four equal sides and four equal angles.) While playing with the manipulative shapes I thought of one of my favorite authors, Ed Emberley and his books that help children (and adults like me who love to draw!) draw animals and monsters and people and cities, etc. all by drawing simple shapes. I showed Mrs. Bearden an Ed Emberley book and she was kind enough to let me share his work with your students.
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So during math centers, we looked at two pictures of a lion, one real, the other drawn. We had conversations about the shapes within the lion–how it’s nose looks like a triangle, how it’s head looks like a rectangle, etc. Then we practiced drawing all the shapes we had identified on white boards with dry erase markers. After that, we followed Mr. Emberley’s tutorial on how to draw his version of a lion, again on the whiteboard. (First by making a rectangle, then another rectangle, then a triangle…) 

Today during math time we practiced drawing shapes again on the whiteboard and then we used cardstock and markers to draw our own lions, still using rectangles and triangles and circles, etc.

Students were allowed to use whatever colors they liked and embellish their lion as they best saw fit–some have freckles! Some have angry eyebrows! We had conversations about how many triangles they used to show the teeth, how many triangles to make the mane, etc.

The results are very colorful and scary and fun and are now greeting passers-by in the halls. 

(And BOY are they BEAUTIFUL! Sorry–this is Mrs. Bearden.  Had to throw in my two cents about how great they are.  AND how great Ms. Holzmueller did as she taught the lesson! Learned a few things myself that I will incorporate tomorrow. 🙂  Really, I did!  Ok…back to the guest post…:) ).

If your student mentioned drawing a lion today know that Mr. Emberley has lots of other fun books they might like, too! (I found two of them in the Robinson library just today!)  And remember it’s just as easy to play “I Spy” with geometrical shapes as it is colors! “I Spy with my little eye something that is a square…” 

Second Grade Math Warm-Ups: Week of April 18-21, 2016

This was a 4-day week at school, but since we’ve moved our MWU to the afternoon (instead of first thing in the morning), it has seemed it’s been easier to make them happen every day.  Maybe it’s just because of the unit we’re in, too, but our conversations about them have been SUPER POWERFUL lately.  Can’t imagine teaching without this part of our day!

Monday

I definitely should have taken a before and after picture of this one.  The circles were all filled up with post-its when we sat down to talk, but we had to work through them and decide which ones sounded like things mathematicians would say about these polygons.  Many of them were vague or didn’t use mathematical terms.  They said things like “they’re different” or “they’re the same.”  We talked through the definition of polygon (hence the words over there) as well as what some mathematical terms were that we should listen for as we narrowed down the choices.  This idea of comparing is something that students are expected to know how to do independently with two different polygons by the end of the unit, so trying some together along the way was crucial.

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Tuesday

This one matches up with both some work on shapes we had done earlier (names and attributes), as well as a replay of the question from the day before to see how they’d do in the same situation with different shapes.  The number of specific, mathematical responses was much greater this time and we had less work to do to make our Venn Diagram make sense.

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Wednesday

This question has a great story to tell (which is SO long and involved I’ll be nice and put it in a different post!), and really gave us lots of math to chew on.  And I thought I would be an easy one.  Those are always the problems that surprise me.

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Do you see the marks on the word HALF up there? Here’s a close-up:

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We’re applying our knowledge of lines, angles and polygons everywhere we look!  This wasn’t even part of the question, but of course was a great part of the discussion!

Thursday

After all our hard work (which I hope you’ll pop over and read about), I wanted to see if they could remember and apply it to a similar but new situation.  Most could see how the knowledge we had gained the day before about halves applied to thirds (and therefore to fourths, fifths, sixths, etc.).

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What did you work on as a mathematician this week?  What warm-ups would you suggest to us that include angles, polygons or fractions?  We’d love to try some more! 🙂

Second Grade Math Warm-Ups: Week of April 11-15, 2016

What? This week I did MWUs every day?  Partly that happened because we actually had every day this week at school, but also because I moved the MWU to a different time of day and it made the timing easier (sometimes mornings can get a little crazy and sometimes I have other things I need them to do instead).  Now (at least for the time being), we’ve moved Writing Warm-Ups to the morning and Math Warm-Ups to right after lunch, and that conversation is then the beginning of our math time together (that part is still the same).  Confused enough now? Don’t worry–the big deal is that I have FIVE MATH WARM-UPS TO SHARE!!  They’re pretty great, too, so I’m glad you stayed through that long intro to check them out. 🙂

Monday

We have been working on subtraction lately, and my kiddos have started to do some amazing thinking with negative numbers as a means of figuring out differences.  It started with just a couple of friends a couple of weeks ago and now probably at least half the class has tried it!  The chart here is similar to the HTO model (which we called Sticks and Dots back then) we used in 1st grade, but connected to an investigation we did with the T-Shirt Factory and refers to the inventory of t-shirts.  The come in Boxes of 100, Rolls of 10 and then loose ones.  Same idea, but inside the context it makes much more sense.  Like most times, you’ll see we did it using two other strategies, as well.  The green numbers on top are from the strategy Making an Easier Problem, in this case by adding 11 to both numbers (which we know is possible because of the idea of constant difference).

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We also tried it with Circle, Split, Subtract and modeled our thinking on a number line.

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And check it out–we got 289 every time!

Tuesday

Another concept we’ve been playing around with is the inverse relationship between addition and subtraction.  This one also asked them to analyze someone else’s thinking.  We tried it by adding up…

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…as well as with our negative number strategy.  Again, we got the same answer both times!

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Wednesday

On Tuesday during math, I gave kiddos a check-in sheet to see what they could do on their own with subtraction, now that we’ve been working on it for a while together, and the last problem was a challenge problem.  Ok, it really isn’t that much harder (just another place), but I wanted to see what kiddos would do when I added 1000s to our work.  Landen and Ava decided to that the BRL chart would probably work the same way if you just added another column, and suggested that we try it together as a math warm-up the next day.  Great idea, kiddos!

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Somehow I took my picture before we had done our work on the chart, so you can’t see it, but believe me–it worked just like they thought it would.  Oh, and when I was using this chart again with someone later that day, we decided that instead of just T for thousands (which doesn’t fit the context of the t-shirt story), we’d say T was Trucks, because you could put 10 boxes on trucks.

Thursday

We’ve been working on both geometry as well as subtraction in math for the last couple weeks (and some still also on money from our last unit), but I decided that we’d use the MWU as the start for our conversation by throwing up some geometry vocabulary I needed to emphasize.  So using examples and non-examples, I had them think about parallel:

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They were able to figure out the meaning (for the most part), although many kept saying it meant “straight” and we had to clarify what they really meant, because ALL of those lines are straight….and while I don’t like math tricks, I did show them that in the word PARALLEL are clues to what it means: PARA for the PAIR of lines, and that the l’s make two parallel lines themselves (ok, well they do if they’re lowercase…see, told I don’t like tricks).

Friday

Today’s MWU was geometry again, related to work we’d done this week, as well as connecting to the work I knew I’d have them do during Math Workshop today.  Win/win! (Oh, and I realize now I mislabeled the trapezoid as a parallelogram.  Oops.  I’ll fix that on Monday. 🙂 ).

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After this conversation we went on a great shape hunt challenge outside, but you’ll have to wait about it.  We’re not quite done yet.  🙂

Note: See that “next” on the bottom?  I’d tried many versions of that extra question this week on math and writing warm-ups.  It seems that when I put “bonus” there, kiddos thought that meant they didn’t have to do it. LOL  So I tried “next” and also “big ?” to help them see that they could do both of them. Or at least start thinking about the answer, since it would be what we’d be talking about anyway.

 

Geometry Creations with Power Polygons

 

We were recently working on geometry in Rm. 202, learning some pretty great things about polygons, angles, area and perimeter.  While I have many things I could share (and probably will!), this post is about an art project we made using some pretty cool manipulatives called Power Polygons.  They are similar to pattern blocks, but kind of on steroids.  Each one is labeled with a letter, that makes then easy to identify and talk about with other mathematicians.


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We spent a couple of weeks learning about angles and polygons, triangles and quadrilaterals.  After we’d gained some new geometry knowledge, I had them put it to use in a Polygon Picture Project:

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It would be GREAT if I had pictures of the final products, wouldn’t it?  Yep, you guessed it, I don’t.  But I do have some pictures of Rm. 202 mathematicians hard at work creating their fabulous pictures!

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Math Warm-Ups January 22-25, 2013

This was a short week because of the MLK holiday on Monday, so we only had four warm-ups this time around.  Most were related to our current geometry unit, except for the last one from yesterday.  I’ll explain that one at the end.

Tuesday

IMG122Besides just knowing polygons and their names, a major focus of this unit is being able to figure out unknown angles using information that is already known.  That septagon that I made is actually created from 3 separate triangle pieces (that we know and have figured out the angles of), so then here I was asking them to use that known information to determine the measure of this new angle.  Many of them also used the idea of a “right angle + some more”, and the fact that it was an obtuse angle in their calculations.  We also focused on the way this question was worded: many went right to telling me WHAT the angle was rather than HOW they figured it out, which is what I was actually asking.  This is an important test-taking strategy that we were able to highlight, as well.

Wednesday

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This question was an extension of what we had just been talking about the day before.  Our focus was on all the different names that one polygon could have, as well as the continued use of known angles to determine unknown ones.  The “G” refers to the way that rhombus is labeled in the set of Power Polygons we use as manipulatives.

Thursday

IMG125This warm-up was a review of old knowledge, but then we used it to connect to our new concepts from this unit.  I reminded them (since of course this seemed like something they did AGES ago!) that area is just like all the work they did with arrays during our study of multiplication.  We also were reminded of how we could use our knowledge of order of operations to correctly write the equation of how we figured out the perimeter.  The lesson following this asked them to be able to create new rectangles based on this one, but with different area/same perimeter  or different perimeter/same area.

Friday

IMG126Hopefully you’ll notice the difference in this one.  This week we were looking at winter benchmarking data noticing that our 5th graders seemed to have a hard time showing that they are solid in computation skills.  It’s clear that we need to do more practice with computation even when it’s not the unit we’re in, as well as more practice with timed situations (the benchmark we use asks them to complete a certain number of problems in 8 minutes).  Other than the benchmark and standardized testing, they aren’t asked to do this.  Simply having more opportunities like that could be helpful.

Math Warm-Ups January 14-18, 2013

This week’s warm-ups are geometry related, as we are at the beginning of a 2D geometry unit now.  My hope was that they were review, since they’ve had similar units for many years.  And for the most part, they were.  Oh, and you’ll notice there are only 3 this week; the morning schedules were a little rushed on Tuesday and Friday, so we skipped them those days.

Monday

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And speaking of having done it before, my kindergartener is actually talking about these very things right now, too!  When I shared this question with him, he was able to tell me which were polygons and which were not!  The definition was simpler in kindergarten, but the idea was the same.  Cool!

Wednesday

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This one was pretty easy, but was a conversation starter for that day.  It helped us take the next step to putting quadrilaterals into categories.

Thursday

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When we first talked about this one, we were unclear about the definition for a parallelogram.  We spent our group time on Thursday clarifying this.

What do you know about geometry?  What questions would you ask for a geometry math warm-up?  Share some with us in the comments!

 

Geometry Challenge for January 23

Today was one of those days when I decided to totally change my plan for math and it worked out tremendously better than the original plans. Let me tell you about it. 🙂

My kids are used to what I call “geometry challenges”, where they have to prove that a statement is true, by using what they know as mathematicians.  The first one we did was to prove that the shortest distance between two points is a straight line.  They worked alone or with a partner to show how that was true, or to find a way to prove that it wasn’t.  Then next one was to prove that a straight angle equals 180 degrees.  With that one, they used Power Polygons with angles that they know to show whether that statement was true or untrue.  Needless to say, they’ve totally rocked each of those situations, and really shown what they know about geometry.

So today I was headed in a totally different direction, but decided to do today’s lesson as a challenge again.  Here is what they were asked to do:

Like in the past, they had amazing things to show for the work on this challenge.  Before I show you what they did, I’m curious to know what your answer would be.  Could you answer this challenge?

Geometry Video

Ok, so the other day I posted about our first lesson in our new geometry unit.  I was a little frustrated by not being able to post videos, because I caught a great conversation about rotational symmetry that one group had.

After some smart thinking by my brother-in-law, I am attempting it again, using our newly created YouTube channel.  Let’s see if it works:

But anyhow, I hope you caught what was happening in that conversation.  The boys were working to put their geometry terms into groups and label them, and got to talking about rotational symmetry related to triangles.  Evan was trying to explain to Harry about how all triangles have rotational symmetry and was showing him with the picture on the post-it.  Harry–and then Dom, who you only hear but not see–help him with the idea that regular triangles, but not all triangles have rotational symmetry.

I love how you ask kids to do one thing, and then they take the conversation to other (and many times deeper) levels.  Great job, kiddos!

(And sorry to those of you who were annoyed by the quality of that video.  I’m still new to this part of blogging and uploading!  I’ll get better, I promise. 🙂 )