Math Problem-Solving Week 7: 2-Dimensional Geometric Shapes

Here is the first week of my Shapes Unit. These are just the problems--I do lots and lots of other activities to get the kids exploring and really thinking about the attributes of shapes. I will detail specific activities tomorrow in a warm-up post.

But for now, here are some problems!

This is a very hands-on unit. I provide my students with lots pattern blocks and other shape tiles so that they can explore and manipulate shapes in a very concrete manner.

Pattern Blocks

Square Color Tiles

Shape Magnets

Day 1

For this problem, I give each student a blackline master of a circle and some colored square tiles. I challenge them to fill the circle completely with the square tiles. They cannot overlap the tiles and they must cover the circle completely--no white spaces left. They will try and try and try--but despite their best efforts, they are unable to complete the challenge.

The most important part of this problem is the discussion that occurs during and afterwards. Why can't they fill the circle with the square tiles? They will inevitably come to the conclusion that they cannot fill the circle with squares because squares have straight edges and circles have a round edge.

I then challenge the students to use the square tiles to see what shapes they are able to make. They quickly discover that they can make different sizes of rectangles and squares. And they try and try to make triangles...and some think they actually do.

This leads to some more really good discussion...Can you make a triangle? Why or why not? Of course the answer is no--and the reasons are a little too complicated for kindergartners to understand (the angles of a triangle must equal 180 degrees and the angles of a square are 90 degrees, which means you could only have 2 angles and a triangle needs 3...and even my head is about to explode right now!) The purpose of this activity is for the kids to explore and wonder...they will start to see that the shape of a square's corners do not fit in a triangle's corners (unless it's a right triangle).

They are building a schema upon which they will add to in the coming years as they learn more and more about geometry!

Download Fill a Circle

Day 2

This is another activity similar to Day 1. I provide the kids with a blackline master of a triangle and pattern blocks. I challenge them to fill the triangle. The same rules apply--you cannot overlap shapes and there can be no white spaces remaining.

I give them all the pattern blocks--even the orange squares and the skinny white parallelograms that won't fit. I let them try and try until they figure out that, because of the shape of the corners (the angles), they won't fit. Again--they are building that schema!

I give the kids paper pattern blocks and have them glue them into their math journals. I also have them fill out a chart with the number of each shape they used. For share time, we take a gallery walk around the room to see the different combinations of shapes the kids used.

Download Fill the Triangle

Download Fill the Triangle Table

Day 3

This activity is based on the Investigations Fill the Hexagon game. I give the students a blackline master with several hexagons on it and pattern blocks. I challenge them to fill the hexagons in as many different ways as they can. Again--I let them figure out that the orange square and skinny white parallelogram aren't going to fit.

This is a challenging activity, because the kids must find different ways to fill the hexagons. They get 2 or 3 quickly, but then they get stuck. It pushes them to really think!

For share time, we make a class chart that shows all the different ways the kids were able to fill the hexagons...

Download Fill a hexagon

Day 4

Here's a fun problem that the kids love. I actually hide 2 shapes in a basket and they get to guess what shapes they are. It is essential that kids have actual shapes to manipulate and count the sides when solving this problem. Most will not use an addition strategy at this point in the year...they will simply guess and check. They will choose 2 shapes and count the sides. If they do not equal 7, they will try again. It is interesting to see which kids will put both shapes back and start all over again from scratch, and which will keep one shape. Watch for the kids that figure out that they have too many or too few sides and choose their second shape accordingly.

(a rhombus, a triangle) Gotta love that kindergarten spelling!

When the kids have found a combination of shapes that equals 7 sides, I say, "That might be it...but it might not be. Can you find 2 more shapes that have 7 sides?"

I have the kids record their answers in their math journals. For share time, we make a class chart recording the different combinations of shapes that have 7 sides. This year, one of my kids figured out that "the triangle always stays the same." He has very good computational fluency, and figured out that it was going to have to be a combination of 3 and 4 sides, and that a triangle is the only shape that has 3 sides!

When we are all done, I open up the basket and reveal the shapes inside--the kids love to see whether or not they were right!

Day 5

So this is the same as yesterday's problem, but taking it a bit further--this time I do not tell them how many shapes I have--just that it's "some." So there are even more possible combinations.

(a hexagon, a square) (a hexagon, a rectangle)

(I love the early attempt at writing equations!)

(square, hexagon) (hexagon, rhombus) (hexagon rectangle) (trapezoid, hexagon) We still haven't mastered organization when recording at this point!

Again, during share time, we make a chart with the different combinations the kids thought of. During the big reveal, the kids discovered that I had included an oval, which added zero sides--they loved that!

Check back tomorrow for some 2-D Shape Warm-up activities!

Comments

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I am so glad to see your post!!!! I would love a copy of the blackline masters you showed above--is that something you could post?
Thanks for your creative sharing!!!
Chris

Posted by: Chris Saundes | 02/06/2012 at 06:32 AM

Thank you so much for sharing this! It couldn't have come at a more perfect time for us!

Posted by: martha brown | 02/06/2012 at 08:38 PM

So glad you are posting again! Your blog is one of my favs! Thanks for sharing all your great ideas!

Posted by: Mary | 02/06/2012 at 09:25 PM

You're back!!!! Yay!!!!
You just made my night :)

Posted by: Shifra | 02/06/2012 at 09:57 PM

I agree. We missed you!! You are so full of great ideas. Keep them coming and we really appreciate yiu time and work.

Posted by: Lisa | 02/07/2012 at 12:13 AM

I would also love a copy of the masters!

Posted by: Susan | 02/07/2012 at 07:14 AM

Your site is awesome. Thanks so much for sharing all that you do!

Posted by: Jen | 02/07/2012 at 09:31 AM

Yay! You are back. I used your site so much at the beginning of the year and then you disappeared. I was worried about you but know how hectic it can be trying to teach, keep up with a blog and have a life! Great to see you back!

Posted by: Kim | 02/07/2012 at 11:09 AM