Exploring geometry!

The second graders recently finished up our unit on 2D and 3D geometry.  This unit provided us with many rich opportunities for hands on learning as the students searched for shapes around our classroom and at home, read books about the subject, created 3D rectangles out of paper, and used mirrors to explore symmetry.  There were many highlights of this unit - here are some of our favorites......

After introducing solid shapes, we read the book Sir Cumference and the Sword in the Cone, by Cindy Neuscwander.  A Swiss mathematician, Leonhard Euler, created a formula that expressed a relationship between the faces, vertices and edges of solid shapes. He discovered that adding the numbers of flat faces of any solid shape to its corresponding vertices (or corner points) and then subtracting that sum from the number of straight edges, the result would be represented by a total of two.  When the result was two, that meant that the solid shape could be classified as a polyhedron. Any solid shapes whose totals were not two cannot be considered polyhedrons.   After reading the book, we discussed and carefully studied the shapes presented in the story.  We created a chart to fill out the number of faces, vertices and edges of each shape, and then applied the equation and gave each shape the "Two's Test." This gave the students opportunity to carefully examine each shape as well as practice with making advanced  and intricate calculations.   This activity quickly became a favorite.  When reflecting back at the end of the unit, many students claimed the Two's Test was their favorite part of studying geometry!

Taking the "Two's Test"

Another thought provoking and fun activity was to create "tricky triangles" or rectangles, and find hidden shapes within shapes.  The students learned there are usually more shapes present than initially thought.  They also devised wonderful strategies to find the various hidden shapes.

Finding hidden triangles

When initially asked to put a group of rectangles in order from smallest to largest, students normally will choose the order based on height.  After we discussed the concept of area and determined how to measure the area of a rectangle by using 1 inch square color tiles, students realized that the tallest rectangles were not always the largest.  This was an excellent exercise on making and testing a prediction.

Ordering rectangles

Which rectangle is the biggest?

Finding the area of a rectangle by using color tiles

The students made 3 dimensional rectangles out of various sizes of paper.  This activity proved challenging at first.  The students weren't sure how to approach creating a 3 dimensional object out of something 2 dimensional.  They needed to fit the sides together, create a top and a bottom, and finally tape it all together so it would eventually become a 3 dimensional box.  After some effort and perseverance, the results were amazing - we had rectangles of all sizes, animals made out of paper shapes, fairy houses, doll beds, and colorful cubes, just to name a few of the creations. What started out as a challenge, ended up being a class favorite.  The possibilities were endless!

colorful cubes!

"Mousey house"

Working on creating a box out of paper

Finally, we explored symmetry, and the properties of symmetrical objects and shapes.  We used mirrors to create perfectly symmetrical designs out of pattern blocks and color tiles.  This was another hands on learning experience that illustrated a mathematical concept in a very tangible way for the students.

mirror images

Exploring symmetry 

Making a chart about symmetry

I can safely say that the 2nd graders are now experts in geometry.  Looking ahead, we will explore more complicated addition and subtraction story problems, using larger numbers.  I have no doubt they will approach this unit with ethusiasm and meet any challenges head on!  

The second grade mathematicians have successfully mastered our first unit, Counting, Coins, and Combinations. They have developed an understanding of the magnitude and sequence of numbers up to 100, developed strategies to solve addition and subtraction problems with totals up to 50 (and beyond!), mastered their combinations of 10, and explored doubling a quantity. These goals were met through a variety of ways. We solved problems in our journals, presented ideas to our classmates, played math games, read and discussed relevant books, and explored materials.

Doubling 

Working at the doubling center

Journal work

Playing Plus 1 or 2 Bingo 

Playing "Double It"

 

Working on doubles arrays

Playing "Double It"

Another new development in math this month has been the introduction of "Math Workshop." After new concepts and topics have been introduced, explored, mastered, and summarized, students have the opportunity to participate in Math Workshop, consisting of various math centers (usually about 4) pertaining to our unit.  A center may have a game to play with a partner, free exploration of math materials and manipulatives, math journal work, or "challenge problems."  This has provided a wonderful opportunity for the students to work with partners, share ideas, and further explore mathematical concepts.

Looking ahead, we are just beginning our unit on geometry.  Students will explore the characteristics and attributes of 2-dimensional and 3-dimensional shapes.  We will do in-depth work with rectangles and rectangular prisms and investigate symmetry.  This has already captured the interest of the second graders, and I'm looking forward to witnessing and guiding their interest, creativity, and enthusiasm!

Playing Tens Go Fish

Exploring and drawing geoblocks

Tens Go Fish

We started the week with an activity called "counting pockets."  We counted the amount of pockets each student had, and recorded the total number.  This was a great exercise on estimating, counting, comparing and combining, as the students collected, represented and interpreted data.

Later in the week, we read the book Math Curse, by Jon Scieszka and Lane Smith.  It is a story about a girl who starts to think of everything as a math problem, and believes her teacher has given her a "math curse." We talked about how everything can appear to be a math problem when you start thinking this way.   Inspired by the book, we made up our own math problems and shared them with the class.  This was an amazing exercise as the students had to think about ways to express themselves and their mathematical ideas.  The problems had to be relevant, challenging enough but not too challenging, and interesting for their peers to solve.  The students loved coming up to the front of the class to write out and present their problems.

Plus 1 or 2 Bingo was also a favorite this week. We worked on our addition combinations while playing games with our friends.  Looking ahead to next week, we'll be learning more games to assist us with combinations of 10.

In closing, here is a link to an excellent article discussing the beauty of math.  Enjoy!

http://blogs.kqed.org/mindshift/2013/10/finding-the-beauty-in-math/

Writing our own problem on the board

Presenting our problem!

Finding a solution in our journals

Problem solving

Playing Plus 1 or 2 Bingo

This week we started to explore coins and their values.  We sorted and counted the various coins and learned two games - Collect 25 Cents and Roll for $1.00.  This provided the children with practical experience adding up coins and making trades for the different coins.

We also started our year long service project - observing and counting birds through eBird.org.  We'll be going outdoors to take a monthly bird count on the Parker property and entering the data into a national database on the eBird website.  We will be graphing our results back in the classroom, as well as completing word problems and other relevant activities.  On our first outing we spotted almost 30 birds!  Now we just have to get better at identifying them.  ;)

Carefully counting coins

Sorting coins

More sorting

Counting birds on the Parker property

Taking careful notes

Playing Roll for $1.00