Focus on Math

Helping children become mathematicians!

Wanted Posters Revisited February 4, 2014

wanted poster picDoing wanted posters for numbers is a great way to have kids think about specific properties of particular numbers. The posters make a great display, too —  and I am always looking for ideas for math bulletin boards!

The idea is useful at lots of grade levels. You could have older students choose a proper fraction (e.g., 5/8), a mixed number (e.g., 4 1/3), or a square or cube root (e.g. the square root of 50).I wrote about these posters before — click here for the link to the previous write-up where you can download the template.

Give them a try and send me a picture of your display!

Mathematically yours,

Carollee

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Math Club for Elementary or Middle School Students November 5, 2013

math club picYou may have heard of math clubs in high schools, but math clubs are a wonderful idea for elementary or middle school students as well. For a number of years I ran a successful weekly math club at the inner city elementary school where I was then teaching. The club was mainly targeted at students in grades 4 to 7 (my school was a K-7 school) although if a grade 3 student were interested in coming, I never turned the child away.

“Euclid Club”, named of course for the Alexandrian Greek mathematician/geometer, met for 30 minutes one day each week after school. It came about simply because I felt there were so many interesting math ideas that just did not fit into my classroom time (or curriculum!) and I wanted the opportunity to share those ideas with kids. Thus Euclid Club was born! I can get pretty excited about mathematics (as anyone who knows me can testify to!) and did not have too much difficulty getting kids to come give the club a try. Our numbers certainly varied over the months depending on what other after-school activities were happening or what other out-of-school activities students were involved in, but we consistently had a pretty good group out at our meetings. I always provided some kind of small snack as well! Certainly not enough to be the main draw, but it was always welcomed by the kids.

There are many benefits to engaging children in math club. For me, first and foremost was that it gave students a chance to build a different perspective about mathematics. Many of them thought of themselves as not being “good” in math and tended to disengage in math in the classroom. The atmosphere in Euclid Club was welcoming, engaging, and lively, and many not only became comfortable with exploring math ideas, but additionally they built a sense of belonging within the club.

So, what kinds of ideas and activities can be explored in that context? Here are some of the things we explored in Euclid Club:
• We learned and played math/thinking games such as Nim, chess, cribbage, etc.
• We examined other number bases, such as base 4, base 2, and base 12. We wrote the value of base 10 numbers in the different bases. We figured out the base 10 value of numbers written in other bases. We added and subtracted in other bases.
• We worked with pentomines, trying to fits sets of pieces into given frames: 6 x 10, 5 x 12, or 8 x 8 (with either the four corners “removed” or the four center squares “removed”).
• We created designs with tangrams.
• We made pattern placemats using cut-out pattern block pieces to make interesting borders on construction paper.
• We used pattern blocks to create designs with one or more lines of symmetry.
• We measured our bodies and compared ratios (e.g., height to arm span; circumference of thumb to circumference of wrist; circumference of wrist to circumference of neck; circumference of neck to circumference of waist, etc.)
• We solved logic puzzles (using ones commercially produced).
• We created tessellations: we found shapes that would tessellate as well as creating our own unusual shapes that would tessellate.
• We made paper quilt squares in a variety of patterns and calculated the fractional part of each colour we used.
• We examined the Fibonacci sequence and looked at real-life examples of where it appears in nature (such as on a pinecone, on flowers, leaves, pineapples, seeds in fruit, etc.
• We created Moebius strips, and marked and cut them to discover interesting properties about them.
• We assigned each letter of the alphabet an amount (a = 1 cent, b = 2 cents, c = 3 cents, etc.) and looked for words whose letters would total $1.00.
• We solved magic squares and then created our own.
• We examined Pascal’s Triangle and looked for patterns on it.
• We created designs with exactly one metre of string glued on to paper (easier to do the basic designing first with dry string, then dip the string in white glue to create the final project).
• We created our own codes using numbers and wrote secret messages to each other.
• We made designs on 100-grid paper using a specific amount of coloured squares (e.g., what designs can be made colouring exactly 50% of the grid? 60%? etc.)
• We created “Guess My Number” puzzles for each other to solve. Each puzzles was to have 3 to 5 clues, first starting with a broad clue and getting more specific each time. (E.g., 1 My number is a prime number less than 30. 2 My number is not part of a pair of twin primes. 3 My number is even.)

I am sure there are other things we did, but those are the ones that I remember at the moment! I am sure you can find other ideas and topics to explore as well.

I hope you will consider giving Math Club a try (but give it a cool name! Kids love that!)

Mathematically yours,
Carollee

 

Tessellations: Fun with Shape and Space May 31, 2013

Escher two birds pic Tessellations are a fun way to play with shape and space, a strand in the mathematics curriculum. A tessellation is a shape or combination of shapes which cover a two-dimensional surface without leaving any gaps. For example, square or rectangular tiles, common in houses, do this nicely, as do other shapes such as equilateral triangles, right triangles, and regular hexagons.

It is easy to create an interesting shape that tessellates by altering a shape that already tessellates. The important thing is to cut out a chunk of the tessellating piece, and then reattach it in such a way that the new altered shape will still be able to tessellate (see illustrations below for possiblilites).

I can hardly think about tessellations without thinking of the work by the Dutch artist M.C. Escher who did some amazing work in tessellations. This is a picture of one of his paintings called “Two Birds”. Check out this link to look at more of Escher’s work in this area.

Creating tessellations is a great activity for home or classroom, and even the most reluctant artist can create unique and wonderful pictures in this way. Thanks to Miss Norris for allowing me to post her students’ examples. Tessellations make a great math bulletin board!

I hope you will give tessellations a try!
Mathematically yours,
Carollee
tessellations how to 1tessellations how to 2 pic

tessellations how to 3 pic

tessellation pic 1 JN

tessellation pic 2 JN

 

Math Bulletin Board: Square Number Towers May 23, 2013

square number tower bb pic Recently I had two of my classes represent visually the idea of “squaring” a number: namely, that a number times itself is literally the area of a square with side length of that beginning number. The students cut squares from centimetre grid paper representing 10 x 10, 9 x 9, … 1 x 1 and them glued them onto construction paper. To each square they added the multiplication fact represented, as well as showing the exponential form of the number. Square numbers show up quite a bit in secondary mathematics, and helping students understand these numbers (as well as memorizing the sequence of them!) is beneficial for them as they move on.

I am always looking for math ideas to display on a bulletin board, and I think this is a good one!
Mathematically yours,
Carollee
square numbers towers 3 pic

 

Tangrams: Seven Shapes, Many Pictures March 13, 2013

bird 1 Tangrams are most likely the oldest and most enduring of all geometric puzzles. Having originated centuries ago in China, tangrams are a set of seven flat shapes, called tans, that are used to form shapes or pictures, usually when given only an outline or a silhouette. A complete set consists of 2 large triangles, a medium triangle, 2 small triangles, a square and a parallelogram, and these 7 pieces can be formed into a huge variety of arrangements.

The math connection for tangrams lies in the visual-spatial opportunities that are generated when students are using them. Visuals come into mathematics in areas such as patterning, graphing, geometry, and measurement, just to name a few. It is easy to disregard the development of visual-spatial skills, but Howard Gardner’s research and writings concerning Multiple Intelligences reveal just how powerful and important these skills are.

In addition to creating pictures and shapes from an outline, it is also good to just be creative yourself with the tans. I recently did just that with three grade 3 classes, asking them to create a bird. I offered no hints or suggestions as to how they might do that; rather, the students just took their sets of tangrams and set to work.

I won’t bother to attach any pictures of tangrams to make – a quick Internet search using your favourite search engine will produce a plethora of such images! Some of the images will show the actual arrangement of the individual tans, and for younger children even recreating those with the “recipe” can still be challenging. Older children (and adults!) can be challenged by the outline or silhouette versions of the patterns.

Sets of patterns are available commercially, but can also be easily cut from a square. Download instructions for cutting a set here.

Taking time to play with tangrams is a fun way to help develop visual-spatial skills in your students (or your own children).

Mathematically yours,
Carollee

PS: Thank you to all of the parents who came to my session at the SD#60 Parent Conference this past Saturday! I enjoyed our time together to talk about math, and I trust you went away with some new ideas for interacting with your children about numbers. I sent you all away with a set of tangrams cut out of fun foam, so here is the promised information about them!

bird goosebird duckbird brownbird 2tangram bird bb

 

Pattern Block Plates — Math Art Grade 2 September 20, 2012

Filed under: General Math,Primary Math Ideas & Problems — Focus on Math @ 2:07 pm
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Well, with the new school year well underway I am delighted to be working with 7 classes of students at Charlie Lake School again this year. I am fortunate to have a room to base my math lessons in — having a base is so much easier than having to truck all my materials and manipulatives around on a cart and I am very appreciative that there is a space for me.

But having a room also means there is a hall bulletin board for displaying student work, and to get the school year going I decided to have the two grade 2 classes each make pattern block plates. Since I have a die cutting machine and the dies to cut some of the pattern block shapes, the students used these construction paper pieces to create their designs.

There were only two instructions:
First, students were to glue a yellow hexagon into the centre of the plate. From there they had free rein as long as they were making a design with a pattern or some symmetry involved. The classes were short — I get one group for 30 minutes and the other for 35, but even within that time frame the students produced some lovely designs. While I was hanging the plates in the hall many of the older students were stopping to admire them, picking out some they particularly liked.

If you have access to pattern block pieces, I encourage you to try the project with your class. Even some older classes would enjoy creating the designs.

(Download the pattern block template here.)

Mathematically yours,
Carollee
Screen shot 2013-01-11 at 11.59.25 AM

 

Math Art: Breaking Apart Numbers December 8, 2011

Filed under: General Math — Focus on Math @ 3:51 pm
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math art 999In looking for a math-related art project that could be displayed on the hall bulletin board, I found this activity on the internet. Although the author (Zachary Brewer) lists this as an activity for adding numbers to equal 999, I believe it is more focused on breaking 999 apart into four components. Breaking numbers apart is a very important thing for students to be able do and understand. John Van de Walle says this about whole-part-part relationships: “To conceptualize a number as being made up of two or more parts is the most important relationship that can be developed about numbers” (Van de Walle & Folk, Elementary and Middle School Mathematics, Can. Ed., 2005, p.98) .

Brewer shows pictures of his art activities on his website and offers a book with templates for all the projects. I have not yet purchased the book with the templates, but, being in a hurry, just created the necessary bits and pieces myself for students to do the activity.

I created a page with the base-10 representations on it: 9-100 grid squares, 9 “ten strips” and 9 tiny ones blocks. I also created a page that has the number 999 in a box along with four blank boxes in which the students would write the numbers that they broke 999 into.

Because I have short blocks with my Wednesday math classes, I prepared the 12″ x “18” pieces of construction paper for the students by drawing two black diagonal lines, creating four spaces on each sheet.

Each student received:

  • a large piece of construction with diagonals marked
  • a page with 999 in base-10 representation (download my version here)*** I have changed this from a .tif to .pdf — it works better now!
  • a small sheet of boxes, one with 999 in it and four to fill in. (download my version here)

Students also needed:

  • four different light-coloured markers, highlighters, or pencil crayons (all work well)
  • a pair of scissors
  • a glue stick

Students were instructed to colour the base-10 page using exactly four colours. They choose the number of 100’s, 10’s and 1’s to colour with each particular colour. They were also to colour one blank “number box” to match each colour they were using on the base-10 representation sheet.

Once all the colouring was done, students cut out the base-10 pieces and glued them onto the construction paper, one colour per section. The blank number boxes were also cut out and glued on with their appropriate colour partners. Each box was then marked with the number that was represented in that particular section. The number box with 999 on it was left white and glued on at the intersection of the lines.

The project produced a great visual representation of breaking apart the 999 into four parts.

I created a modification of the original project by choosing to have one class split 500 into two parts. Students were given a piece of 9″ x 12″ construction paper divided in half with a vertical line. The piece of paper with the base-10 representation for colouring had 4-100 grids, 9-10 sticks, and 10-units blocks.

The click here for a link to Brewer’s webpage where you can view this project and his other art projects. Keep in mind that, although he lists them for grades 2,3, and 4, topics may correlate to other grades as well. For instance, his visual representation of square numbers would be appropriate for any class working with that concept.

My classes enjoyed the activity and the bulletin board looks great!
Mathematically yours,
Carollee