# Focus on Math

## Helping children become mathematicians!

### Developing Math VocabularySeptember 12, 2013

Mathematics, like many subject areas, has some terms specific to discipline. Additionally, there are words that have uses in everyday language but a specific meaning in math (like “product”, “root”, and “obtuse” just to name a few). Within mathematics itself are some strands that are particularly vocabulary rich, such as geometry and measurement.

There is also the issue in most schools where some portion (in some cases a large portion) of the student population are English Language Learners , ELL, (or termed English as a Second Language students, ESL).

Clearly there is a need for teachers to be proactive regarding helping students learn the various terms that we use regularly in the mathematics classroom.

One easy way to support math vocabulary is a make a Math Words chart that hangs in the classroom, always visible to students. Now, some teachers, particularly in the elementary grades create word walls of general vocabulary terms for young learners, and this is a great idea. Many that I have seen have individual words written on cards and placed alphabetically on the wall. That is a great idea, but I must confess one that for me was not very easy to keep up with on a regular basis.

I am suggesting, instead, that you give math its own sheet so you can add words easily at any time. You need only start with a few words at the beginning of the year and ask your students for suggestions of words to be included. As new words come up in the course of the year, add them. I have often had students in my class prompt me to do just that – they would stop me during our math work and inform me that a certain word needed to be added to the chart. Students used the chart regularly when writing about their thinking. In fact, many times I would see a student sitting, not knowing what to write, scanning the Math Words chart. Finally one term would spark something for him, and the writing could begin.

Having the words posted also reminded us all to use the words in our math discussions. Instead of calling a blue or tan Pattern Block a “diamond”, we would use the correct mathematical term “rhombus”.

The picture of the chart posted here is clearly one used in an primary grade, but the chart is easily adapted to any level. If a phrase is used (such as “ten frames”) one colour is used to show it is a phrase. Otherwise words are written in any colour, multiple words to a line. If possible a small symbol or “cue” is added beside a term to prompt students to remember the meaning of the term.

In particular units of study (such as angles) where there are many new terms, it may be helpful for students to do deeper vocabulary work with the various terms. Using a Frayer Model is helpful for that. (Click here for information about that.)

I hope you will put up a Math Words chart today if you do not already have one up!
Mathematically yours,
Carollee

### Tessellations: Fun with Shape and SpaceMay 31, 2013

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

### Math Bulletin Board: Square Number TowersMay 23, 2013

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

### Tangrams: Seven Shapes, Many PicturesMarch 13, 2013

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!

### Math Bulletin Board: Creating Patterns with a Green Triangle as the 7th ElementJanuary 10, 2013

Often when we do patterns in primary classrooms, we have students extend them, name them, and even create them. But if we ask students to work with patterns in the context of a problem-solving task, the thinking can be even richer.

I recently had both of my grade two math classes create patterns with pattern block pieces. (I was using die cut paper versions of the blocks as I intended to have the students glue down their final product.) I started the lesson by having them create a pattern with the green triangle as the 6th element of the pattern. As I had expected, every child was quickly successful with that. The fact that 6 has factors of both 2 and 3 meant that students creating common patterns such as AB, AAB, ABB, or ABC ending with a green triangle would easily end up repeating the triangle as the 6th element.

The second part of the challenge was significantly more difficult: I asked students to create a pattern with the green triangle as the 7th element of the pattern. Most students were initially stumped as to how to do this. Some just created longer versions of their initial pattern and had to be encouraged to carefully check the 7th element of their pattern. Although the students started out working in a ‘trial and error’ manner, most moved eventually to the point of being able to predict whether or not a green triangle would “land” in the correct spot.

In the end, all but one student was successful in the time frame I had for the lessons (approximately 35 minutes for both parts). I was happy with the thinking and talking that went on in the class as students worked to create and then glue down their patterns.

Pictured here is the bulletin board made from the students’ work.

I would encourage you to do a problem-solving task with your primary students. Of course, feel free to borrow mine! I’d love to hear how it goes with your students.

Mathematically yours,
Carollee

### Math Alphabet PostersSeptember 24, 2012

One of the teachers in my district (thanks, Angela G.!) sent me a link recently to a site where one can download a set of alphabet posters. The wonderful thing about them is that they have a math focus! The picture/word for every letter makes reference to a math idea. Some of the words may be a bit advanced for an early primary class, but the set is certainly useful for later elementary grades, or even middle school classes.

I have printed these off, laminated them, and hung them in my room at Charlie Lake School, and, I must say, they look wonderful. Thank you to the creator, “Little Lovely Leaders”, from the Teachers Pay Teachers website for this resource. At the time of posting, the pdf file of the posters is free to download, so if you are at all interested I suggest you don’t delay 🙂