Focus on Math

Helping children become mathematicians!

Patterns in 100 Charts: A Treasure of Learning March 21, 2013

Screen shot 2012-04-22 at 3.18.39 PM Are you looking for a great activity to do with your elementary-aged children? Consider playing with a 1-to-100 chart (often called a 100 chart), or its first cousin, the 0-to-99 chart. These visual organizations of numbers are a staple in primary classrooms, but both bear looking at deeply and often.

One great thing to do is to examine the patterns are created when you colour or highlight various skip counting patterns on the chart. Often we think of skip counting by 2, by 5 and by 10. But if you consider each of the skip counting patterns (by 2, 3, 4, 5, 6, etc) you are also playing with the multiples of those numbers. When students in grades 3-6 practice multiplication facts, they usually do not go beyond x10 or in some cases 12. By looking at the skip counting all the way to 100, you can explore the repeating patterns that show up. Some of the patterns are particularly interesting! (Do you know how a knight moves on the chessboard? Try looking for that pattern in the skip counts.)

As an intermediate classroom teacher, I always had my class do these colouring patterns and we stapled the sheets into a little booklet that they kept in their “math toolkits”. We revisited them throughout the year.

Do some general exploring of patterns, too. Just let kids “notice” some things. If you need a few prompts, consider these:
What patterns happen in vertical columns?
What patterns happen in horizontal rows?
Compare the various diagonal rows?
What do you notice when you colour every number with the digit 4 in it? With 5?
What is the same in each of the above? What is different?

I have provided mini-100 charts and mini 0-99 here for you to download for use in your colouring and comparing activities. I hope you will try some with a class or with your own child. Enjoy!

Mathematically yours,


What Math Ideas is Your Child “Catching” from You? March 18, 2013

Filed under: General Math,Parents — Focus on Math @ 3:37 pm

Screen shot 2013-03-18 at 3.35.03 PM “Values are caught, not taught.” That is a quote from Dr. James Dobson, a psychologist who has written much about family relationships. Dobson contends that if you want to teach your children personal values such as respect, honesty, integrity, and tolerance, then you have to live those values. It is not good enough to have conversations with children about them to try to teach those values, but how you live day after day in front of your children is really basis of the lesson.

So, why talk about values in a math blog? Because I believe there are many parents unintentionally “teaching” their children their own negative values or beliefs about math as they say things in front of their children that clearly transmit those feelings. Statements such as, “Oh, I was never very good at math,” or “I never understood any of this stuff,” or “I hated math class!” send the negative message loud and clear. Children end up being afraid of math and believing that they will do poorly just at their parents did.

So what actions can parents take to encourage their children mathematically? First, stop all the negative talk! Even if you feel it, don’t say it! Rather, begin to notice where math shows up in real life and talk about that. (Let me interject here that lots of folks think they don’t use math much, but stop and think about it. Math shows up when we spend money, when we measure for cooking or crafting or building, when we tell time, estimate distances, and buy paint for the bedroom. It shows up on the scale at the weigh-in, when we figure out the amount of a discount or the amount of a tip. Math shows up everywhere!)

Play games with your children, especially those that use dice and cards, or any game in which you have to keep score. Crib is a great game for adding! Play Monopoly, the older version (not the newer one with the electronic banking) where you have to figure out the money being exchanged. Play logic games like chess, checkers, Othello (aka Reversi). Get children involved in Sudoku. (Download a daily kid-version of Sudoku here.)

Any teacher can tell you that if a child has a positive attitude toward mathematics, that goes a long way to helping the child actually learn math. A negative attitude causes a child to just shut down from the beginning – it is like the learning stops before it has even begun.

Your words matter. What you say in front of your kids about math matters. Keep it positive!
Mathematically yours,


My newly launched sites :) March 14, 2013

Filed under: General Math — Focus on Math @ 4:22 pm

Screen shot 2012-03-12 at 10.03.39 AM In honor of Pi Day (3/14) my new website and face book page have been published. Please connect with me here!

Pi Day is celebrated on March 14th (3/14) around the world. Pi (Greek letter “π” , is the symbol used in mathematics to represent a constant — the ratio of the circumference of a circle to its diameter — which is approximately 3.14159.

Pi has been calculated to over one trillion digits beyond its decimal point. As an irrational and transcendental number, it will continue infinitely without repetition or pattern. While only a handful of digits are needed for typical calculations, Pi’s infinite nature makes it a fun challenge to memorize, and to computationally calculate more and more digits.
Mathematically yours,


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,

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


Strike it Out: a Primary Game from NRICH March 5, 2013

Filed under: Basic Facts,General Math,Parents,Primary Math Ideas & Problems — Focus on Math @ 12:06 pm
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Screen shot 2013-03-05 at 8.43.25 AM One thing that I came across recently on the NRICH math website is an quick primary students’ game for practicing addition and subtraction with numbers to 20. On the particular webpage for “Strike it Out”, they offer a poster (a picture of which is posted here), a short video clip of the game, and a power point file all which give the instructions for the game.

I had each of my grade two math classes playing this game recently as a warm-up activity, and they loved it! The games go quickly for the most part – of course, some of the pairs of students were slower at the game, but those students were still engaged and trying their best.

The rules, simply, are these:
• Using a number line marked 0-20, one student begins by creating and recording an addition or subtraction equation, e.g., 4 + 10 = 14. On the number line he crosses out the 4 and 10 and circles the 14. His turn is over.
• The partner must now create a new addition or subtraction equation, but it must use the number 14 as one of the first two numbers, e.g., 14 – 6 = 8. She would crosses out the circled 14, crosses out the 6, and circles the 8. Her turn is over.
• The 8 must be used now by the first partner in his new equation, with the recording and crossing out and circling continuing.
• Play continues until one of the partners cannot make a correct number sentence, and the player who made the last correct equation wins.

Although there are many possibilities for equations near the beginning of the game, there are fewer possibilities as the game progresses. I watched students doing a lot of mental math trying to come up with appropriate equations. The students who needed support had a set of ten frames on the table to use to help the visualize and calculate.

I am including for download the game board page I made for students to use. (Cut the page in half to use.) Two students play on a single game board at a time.

There are lots of other great ideas on the NRICH math site for many different levels. I hope you will take some time and explore what is there!

Mathematically yours,

Link to game on the NRICH math site here

Download the game board here.