# Focus on Math

## Helping children become mathematicians!

### Math Club for Elementary or Middle School StudentsNovember 5, 2013

You 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

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### Math BowlingOctober 1, 2013

This “Math Bowling” activity is one that students tend to love! It is great for practicing math facts as well as for stretching students’ thinking.

The activity is done as follows (students alone or in pairs):
Roll three dice (your choice whether to use regular six-sided dice or include one or more different dice, such as a ten-sided die). Write the numbers in the boxes marked “strike”. Using all three numbers each time exactly once, students work to write equations to equal each of the numbers 1 to 10 of the “pins” marked on the sheet and thus “knock them down”. Students may use whatever operations they understand: addition, subtraction, multiplication, and division are standard, but students may also use exponents, roots, and factorials if those are in their realm of mathematical knowledge.

For instance, if the numbers rolled are 2, 3, and 6, students might “knock down”
1 = 6 – 2 – 3 OR 1= 6/(2 x 3)
3 = [( 3!)/6] + 2
4 = (2 x 6) ÷ 3
5 = 6 + 2 – 3
6 = (6 ÷ 2) + 3
7 = 3 + 6 – 2
9 = (6 ÷ 2) x 3

If the students did equations for those 7 numbers/pins, that would constitute the first throw of the ball. Since all the pins are not knocked down, the player may roll the dice a second time, record the numbers in the boxes marked “spare” and try to knock down the three remaining pins using that second set of numbers to score a spare. If that is not accomplished, the student scores the number of pins knocked down in the two “throws”.

If you wish, as players take multiple turns, you can calculate scores in the manner that 10-pin bowling is actually scored. As someone who was on a youth bowling league in my younger days, I know the scoring system well. There is some good math in the score keeping, too! If you are not familiar with that scoring system, here is a website which will walk you through the scoring process.

http://www.bowling2u.com/trivia/game/scoring.asp

I hope you will give math bowling a try with your class.
Mathematically yours,
Carollee

### Simplifying Radicals — Play the Game!October 29, 2012

Filed under: General Math,Middle School/Secondary School Math — Focus on Math @ 3:31 pm
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After reading about the game that Richard DeMerchant created for practicing the skill of approximating square roots, Katie Wagner (a friend and colleague) adapted the idea and created a game for practicing the skill of simplifying radicals! I think this is another winner, and hope that you will try this in your secondary classroom as it fits into your curriculum.

Thanks for sharing this, Katie. Link to Katie’s game here.

Mathematically yours,
Carollee

### Approximating the Square Root of Numbers — Play the Game!October 13, 2012

For those teachers who are looking for a way to have their students practice approximating square roots in an interesting manner, Richard De Merchant (a friend and colleague) has created a game for just such a purpose.

He explains how to play the game and adds some other helpful tips on his blog Math in the Middle (click here for the link to this particular post).

If this is something your students need practice with, then I heartily recommend that you check out this game 🙂

Mathematically yours,
Carollee

### Dot Plate Workshop: Early Numeracy ConceptsOctober 9, 2012

This week some of the teachers in the district attended a workshop held here at the SD#60 board office. Our focus for the session was early numeracy, in particular, number relationships that are important for young learners. We focused on these “big four” relationships:
• One more/one less (extending to two more/two less)
• Visual/spatial relationships
• The benchmarks or anchors of 5 and 10
• Whole-part-part

I particularly refer to the whole-part-part relationship in that manner (as opposed to part-part-whole often used by others). I like stating “whole” first because the emphasis of that relationship is that a number can be pulled apart into two smaller parts, not the joining together of two parts to make a larger whole. This distinction is not just a matter of semantics, but rather a spotlighting of the pulling apart. “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, 2005).

Understand that there is a lot of counting that must take place as children work to build these relationships. They must repeatedly work with counters as well as dice, dominoes, ten frames, dot cards, dot plates, and other things that show patterned arrangements of numbers to build a deep understanding about the numbers, first 1-10, then extending to 20, to 100 and beyond.

The workshop participants went home with a set of dot plates they made from small paper plates and bingo daubers (see photo). They also took home 4 sets of small dot cards printed on colourful cardstock. Lastly they took away larger paper plates with dot patterns on them (the patterns from either mini dot cards or mini ten frames) that could become spinners for games or made into activities for math centres.

One other tool that we talked about was a grid of tools that both the teacher and students could use for representing numbers. When one looks at the grid and possible combinations of materials, it is easy to see that having a few good tools on hand allows for many different ways for young children to be involved in representing number.

Download the Representing Number Grid here.

I hope you will think deeply about the ways you are having your young learners interact with numbers! You are laying the foundation for later mathematical learning.

Mathematically yours,
Carollee

PS My apologies to the participants — I had intended to post this blog by the end of last week and did not get to it, and over the weekend I did not have access to the visuals I wanted to post with it. So, hopefully, this is a case of better late than never!

Reference
Van de Walle, J. and Folk, S. (2005). Elementary and Middle School Mathematics: Teaching Developmentally (Canadian Edition). Pearson: Toronto.