The Meaning of Equality April 23, 2011

I was in Indianapolis, Indiana recently at the National Council of Teachers of Mathematics (NCTM) National Conference. First of all, let me say that it was a fabulous meeting of minds! I am full of new ideas to try with my students and to share with teachers in my district.

I was honoured to get to present at the conference. I did my workshop “Packing a Powerful Punch with Patterns” which is about using patterns (especially pictorial ones) to help younger students build algebraic thinking. One of the important points in the workshop is about equality. We, as teachers, need to make sure we offer lots of opportunities for students to build an understanding of this concept. We use the term frequently in our classrooms, saying things like “two plus three equals five” referring to the symbolic notation of that: 2 + 3 = 5. Day after day, week after week, month after month, year after year we use the term “equals”, but seldom do we stop and check to see if the students understand the term as we mean it. It is most likely that they do not. Studies have shown that students then to think that “equals” means “put the answer here”, or “now do the operation”. They tend to have no reference point for the idea that whatever is on one side of the equal sign has the same value as what is on the other side.

Teachers can help students with this by doing a few simple things. First, try writing equations with the “answer” on the left: 5 = 2 + 3. When children see that for the first time, they tend to tell you that you have written it incorrectly! Another great thing to try is to write equations such as 2 + 3 = 4 + 1. You can also leave out any one part of that equation and have students solve it. Again, they are likely to have a misunderstanding and tell you that 2 + 3 does NOT equal 4 since that is where they are used to stopping in their thinking. Using actual balance scales with small blocks or other regularly-sized manipulatives is a great way to help students develop this important concept.

So, the next time you are using equations in a lesson, take some time and find out how well your students understand equality. It’s worth putting some time into this topic!

Mathematically yours,
Carollee

100 DAY! April 7, 2011

Many elementary classes (especially primary ones K-3) celebrate the 100th day of school, which, depending on the particular school calendar, usually happens around the middle of February. I would like to propose another chance to celebrate 100 day, and that is April 10 as it is the 100th day of the calendar year (April 9 if it is leap year!).

There are many really wonderful things to do to celebrate and explore the number 100. One of my favourites is to look for words worth 100 cents or $1.00. The letters of the alphabet are assigned a value beginning with a = 1 cent, b = 2 cents, c = 3 cents, etc. (see illustration) and from there students begin to put together their words, aiming for 100. The $1.00 Word Riddle Book by Marilyn Burn is full of clues to help puzzlers of any age find some of these special words.

Here are a few clues to get you started:

* a zoo animal (at least two different ones)
* items found in a public washroom
* a fall (or Halloween) word
* a famous scientist (who had something to do with milk…)
* a particular golf club
* a number less than 50
* a place to keep memories
* a sea creature
* items worn in the winter
* a Thanksgiving word
* better than good

Looking at prefixes or suffixes can be helpful. For instance, adding -ed to a word adds 9 cents (adjusting the main target to 91 cents); adding -ing to a word adds 30 cents; and adding -s to a word adds 19 cents.

I hope you’ll try the activity with the children in your life, and be sure to post any words you find! Celebrate 100 Day!

Mathematically yours,
Carollee

More on 100 Day! April 5, 2011

With the 100th day of the calendar year coming up soon, I thought I would post a few more ideas for activities involving 100. Hopefully some of them will be useful to you with your students. So in no particular order…

• Read 100 Hungry Ants to your kids and have them divide 100 by other numbers. Ask how many groups? How many in each group? How many left over? (A 100 dot array is a useful tool here — kids can circle groups they are making right on a small 100 dot array and to figure out the answer for each group size.)

• Give young students (grade 1 or 2) a 100 chart (either 0 to 99 or 1 to 100) and say random numbers for them to find and cover with a bingo chip.

• Have students figure out how far to 100 (or to 100%). Again, a 100 dot array is a useful tool. Given a certain number or percentage, e.g., 23 or 23%, have students figure out how much is needed to get to 100 or 100%.

• Pour out 100 candies such as jelly beans, Skittles, or Smarties and graph them by colours.

• Have students close their eyes and stand when they think 100 seconds have passed.

• Cut pieces of string, estimating 100 cm. See who can come closest to the actual amount (graph the estimated lengths).

• Have students bring in 100 of the same item from home (e.g., pieces of macaroni, Lego blocks, pieces of gum, mini marshmallows, bobby pins, etc) and weigh the different amounts.

• Have students jump rope 100 times and then take their pulses. Graph and compare.

• Hold a 100 second race.

• Create pictures using only 100 cm of yarn or string.

• Use large 10 x 10 grids and have students colour them in two colours to make a pattern or picture.

There are lots of things that can be done to celebrate the day. I am doing several of these activities with my eight classes of students at Charlie Lake School this week. No matter your grade, it is always great to put some fun in math!

Mathematically yours,
Carollee