Friday, October 2, 2009
Monday, July 27, 2009
Using Children's Books to foster Numeracy: useful websites
Articles about Using Children's Literature to teach Mathematics
Promoting Emergent Literacy and Numeracy Through Children's Literature
http://www.cayc.ca/promolit.pdf
Curriculum: Math and Literature—A Match Made in the Classroom!
http://www.education-world.com/a_curr/curr249.shtml
Book Lists:
Marilyn Burns Classroom Library
http://teacher.scholastic.com/products/statehomepages/nm/pdfs/NM_BurnsGK.pdf
Books for Teaching Math Concepts
http://www.education.uiowa.edu/crl/bibliographies/documents/BooksforTeachingMathConceptsupdatedforweb2009.pdf
Lesson Plan Ideas:
Share 2 Learn: Literature ad Math
http://www.share2learn.com/mathliterature.html
Illuminations: Mathematics and Children's Literature
http://illuminations.nctm.org/LessonDetail.aspx?ID=U83
Utah Education Network: How Big is A Foot
http://www.uen.org/Lessonplan/preview.cgi?LPid=10729
Exemplars: How Big is a Foot
http://www.uen.org/Lessonplan/preview.cgi?LPid=10729
Find the story for the above 2 lessons at
http://www.vidyaonline.net/arvindgupta/kingsfoot.pdf
General Resources:
Home Page for New Math Teachers
http://terri.clarityconnect.com/terri.html
Wednesday, July 15, 2009
Numeracy on the Bus
This morning, on the bus ride up to Burnaby Mountain, as I stared mindlessly at the propaganda lining the bus walls, I happened upon the following claim:
“Glasses for Half the Price!”, followed by a website address.
As I am counting the days until my insurance coverage will kick in to pay for new glasses, this spoke to me. “Right on!” I thought, “I need new glasses, half price is a great deal! I’ll get my glasses from there and that way be sure that insurance will cover the whole amount!”
As I was on the bus halfway up the mountain, I couldn't immediately log on to the web and check it out, so I got to using my numeracy skill to think about the claim and if I really believed them.
Half of the Price….. hmm, what price are they referring to? What store’s pricing are they comparing themselves to? Lenscrafters? Cheap-O Optical? Who? In my experience, the price of frames and lenses vary greatly from place to place.
And when they speak of ‘glasses’ are they referring to just the frames? Or frames and lenses? Or maybe just the lenses?
Last year I did some comparison shopping and found significant differences in similar frames, and I found some deceptive advertising from a major eyeglass retailer when they offered free lenses. The ‘free’ lenses only went with certain frames, whose prices seemed to be inflated to compensate for the gift of the basic lenses. Also, the free lenses were the most basic style and they were kind enough to inform customers of how they deserved a much better quality of lenses with all the latest technology…which they again were pleased to offer at a price.
When they had finally priced out my ‘sale’ offer eyeglasses, I was presented with an estimate of over $500… My insurance covers up to $275 dollars, so a quick calculation told me I would have to cover the other (500-275) $225. No way.
I ended up buying a very similar frame with high quality lenses from Factory Optical, a locally owned, low-key operation and they cost me $178. Now, I realize the other store has more expenses: they are in a mall, their store is fancy, you get your glasses in an hour blah, blah, blah. I don’t care that the store was off the beaten path or that I had to wait a week for the glasses. My Utility factor was based on quality and price, not convenience.
And, as hoped, I got some nice glasses for a good price.
Anyways, back to the ad on the bus. Thinking about the bus ad brought the memory of last years glasses shopping into the forefront of my thoughts and I was skeptical.
Assuming the ad spoke of a complete pair of glasses, I still didn’t know what their baseline for ‘half-price’ was.
Half off of the big box store price of about $500 would be (500/2) 250, making the ad’s offer $250 for eyeglasses. That’s still (250-178) $72 more than what I paid last year and not really such a good deal for me.
ON the other hand, if they are referring to the Factory Optical price of $178 and taking half off of that, that would mean I could get my glasses for $89, which would be a great deal.
I decided to investigate their website: [www.clearlycontacts.ca] to price a pair of glasses similar to the pair I bought last year (using that as a type of scale for comparison)
This is what I came up with
[ www.clearlycontacts.ca/glasses/frames/hugo-boss-47-dark-tortoise/prod25079.html ]
A similar styled pair, similar designer brand, and lenses included for only $98! (plus taxes, I would assume)
If this pair is $98, I guess they are assuming you would usually pay (98 x2) $196 for these glasses, which makes their price point close to Factory optical’s pricing than the other store’s. I guess their claim of “Glasses for Half the Price” was pretty accurate.
“Glasses for Half the Price!”, followed by a website address.
As I am counting the days until my insurance coverage will kick in to pay for new glasses, this spoke to me. “Right on!” I thought, “I need new glasses, half price is a great deal! I’ll get my glasses from there and that way be sure that insurance will cover the whole amount!”
As I was on the bus halfway up the mountain, I couldn't immediately log on to the web and check it out, so I got to using my numeracy skill to think about the claim and if I really believed them.
Half of the Price….. hmm, what price are they referring to? What store’s pricing are they comparing themselves to? Lenscrafters? Cheap-O Optical? Who? In my experience, the price of frames and lenses vary greatly from place to place.
And when they speak of ‘glasses’ are they referring to just the frames? Or frames and lenses? Or maybe just the lenses?
Last year I did some comparison shopping and found significant differences in similar frames, and I found some deceptive advertising from a major eyeglass retailer when they offered free lenses. The ‘free’ lenses only went with certain frames, whose prices seemed to be inflated to compensate for the gift of the basic lenses. Also, the free lenses were the most basic style and they were kind enough to inform customers of how they deserved a much better quality of lenses with all the latest technology…which they again were pleased to offer at a price.
When they had finally priced out my ‘sale’ offer eyeglasses, I was presented with an estimate of over $500… My insurance covers up to $275 dollars, so a quick calculation told me I would have to cover the other (500-275) $225. No way.
I ended up buying a very similar frame with high quality lenses from Factory Optical, a locally owned, low-key operation and they cost me $178. Now, I realize the other store has more expenses: they are in a mall, their store is fancy, you get your glasses in an hour blah, blah, blah. I don’t care that the store was off the beaten path or that I had to wait a week for the glasses. My Utility factor was based on quality and price, not convenience.
And, as hoped, I got some nice glasses for a good price.
Anyways, back to the ad on the bus. Thinking about the bus ad brought the memory of last years glasses shopping into the forefront of my thoughts and I was skeptical.
Assuming the ad spoke of a complete pair of glasses, I still didn’t know what their baseline for ‘half-price’ was.
Half off of the big box store price of about $500 would be (500/2) 250, making the ad’s offer $250 for eyeglasses. That’s still (250-178) $72 more than what I paid last year and not really such a good deal for me.
ON the other hand, if they are referring to the Factory Optical price of $178 and taking half off of that, that would mean I could get my glasses for $89, which would be a great deal.
I decided to investigate their website: [www.clearlycontacts.ca] to price a pair of glasses similar to the pair I bought last year (using that as a type of scale for comparison)
This is what I came up with
[ www.clearlycontacts.ca/glasses/frames/hugo-boss-47-dark-tortoise/prod25079.html ]
A similar styled pair, similar designer brand, and lenses included for only $98! (plus taxes, I would assume)
If this pair is $98, I guess they are assuming you would usually pay (98 x2) $196 for these glasses, which makes their price point close to Factory optical’s pricing than the other store’s. I guess their claim of “Glasses for Half the Price” was pretty accurate.
Numeracy at T and T Market
The other day I arrived at the SFU Surrey Campus with time to spare, so I headed over to T and T Market in search of unusual and yummy food products imported from nations around the world.
I came across NesCafe 3 in 1 instant coffee packets imported from Malaysia. These are packets of instant coffee, creamer and sugar, individually packaged for your convenience. Thirty packages to a bag, each bag costing $8.69.
This was significant to me for 2 reasons: 1. I am a coffee fanatic and 2. I am cheap.
“Hmmm…”, I thought “Should I buy this to take to school? I could have my coffee and spend less money!” In order to make the decision, I considered several things.
If 30 cups cost $8.69, how much does that work out per cup? -Rounding it up to $9, that would be 9.00 divided by 30, which would be about 30 cents per cup.
How much of a savings per cup is that compared to what I would usually spend at the SFU coffee shop? - In a best case scenario, where I bring a mug and at SFU Bby (where coffee is cheaper), at Renaissance coffee, I spend 1.35 for a refill cup. That means I would save 1.05 per cup.
I usually have 2 cups every day I at class, so that means spending 2.10 each day. For four days a week on campus per week, I am saving about $8.40. Not too bad!
But… then I started to thinking… Do I really want to be drinking instant instead of brewed coffee? Does the savings make it work it?
So, I did a quick little analysis of the Utility factors involved:
UT for delicious taste of a brewed cuppa joe: 10
UT for spending $1. 35 per cup: -9
Total for brewed: 1
UT for somewhat less delicous taste of instant 5
UT for spending the minimal amount of $.30 9
Total for instant: 14
It became obvious that I was willing to opt for the mediocre coffee with the thrifty price tag, so I bought the big bag of Nescafe 3 in 1!
I came across NesCafe 3 in 1 instant coffee packets imported from Malaysia. These are packets of instant coffee, creamer and sugar, individually packaged for your convenience. Thirty packages to a bag, each bag costing $8.69.
This was significant to me for 2 reasons: 1. I am a coffee fanatic and 2. I am cheap.
“Hmmm…”, I thought “Should I buy this to take to school? I could have my coffee and spend less money!” In order to make the decision, I considered several things.
If 30 cups cost $8.69, how much does that work out per cup? -Rounding it up to $9, that would be 9.00 divided by 30, which would be about 30 cents per cup.
How much of a savings per cup is that compared to what I would usually spend at the SFU coffee shop? - In a best case scenario, where I bring a mug and at SFU Bby (where coffee is cheaper), at Renaissance coffee, I spend 1.35 for a refill cup. That means I would save 1.05 per cup.
I usually have 2 cups every day I at class, so that means spending 2.10 each day. For four days a week on campus per week, I am saving about $8.40. Not too bad!
But… then I started to thinking… Do I really want to be drinking instant instead of brewed coffee? Does the savings make it work it?
So, I did a quick little analysis of the Utility factors involved:
UT for delicious taste of a brewed cuppa joe: 10
UT for spending $1. 35 per cup: -9
Total for brewed: 1
UT for somewhat less delicous taste of instant 5
UT for spending the minimal amount of $.30 9
Total for instant: 14
It became obvious that I was willing to opt for the mediocre coffee with the thrifty price tag, so I bought the big bag of Nescafe 3 in 1!
Numeracy in my coffee cup
Each morning, I wake up before my husband and the first thing I do is put on a pot of coffee. I then proceed to make lunches, unload/ reload the dishwasher, and tidy up the kitchen.
Eventually, my husband rolls out of bed and tumbles into the living room, turns on the morning news and mumbles something about wanting coffee. Being the Good Wife that I am, I reason to myself that he is not a morning person, poor fellow, I should really get him a cup of coffee and set his day off to a nice start as kindness is the foundation of the respect and love I have for him.
Simultaneously, my inner B. is thinking that this lazy oaf needs to get off the bloody couch and get his own (BLEEP)ing coffee, what does he think this is, a restaurant? So what do I do? Of course, being the Good Wife, I take down the cups from the shelf and proceed to get my beloved a cup of coffee, sweetened with a toach of organic sweet cane, just as he likes it…
But, my inner B. is not willing to go down without a fight, so I choose those cups carefully. Cup A and Cup B are, at first glance, quite similar but I know the differences (insert evil laughter here).
Both cups are the same height, but Cup B is a more square shape and has a larger diameter than the circular, smaller diametered Cup B. When filled Cup B holds more than Cup A. When I fill them to the same height (fairsy-sharesy!), whomever gets Cup B gets more coffee. Whomever gets more coffee WINS! Of course I take Cup B, I WIN! TAKE THAT YOU LAZY BUM! (more evil laughter)
“Nothing, Honey, just talkin’ to myself, here’s your coffee. Enjoy!”
I am avenged, yet my husband, in his blissful innumerate ignornace, doesn’t suspect a thing…
Eventually, my husband rolls out of bed and tumbles into the living room, turns on the morning news and mumbles something about wanting coffee. Being the Good Wife that I am, I reason to myself that he is not a morning person, poor fellow, I should really get him a cup of coffee and set his day off to a nice start as kindness is the foundation of the respect and love I have for him.
Simultaneously, my inner B. is thinking that this lazy oaf needs to get off the bloody couch and get his own (BLEEP)ing coffee, what does he think this is, a restaurant? So what do I do? Of course, being the Good Wife, I take down the cups from the shelf and proceed to get my beloved a cup of coffee, sweetened with a toach of organic sweet cane, just as he likes it…
But, my inner B. is not willing to go down without a fight, so I choose those cups carefully. Cup A and Cup B are, at first glance, quite similar but I know the differences (insert evil laughter here).
Both cups are the same height, but Cup B is a more square shape and has a larger diameter than the circular, smaller diametered Cup B. When filled Cup B holds more than Cup A. When I fill them to the same height (fairsy-sharesy!), whomever gets Cup B gets more coffee. Whomever gets more coffee WINS! Of course I take Cup B, I WIN! TAKE THAT YOU LAZY BUM! (more evil laughter)
“Nothing, Honey, just talkin’ to myself, here’s your coffee. Enjoy!”
I am avenged, yet my husband, in his blissful innumerate ignornace, doesn’t suspect a thing…
Tuesday, July 14, 2009
Numeracy at Music School
My son has been taking piano lesson at a neighborhood music school. They recently sponsored a recital at the church down the street where many of the students made their parents proud by singing, playing various instruments and generally looking extremely adorable.My son was the youngest little one of all and I was truly impressed by the composure and grace
he exhibited while he sat at the enormous grand piano and tickled the ivories. While thining about examples of numeracy in daily life, I got to thinking about music and all the numeracy exhibited in interpreting a piece.
I decided to look at the simple piece my son played at his recital, a variation of the 'Mary had a Little Lamb' melody.
This is whay I came up with in a sort of list form:
Child needs to know how to count to understand notes and note length
Child needs to understand idea of fraction (whole, half, quarter and eighth notes)
Child needs to understand syllables (ie counting them out) in a world to be able to match the words and the notes
Child needs to be able to grasp connection between symbol and what it stands for, in this case, what does a note mean? how does this symbol relate to how long this sound should last?
Child needs to understand the ideas of 'slower/faster', 'louder/softer' in relation to what is played, using a type of scale to measure (using a song as the scale to measure against - ie I play it, now you pay it faster/slower/softer/louder)
I can see why music is considered closely to mathematics, the concepts are clearly related. I keep telling my little guy that he likes math, so it is logical that he likes music and he agrees!
Numeracy in a Public Service Announcement
The BC gaming commission has produced a new ad for TV aimed at helping the viewer understand the idea of simple probability.
Have a look at it. http://www.bclc.com/documents/GameSense_Conform_bar.wmv
It's funny and I think it attempts to portray the concept that the probability of an event happening (in this case, a girl accepting the guy's advances) as being independent of the number of times you repeat that event.
In the case in this ad, the chances of the girl accepting his advances do not improve despite the number of times he attempts to get her attention.
I see this like a simple probability experiment, much like flipping a coin. The probability of you flipping a specific side (heads or tails) on any given flip does not change, regardless of how many times you flip that coin.
Looking at the situation portrayed in the ad as a probability experiment, the probability of the woman saying yes is one out of two possible outcomes (yes or no).
Expressed mathematically this is:
P(yes) = ½ or 50%
Interestingly, the probability of her saying yes is also 50% for any given attempt.
Hmm... in that case, if this was really like the coin flip experiment it would have had to have been a woman with no short-term memory. In order for this to be a truly random event, she would have had no memory of him having asked her before. As she does have a memory of his advances, this is influencing her response. In this woman's case, her memory will either cement her decision to refuse him or eventually he will wear her down and she will accept. Not random at all.
I realize the point of the Public Service Ad is to hep people realize that repeated play in a casino game is not making the probability of them winning any better, but perhaps the depiction they chose is not the best suited to their message, as the event they are depicting doesn't really convey that message when you start to dissect it.
Have a look at it. http://www.bclc.com/documents/GameSense_Conform_bar.wmv
It's funny and I think it attempts to portray the concept that the probability of an event happening (in this case, a girl accepting the guy's advances) as being independent of the number of times you repeat that event.
In the case in this ad, the chances of the girl accepting his advances do not improve despite the number of times he attempts to get her attention.
I see this like a simple probability experiment, much like flipping a coin. The probability of you flipping a specific side (heads or tails) on any given flip does not change, regardless of how many times you flip that coin.
Looking at the situation portrayed in the ad as a probability experiment, the probability of the woman saying yes is one out of two possible outcomes (yes or no).
Expressed mathematically this is:
P(yes) = ½ or 50%
Interestingly, the probability of her saying yes is also 50% for any given attempt.
Hmm... in that case, if this was really like the coin flip experiment it would have had to have been a woman with no short-term memory. In order for this to be a truly random event, she would have had no memory of him having asked her before. As she does have a memory of his advances, this is influencing her response. In this woman's case, her memory will either cement her decision to refuse him or eventually he will wear her down and she will accept. Not random at all.
I realize the point of the Public Service Ad is to hep people realize that repeated play in a casino game is not making the probability of them winning any better, but perhaps the depiction they chose is not the best suited to their message, as the event they are depicting doesn't really convey that message when you start to dissect it.
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