Sometimes I cringe to think about the way I used to have the kids solve word problems. In our standard problem solving model, where the first "box" requires the kids to write down important information from the problems, I would have them start at the beginning of the story and write all of the numbers with their corresponding units. But this can lead to a really packed, overbogged-down first box...
Last week, I gave the kids this problem:
Mr. Teacher has 37 hats, 28 baseballs, 19 gloves, and $640.00. He bought 3 cookies for 50 cents each. How many more hats does he have than gloves?
With my OLD technique for problem solving, most of my kids probably would have bogged down on all of the extra information. But with the NEW way, nearly everyone in the class got the question correct.
Now, instead of starting at the beginning, I have the kids start at the end. They always write the QUESTION first, and then focus in on the unit that the question is asking them to count. In this case, it's only hats and gloves. The kids were able to ignore the baseballs, the dollars, and the cookies.
The few kids who DIDN'T get the question correct are the ones who still think "how many more" is a prompt to add instead of subtract.
I have a low group of kids this year, and they have trouble retaining concepts. But they are definitely getting better at problem solving, especially when the target the question and the important units first.
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Showing posts with label word problems. Show all posts
Showing posts with label word problems. Show all posts
Wednesday, November 16, 2011
Saturday, February 19, 2011
TMI
As I posted about a few weeks ago, I've been trying a new method with word problems with my kids. One that has them focus more on the question first and only on the aspects of the problem that they really need. I've been pretty encouraged by how it's gone. Clearly, some of the kids are still a little tied to the old system, which makes me think that if I start the new method from day 1 next year, it will be even better.
Still, the kids this year are coming along pretty well. On Wednesday, I had a problem solving day. I gave each pair of kids a word problem that had extra information or some other trick in it, and had them work together to solve it on a big piece of paper. I found that the kids weren't quite as far along the slope as I had thought they were. Some of them weren't paying attention to the units or dividing when they should be multiplying, or making their tables all wrong. A lot of the extra information was being included in the "See" box, when it should be ignored. But we talked about things, and I think got a lot set right.
Then on Thursday, I presented them with "The Big One." I made up the biggest, longest, most complicated problem that I've given them all year. Here's what it said:
Billy and his 3 friends caught 18 worms on Saturday. Then they went to a restaurant and bought 5 hamburgers for a total of $10.50. Each boy ate 12 french fries. Each boy got 3 napkins. Then they saw 6 of their friends. How many french fries did Billy and his friends eat in all?
I set them loose on this bad boy, and I was very pleased to see most of them get it right. For the most part, the kids did not circle or include the extra information in the "see" box. Nobody got fooled by the napkin sentence. Even the kids who got it wrong, were close. They only counted 3 boys and forgot Billy, or they added the 6 friends who were seen at the end.
This gives me hope that maybe my kids ARE becoming better "math detectives" after all!
Now if I could just get them to learn their times tables!!!
Still, the kids this year are coming along pretty well. On Wednesday, I had a problem solving day. I gave each pair of kids a word problem that had extra information or some other trick in it, and had them work together to solve it on a big piece of paper. I found that the kids weren't quite as far along the slope as I had thought they were. Some of them weren't paying attention to the units or dividing when they should be multiplying, or making their tables all wrong. A lot of the extra information was being included in the "See" box, when it should be ignored. But we talked about things, and I think got a lot set right.
Then on Thursday, I presented them with "The Big One." I made up the biggest, longest, most complicated problem that I've given them all year. Here's what it said:
Billy and his 3 friends caught 18 worms on Saturday. Then they went to a restaurant and bought 5 hamburgers for a total of $10.50. Each boy ate 12 french fries. Each boy got 3 napkins. Then they saw 6 of their friends. How many french fries did Billy and his friends eat in all?
I set them loose on this bad boy, and I was very pleased to see most of them get it right. For the most part, the kids did not circle or include the extra information in the "see" box. Nobody got fooled by the napkin sentence. Even the kids who got it wrong, were close. They only counted 3 boys and forgot Billy, or they added the 6 friends who were seen at the end.
This gives me hope that maybe my kids ARE becoming better "math detectives" after all!
Now if I could just get them to learn their times tables!!!
Wednesday, February 09, 2011
How I Met Your Word Problem
Over Christmas break, I had a bit of an epiphany. Not THE Epiphany, January 6, when the Wise Men visited the newborn Jesus, and the day that you are supposed to take down your Christmas tree (though my mother-in-law leaves her tree up year round). But a teaching epiphany all the same.
I came up with a game plan in my head for a better way to teach the kids to solve word problems. Thankfully, I did have a week or so to implement it before all these crazy inclement weather days started piling up (we're on our FIFTH today). The kids are taking to it somewhat slowly, but when they do, I think it's really effective.
It's also one of those things that I'm kind of kicking myself in the butt for never having thought of before. I have a nagging feeling that many of you reading this will say, "And just why the heck haven't you been doing it this way ALWAYS?? Duh!!" Nevertheless, I'll attempt to explain.
In Dallas, we have a problem solving model that we have to use. It's called See-Plan-Do-Reflect, or SPDR. The kids make a giant plus sign, +, and each quadrant has its own purpose. Let me write a typical word problem, and I'll try to explain the old way first, and then the new way.
Timmy has $13.00. He bought 32 apples in 4 crates. Each crate had the same number of apples. How many apples were in each crate?
Step number 1 remains the same, and always will. READ the problem. I can't stand it when kids just see 13, 32, and 4 and add them all. So they have to read it through once first.
BEFORE, I would have them start at the very beginning and put every number they saw into the "See" box. They would wind up with something like this:
T -> $13.00
He bought 32 apples
There are 4 crates
How many apples were in each crate?
Then they draw the 4 operation signs off to the side and take a good look at the units in their box. If the units are the same (apples and apples) or the same TYPE of thing (dogs and cats, or boys and girls), they know they can only add or subtract and can eliminate the other two operations. If the units are different (apples and crates, or candy and bags), they can eliminate addition and subtraction.
In the "Plan" box, they would draw a picture. I've taught them to always circle the word "each" and to put a box around whatever unit comes after that word -- in this case, "crate." The box tells them what to draw. They need to draw 4 crates (they draw circles to keep it simple), and put the correct number of apples (tally marks) in each crate. If the sentence that said "each crate" already tells them the number of apples in each crate, they put that number or that many tally marks in each circle. If the question ASKS how many apples were in each crate, then they don't know the number yet, so they leave the circles empty and divide up the 32 tally marks.
In the "Do" box, they write the number sentence (32 / 4) and do any adding, subtracting, or any other operation they need to do.
Finally, in the "Reflect" box, they check their work by fact family if possible (ie, 8 X 4) and they write a sentence that answers the question. "There are 8 apples in each crate."
For some kids, this way has worked really well. For some kids, the "see" box takes forever because they are unsure how to decide if a number is important to the problem or not. So here's where I think my NEW way helps.
Same word problem. But now, after reading the problem, the very first thing I have the kids do is focus on the question. Instead of starting at the beginning, and putting all the numbers in the "see" box, they start at the question, and circle the unit that the question is asking them to count. This question starts with, "How many apples," so apples becomes the most important unit in the story.
As opposed to the old method, the kids now write the question first in the "see" box and then go back to the story to find instances that give a number with the target unit. In this problem, they would find 32 apples. Any sentences that also mention apples AND have the word "each" or "every" in them provide a brand new unit that is important. Since the question in this problem asked how many apples were in "each crate," crates are now important as well, so they need to add the 4 crates to the "see" box.
Their "see" box now looks like this:
How many apples are in each crate?
He bought 32 apples.
There are 4 crates.
The $13.00 never even comes into play because dollars are not asked for in the question, nor are they mentioned after "each" anywhere in the story.
The Plan, Do, and Reflect boxes remain pretty much the same as the old version, but the kids seem to have a much better grasp of how they are related now that they have keyed in on what the problem was really asking them to look for.
This is what caused me to have a long hard think about this and to have my "flux capacitor" moment in the first place. We had given a test where one of the questions talked about a kid having a bunch of books and wanting to make stacks. The question asked, "How many stacks can he make?" and a lot of the kids were writing answer sentences that said, "He can have 24 books," or "He can have 8 books in each stack." But the question asked for STACKS, not BOOKS!!
I am hoping that this new way will really help the kids focus on the unit in question, not just any unit in the story.
I came up with a game plan in my head for a better way to teach the kids to solve word problems. Thankfully, I did have a week or so to implement it before all these crazy inclement weather days started piling up (we're on our FIFTH today). The kids are taking to it somewhat slowly, but when they do, I think it's really effective.
It's also one of those things that I'm kind of kicking myself in the butt for never having thought of before. I have a nagging feeling that many of you reading this will say, "And just why the heck haven't you been doing it this way ALWAYS?? Duh!!" Nevertheless, I'll attempt to explain.
In Dallas, we have a problem solving model that we have to use. It's called See-Plan-Do-Reflect, or SPDR. The kids make a giant plus sign, +, and each quadrant has its own purpose. Let me write a typical word problem, and I'll try to explain the old way first, and then the new way.
Timmy has $13.00. He bought 32 apples in 4 crates. Each crate had the same number of apples. How many apples were in each crate?
Step number 1 remains the same, and always will. READ the problem. I can't stand it when kids just see 13, 32, and 4 and add them all. So they have to read it through once first.
BEFORE, I would have them start at the very beginning and put every number they saw into the "See" box. They would wind up with something like this:
T -> $13.00
He bought 32 apples
There are 4 crates
How many apples were in each crate?
Then they draw the 4 operation signs off to the side and take a good look at the units in their box. If the units are the same (apples and apples) or the same TYPE of thing (dogs and cats, or boys and girls), they know they can only add or subtract and can eliminate the other two operations. If the units are different (apples and crates, or candy and bags), they can eliminate addition and subtraction.
In the "Plan" box, they would draw a picture. I've taught them to always circle the word "each" and to put a box around whatever unit comes after that word -- in this case, "crate." The box tells them what to draw. They need to draw 4 crates (they draw circles to keep it simple), and put the correct number of apples (tally marks) in each crate. If the sentence that said "each crate" already tells them the number of apples in each crate, they put that number or that many tally marks in each circle. If the question ASKS how many apples were in each crate, then they don't know the number yet, so they leave the circles empty and divide up the 32 tally marks.
In the "Do" box, they write the number sentence (32 / 4) and do any adding, subtracting, or any other operation they need to do.
Finally, in the "Reflect" box, they check their work by fact family if possible (ie, 8 X 4) and they write a sentence that answers the question. "There are 8 apples in each crate."
For some kids, this way has worked really well. For some kids, the "see" box takes forever because they are unsure how to decide if a number is important to the problem or not. So here's where I think my NEW way helps.
Same word problem. But now, after reading the problem, the very first thing I have the kids do is focus on the question. Instead of starting at the beginning, and putting all the numbers in the "see" box, they start at the question, and circle the unit that the question is asking them to count. This question starts with, "How many apples," so apples becomes the most important unit in the story.
As opposed to the old method, the kids now write the question first in the "see" box and then go back to the story to find instances that give a number with the target unit. In this problem, they would find 32 apples. Any sentences that also mention apples AND have the word "each" or "every" in them provide a brand new unit that is important. Since the question in this problem asked how many apples were in "each crate," crates are now important as well, so they need to add the 4 crates to the "see" box.
Their "see" box now looks like this:
How many apples are in each crate?
He bought 32 apples.
There are 4 crates.
The $13.00 never even comes into play because dollars are not asked for in the question, nor are they mentioned after "each" anywhere in the story.
The Plan, Do, and Reflect boxes remain pretty much the same as the old version, but the kids seem to have a much better grasp of how they are related now that they have keyed in on what the problem was really asking them to look for.
This is what caused me to have a long hard think about this and to have my "flux capacitor" moment in the first place. We had given a test where one of the questions talked about a kid having a bunch of books and wanting to make stacks. The question asked, "How many stacks can he make?" and a lot of the kids were writing answer sentences that said, "He can have 24 books," or "He can have 8 books in each stack." But the question asked for STACKS, not BOOKS!!
I am hoping that this new way will really help the kids focus on the unit in question, not just any unit in the story.
Sunday, April 04, 2010
"Reasonable" Math Problems
Here is the post that showed up on I Want to Teach Forever on April Fool's Day, reposted in its entirety here:
As I mentioned the other day, we have dived in headfirst to the "tough stuff" of the 3rd grade curriculum. Word problems, 2-step problems, and now, "Reasonable" problems. It's pretty ironic, but even with 4 years of high school math under my belt, 3 ½ years of college math and engineering, and 2 years of graduate school math and engineering, I had NEVER come across this type of math problem in my life until I started teaching 3rd grade.
Here's a typical problem:
Mr. Sutton buys 4 tools at the hardware store. The least expensive tool is $10, and the most expensive tool is $20. What is a reasonable total for all 4 tools?
In my opinion, Mr. Sutton should look at his receipt and find the exact prices of each tool and add them, or at least round them and add. This lowest and highest deal is silly. Yet teach it we must.
Oh, and there's also a second kind of reasonable question.
Suzy the Squirrel can bury 3 to 5 nuts every day. How many days will it take her to bury 40 nuts?
Nevermind the fact that I always have to stop and deal with giggle fits every year when we do this problem in class (the kids giggle, too. NUTS!), but I think this kind is more difficult than the first because it requires something beyond just adding to find a total.
Speaking of unreasonableness, I have been working on getting my honeymoon booked. My fiancé and I have decided upon Turks and Caicos (mostly just because it is incredibly fun to say), and a 5 night stay at an all-inclusive resort there. However, the airfare is redonkulous!! Almost 700 bucks per person! Of course, if it was some of my kids charging me airfare, it wouldn't be so bad, because 2 people at 700 dollars each would only be 702 dollars. Possibly even 698 dollars. However, in the real world, it's so much more than that.
Ideally, my book would win the Amazon Breakthrough Novel Contest and the $15,000 prize that goes along with it. Realistically, though, that's probably not going to happen. Any chance everyone could encourage their friends and neighbors to buy a couple of copies of Learn Me Good? On the Kindle even?
Coach K has already come through and delivered on my request. Somehow I doubt he's going to come to the wedding, but at least he gave me my early present.
Is it still "reasonable" to think that Duke can win it all?
As I mentioned the other day, we have dived in headfirst to the "tough stuff" of the 3rd grade curriculum. Word problems, 2-step problems, and now, "Reasonable" problems. It's pretty ironic, but even with 4 years of high school math under my belt, 3 ½ years of college math and engineering, and 2 years of graduate school math and engineering, I had NEVER come across this type of math problem in my life until I started teaching 3rd grade.
Here's a typical problem:
Mr. Sutton buys 4 tools at the hardware store. The least expensive tool is $10, and the most expensive tool is $20. What is a reasonable total for all 4 tools?
In my opinion, Mr. Sutton should look at his receipt and find the exact prices of each tool and add them, or at least round them and add. This lowest and highest deal is silly. Yet teach it we must.
Oh, and there's also a second kind of reasonable question.
Suzy the Squirrel can bury 3 to 5 nuts every day. How many days will it take her to bury 40 nuts?
Nevermind the fact that I always have to stop and deal with giggle fits every year when we do this problem in class (the kids giggle, too. NUTS!), but I think this kind is more difficult than the first because it requires something beyond just adding to find a total.
Speaking of unreasonableness, I have been working on getting my honeymoon booked. My fiancé and I have decided upon Turks and Caicos (mostly just because it is incredibly fun to say), and a 5 night stay at an all-inclusive resort there. However, the airfare is redonkulous!! Almost 700 bucks per person! Of course, if it was some of my kids charging me airfare, it wouldn't be so bad, because 2 people at 700 dollars each would only be 702 dollars. Possibly even 698 dollars. However, in the real world, it's so much more than that.
Ideally, my book would win the Amazon Breakthrough Novel Contest and the $15,000 prize that goes along with it. Realistically, though, that's probably not going to happen. Any chance everyone could encourage their friends and neighbors to buy a couple of copies of Learn Me Good? On the Kindle even?
Coach K has already come through and delivered on my request. Somehow I doubt he's going to come to the wedding, but at least he gave me my early present.
Is it still "reasonable" to think that Duke can win it all?
Monday, March 29, 2010
Crunchy Time
3rd grade math TAKS test is on April 27th. That doesn't leave us with too much time left.
Aside from kids still struggling with the concepts, we have at least covered a lot of the material. Operations, patterns, rounding, measurement, fractions, geometry, etc.
The past few weeks and the next few weeks have been and will be over tougher stuff: The Word Problems.
Most word problems follow some sort of logical path. Most 3rd graders do not. So while it might make perfect sense that if somebody gives away 5 pencils, they should then have LESS pencils than they started with... prompting subtraction...that's not always the way it works out.
Last week, we focused on Two-Step Word Problems. Talk about your basic whipping. There are THREE numbers in the problem now?? We HAVE to add/subtract them all at the same time!!
Usually, when we walk through a problem together, logic prevails. The kids, even the low ones, can tell me when they should add, when they should subtract. The problem arises when the kids face the questions on their own. The main problem being that many of the kids don't actually read the problem or think about what the words mean.
Remember that Far Side cartoon captioned, "What dogs hear?" where the owner said, "Spot, fetch my slippers! Good boy, Spot, that's a good boy, Spot!" and the dog hears, "Spot, blah blah blah blah blah blah, Spot, blah blah blah blah Spot!"
Word problems act in much the same way for a lot of kids.
Blah blah blah blah blah blah 15 blah blah. Blah blah blah blah blah blah 3 blah blah. Blah blah blah blah blah?
Ooooooh, I spy, with my tiny little eye, two numbers!! The magic 8 ball in my head says to.... ADD them!
Then the teacher, ME, reads their answer and wonders why the heck each friend has 18 hotdogs, if Alex started with 15 hotdogs and split them up evenly among 3 friends. (Nevermind the fact that they added hotdogs and friends and magically turned them all to hotdogs.)
We start "Reasonableness"-type questions tomorrow. A bit too unreasonable, if you ask me.
Aside from kids still struggling with the concepts, we have at least covered a lot of the material. Operations, patterns, rounding, measurement, fractions, geometry, etc.
The past few weeks and the next few weeks have been and will be over tougher stuff: The Word Problems.
Most word problems follow some sort of logical path. Most 3rd graders do not. So while it might make perfect sense that if somebody gives away 5 pencils, they should then have LESS pencils than they started with... prompting subtraction...that's not always the way it works out.
Last week, we focused on Two-Step Word Problems. Talk about your basic whipping. There are THREE numbers in the problem now?? We HAVE to add/subtract them all at the same time!!
Usually, when we walk through a problem together, logic prevails. The kids, even the low ones, can tell me when they should add, when they should subtract. The problem arises when the kids face the questions on their own. The main problem being that many of the kids don't actually read the problem or think about what the words mean.
Remember that Far Side cartoon captioned, "What dogs hear?" where the owner said, "Spot, fetch my slippers! Good boy, Spot, that's a good boy, Spot!" and the dog hears, "Spot, blah blah blah blah blah blah, Spot, blah blah blah blah Spot!"
Word problems act in much the same way for a lot of kids.
Blah blah blah blah blah blah 15 blah blah. Blah blah blah blah blah blah 3 blah blah. Blah blah blah blah blah?
Ooooooh, I spy, with my tiny little eye, two numbers!! The magic 8 ball in my head says to.... ADD them!
Then the teacher, ME, reads their answer and wonders why the heck each friend has 18 hotdogs, if Alex started with 15 hotdogs and split them up evenly among 3 friends. (Nevermind the fact that they added hotdogs and friends and magically turned them all to hotdogs.)
We start "Reasonableness"-type questions tomorrow. A bit too unreasonable, if you ask me.
Thursday, March 11, 2010
Unaccountable talk
Last week, I assigned a homework over missing information that some of the kids did great on and some didn't get at all. The sort of question like "Sherri has 7 bookshelves. She wants to find the total number of books that she has. What information does she need to find the total number of books? (The answer being: what color her shirt is. Just kidding. She needs to know how many books are on each shelf.)
So I paired up the kids who had gotten all 3 questions right with the kids who had not and had them go over their answers and their reasoning. As they did this, I walked around and listened in.
I happened to overhear one boy asking the girl he was paired with, "So you probably didn't even read this problem, did you? You weren't paying attention, and that's why you got it wrong!" The girl replied, "Yes, I was paying attention," to which the boy responded, "Come on, you weren't, were you?
I had to ask the boy to be just a bit nicer in his "help."
Today, we were looking at word problems. I've been trying to help the kids decide what operation they should use by looking at the units. If the units are the same (ie, 10 bears and 5 more bears), they can add or subtract. If the units are different (ie, 10 bears and 5 cages), they should multiply or divide.
The problem I had tasked them with talked about M&Ms and Skittles and asked how many more M&Ms there were than Skittles. They were discussing what to do in pairs. One little girl (NOT my brightest) was telling her partner that they should multiply or divide because M&Ms and Skittles are different things. The boy, instead of just telling her she was wrong was asking probing questions. "What are they?" he asked. "They are the units," she said. He answered, "But what ARE they? Are they nails and boxes? How are they different?"
He was (correctly) trying to get her to see that they were both types of candy and thus the same, but I had to walk away or risk laughing out loud at their conversation.
Finally, on our way out to the buses today, one of my little girls told me that when her dad got out of jail (!) they were going to move away from the United States. I figured she meant to Mexico, so I was being facetious when I asked, "You will move to Japan?" "No!" she answered. "The moon?" I asked. "No!" again. When I asked her where, she replied, "To Miami."
Geography just is not her strong suit.
So I paired up the kids who had gotten all 3 questions right with the kids who had not and had them go over their answers and their reasoning. As they did this, I walked around and listened in.
I happened to overhear one boy asking the girl he was paired with, "So you probably didn't even read this problem, did you? You weren't paying attention, and that's why you got it wrong!" The girl replied, "Yes, I was paying attention," to which the boy responded, "Come on, you weren't, were you?
I had to ask the boy to be just a bit nicer in his "help."
Today, we were looking at word problems. I've been trying to help the kids decide what operation they should use by looking at the units. If the units are the same (ie, 10 bears and 5 more bears), they can add or subtract. If the units are different (ie, 10 bears and 5 cages), they should multiply or divide.
The problem I had tasked them with talked about M&Ms and Skittles and asked how many more M&Ms there were than Skittles. They were discussing what to do in pairs. One little girl (NOT my brightest) was telling her partner that they should multiply or divide because M&Ms and Skittles are different things. The boy, instead of just telling her she was wrong was asking probing questions. "What are they?" he asked. "They are the units," she said. He answered, "But what ARE they? Are they nails and boxes? How are they different?"
He was (correctly) trying to get her to see that they were both types of candy and thus the same, but I had to walk away or risk laughing out loud at their conversation.
Finally, on our way out to the buses today, one of my little girls told me that when her dad got out of jail (!) they were going to move away from the United States. I figured she meant to Mexico, so I was being facetious when I asked, "You will move to Japan?" "No!" she answered. "The moon?" I asked. "No!" again. When I asked her where, she replied, "To Miami."
Geography just is not her strong suit.
Tuesday, October 20, 2009
Docents and gallery walks
Today was a really good day for math class. We had designated it as a Problem Solving day, so I had the kids work in groups to solve word problems. We've been going over subtraction for the past couple of weeks, so I had written up 5 subtraction word problems -- none of which used the word "left" -- and gave one to each group.
The groups then copied the problem onto a larger piece of posterboard and went through the steps of solving the problem.
For the most part, the kids worked well together, talked out the problems, and took their fair share of the work. We had made up a rubric for groupwork beforehand, and the kids graded themselves and their partners after they were done with the problem.
After that, though, the really enjoyable part began. I posted the problems on the walls around the room and had each group choose a "docent" -- a group member to stand by the poster and answer any questions or explain the process to the groups that would rotate around during the gallery walk.
Once the gallery walk began and groups were checking out each other's work, I walked around and listened in. I really enjoyed hearing discussions of which number in the problem was the "whole" and which were the "parts;" how "difference" means the same thing as "how many more;" how you are supposed to round numbers if the question has the word "about" in it; how there is no possible way 38 dogs still need to be fed if there were only 21 dogs to begin with and 17 of them have already been fed.
I still have some incredibly low kids in my class, there is no way around that. But I also have a large group of kids that are really beginning to show great thinking skills and the ability to share their reasoning.
The groups then copied the problem onto a larger piece of posterboard and went through the steps of solving the problem.
For the most part, the kids worked well together, talked out the problems, and took their fair share of the work. We had made up a rubric for groupwork beforehand, and the kids graded themselves and their partners after they were done with the problem.
After that, though, the really enjoyable part began. I posted the problems on the walls around the room and had each group choose a "docent" -- a group member to stand by the poster and answer any questions or explain the process to the groups that would rotate around during the gallery walk.
Once the gallery walk began and groups were checking out each other's work, I walked around and listened in. I really enjoyed hearing discussions of which number in the problem was the "whole" and which were the "parts;" how "difference" means the same thing as "how many more;" how you are supposed to round numbers if the question has the word "about" in it; how there is no possible way 38 dogs still need to be fed if there were only 21 dogs to begin with and 17 of them have already been fed.
I still have some incredibly low kids in my class, there is no way around that. But I also have a large group of kids that are really beginning to show great thinking skills and the ability to share their reasoning.
Tuesday, February 03, 2009
I'd like to use a life line
We've been doing division in class lately. Perhaps other school districts start teaching division before third grade, for almost all of our kids, they are learning and practicing division for the first time.
It makes me very happy when one of my kids can actually explain to me what a division problem means. Most of my kids probably could NOT explain it, but one of my girls did today, so I was pleased.
I asked why we could not do 3 divided by 15. She explained it perfectly, saying that we could not start with three things and put them into 15 equal groups because there weren't enough things to start with.
On the other side of logic, I wrote this word problem on the board today:
Erin wants to share her cookies with her 2 sisters. She has 18 cookies. How many cookies will each sister get?
I let my kids work with a partner and gave them a few minutes to come up with a picture, a number sentence, and an answer.
Every one of them told me the answer was 9 cookies. Wait, I take that back. Every one of them told me that 18 divided by 2 was the way to solve the problem. One girl said that 18 divided by 2 equaled 7.
When I told them (much to their shock) that 9 cookies was NOT the answer to the problem, and that I would give them a couple more minutes to go back and very carefully read the problem again, they all saw the trick and came up with the right answer.
I'm just not sure how to teach the skill of carefulness and scrutiny. Especially when I have a group of kids that don't really want to read the words but would rather just grab the numbers and perform a random operation on them...
It makes me very happy when one of my kids can actually explain to me what a division problem means. Most of my kids probably could NOT explain it, but one of my girls did today, so I was pleased.
I asked why we could not do 3 divided by 15. She explained it perfectly, saying that we could not start with three things and put them into 15 equal groups because there weren't enough things to start with.
On the other side of logic, I wrote this word problem on the board today:
Erin wants to share her cookies with her 2 sisters. She has 18 cookies. How many cookies will each sister get?
I let my kids work with a partner and gave them a few minutes to come up with a picture, a number sentence, and an answer.
Every one of them told me the answer was 9 cookies. Wait, I take that back. Every one of them told me that 18 divided by 2 was the way to solve the problem. One girl said that 18 divided by 2 equaled 7.
When I told them (much to their shock) that 9 cookies was NOT the answer to the problem, and that I would give them a couple more minutes to go back and very carefully read the problem again, they all saw the trick and came up with the right answer.
I'm just not sure how to teach the skill of carefulness and scrutiny. Especially when I have a group of kids that don't really want to read the words but would rather just grab the numbers and perform a random operation on them...
Saturday, December 06, 2008
Word Problem mania
Happy weekend, people! I don't know about everyone's schedule across the nation, but I think it's safe to say most of us only have TWO more weeks of school before a nice long Christmas break! And for yours truly, it's only ONE more week before I get to take a nice long trip to Disney World with the family, and then only TWO more DAYS when I get back!!! As Mickey Mouse would say, "YIPPPEEEE!"
In other news worth of a "YIPPPEEEE!!" Learn Me Good has passed the 100,000 mark! This happened sometime about 2 days ago, thanks to majorly increased traffic from the Christmas Carnival! What can I say, I'm a numbers guy, so this is exciting to me.
This week's Mr. Teacher column on education.com is titled, "No More Field Trips," and it is a bit of a lament, seeing as how we were told at the beginning of the year that there was no money to pay for buses to take us anywhere. We're going to have a few people come to us, though, so all is not as Dickensian as it may seem...
A question for everyone reading this: Have you ever read Joel's blog -- So You Want to Teach? If so, you know what an incredibly insightful look at the teaching profession it is. Joel is a music teacher in South Texas, and (unlike SOME people attached to my head) his posts are not just feeble attempts to garner laughter, but rather deeply thoughtful musings about ways teachers can improve themselves, things to destress, and strategies to be more effective with kids and colleagues.
Currently, Joel seems to be concerned that his blog has shown up on some "marketing" searches, but I think that anybody who reads it on a regular basis (which I certainly do) knows where the meat of the matter is. The guy's really good. If you have NOT ever read So You Want to Teach? for whatever reason, stop what you are doing and go peruse the archives! You'll enjoy it, I guarantee!
Another great blogger, the Educat (she's ramblin! and quite possibly gamblin!) has tagged me with a meme she made up herself. I don't particularly enjoy memes (especially having to tag other people, as I always feel like I'm passing on a chain letter), but since the Educat broke her own rule not to meme I feel I can do the same for her.
Her meme is called Seven Posts about the Same Topic. Her directions are as follows:
Find old entries on your blog that center around the same topic and give us the links to them. We'll get to know your back catalog and your hits will shoot up (even if it's false inflation and only for a short time).
She chose the topic of State Testing. I probably have at least 7 posts about that topic as well (including one of my favorites, with the Six Flags height stick analogy here), but I think I'll choose a different topic.
My topic will be WORD PROBLEMS!! (I am, after all, a math teacher)
We'll start with the most recent example, which was relayed to me by another teacher at the school. That of a word problem which showed up written on the inside of a playground slide. When she first told me there was some grafitti I was a bit worried, but as long as all the computation is shown, I'm ok.
Next is a selection from last year, where I was big into suggesting the my students make the problems relative to their own lives. Who cares if Larry bought 14 cupcakes! Let's say YOU bought 14 cupcakes! Or someone you KNOW bought 14 cupcakes! My kids worked one of my teaching buddies into a problem with great results.
A short post here, where one of our math tutors came and told me about a rather frugal comment made to her by one of my kids.
Here's a post about some creative thinking from one of my new kids when it came to a word problem where the answer seemed mathematically obvious. Way to think outside the box!
Almost 2 years ago, I thought I had discovered that the 4 Gospel writers might very well have been poor math students.
Here's one from way back when, from a time I had my kids write their own word problems and share them with the class. Some were good, some not so much.
And to wrap things up, here's an idea I had for a brand new game show called Are You More Cynical Than a 3rd Grade Teacher? Word problems of a different sort.
OK, I think that's 7! Now comes the crappy part of memes, when I need to tag other people to continue the wave. I think I'll start with my "ghosts" from the recent Scrooge Carnival and tag:
Joel
Elementary History Teacher
Mrs. Bluebird
Mamacita
PS Don't forget to sign my guestbook at the bottom of the page!
In other news worth of a "YIPPPEEEE!!" Learn Me Good has passed the 100,000 mark! This happened sometime about 2 days ago, thanks to majorly increased traffic from the Christmas Carnival! What can I say, I'm a numbers guy, so this is exciting to me.
This week's Mr. Teacher column on education.com is titled, "No More Field Trips," and it is a bit of a lament, seeing as how we were told at the beginning of the year that there was no money to pay for buses to take us anywhere. We're going to have a few people come to us, though, so all is not as Dickensian as it may seem...
A question for everyone reading this: Have you ever read Joel's blog -- So You Want to Teach? If so, you know what an incredibly insightful look at the teaching profession it is. Joel is a music teacher in South Texas, and (unlike SOME people attached to my head) his posts are not just feeble attempts to garner laughter, but rather deeply thoughtful musings about ways teachers can improve themselves, things to destress, and strategies to be more effective with kids and colleagues.
Currently, Joel seems to be concerned that his blog has shown up on some "marketing" searches, but I think that anybody who reads it on a regular basis (which I certainly do) knows where the meat of the matter is. The guy's really good. If you have NOT ever read So You Want to Teach? for whatever reason, stop what you are doing and go peruse the archives! You'll enjoy it, I guarantee!
Another great blogger, the Educat (she's ramblin! and quite possibly gamblin!) has tagged me with a meme she made up herself. I don't particularly enjoy memes (especially having to tag other people, as I always feel like I'm passing on a chain letter), but since the Educat broke her own rule not to meme I feel I can do the same for her.
Her meme is called Seven Posts about the Same Topic. Her directions are as follows:
Find old entries on your blog that center around the same topic and give us the links to them. We'll get to know your back catalog and your hits will shoot up (even if it's false inflation and only for a short time).
She chose the topic of State Testing. I probably have at least 7 posts about that topic as well (including one of my favorites, with the Six Flags height stick analogy here), but I think I'll choose a different topic.
My topic will be WORD PROBLEMS!! (I am, after all, a math teacher)
We'll start with the most recent example, which was relayed to me by another teacher at the school. That of a word problem which showed up written on the inside of a playground slide. When she first told me there was some grafitti I was a bit worried, but as long as all the computation is shown, I'm ok.
Next is a selection from last year, where I was big into suggesting the my students make the problems relative to their own lives. Who cares if Larry bought 14 cupcakes! Let's say YOU bought 14 cupcakes! Or someone you KNOW bought 14 cupcakes! My kids worked one of my teaching buddies into a problem with great results.
A short post here, where one of our math tutors came and told me about a rather frugal comment made to her by one of my kids.
Here's a post about some creative thinking from one of my new kids when it came to a word problem where the answer seemed mathematically obvious. Way to think outside the box!
Almost 2 years ago, I thought I had discovered that the 4 Gospel writers might very well have been poor math students.
Here's one from way back when, from a time I had my kids write their own word problems and share them with the class. Some were good, some not so much.
And to wrap things up, here's an idea I had for a brand new game show called Are You More Cynical Than a 3rd Grade Teacher? Word problems of a different sort.
OK, I think that's 7! Now comes the crappy part of memes, when I need to tag other people to continue the wave. I think I'll start with my "ghosts" from the recent Scrooge Carnival and tag:
Joel
Elementary History Teacher
Mrs. Bluebird
Mamacita
PS Don't forget to sign my guestbook at the bottom of the page!
Saturday, November 22, 2008
Tagging the playground
A couple of days ago, a teacher approached me in the hall and asked if I had a boy named "A" in my class. I replied that I did not, but that I knew who he was and which 3rd grade class he was in. The teacher told me that she thought he might be responsible for some graffiti out on the playground, as some writing had been found on the inside of one of the slides with "A's" name on it.
I asked her what it said, fully expecting her to say that someone had spelled "F-U-K" or "B-I-C-H-T." Instead, she said that the graffiti had said, "A has 25 hot wheels cars. His friend has 19 hot wheels cars. How many cars in all?"
"A" is a MATH graffiti artist!!! SCORE!!! Just kidding, nobody should be defacing the school property. But hey, if you've got to write something onto the side of a public facade, why not let it be something that is likely to stimulate brain cells??
I asked her what it said, fully expecting her to say that someone had spelled "F-U-K" or "B-I-C-H-T." Instead, she said that the graffiti had said, "A has 25 hot wheels cars. His friend has 19 hot wheels cars. How many cars in all?"
"A" is a MATH graffiti artist!!! SCORE!!! Just kidding, nobody should be defacing the school property. But hey, if you've got to write something onto the side of a public facade, why not let it be something that is likely to stimulate brain cells??
Thursday, October 18, 2007
It's nice to have friends
Our Problem of the Day this morning read as follows:
Mister Teacher scored 148 points playing basketball. His friend scored 99 points playing basketball. How many more points did Mister Teacher score?
When solving a problem such as this, my kids know that they need to draw a picture to show what is happening in the story. This can be done by putting the large numbers into circles and either putting the circles into a box to show that they are being put together, or by drawing an arrow from one number to the next to show that something is being taken away. The kids are also supposed to label the circles with something that will make them stand apart.
So for the circle with the number 148 in it, the kids wrote, "Mister Teacher" above it. But instead of writing, "friend" above the 99 point circle, several of my kids called me over to ask, "Instead of writing 'friend,' can we write 'Ed U Cater?'"
Ed is of course a fellow teacher at my school. Obviously these kids recognize that he and I are friends.
Now if they would only realize that Mrs. Math and I are NOT married to each other...
Monday, April 09, 2007
Bargain hunters
On Thursday, which was basically our Friday last week, one of the math tutors who works next door to me came over and told me a funny story.
She had been working on a word problem with some of my kids that read, "Mary went to the store and bought 2 pairs of shoes. Each pair of shoes cost $25. How much money did Mary spend at the store?"
One of my kids, A, leaned over to the tutor and said, "Mary should have gone to the Family Dollar store."
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