I had a pretty great experience with my Grade 12's today using these made-up data sets to discuss with kids how to find multiple modeling functions and then how to narrow them down to one using either asymptotic behavior or the meaning of that type of function. I used it in conjunction with the function types handout that I had given them before, and they were able to ask me some good questions about the differences between functions and how do you know which one is the most appropriate, when a few look very similar?
Even though I wish that they could have come up with the handout information themselves about various function types, it was very valuable to hear them ask those relevant questions, and some of them (the ones who had brought laptops from home) were able to play around with plotting points, setting up sliders for parameter values, and then estimating best fit equations all in GeoGebra. Pretty great, for one day! (The rest of the kids plotted points in their graphing calcs and practiced looking through the functions to find possibilities.)
In the end, I passed out our official IB task and they looked over it and nobody panicked. I think that is a good sign.
Thursday, November 17, 2011
Wednesday, November 16, 2011
An Unexpected Math Encounter
I forgot to write about this:
I went to a cabaret / dance thing last weekend. (It was more of a dance thing than a cabaret thing, which was totally cool except that I had thought it'd be more of a cabaret thing and wore heeled boots and danced with my boots on a slippery wooden floor all night.) At the entrance, there was a sign:
"Pay 9,50 Euros OR toss a die to try your luck. If you roll 1, you pay 7 Euros to get in. If you roll 2, you pay 8 Euros to get in. If you roll 3, you pay 9 Euros... etc. Up to a possible 12 Euros for entrance."
That made the math teacher in me happy to know that somebody paid attention in their math class. :)
I went to a cabaret / dance thing last weekend. (It was more of a dance thing than a cabaret thing, which was totally cool except that I had thought it'd be more of a cabaret thing and wore heeled boots and danced with my boots on a slippery wooden floor all night.) At the entrance, there was a sign:
"Pay 9,50 Euros OR toss a die to try your luck. If you roll 1, you pay 7 Euros to get in. If you roll 2, you pay 8 Euros to get in. If you roll 3, you pay 9 Euros... etc. Up to a possible 12 Euros for entrance."
That made the math teacher in me happy to know that somebody paid attention in their math class. :)
Tuesday, November 15, 2011
Fun with Ratios and Thinking About Functions
My middle-schoolers are coming along nicely in their conceptual understanding. I would like to share one project that my 7th-graders are working on currently. It's an old ratios assignment from when I taught middle-schoolers way back when, but still one that gets kids all riled up and excited, apparently.
First, I want to share a neat little trick with teaching ratios. My first and second years of teaching, I had a lot of trouble getting kids to "see" how to convert part-to-part ratios (such as girls:boys = 3:2) to part-to-whole ratios (such as girls:total = 3:5). I used all these hands-on manipulatives and guided exercises, but to no avail! My third year, I finally figured it out. All this time I had been trying to explain ratios, when instead I should have been letting kids observe ratios, because ratios are an intuitive concept!
So, nowadays I teach ratios problems using tables of values. The tables always start with zeros, because I want to continuously reinforce the connection between direct variations and ratios problems.
I've noticed that this way, no matter if the kids are starting with a part-to-part or part-to-whole ratio as given in the problem, they can always manage to find the other missing parts. And also, they can see how every part (or column) scales equally, thereby leading naturally to the idea of a scale factor. When the problem then asks, "How many boys would there be, if there are 966 girls?" they can figure out easily which column 966 goes into, and then extend (fairly easily, with a bit of practice) the idea of scale factors to find the other column values. --And this is with my Grade 7s, who had never before seen any ratios problems! In the past, when I used the same method with my 8th-graders, I didn't have to teach them anything at all; they could just observe the pattern and figure out the scale factor shortcut when they felt tired of extending the table tediously.
Anyway, following some practice of the table method, I finally introduced cross multiplication. The kids were mad at me; they thought that setting up and solving proportions was way more difficult than making the tables! I made them practice both methods so that in the future, should a teacher require cross multiplication and/or the problem involves decimals, it'd still be in their arsenal. But, I am happy that their conceptual understanding is strong enough to want to replace the cross multiplication.
In any case, back to the ratios project. The kids are given the specs of an original shape and partial specs of a new shape. They need to use their understanding of part-to-part and part-to-whole ratios in order to find the scale factor and to scale all sides appropriately. In the end, they measure and cut out both versions (initial and final), and in groups of 3 write out an explanation of the entire process -- which everyone has to agree upon -- and create an explanatory poster.
I like this project, because it allows me to differentiate easily. Some groups have scale factors that are whole numbers, and others have scale factors that are unit fractions (ie. 1/n where n is an integer), while others have scale factors that are non-unit fractions. Since they're not told what the scale factors are, finding it can be a bit tricky when it is a non-unit fraction.
Anyway, so far, it's going swimmingly! The kids have almost all finished measuring and cutting out their two shapes and are working on the final written explanations. If that sounds like fun to you, here are the project prompts I used this year (excluding the instructions for the posters) and the warmup exercise I used to introduce the idea of geometric scaling.
Love projects!
---------------------
For Grade 8, we are wrapping up two application assignments of the functions we have been learning. I did Dan's cup-stacking activity with them and they enjoyed it immensely -- 3 or so groups came within 1 cup of the final result! I also did a traditional profit and revenue assignment with them. It was the first time I felt like we were getting into complicated application, and although it surely challenged them conceptually, I could see that some of them, at least, enjoyed the discussions about why it makes sense that profit and revenue are both shaped like a parabola.
Today, I taught them to graph linear functions. But I did so by tying it firmly into the meaning of slope and y-intercept inside a word problem, so that every time they look at an equation like y=3x/5 + 2 they will think to themselves that 2 is the starting value (such as # vacation days at the beginning of the year) and 3/5 is a rate -- 5 describing "how often" it happens and 3 describing "what actually happens." (For example, every 5 months you gain 3 vacation days.) It was the first time I did graphing by connecting it to my Mad Libbs worksheet on interpreting linear functions, and it worked really beautifully!!! Not a single kid was lost in the graphing of equations, when they were just thinking about the meanings of the rate and the starting value and putting that into graphical form. Kids were even figuring out for themselves the idea of rise and run in a fractional slope, even though they had never learned this before!!
:) Yay to experimenting. Small changes, big impact!
Addendum 11/16/11: Today I gave my kids a bunch of graphs for them to write equations for. Using just their understanding of the meanings of parameters inside the slope-intercept equation as related to word problems, they were able to easily look at graphs and to write those equations without messing up! This has been the smoothest teaching of writing equations EVER.
First, I want to share a neat little trick with teaching ratios. My first and second years of teaching, I had a lot of trouble getting kids to "see" how to convert part-to-part ratios (such as girls:boys = 3:2) to part-to-whole ratios (such as girls:total = 3:5). I used all these hands-on manipulatives and guided exercises, but to no avail! My third year, I finally figured it out. All this time I had been trying to explain ratios, when instead I should have been letting kids observe ratios, because ratios are an intuitive concept!
So, nowadays I teach ratios problems using tables of values. The tables always start with zeros, because I want to continuously reinforce the connection between direct variations and ratios problems.
I've noticed that this way, no matter if the kids are starting with a part-to-part or part-to-whole ratio as given in the problem, they can always manage to find the other missing parts. And also, they can see how every part (or column) scales equally, thereby leading naturally to the idea of a scale factor. When the problem then asks, "How many boys would there be, if there are 966 girls?" they can figure out easily which column 966 goes into, and then extend (fairly easily, with a bit of practice) the idea of scale factors to find the other column values. --And this is with my Grade 7s, who had never before seen any ratios problems! In the past, when I used the same method with my 8th-graders, I didn't have to teach them anything at all; they could just observe the pattern and figure out the scale factor shortcut when they felt tired of extending the table tediously.
Anyway, following some practice of the table method, I finally introduced cross multiplication. The kids were mad at me; they thought that setting up and solving proportions was way more difficult than making the tables! I made them practice both methods so that in the future, should a teacher require cross multiplication and/or the problem involves decimals, it'd still be in their arsenal. But, I am happy that their conceptual understanding is strong enough to want to replace the cross multiplication.
In any case, back to the ratios project. The kids are given the specs of an original shape and partial specs of a new shape. They need to use their understanding of part-to-part and part-to-whole ratios in order to find the scale factor and to scale all sides appropriately. In the end, they measure and cut out both versions (initial and final), and in groups of 3 write out an explanation of the entire process -- which everyone has to agree upon -- and create an explanatory poster.
I like this project, because it allows me to differentiate easily. Some groups have scale factors that are whole numbers, and others have scale factors that are unit fractions (ie. 1/n where n is an integer), while others have scale factors that are non-unit fractions. Since they're not told what the scale factors are, finding it can be a bit tricky when it is a non-unit fraction.
Anyway, so far, it's going swimmingly! The kids have almost all finished measuring and cutting out their two shapes and are working on the final written explanations. If that sounds like fun to you, here are the project prompts I used this year (excluding the instructions for the posters) and the warmup exercise I used to introduce the idea of geometric scaling.
Love projects!
---------------------
For Grade 8, we are wrapping up two application assignments of the functions we have been learning. I did Dan's cup-stacking activity with them and they enjoyed it immensely -- 3 or so groups came within 1 cup of the final result! I also did a traditional profit and revenue assignment with them. It was the first time I felt like we were getting into complicated application, and although it surely challenged them conceptually, I could see that some of them, at least, enjoyed the discussions about why it makes sense that profit and revenue are both shaped like a parabola.
Today, I taught them to graph linear functions. But I did so by tying it firmly into the meaning of slope and y-intercept inside a word problem, so that every time they look at an equation like y=3x/5 + 2 they will think to themselves that 2 is the starting value (such as # vacation days at the beginning of the year) and 3/5 is a rate -- 5 describing "how often" it happens and 3 describing "what actually happens." (For example, every 5 months you gain 3 vacation days.) It was the first time I did graphing by connecting it to my Mad Libbs worksheet on interpreting linear functions, and it worked really beautifully!!! Not a single kid was lost in the graphing of equations, when they were just thinking about the meanings of the rate and the starting value and putting that into graphical form. Kids were even figuring out for themselves the idea of rise and run in a fractional slope, even though they had never learned this before!!
:) Yay to experimenting. Small changes, big impact!
Addendum 11/16/11: Today I gave my kids a bunch of graphs for them to write equations for. Using just their understanding of the meanings of parameters inside the slope-intercept equation as related to word problems, they were able to easily look at graphs and to write those equations without messing up! This has been the smoothest teaching of writing equations EVER.
Monday, November 7, 2011
On Being Truthful
Today, when I was grabbing something out of my closet, my 7th-graders came into my room to get ready to start our class. One of the last kids to come in did not see me behind the open closet door, and she cheered loudly when she thought that I was absent. She was immediately embarrassed when she realized that I was present (and standing quite close to her), and her friends all laughed.
Innocent mistake. I would have just let it go, except when class started a few moments later and a few kids were still giggling about it, I steadied the class and I asked her if she had something to tell me about how she felt about my class. She said no, that [they] like [me]. And I added softly, "Because I would never cheer even when a kid who's really difficult misses my class. What you said... hurt my feelings."
I wasn't mean about it, even though the kid had embarrassed me (intentionally or not). I think that's something that I've learned to do with grace in the last few years. During the class, the kid tried to sneak me a couple of quick apologies, and then after class she hung around and explained that she was sorry that she had been offensive, that she hadn't meant for it to be hurtful but that she was hoping for some free time today to work on something during class.
I appreciated her for her apology. As a teacher of middle-schoolers, I understand that I cannot take these things personally. But, I think it was the first time I embraced the truth and frankly told a kid that what they said was hurtful to me. And hopefully, the next time it will make her think twice about being inadvertently hurtful to someone else.
I am trying to model for my kids the kind of adult I hope they would grow up to be. That's the most difficult task of all, because I'm not sure I am that person all the time. I think this year I am closer than the years before, because I am much more aware of it. But I've still got ways to go.
Innocent mistake. I would have just let it go, except when class started a few moments later and a few kids were still giggling about it, I steadied the class and I asked her if she had something to tell me about how she felt about my class. She said no, that [they] like [me]. And I added softly, "Because I would never cheer even when a kid who's really difficult misses my class. What you said... hurt my feelings."
I wasn't mean about it, even though the kid had embarrassed me (intentionally or not). I think that's something that I've learned to do with grace in the last few years. During the class, the kid tried to sneak me a couple of quick apologies, and then after class she hung around and explained that she was sorry that she had been offensive, that she hadn't meant for it to be hurtful but that she was hoping for some free time today to work on something during class.
I appreciated her for her apology. As a teacher of middle-schoolers, I understand that I cannot take these things personally. But, I think it was the first time I embraced the truth and frankly told a kid that what they said was hurtful to me. And hopefully, the next time it will make her think twice about being inadvertently hurtful to someone else.
I am trying to model for my kids the kind of adult I hope they would grow up to be. That's the most difficult task of all, because I'm not sure I am that person all the time. I think this year I am closer than the years before, because I am much more aware of it. But I've still got ways to go.
Intro to IB Type 2 Task
This entry is for you IB math(s) teachers out there. I pulled together an introduction slideshow for the Type II task to make it super clear for kids what the mathematical modeling process needs to look like.
Here is the Prezi, and if you wish to make it fullscreen, just click on the "More" button in the lower right corner of the Prezi presentation to see that option. The plan is to walk the kids through the various steps of modeling, and then to jump right into helping them install Autograph (30-day trial version) on their laptops, and then to play around with the program a bit in class, and then to go over the function basics again, and then to take them through an easy sample task.
This is, of course, meant to be used as a follow-up discussion assuming that your kids have already seen these awesome demo videos Part 1 and Part 2 that I had found on the web.
PS. Also, to help kids keep track of all the function types and features, I made this rather comprehensive handout that you are welcome to take. I know, it's not perfect. I wish kids could just all look at data sets and figure out on their own what functions make sense based on their own awesome mathematical understanding, but I don't think I have enough time with my 12th-graders to make that happen overnight, so I'm giving them this as a bit of help, and I will go over it with them as a class to make sure that they are taking notes and trying to understand the important features of each graph. Better than them going on the internet and copying and pasting things they don't understand, no??
Here is the Prezi, and if you wish to make it fullscreen, just click on the "More" button in the lower right corner of the Prezi presentation to see that option. The plan is to walk the kids through the various steps of modeling, and then to jump right into helping them install Autograph (30-day trial version) on their laptops, and then to play around with the program a bit in class, and then to go over the function basics again, and then to take them through an easy sample task.
This is, of course, meant to be used as a follow-up discussion assuming that your kids have already seen these awesome demo videos Part 1 and Part 2 that I had found on the web.
PS. Also, to help kids keep track of all the function types and features, I made this rather comprehensive handout that you are welcome to take. I know, it's not perfect. I wish kids could just all look at data sets and figure out on their own what functions make sense based on their own awesome mathematical understanding, but I don't think I have enough time with my 12th-graders to make that happen overnight, so I'm giving them this as a bit of help, and I will go over it with them as a class to make sure that they are taking notes and trying to understand the important features of each graph. Better than them going on the internet and copying and pasting things they don't understand, no??
Wednesday, November 2, 2011
Responding to Student Needs
I've been slowly reading Lost at School as part of a professional book club at work. Honestly, I don't think much of the book is ground-breaking stuff, but it's a nice common-sense teaching book to spark some common-sense teaching discussions. It provides a good focal point at work for discussions about what is important to all of us, rather than discussions about our individual concerns.
Here is a quote that I liked that helps me view my current experience through a different lens:
I think this really nicely outlines all of the things that are on my mind constantly, as I struggle to grow into being a "good" teacher for my kids.
* My Grade 7's have a few lagging performers who haven't yet figured out that math is important and they need to come see me outside of class for help, so (in response) I weave all of their review of past topics that they're still weak with into our normal class. Every test is cumulative and hits every past topic, and we review accordingly beforehand. I also send daily emails home to let parents know when their kids miss an assignment. And, once every few weeks we play a game that reviews an old skill that I want them to fully master.
* My Grade 8's are a bimodal group, so I need to balance between keeping the really advanced kids challenged and giving the strugglers time to work on their factoring skills when the leading coefficient isn't 1. I do so by introducing every factoring tool possible (looking at graphs & using quadratic formula), and also giving the top-top kids extra graphing calculator assignments to work on independently.
* My Grade 9's are the lowest group in the grade, so there are kids in the group with serious language issues, others with no mathematical memory past the current day, and a few kids who are working very hard to bridge the gap of their learning. I need to provide tasks that are accessible to all kids and allow them to work at their individual paces, and I give them free reign to correcting/re-doing all old assignments as many times as they want. Frequent assessment with clear skills expectations is key to making sure all kids are given regular feedback, and I've met half of their parents already to discuss my concerns about the kids.
* My Grade 11's are a mixture of returning kids and new kids to the school. The returning kids are much more experienced with the first topics of the year, but to ensure that all kids have a fair shot at the IB exam, I'm teaching them all from scratch to make sure the new kids get proper training. Again, it's a balance act of approaching the topic from many angles to ensure that the returning kids are challenged and enriched and pushing the new kids along with some urgency to make sure they do a bit of extra homework to keep moving at the same pace as the others. In the longer run, I've worked out with a colleague that she can transfer the kids who need a bit more nurturing into my group, in exchange for moving kids who wouldn't mind/could handle moving at a much faster pace into hers. We're both happy with that arrangement and think it will maximize the benefit to all kids.
* My Grade 12's have a lot of gaps in their knowledge. They basically don't know/remember anything they are supposed to know from Year 11, and so I've been interleaving as much of old material as possible into current topics to help them review. I know that in the spring, I will have to do some very heavy-duty concept-mapping and explicit learning strategies like algorithm flashcards to get them familiar with the basic concepts of each topic, before we can start doing integrated review and test prep. I am prepared to make that happen and I have a plan for how to help them be successful. (It'll involve topic-based worksheets / individual tests when they're ready / moving on to individually review the next topic when both they and I agree they've mastered the basic ones, or repeating the cycle until they do improve.)
It's stretching me professionally to consider the various academic and emotional needs of my many groups and to attempt to address individual needs within each group. But, I am loving the challenge! :)
(...Now, if only someone could tell me if it's having any actual effect on the kids...)
Here is a quote that I liked that helps me view my current experience through a different lens:
Good teaching means being responsive to the hand you've been dealt.
It goes without saying that each group of kids is different. The task with each group is to get a handle on its collective strengths and limitations and work toward building a community where each member feels safe, respected, and valued. But that takes time and concentrated effort. It doesn't happen by itself. And it looks different every year. That's what it means to be responsive.
It also goes without saying that every individual in a classroom is different. [...] The ultimate challenge is to be responsive in both ways -- to the group and to the individuals in it -- simultaneously.
I think this really nicely outlines all of the things that are on my mind constantly, as I struggle to grow into being a "good" teacher for my kids.
* My Grade 7's have a few lagging performers who haven't yet figured out that math is important and they need to come see me outside of class for help, so (in response) I weave all of their review of past topics that they're still weak with into our normal class. Every test is cumulative and hits every past topic, and we review accordingly beforehand. I also send daily emails home to let parents know when their kids miss an assignment. And, once every few weeks we play a game that reviews an old skill that I want them to fully master.
* My Grade 8's are a bimodal group, so I need to balance between keeping the really advanced kids challenged and giving the strugglers time to work on their factoring skills when the leading coefficient isn't 1. I do so by introducing every factoring tool possible (looking at graphs & using quadratic formula), and also giving the top-top kids extra graphing calculator assignments to work on independently.
* My Grade 9's are the lowest group in the grade, so there are kids in the group with serious language issues, others with no mathematical memory past the current day, and a few kids who are working very hard to bridge the gap of their learning. I need to provide tasks that are accessible to all kids and allow them to work at their individual paces, and I give them free reign to correcting/re-doing all old assignments as many times as they want. Frequent assessment with clear skills expectations is key to making sure all kids are given regular feedback, and I've met half of their parents already to discuss my concerns about the kids.
* My Grade 11's are a mixture of returning kids and new kids to the school. The returning kids are much more experienced with the first topics of the year, but to ensure that all kids have a fair shot at the IB exam, I'm teaching them all from scratch to make sure the new kids get proper training. Again, it's a balance act of approaching the topic from many angles to ensure that the returning kids are challenged and enriched and pushing the new kids along with some urgency to make sure they do a bit of extra homework to keep moving at the same pace as the others. In the longer run, I've worked out with a colleague that she can transfer the kids who need a bit more nurturing into my group, in exchange for moving kids who wouldn't mind/could handle moving at a much faster pace into hers. We're both happy with that arrangement and think it will maximize the benefit to all kids.
* My Grade 12's have a lot of gaps in their knowledge. They basically don't know/remember anything they are supposed to know from Year 11, and so I've been interleaving as much of old material as possible into current topics to help them review. I know that in the spring, I will have to do some very heavy-duty concept-mapping and explicit learning strategies like algorithm flashcards to get them familiar with the basic concepts of each topic, before we can start doing integrated review and test prep. I am prepared to make that happen and I have a plan for how to help them be successful. (It'll involve topic-based worksheets / individual tests when they're ready / moving on to individually review the next topic when both they and I agree they've mastered the basic ones, or repeating the cycle until they do improve.)
It's stretching me professionally to consider the various academic and emotional needs of my many groups and to attempt to address individual needs within each group. But, I am loving the challenge! :)
(...Now, if only someone could tell me if it's having any actual effect on the kids...)
Friday, October 21, 2011
A Move-Around Friday Algebra Activity
I just had a really fun (and mostly productive) Friday afternoon with my Grade 7's! :) We had been working on drawing and solving some simple algebra balances, and I wanted to give them a bit more practice without it being too boring on a Friday afternoon.
This is how I structured it:
* Each kid gets a strip of one equation. They take a sheet of scrap paper and draw the balance scale that corresponds to that equation (They can ask me for help, of course, but NOT for me to see if it's correct).
* They go tape their algebra scales up around the room. (The kids were very silly about this; they taped them on all kinds of surfaces like the fan, the clock, and our lights.) The equation is written above the picture in nice, big letters with markers.
* They go stand in front of a scale that's not theirs and double-check the balance scale that has been drawn, fixing it if necessary. (I should have had them rotate once more to get a second look, but all of the mistakes except for 1 were caught.) When/if in doubt, I went over and took a look myself before they made any changes to the already-drawn scales.
* I handed out an answer sheet with the equations written on it. They are to roam around the room and find the balances that have already been drawn, and then solve them. Some of them are easier to solve than others; some of them required the kids to copy down the balance in order to work it out. (Each equation had a number/index, to make it easy for us to go over the answers in the end.)
* Since some of the kids were absent today, we needed to do two rounds of this in order to finish all the equations. The second time they sat down to draw the balances, they worked in pairs to make sure their drawings were definitely correct.
In the end, I went over the answers and asked the kids if they had questions, and everyone said that they understand the concept (but made some arithmetic mistakes)!! :) :) SCORE. It is a shame that some of my kids were absent today because of a soccer tournament, so next week I'll still have to think of a way to help those kids bridge their understanding gap. But, I think today was a very smooth run!!
Here is the material, if you wish to do this. Notice that I intentionally included parentheses into every problem; I really wanted kids to be able to see 5(x + 2) as drawing x and +2 each five times. I also threw in some "no solutions" and "all solutions" ones in there; the kids particularly liked those. :)
This is how I structured it:
* Each kid gets a strip of one equation. They take a sheet of scrap paper and draw the balance scale that corresponds to that equation (They can ask me for help, of course, but NOT for me to see if it's correct).
* They go tape their algebra scales up around the room. (The kids were very silly about this; they taped them on all kinds of surfaces like the fan, the clock, and our lights.) The equation is written above the picture in nice, big letters with markers.
* They go stand in front of a scale that's not theirs and double-check the balance scale that has been drawn, fixing it if necessary. (I should have had them rotate once more to get a second look, but all of the mistakes except for 1 were caught.) When/if in doubt, I went over and took a look myself before they made any changes to the already-drawn scales.
* I handed out an answer sheet with the equations written on it. They are to roam around the room and find the balances that have already been drawn, and then solve them. Some of them are easier to solve than others; some of them required the kids to copy down the balance in order to work it out. (Each equation had a number/index, to make it easy for us to go over the answers in the end.)
* Since some of the kids were absent today, we needed to do two rounds of this in order to finish all the equations. The second time they sat down to draw the balances, they worked in pairs to make sure their drawings were definitely correct.
In the end, I went over the answers and asked the kids if they had questions, and everyone said that they understand the concept (but made some arithmetic mistakes)!! :) :) SCORE. It is a shame that some of my kids were absent today because of a soccer tournament, so next week I'll still have to think of a way to help those kids bridge their understanding gap. But, I think today was a very smooth run!!
Here is the material, if you wish to do this. Notice that I intentionally included parentheses into every problem; I really wanted kids to be able to see 5(x + 2) as drawing x and +2 each five times. I also threw in some "no solutions" and "all solutions" ones in there; the kids particularly liked those. :)
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