In general, I see two ways the materials found in this reading section could be used: 1. Once a concept is introduced, I can see the Level 1, 2, 3, and Einstein level problems for that concept being used as 5-10 minute warm ups/ brain teasers at the beginning of the PGP period. Students could then share their solutions to the problems on the ACTIVboard so that all can view various ways of arriving at the same answer. 2. Each chapter could also be used as a mini unit/break between longer project based units. Students could spend 2-3 class periods learning a concept, practicing it by doing the Level 1, 2, 3, and Einstein level problems individually or in a small group, and then making up their own problems to be shared with the group through: • writing/illustrating story problems • storytelling • constructing manipulatives (formula machine, money, clocks, thermometers) • making a “What Number am I?” Power Point • creating a story problem Bookr • using calculators on laptops, iTouches, iPads, etc…

I think the material in these chapters could be used in various ways: as warm-ups, as mini-lessons or as a springboard for projects.

For example, after working through problems in Chapter 12, Magic of Math (p. 113), students could create a probability story to share. This could then lead to creating a game where probability is used to play (and win).

The problems presented in Chapters 10-18 would all make excellent warm-ups. Each problem continues to present such practical applications. I particularly liked the “to scale” problems in chapter 11, Level 2…I would develop this into an architectural unit, using the 10 Wonders of the Ancient World as models. This concept of scale would be utilized in a two-fold unit: one-dimensionally and two-dimensionally. A one-dimensional project would incorporate an ancient floor plan, using ¼”=’s 1’, and a two-dimensional project would manifest itself as a three dimensional object as the end result. Perhaps, choosing the Pyramid of Giza, and using a different scale I/2”=’s 50’, figure the dimensions and then constructing the pyramid to scale. Again, you are incorporating multiple learning styles within the problem. I had to chuckle at the headings in Chapter 16! I am now experiencing the second generation chants of “When are we getting there?”

Well, since I am still in my “Canadian mode”, and the country is currently under an extreme heat alert, I came across the problem in Chapter 13, problem # 2 concerning temperature and had a Nanette “Ah-ha” moment. Since Houston has such mild winter temperatures, compare a city in another country that uses Celsius and has very “winter” temperatures. Chart, or graph, the extreme differences, say the entire month of January, and compare. If one is really “math inclined”, you could go one step further and convert precipitation…rain versus snow…using the metric system. That thrills me not! Another “Ah-ha” moment for me….I Googled various Canadian and European cities for temperatures…all were in Fahrenheit. Used Google Canada, or Google France, and temperatures were then shown as Celsius. Wow!

Does three make it unanimous? I am in full agreement with Eleanor’s and FMoores’ assessments that all of Zaccaro’s material in his Math Challenge text could be used as warm-ups, mini-lessons and springboards for projects.

Well, we are all in agreement that the problems are tailor made for "warm ups". :-)

"How Tall is It" (pp 104- 113) would be a fun one to take outside on a sunny day. The kids would love to know the "secret method" for figuring out how tall the trees are.

Any of the problems in the book could easily be turned into a trading card (http://bighugelabs.com/deck.php) which the kids could then share with each other.

Chapter 15, How Far Away is It (pp145 -152 ) and Chapter 16 "When Are We Going to Get There" (pp 153 -167 ) would make an interesting addition to that old chestnut, the Animal Project - students could compute the distance their animal could travel or how long it would take them to cover a specific distance. The distances could be plotted on a map on the ActivBoard.

That's a great idea to go outside and actually find out how tall a tree, or the school building, is! I have done this with my regular class, and the kiddos loved it.

KHarrell - My first look at this book was to designate one of our sessions as a math day and go through the actual process – could be that I lack mathematical knowledge and I will have to go step by step through the book to get to the Einstein levels. I know that most of my students are labeled GT in Math, so I know I need to do math. Once we have learned the processes, then I agree with the rest of the group – we can do it as brain teasers at the first of class. I can also see this being used when I only have a few show up..have it ready to go so that I never have any “lag time”. I can see the students working in groups to solve and possibly creating problems for each other. My sister just came back from South Africa (her son is PGP alumni) and the first thing she said when we were visiting about her trip was…she wished the boys had more experience in changing money…one entire unit in this book is that….we could integrate the “math concept” in with some other item that we are studying….then students could see how math is used in “real life”. In response to all…yes..these would make wonderful warm up lessons. In response to Nanette – now that I read your comment – yes…your temperature – what a way to introduce research and using the internet in a simple short way…also support a science lesson and if we looked, I’m sure that we could find some novel that talks about temperature…maybe not for PGP for for GT! With temperature we could cover a lot of ground! Maybe a whole “unit” of study!

I think these activities would work perfectly for warm-ups or for fillers at the end of the PGP time when you have a couple of minutes left over. They may also be a jumping off point for a new lesson or project. They are tailor-made to use with a document camera or an activboard. I especially thought so with chapter 14, “Let’s Share”. If you begin with the money problems using the money in the inspire software, it becomes very real to the kids, maybe even more so than play money. And my kids just love to do anything on the board! They could take turns working through the problems and even creating their own to assign to a classmate. I also think the boards lend themselves quite easily to the negative number problems in chapter 13. Being able to draw it out as they visualize it is very important for my kiddoes and I can definitely see them doing that with some of the problems in this chapter. It would also be fun to go outside on a sunny day and work the problems involving shadows as in chapter 11 “How Tall is It?” Anything that gets them up and moving around or manipulating objects is a winner in my book!

@ Of Life,... I love the idea of making them into trading cards! We've done those so many times with other projects, but it never occurred to me to do it with math, too! You rock!

@KHarrell...I, too, have students who are GT in math and I know I have underserved them! I like the idea of making one day a math day and one day a LA day. I'm sure there would be times when we could combine them or be flexible in other ways, but you've given me something else to think about.

As a PGP teacher, I'd love to make this a "standard" part of the week. I usually meet with my PGP students twice/week... it works best with the library schedule and with the Primary class schedule to pull them out multiple times per week. I am not sure we'd get to it every time we met, but if we spent 1 of our 2 times per week working with this book and the activities, I think that would be ideal. I know that my students coming in to PGP this year have some interesting challenges... many of them are identified in Mathematics, and I also know that many of them have fine motor issues, so having them sit and do journals or problem-solving is not going to be the best way to have them "warm up" or "close" the day/week. However, these math problems are so interesting and so applicable that I think projecting them on the ActivBoard or with a document camera would be ideal. They will also be a good way for me to get several of my very headstrong and independent boys to work together. For example, I'd love to have them take Chapter 8 - How Many Legs are There, and just run with it, starting with these problems projected for them to solve... perhaps we could do them first individually and then work as a group on the harder levels.

Sorry... my entire paragraph didn't paste... I am not doing so well in the comment boxes this summer!

As a follow up to my post above, I also love Chapter 13.. What are these Strange Numbers... I see that we could begin a study of positive and negative numbers using Chapter 13 as a jumping off point... it would be a perfect way to explore an extremely complex numerical study. I think it's perfect to do it with money... it's easier for students to understand when they're in the "negative" in a monetary way. And then to follow up with temperature in the harder levels is perfect. Would be fun in the wintertime if we actually have a winter again this year.

In response to Of Life... LOVE the trading card idea - let's do this! Great idea to make them into trading cards.

Also, I love the thought of tacking some of these more challenging problems on to an animal unit. Our 2nd grade does a non-fiction study on animals and many of these problems would be perfect "piggybacking" during those weeks of research when most of our G/T students are finished before the rest of the class.

In response to MelScales... oooh, I love the idea of letting them work them on the ActivBoard! As I don't have one, I don't even think about how that will change what I do with my PGP students! In thinking about how to use it when I finally do get my board, I think this would be an awesome idea!!

I would want to work at the Level 1 and 2 the first semester to build the self esteem ans self confidence with our students. I would identify the MATH/Science PGP students and try to group if needed with LA students. Given a problem, the team would have to solve and discuss who would present the solution to the group. Friends learn from friends!!! Instead of journaling the team would teach the solution to the group. Of course there would be modeling by teacher to set expectations and guidelines. I think the chapter, "Let's Share" would be a great chapter to start with and tie in SHARING. Great for the PRIMARY students.

As a PGP teachers, this material could be used to add depth and complexity to what they are learning in the classroom. I would like to find out how I might choose chapters that seque from what they are learning in their classrooms. The activities could be used as a warm up or as a challenge in game form also. Even teams could work on answers together so they can problem solve together. It would even be good to allow them to do some real time technology collaboration using a tool such as wall wisher where they can actually see each others thoughts in trying to figure out the problem together. I had some students last year who definitely could have benefitted from this added enrichment in math.

As I stated in my answer to Session 1 question 1 (and has been repeated by many other commenters here), I believe these math problems would best be used as a warm-up or early finisher activity. They are "bite-sized", engaging, easy to start/stop working on, and relatively self-directed. I would try to assign warm-up problems that are aligned with whatever topic is being covered in the regular PGP lesson if possible (e.g. using the pyramid height question on page 108 or the doll house construction question on page 110 in conjunction with the architecture unit). I think the PGPers would find these problems challenging and will get a kick out of comparing their unique solution strategies with their buddies.

At Ridgecrest Elementary, we are always strategic at planning for TAKS. Our population is at risk and teachers will jump through any available hoop to boost their students up for the math TAKS. Estimating is always a part of the math test and chapter 12 just jumps right out with teaching students to make smart guesses. I can see teachers heavily using the problems in this chapter for that purpose.

Chapter 16 on when will we get there could be used periodically all year long. Teachers could start the year with discussing summer vacation travel. It could be brought back into play at Thanksgiving or Christmas. Students could estimate differences in time taken to get to school, comparing walking with riding the bus, or being dropped off by parents.

Chapter 18 covers weight in a creative fashion. Many students have difficulty getting “under” or having a deep understanding of units of weight. They can be taught the units and conversion, and be able to work through problems but often without a clear understanding of how much things really weigh. They may have only a vague notion of the real differences between a ton and an ounce. The problems in this chapter help them dig a little deeper.

I agree with Eleanor and Nanette G about using these math problems as warm-ups, especially the month before TAKS. The problems and the layout of this books really lend themselves to a quick visit, solve the problem, get their little brains going and repeat it the next day. Short and interesting doses keep their attention. The problems in this book can really be approached as a daily treat, not the usual math grind.

In response to Viking, I agree that this book (as well as just about any GT tool) can and should be offered up to all students for their mental stimulation. The helpful hints for problem solving covered in this book would be great tools for any student preparing for TAKs Math tests.

Head Squirrel If your kiddos have Fine Motor skill issues you might try letting them blog. The kids I had last year would MUCH rather type - even it was just hunt n' peck than struggle with a pencil and paper. To be honest -so would I!

I see this book being used throughout the year with emphasis in the beginning to learn the layout and pattern. To be honest, my PGP students did not benefit much in the area of math. As a campus admin team, we have decided this area must be addressed. While one book is usually not the end-all-be-all answer, this particular title is a substantial start and will take us far.

My PGP group is very small, so I can also confer with my Math SIS and two classroom teachers to make sure I provide the right kind of challenges.

While I can't cite a particular page number, the entire concept of questioning is applicable. Students need to learn to right good, concise questions. The author does a great job of this throughout the book.

Viking, I liked your suggestion of using a particular chapter and relating it to different times of the year when that same interest arises (Chapter 16 distance/travel time).

NanetteG, the idea of creating a topic of study centered around one of the chapters is great! This is a great starter to developing a research problem/question that can go much deeper than just a mathematical concept.

Oh Guusje, how I see your little brain moving to technology. The ActivBoard is the IN THING. The trading cards were a huge success when we mutated the animals. What a blast and laughs were shared by all. The children what technology and have no fear. Give them a problem, let them solve it and give them a choice of technology to present their solution. Creativity and thinking outside the box.

In general, I see two ways the materials found in this reading section could be used:

ReplyDelete1. Once a concept is introduced, I can see the Level 1, 2, 3, and Einstein level problems for that concept being used as 5-10 minute warm ups/ brain teasers at the beginning of the PGP period. Students could then share their solutions to the problems on the ACTIVboard so that all can view various ways of arriving at the same answer.

2. Each chapter could also be used as a mini unit/break between longer project based units. Students could spend 2-3 class periods learning a concept, practicing it by doing the Level 1, 2, 3, and Einstein level problems individually or in a small group, and then making up their own problems to be shared with the group through:

• writing/illustrating story problems

• storytelling

• constructing manipulatives (formula machine, money, clocks, thermometers)

• making a “What Number am I?” Power Point

• creating a story problem Bookr

• using calculators on laptops, iTouches, iPads, etc…

I think the material in these chapters could be used in various ways: as warm-ups, as mini-lessons or as a springboard for projects.

ReplyDeleteFor example, after working through problems in Chapter 12, Magic of Math (p. 113), students could create a probability story to share. This could then lead to creating a game where probability is used to play (and win).

Session 2-Question 1

ReplyDeleteThe problems presented in Chapters 10-18 would all make excellent warm-ups. Each problem continues to present such practical applications.

I particularly liked the “to scale” problems in chapter 11, Level 2…I would develop this into an architectural unit, using the 10 Wonders of the Ancient World as models. This concept of scale would be utilized in a two-fold unit: one-dimensionally and two-dimensionally. A one-dimensional project would incorporate an ancient floor plan, using ¼”=’s 1’, and a two-dimensional project would manifest itself as a three dimensional object as the end result. Perhaps, choosing the Pyramid of Giza, and using a different scale I/2”=’s 50’, figure the dimensions and then constructing the pyramid to scale. Again, you are incorporating multiple learning styles within the problem.

I had to chuckle at the headings in Chapter 16! I am now experiencing the second generation chants of “When are we getting there?”

Session 2-Question 2

ReplyDeleteWell, since I am still in my “Canadian mode”, and the country is currently under an extreme heat alert, I came across the problem in Chapter 13, problem # 2 concerning temperature and had a Nanette “Ah-ha” moment.

Since Houston has such mild winter temperatures, compare a city in another country that uses Celsius and

has very “winter” temperatures. Chart, or graph, the extreme differences, say the entire month of January, and compare. If one is really “math inclined”, you could go one step further and convert precipitation…rain versus snow…using the metric system. That thrills me not!

Another “Ah-ha” moment for me….I Googled various Canadian and European cities for temperatures…all were in Fahrenheit. Used Google Canada, or Google France, and temperatures were then shown as Celsius. Wow!

Does three make it unanimous? I am in full agreement with Eleanor’s and FMoores’ assessments that all of Zaccaro’s material in his Math Challenge text could be used as warm-ups, mini-lessons and springboards for projects.

ReplyDeleteWell, we are all in agreement that the problems are tailor made for "warm ups". :-)

ReplyDelete"How Tall is It" (pp 104- 113) would be a fun one to take outside on a sunny day. The kids would love to know the "secret method" for figuring out how tall the trees are.

Any of the problems in the book could easily be turned into a trading card (http://bighugelabs.com/deck.php) which the kids could then share with each other.

Chapter 15, How Far Away is It (pp145 -152 ) and Chapter 16 "When Are We Going to Get There" (pp 153 -167 ) would make an interesting addition to that old chestnut, the Animal Project - students could compute the distance their animal could travel or how long it would take them to cover a specific distance. The distances could be plotted on a map on the ActivBoard.

In response to "Of Live, Education,...,

ReplyDeleteThat's a great idea to go outside and actually find out how tall a tree, or the school building, is! I have done this with my regular class, and the kiddos loved it.

KHarrell - My first look at this book was to designate one of our sessions as a math day and go through the actual process – could be that I lack mathematical knowledge and I will have to go step by step through the book to get to the Einstein levels. I know that most of my students are labeled GT in Math, so I know I need to do math. Once we have learned the processes, then I agree with the rest of the group – we can do it as brain teasers at the first of class.

ReplyDeleteI can also see this being used when I only have a few show up..have it ready to go so that I never have any “lag time”. I can see the students working in groups to solve and possibly creating problems for each other. My sister just came back from South Africa (her son is PGP alumni) and the first thing she said when we were visiting about her trip was…she wished the boys had more experience in changing money…one entire unit in this book is that….we could integrate the “math concept” in with some other item that we are studying….then students could see how math is used in “real life”.

In response to all…yes..these would make wonderful warm up lessons.

In response to Nanette – now that I read your comment – yes…your temperature – what a way to introduce research and using the internet in a simple short way…also support a science lesson and if we looked, I’m sure that we could find some novel that talks about temperature…maybe not for PGP for for GT! With temperature we could cover a lot of ground! Maybe a whole “unit” of study!

I think these activities would work perfectly for warm-ups or for fillers at the end of the PGP time when you have a couple of minutes left over. They may also be a jumping off point for a new lesson or project. They are tailor-made to use with a document camera or an activboard. I especially thought so with chapter 14, “Let’s Share”. If you begin with the money problems using the money in the inspire software, it becomes very real to the kids, maybe even more so than play money. And my kids just love to do anything on the board! They could take turns working through the problems and even creating their own to assign to a classmate. I also think the boards lend themselves quite easily to the negative number problems in chapter 13. Being able to draw it out as they visualize it is very important for my kiddoes and I can definitely see them doing that with some of the problems in this chapter. It would also be fun to go outside on a sunny day and work the problems involving shadows as in chapter 11 “How Tall is It?” Anything that gets them up and moving around or manipulating objects is a winner in my book!

ReplyDelete@ Of Life,... I love the idea of making them into trading cards! We've done those so many times with other projects, but it never occurred to me to do it with math, too! You rock!

ReplyDelete@KHarrell...I, too, have students who are GT in math and I know I have underserved them! I like the idea of making one day a math day and one day a LA day. I'm sure there would be times when we could combine them or be flexible in other ways, but you've given me something else to think about.

ReplyDeleteAs a PGP teacher, I'd love to make this a "standard" part of the week. I usually meet with my PGP students twice/week... it works best with the library schedule and with the Primary class schedule to pull them out multiple times per week. I am not sure we'd get to it every time we met, but if we spent 1 of our 2 times per week working with this book and the activities, I think that would be ideal. I know that my students coming in to PGP this year have some interesting challenges... many of them are identified in Mathematics, and I also know that many of them have fine motor issues, so having them sit and do journals or problem-solving is not going to be the best way to have them "warm up" or "close" the day/week. However, these math problems are so interesting and so applicable that I think projecting them on the ActivBoard or with a document camera would be ideal. They will also be a good way for me to get several of my very headstrong and independent boys to work together. For example, I'd love to have them take Chapter 8 - How Many Legs are There, and just run with it, starting with these problems projected for them to solve... perhaps we could do them first individually and then work as a group on the harder levels.

ReplyDeleteSorry... my entire paragraph didn't paste... I am not doing so well in the comment boxes this summer!

ReplyDeleteAs a follow up to my post above, I also love Chapter 13.. What are these Strange Numbers... I see that we could begin a study of positive and negative numbers using Chapter 13 as a jumping off point... it would be a perfect way to explore an extremely complex numerical study. I think it's perfect to do it with money... it's easier for students to understand when they're in the "negative" in a monetary way. And then to follow up with temperature in the harder levels is perfect. Would be fun in the wintertime if we actually have a winter again this year.

In response to Of Life... LOVE the trading card idea - let's do this! Great idea to make them into trading cards.

ReplyDeleteAlso, I love the thought of tacking some of these more challenging problems on to an animal unit. Our 2nd grade does a non-fiction study on animals and many of these problems would be perfect "piggybacking" during those weeks of research when most of our G/T students are finished before the rest of the class.

In response to MelScales... oooh, I love the idea of letting them work them on the ActivBoard! As I don't have one, I don't even think about how that will change what I do with my PGP students! In thinking about how to use it when I finally do get my board, I think this would be an awesome idea!!

ReplyDeleteI would want to work at the Level 1 and 2 the first semester to build the self esteem ans self confidence with our students. I would identify the MATH/Science PGP students and try to group if needed with LA students. Given a problem, the team would have to solve and discuss who would present the solution to the group. Friends learn from friends!!! Instead of journaling the team would teach the solution to the group. Of course there would be modeling by teacher to set expectations and guidelines. I think the chapter, "Let's Share" would be a great chapter to start with and tie in SHARING. Great for the PRIMARY students.

ReplyDeleteAs a PGP teachers, this material could be used to add depth and complexity to what they are learning in the classroom. I would like to find out how I might choose chapters that seque from what they are learning in their classrooms. The activities could be used as a warm up or as a challenge in game form also. Even teams could work on answers together so they can problem solve together. It would even be good to allow them to do some real time technology collaboration using a tool such as wall wisher where they can actually see each others thoughts in trying to figure out the problem together. I had some students last year who definitely could have benefitted from this added enrichment in math.

ReplyDeleteAs I stated in my answer to Session 1 question 1 (and has been repeated by many other commenters here), I believe these math problems would best be used as a warm-up or early finisher activity. They are "bite-sized", engaging, easy to start/stop working on, and relatively self-directed. I would try to assign warm-up problems that are aligned with whatever topic is being covered in the regular PGP lesson if possible (e.g. using the pyramid height question on page 108 or the doll house construction question on page 110 in conjunction with the architecture unit). I think the PGPers would find these problems challenging and will get a kick out of comparing their unique solution strategies with their buddies.

ReplyDeleteAt Ridgecrest Elementary, we are always strategic at planning for TAKS. Our population is at risk and teachers will jump through any available hoop to boost their students up for the math TAKS. Estimating is always a part of the math test and chapter 12 just jumps right out with teaching students to make smart guesses. I can see teachers heavily using the problems in this chapter for that purpose.

ReplyDeleteChapter 16 on when will we get there could be used periodically all year long. Teachers could start the year with discussing summer vacation travel. It could be brought back into play at Thanksgiving or Christmas. Students could estimate differences in time taken to get to school, comparing walking with riding the bus, or being dropped off by parents.

Chapter 18 covers weight in a creative fashion. Many students have difficulty getting “under” or having a deep understanding of units of weight. They can be taught the units and conversion, and be able to work through problems but often without a clear understanding of how much things really weigh. They may have only a vague notion of the real differences between a ton and an ounce. The problems in this chapter help them dig a little deeper.

I agree with Eleanor and Nanette G about using these math problems as warm-ups, especially the month before TAKS. The problems and the layout of this books really lend themselves to a quick visit, solve the problem, get their little brains going and repeat it the next day. Short and interesting doses keep their attention. The problems in this book can really be approached as a daily treat, not the usual math grind.

ReplyDeleteIn response to Viking, I agree that this book (as well as just about any GT tool) can and should be offered up to all students for their mental stimulation. The helpful hints for problem solving covered in this book would be great tools for any student preparing for TAKs Math tests.

ReplyDeleteHead Squirrel

ReplyDeleteIf your kiddos have Fine Motor skill issues you might try letting them blog. The kids I had last year would MUCH rather type - even it was just hunt n' peck than struggle with a pencil and paper. To be honest -so would I!

I see this book being used throughout the year with emphasis in the beginning to learn the layout and pattern. To be honest, my PGP students did not benefit much in the area of math. As a campus admin team, we have decided this area must be addressed. While one book is usually not the end-all-be-all answer, this particular title is a substantial start and will take us far.

ReplyDeleteMy PGP group is very small, so I can also confer with my Math SIS and two classroom teachers to make sure I provide the right kind of challenges.

While I can't cite a particular page number, the entire concept of questioning is applicable. Students need to learn to right good, concise questions. The author does a great job of this throughout the book.

Viking, I liked your suggestion of using a particular chapter and relating it to different times of the year when that same interest arises (Chapter 16 distance/travel time).

NanetteG, the idea of creating a topic of study centered around one of the chapters is great! This is a great starter to developing a research problem/question that can go much deeper than just a mathematical concept.

Oh Guusje, how I see your little brain moving to technology. The ActivBoard is the IN THING. The trading cards were a huge success when we mutated the animals. What a blast and laughs were shared by all. The children what technology and have no fear. Give them a problem, let them solve it and give them a choice of technology to present their solution. Creativity and thinking outside the box.

ReplyDelete