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United We Solve: 116 Math Problems for Groups, Grades 5-10, by Tim Erickson
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Math need not be a lonely endeavor! This is a collection of 116 mathematics problems designed especially for groups. The problems focus on proportional reasoning, spatial visualization, and learning to generalize from patterns -- central pillars of any math curriculum. The book includes help for the teacher, a topics grid, and connections to several high-quality middle-grades math programs.
- Sales Rank: #472366 in Books
- Published on: 2015-06-23
- Original language: English
- Dimensions: 11.00" h x .44" w x 8.50" l,
- Binding: Paperback
- 192 pages
About the Author
Tim Erickson is a mathematics and science curriculum developer. He is also the author of Get It Together.
Most helpful customer reviews
70 of 70 people found the following review helpful.
Great Math and Great Design for Cooperative Work
By Daryl Anderson
This book is a treasure in my chest. I have a long shelf of project-books, activity-books and all the rest that I bought to add some spice to the day in math class. This is my "go to" book. I use it every year, repeatedly. I use it in my "accelerated" classes and I use it in my "math lab" classes.
The math selections are outstanding in both interest and challenge levels - they also scale up to allow very bright students to be engaged. And if, like me, you've slogged through too many lame "cooperative learning" books and activities to count, you will be pleased with the design of that element of the program.
The book organizes more than 100 problems into 24 categories within 4 groups, "Patterns", "Spatial", "Proportion" and "Open". Each problem provides 4 printed clues which provide pieces necessary to solve an overall problem. Here is an example from the "Product Chain" category of "Proportion", a rather unusual zoo:
* Rodelians feed every night. Each rodelian eats five snoppets.
* Snoppits feed every night. Each snoppit eats three quigs.
* Pipworts feed every night. Each Pipwort eats four dorblatts.
* Quigs feed every night. Each quig eats twelve pipworts.
The problem, in this case, is itself stated in pieces spread over the 4 clues. The group is ultimately asked to propose a method or rule for finding out how many dorblatts will be needed to keep a given number of rodelians alive.
This is an intriguing enough problem, mathematically, for 4 average 6th graders, but the challenge is multiplied by the "cooperative learning" design. Each student receives one clue but they are not allowed to show their clue to the others in their group. They can draw and illustrate their clue to show to others and they can even read it aloud - just not show it. At first this seemed an oddly crafted constraint but, after using the "UWS" problems for 5 years now I see that it is just the right touch. When denied only the visual access to their partners' clues, the kids tend to switch out into first reading them aloud - feeling, sometimes, like they are 'beating the system'. But, inevitably, just hearing it is not enough for their group-mates and they have to hunker down and reread, understand and restate or illustrate their clue in order to get anywhere.
other notes:
The clues are not numbered. For a problem like the one noted above, the group themselves have to discover and organize the sequence of relationships and solution steps.
For most problems two "hint" clues are provided as what we now call "lifelines". These usually provide not extra data but prompts for looking at the overall problem from a different view (e.g., for the above "Hint: One way to test your scheme is to see if it works if there is only one rodelian, or two."
NO ANSWERS ARE PROVIDED to the teacher! I hated this, then I loved it! As a practical necessity I eventually wrote up an answer 'bank' I could refer to - but with my accelerated classes I found it even more worthwhile. They so often rush to an answer then rush to me for 'validation' - something I'm always trying to shake them of. It introduced a real element of meta-learner challenge when I would reply to their "is this right?" by saying "I don't know. Its up to you and your group to decide if you are confident enough of your answer to move on to a harder problem."
The problems are organized one-per-page in the spiral book and are intended to be photocopied and then cut out. I store the 6 clue papers, each about 4" x 3.5", in envelopes and try to keep 7 or 8 copies of each so that 28 or 32 kids can be working on the same problem if necessary.
As mentioned before, the problems within each of the 24 categories are mathematically similar but get harder to solve in the order that they appear in the book. I usually set out a "suite" which allows an open-ended element to keep the brighter kids engaged.
Groups of three are easily accommodated by simply allowing one member to `work' two clues.
I have used the book with 6th and 7th graders. It is labeled as being for grades 5-10. At either end of that range, my impression is that still roughly half of the problems are appropriate. It is a great match for grades 7 and 8.
Some of the especially interesting categories of problems include "Nim Games", some nice "3D point of view" ones, Calculator based, "Mystery Ops", and my favorite, "Alien Number Systems". There are even two neat problems that demonstrate `fractal automata' solved using paper grids and colored pencils. Nice, nice, nice !
Once you've seen a few of these problems you might think you could make up your own and, in fact, the book encourages you to do so. That being the case, I have to say I've never done so. The sheer number of problems in this one book is more than adequate unless one wanted to actually build a curriculum around their use. If you ever feel you have "used up" "United We Solve" you can check out their second volume, "Get it Together - math Problems for Groups", which is pegged to grades 4-12.
16 of 19 people found the following review helpful.
Hurray!
By A Customer
I was teaching Math for Liberal Arts at a community college and could not get the students to loosen up and try solving non-standard problems UNTIL I started using problems from this book. The problems are fun for everyone and the value of group work becomes clear.
16 of 22 people found the following review helpful.
GREAT BOOK
By A Customer
Great book for any teacher that wants to SHUT UP and let the students do the talking !!!!
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