Yesterday I said that I would share puzzle sites that I have accumulated over time. I have blogged about this in the past, but here is an updated list of my go-to sites when I am searching for something fun:
A+ Click Math and Logic Problems
Simon Tatham’s Portable Puzzle Collection
And here is one site to make your own puzzles:
I am sure that there are many other great sites that are not on the list. Please send me your favourites.
I have been reading about Sarah Carter’s puzzle table and I love the idea. She has four posts where she talks about the types of puzzles that she uses, and you can read them here and here and here and here. I am not sure if I have anywhere to set up a table for this and I may have to modify the idea, but I still went ahead and ordered the Puzzle Box books that she mentioned from Amazon. I can’t wait for them to arrive!
In her Puzzle Table: Weeks 7-9 post she wrote about the H and T puzzles which I have seen before. She got them from a website called Puzzles.ca. I think I may have some hard copies of these puzzles in my classroom at school, but I wanted a digital copy and so I started searching online. I didn’t find them on that site, but I did find them on the Puzzle Playground website which has both the H and T puzzles, along with an M puzzle. You can access them here. I know that I also have the F puzzle at school and was looking for a digital copy of that one, as well. Puzzle Playground doesn’t have a copy, but Math is Fun has a version which you can access here. You should also check out the Puzzle Playground Manipulative Puzzles section for some other great options.
In her Puzzle Table: Weeks 1-6 post she mentioned the Four Aces puzzle which she also got from Puzzles.ca. I also could not find this puzzle there nor anywhere else that I searched online. I went back to the Puzzles.ca website and contacted the website designer and requested a copy. He kindly sent me the pdf of the puzzle and gave me permission to share it here. He also said that other DIY puzzles (manipulative puzzles) will eventually return to his website. Puzzles.ca also has a variety of other puzzles and games which you can either play online or print, including Mathdoku.
I have also scoured through some of my other resource books and have found a few puzzles that I like from the following books:
I have many more online puzzle sites to search through and I should have quite the collection by the time I am done. I will share those links another day.
I like to find different ways for students to understand the invert and multiply algorithm and this summer I have seen some good ideas for representing division of fractions.
First I will direct you to Graham Fletcher’s blog, GFletchy. Earlier this year he wrote about his method which I like for daily use in the classroom. His strategy is to have students find ways to turn the denominator into one whole. In his post he also directs you to two other sources for this topic. One source is Fawn Nguyen who wrote about a rectangular model, an interesting model for conceptual understanding. The other source is Christopher Daniel’s blog, Overthinking My Teaching. He discusses a model I had never heard of before, using common numerators to divide fractions.
I also want to share an online widget that I found years ago called the DIM Calculator. This widget allows students to enter any two fractions then follow the instructions to learn why invert and multiply works.
I have used the DIM Calculator in the past, but I will definitely be introducing these other ideas to my students in the future.
Last year, one of the activities I did during the first week of school was called “Barrels of Mystery”. I bought two packages of Monkey Key Chains from Party City, which are basically mini barrels of monkeys. I took off the key chains from the barrels and opened them up to remove the monkeys, and then I used a permanent marker to number each barrel from 1 to 24. Inside of the barrels I put small objects such as nails, rice, dice, coins, paperclips, buttons, marbles, magnets, screws, and yes, I also put in some of the monkeys. Each barrel received a different item except for the rice barrel, which was filled halfway with rice. The students were not told any of the objects that were inside. They had to come up with strategies to identify what was in each barrel and they also had to give reasoning for their thoughts. I told the students that I would not tell them anything about the contents of the barrels, but I would provide tools or objects upon request. They just needed to figure out what to request.
Each student came up and selected a barrel. At first there was a lot of shaking of barrels, and there was only shaking of barrels. Then the students started getting creative. They asked for magnets. They asked for scales and balances. They also asked for empty barrels (and I had kept a few off to the side). They compared empty barrels to their assigned mystery barrels to determine the weight of their item. Once they had an idea of what might be inside the barrel they then asked me for that item and then weighed the item to see if they were correct. I had never done this activity before and I honestly had no idea how successful they would be, but they used good deduction skills and I was quite impressed. I think I will use this activity again this year. If you have any ideas of how to make it better, please send them my way.
You can access the student handout here.
My favourite math task of all time is a financial planning assignment. I have blogged about this previously, but I think it is worth mentioning again. The assignment is called “Making Ends Meet”. It was created years ago with a teaching partner, but it has grown and developed over the years. In this task students take the role of new university graduates who are just moving out on their own. They need to determine how they will pay all of their costs on an entry-level salary. I created a list of entry-level jobs and their salaries. I cut up the list so that each item on the list is on a separate sheet of paper. The papers go into a jar, and then students pick their career out of a jar. I think I need to update the list for next year, as many starting salaries have increased since I first created the list.
After the initial excitement dies down, students begin to move on to the first part of the task, which is calculating take home pay after federal and provincial deductions. I chose to leave off EI (employment insurance) and CPP (Canada Pension Plan) deductions this year, but may put them back on in the future. After determining the yearly net salary the students then determine the monthly net salary, and then the real fun begins. The students proceed to determine the various costs that they will have, including food, housing, utilities, transportation, medical expenses, miscellaneous expenses, and savings. During this phase of the assignment I usually have many students trying to negotiate with me if they really need certain items or with how many people they can share a rental apartment or house, and the buzz in the room is full of excitement. As students are trying to find somewhere to live I encourage them to consider distance to work, safety of the neighbourhood, and proximity to public transportation. Students then come up with a monthly budget, hopefully including a portion for savings. In this phase of the task the students are free to talk with one another and share ideas.
The last phase of the task requires the students to answer questions under a “test” situation and the students are not allowed to share ideas at this point. The amount and content of questions has varied from year to year, but the general theme is that they need to analyze the effectiveness of their budget compared to financial planning strategies and they need to deal with and pay for 2 of 19 potential unexpected problems (flood, broken glasses, etc). I created a numbered list of those problems. I have assigned the problems in various ways in the past, but this year I had each student randomly pick two numbers between 1 and 19 and then I assigned those two unexpected problems to the student.
The students and parents all love this assignment. Students in grade 8 do not pay for much on their own, and for many this gave them their first exposure to what is involved with living on your own. This year I had a student actually thank me for making her realize how expensive life really is, and she said that she was now a lot more appreciative of all that her parents do for her.
You can access the main task here. The “test” situation portion is not part of this handout, as I don’t want my students to access it online.
Have a wonderful day.
I am always searching for good real world project ideas to incorporate into my science curriculum. One of the units I taught last year was electricity, and part of that unit involved teaching about the sources for generation of electricity. I wanted to create an assignment where the students had to analyze a city’s needs in order to determine the best renewable or non-renewable source to generate electricity. It was for grade 6, and so I did not want the city descriptions to be too complex. I began writing my ideas, and as I was researching I came across a website that had already done exactly what I wanted. The project is called “The Energy Sources Project”, and you can find the link to it here. Click on the project descriptions to read about five cities and their various needs.
I put my students into groups of 3-4 students and presented them with the city scenarios. I had put each scenario into a separate Google Drive folder and then shared the folder with all group members. On the original website there are specific questions provided for the students to answer, but I modified them for my own needs. The questions on the site gave environmental and economic questions, but I needed to adapt them to meet the requirements of the International Baccalaureate rubrics that we use at our school. In the Real World rubric the students need to discuss either environmental, political, social, cultural, moral, or ethical factors and so I wanted to expand the question set to allow for this. I left off moral and ethical questions as I thought they might be more difficult for this assignment, and they are not required to choose those factors. I gave guiding questions as this was the first unit in grade 6 and students were just beginning to use this rubric, and thus needed a place to start their research. Below you can see how I modified the assignment.
Task:
As members of the Harrisburg/Wallen/Oxford/Mayberry/Jasper Power Company, you must develop a plan to present to city members at the upcoming town meeting. Read your assigned scenario, and then together with your group members decide which type of energy source would be best for the town. Things to consider when planning your presentation include:
Power Plant Selection
-What are possible energy sources that your power plant could utilize?
-Which is the best energy source for your power plant to utilize and why?
-How does the selected energy source work? How will it generate the power needed to provide electricity to your residents?
– What will be the location of the power plant within the city?
Environment
-Is your energy source renewable or nonrenewable?
-How will the power plant and its location affect the environment positively and/or negatively?
– Are there waste products produced? How will these affect the environment?
– Are there any benefits to using this form of energy? Any risks?
-Are there other environmental issues to be considered?
Cost
-How much would it cost to construct a power plant that would supply enough energy for the city of your size?
-How is the city going to pay for the power plant (tax options, grants, etc.)?
-What other costs might be involved with the creation and upkeep of the power plant?
-Are there other cost issues to be considered?
Politics
-What government officials need to be consulted about the chosen energy source/power plant and its location?
-What government officials might be involved with ensuring the power plant is operating in a safe manner?
-Are there other political issues to be considered?
Social/Culture
-How might the power plant and its location affect the residents of the city and their daily life?
-How might the power plant and its location affect visitors to the city?
-Are there any potential health issues related to the power plant and its operation?
-Are there any education issues for the residents related to the power plant and its operation?
-Are there other social or cultural issues to be considered?
I am thankful for the many people in the #MTBoS community who readily share ideas and documents, and some days I am overwhelmed by the abundance of resources through which to sift. Like others, I am hopeful that a #teachscience community will flourish, as well.
In reading the tweets and blogs of others, I have been thinking a lot about ways to better engage students. I have begun to compile a list of structures, methods, and routines to use in the classroom in order to spark curiousity, inquiry, and eager attitudes from my math and science students. Below is what I have so far:
2 Truths and a Lie – Read about how to use them at Mr. Orr is a Geek.com or at Math=Love
Always, Sometimes, Never – Read about how to use it here and you can find many examples online
Row Games – Described here
Card Sorts – Instructions can be found on The Teacher’s Toolkit
Question Stacks – Again, go to Math=Love for wonderful samples
Connecting Representations – Visit Fostering Math Practices and New Visions for Public Schools
Contemplate then Calculate – Again, visit Fostering Math Practices and New Visions for for Public Schools
Estimation 180 – Estimation challenges from Andrew Stadel
Entry/Exit Tickets – Used at the beginning or end of a class, read about them here
Graphing Stories – Go to the website by the same name or read Dan Myer’s ideas on dy/dan
Four Corners – Read about this strategy here or here
My Favourite No – Watch the video on The Teaching Channel
Notice/Wonder – Read about it here and then search Google for other samples
3 Act Math – Definitely read about it on Dan Meyer’s blog
Which One Doesn’t Belong – Visit the fabulous website to see how these puzzles work
Would you Rather – Visit the website by the same name for samples
Who Am I? – Try them out here…and thanks to Matt Coaty for reminding me that this should be on the list
Add Them Up – Read about it from Sara Van Der Werf
Tarsia Puzzles – Download the free software here (only on PC) and then visit Mr. Barton Maths site for samples
Build an Army/Top Trumps – Again visit Mr. Barton Maths to see what he does for Build an Army and then read about how to incorporate the Top Trumps card game into the classroom here
War – Read about how to use the card game in math class here and here
Game Shows – Find templates for Are You Smarter than a Fifth Grader, Jeopardy, Bingo, Family Feud, and Who Wants to Be a Millionaire here
Escape/Breakout – Explore with digital games at BreakoutEDU or here and learn how to create your own game here and here
*The following list items are thanks to @druinok and the responses to her call for structure ideas:
3 Reads – Read about this on Fostering Math Practices (suggestion from Kim Charlton @Logical Poetry)
O.G. Mistake – A new spin to use instead of question stacks, read about it on Julia Anker’s blog
Open Middle – I actually originally had this on the list, but must have accidentally deleted it, visit the Open Middle website to read about it and explore an abundance of problems (suggestion from @Dsrussosusan)
Give One, Get One – Suggested by @druinok, I think I could make use of this in my science lessons, read about it here
Find Someone Who – Also suggested by @druinok, read about it here
Math Hospital – Also suggested by @druinok, a type of find and fix the error strategy, read about it here
Let me know what else should be on this list.
I cannot remember where I first came across this resource, but if you or your students are into apocalypse scenarios, then this might be a good resource for you. There are 25 zombie based questions, including worked solutions and pdf handouts of the problems. I am thinking that it might be a good activity for the last few days before winter or spring break, when a portion of my students have already left for vacation. I may even take some of the problems and make an escape game activity.
Access the resource here.
