You can adapt this idea to other topics too, but these are the ones I have made so far.
After trying a few different topics with these puzzles, I noticed that they really motivate students to find more efficient mathematical methods and develop their own shortcuts to try to solve them faster! ... Awesome for critical thinking!!
Here's how to do it:
Three of these are puzzle-style activities in which students have to spin three layers of plates. The goal is to line up the numbers so that each set of three numbers will meet the criteria.
For these ones, I pressed a paper between two plates to get an imprint of the circle. I cut it out to the right size and made a little template. I folded to make 8 sectors. I traced a candle for the center circle, then eyeballed the halfway point from that circle to the edge to make the three layers of numbers.
I kept this template and now I re-use it each time. I just lay it under the plates while I create each activity.
Once you have a template set under the first plate, go around and copy the innermost set of numbers (see my photos below for sets of numbers that work for each puzzle). Set another plate on top and do the next circle of numbers, then lay the third plate for the outermost set of numbers.
For the puzzle-style activities, I try to make them only have one correct answer (If one ends up with more than one solution, no problem - you'll just get a good conversation going about it!). I found it helped to put a little arrow on one layer to point out one row to record as a "check row." This makes it easier to grade. If you use this as a station, the students just need to record that set of 3 numbers, and you can check answers in one second.
Triangle Inequality Theorem Puzzle
For the Triangle Inequality Theorem one, students must spin the three layers of plates until they can get ALL 8 sets of numbers to represent the 3 side lengths of POSSIBLE triangles at the same time.
This offers a great critical thinking challenge and really reinforces the concepts behind the side lengths of triangles. By the time they test and spin a few times, the students get a ton of practice with the theorem.
They start analyzing patterns in an attempt to test cases more quickly. It's a pretty good challenge!
The image shows the solution, so the "check row" for students to record if they get it would be 818.
Triangle Sum Theorem Puzzle
This one is similar, but takes even more thinking. Two of the layers have angle measures, and the third has the triangle classification.
As they spin and test to find the solution to this puzzle, students have to first determine what the third angle measure will be (using triangle sum theorem - 180 degrees). Then, they can think about the classification. Again, they will develop shortcuts on their own as they work.
The motivation to solve the puzzle leads them to find their own ways to become more mathematically efficient!
Again, the solution is shown here. The set for a "quick check" would be 64, 58, acute.
Integer Addition Puzzle
You can never have too much practice with integers in Pre-Algebra. I love this one for switching it up.
The 3 layers have to be arranged so that each set of 3 numbers adds up to 10. You can easily make a huge set of these, each with different "goal" numbers.
These work a little differently.....
Once I discovered the joys of my little plastic plate rotation stations, of course I could not get enough. I decided to make a few to add a little fun to Algebra 1.
Instead of using a table on a worksheet, students can manipulate the plate and try to figure out the rule.
It's not too fancy, but you can use basic or more challenging function rules and show the idea of a function in a different way for those hands-on / visual learners. Some kids enjoy using these for practice.
I just draw the function machine on the top layer, and arrange my input and output values on the bottom layer. As the kids spin it, they try to find the function rule that defines each relationship.
The colored one is a "basic" level. The rule is f(x) = 2x + 1.
The other is more challenging. The rule is f(x) = x^2 - x.
Rotations on the Coordinate Plane
These are a fun addition to transformations. I put the coordinate plane on the bottom of one plate, and the students use a dry-erase marker on the top plate.
Everything spins so smoothly and stays aligned. It is the best way I have found so far to do rotations manually.
It helps to mark off a line every 90 degrees for reference. You can do more marks if you want to do other rotations. Click here to download the jpg image file for the coordinate plane if you do not have a printable one in this size already.
This video shows a little more detail if you are interested in making a set for your class. Click the image to head over to the "Tools for Teaching Teens" video blog site to watch!
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