At the high school level, activities have to be meaningful and engaging at the same time.  A card sorting activity can be a great way to achieve this goal.

For some topics, a hands-on card sort can offer quite a bit more than a basic worksheet could.  Don't worry; the prep work is minimal.  A few minutes with the paper cutter can be more than worth it when you see your students really thinking critically and differentiating between categories.

If you allow students to work with a partner and discuss, you can incorporate visual, auditory, and kinesthetic learning styles all into one activity.  You may hear some great conversations as students determine how to sort each card.

Card sorts are versatile - you can assign one as homework, set up a learning station, or do a full-class, partner, or group structure.  Here are three different ways that you can implement a card sorting activity in your high school math classroom.

I've listed three great ways to use card sorts, and each is great in different situations, which I will describe, but my favorite is the pocket style (#2).  This setup is amazing for maximizing all the benefits of a card sort.  They get the critical thinking going with a variety of information, but can also be re-used as a study guide later on.  Everything, including the answer key, fits right inside the pocket for re-working or studying later on.

You can even layer the pockets to make sub-groups!  I show this tip in the video (link below).

Try groups of 2 or 3 students.  Set up your card sort at the table.  Have students work together to sort the cards into the correct category. 

Card sorting activities are a great addition to your interactive notebook.  You can make a very simple "quick-fold pocket" out of a rectangular paper.  Students can then sort cards directly into their notebook.  If you prefer not to type and print these, students can just write labels themselves, cut the rectangles, and make the pockets in a couple minutes.  Limit yourself to three or four categories for the best card sorting results.

Be sure to include as much variety in the given information as possible.  In the Congruent vs. Similar sort, I use written explanations about all different situations to get students thinking (perimeters, diagonals, lengths, etc.).  I also include diagrams with missing information.  Students must use properties to find some angle measures before they can even determine whether the figures are similar or congruent.  I also include transformed figures on the coordinate plane.  These are amazing for critical thinking if you really get creative with your input information on each card.

Another option is to have your entire class work together to sort a set of cards.  This is easiest for you to prep.

Hand out one card to each student.  Write the labels for your categories on the board.  Have them come up one at a time and read the card aloud, then stick it to the board in the appropriate category.

Give the entire class a chance to think and dispute.  Offer some challenging cards and get a discussion going.  An "Always, Sometimes, Never" card sort works really well for a full-class card sort.  Get your students thinking critically.  Click here to purchase "Always, Sometimes, Never" Card sets to use.  Encourage students to offer examples and counterexamples.  Have them test cases and prove why they chose the category that they did.

"Always, Sometimes, or Never True" ??  (Click images for link)

Get your students thinking critically!  The "always, sometimes, never" activity series incorporates higher level thinking.

Students have to test cases and determine whether each statement is "always true," "sometimes true," or "never true."

The activities come with an option of two formats - a worksheet and a card sort. 

Check out this new freebie that focuses on points, lines, planes, and angles.

Check out more "always, sometimes, never" activities for secondary math.

To make your lesson on surface area fun AND help students really understand the concept, try adding a special "dissection lab" day into your middle school geometry unit.

Students really need to get hands-on with nets of 3d figures in order to understand the concepts behind the formulas for surface area.

I think it is a huge mistake to just present students with the formulas and teach them how to plug in.  Obviously, the formulas can be useful, but if students develop the formulas themselves, they can then reproduce them at any time without memorizing.  They also actually understand the process and why it works.

Print nets on colored paper and tape them together ahead of time.  When you start class, set up like a science lab and tell students that their job is to "dissect" the specimen in front of them and then find the total area of all of the "skin." 

Students will need a ruler and scissors.

Here are some additional items you can put out to make it a little more fun (optional):
- foam trays
- tweezers
- small scissors
- push pins

Start by laying out the assembled 3d shapes on trays.  Lay out the dissection tools, and instruction & recording sheets (see link below).  Students start by taking measurements before they are allowed to cut.

Try a simple polyhedron first (a cube or rectangular prism).  Once students take measurements, have them record the types of faces and how many there are of each.  Allow them to find the total surface area on their particular figure, then develop a formula for the surface area of ANY rectangular prism/cube.

When you introduce the cylinder, give the same prompt and structure, but try to avoid giving hints.  Once students "unroll" the cylinder and lay it flat, allow them to figure out that the length of the rectangle is equal to the circumference of the circle.  This hands-on exploration will activate their brains and help them make the connections!

After opening up the "specimen," students take detailed measurements of all the faces in the net.  They calculate the surface area, then develop a formula.

Here is the net I use - Download Net (free)

You can also buy worksheets to guide your students through the cylinder dissection activity.  Click the image below for more information.

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