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2/20/2015 32 Comments

3 Ways to Use Card Sorts in High School Math

Different Ways to Use a Card Sort to Maximize Critical Thinking

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).

1. Station or Group

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.

End Behavior for Polynomial Functions Activity for Algebra or Pre-Calculus

"End Behavior for Polynomial Functions" Card Sort

Card sets should have problems, questions, or statements that fit the topic (I like to include a mix of equations, word phrases, and graphs when appropriate)
Limit the set to 20-40 cards, depending on the work required for the topic.
In addition to the cards, print a sheet with the categories listed (or a box on the table for each category).
Laminate the cards and the sorting mat for future use - Prep once and use each year!

If the categories can overlap with some cards fitting into more than one, try a Venn Diagram style sorting mat.

If you want students to document their work, set out a camera. They can write the names of group members on the laminated sheet using a dry-erase marker and snap a photo. You will have a set of images to look through to assign grades for completion of the activity or learning station.

Decide whether to supply a key for students to check answers.

Always, Sometimes, or Never in High School Math

Activity for Sorting Triangles by Properties

"Always, Sometimes, Never" Activity for Triangles

2. Interactive Notebook: Sorting Pockets

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.

There are a couple HUGE advantages to this structure:

Students keep the cards in the notebook pockets and have plenty of examples in their notes.
With an included answer card, students can re-do the activity at home at any time as a review. They have a study guide full of examples to practice and check.

Hand out answer cards after students have finished sorting the cards. They can check work and ask questions. Then, have them tuck the answer cards into the back of each pocket for later.

Discriminant Activity for Quadratic Equations - Sort by Number of Real Roots

"Discriminant for Quadratics" Card Sort

Algebra Activity Using Discriminant for Quadratics

For this card sort (interpreting a discriminant), I used a mix of card formats. Some are graphs, some are equations, and some are word phrases about the discriminant of a quadratic. This helps students to identify how many roots are present from a variety of given information.

This type of activity is also easy to differentiate. I add an extra set of cards for students who are ready. In this particular set, I included ten additional cards in which the quadratic equation is not already set equal to zero. Think about how your topic can be differentiated and offer different cards to groups with different needs. Click the images for links to the resources.

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.

Click the image to check out my video about setting up and implementing this type of card sort in your classroom: A Better Way to Do Card Sorts.

3. Whole Class Activity

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)

To Read Next:

32 Comments

2/15/2015 5 Comments

Always True, Sometimes True, or Never True - Free Activity

Points, Lines, Planes, and Angles in Geometry - Always, Sometimes, or Never True Activity

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.

If you like it, you can also download a FREE TEMPLATE to make your own "always, sometimes, never" activity for any topic!

In the worksheet version, students color each circle, and in the sorting version, they place the cards in the correct category. These activities are versatile and can be used as independent work, whole-class activities, partner work, or learning stations. You can print the cards on colored cardstock and laminate them to re-use each year.

Always, Sometimes, or Never Activity Template

Always, Sometimes, Never: Self-Checking Critical Thinking with Points, Lines, and Planes in Geometry

Higher Level Critical Thinking - Free Geometry Download - Points, Lines, Planes, and Angles

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

Discovery: Surface Area

Teaching Surface Area of a Cylinder with a Hands-On Discovery Lesson Plan

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.

Dissecting 3D shapes to understand surface area

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!

Dissection Activity for Discovering Surface Area

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.