Calculus Challenges for End of Year Review

This post has been a little while in coming since the end of the school year meant a lot of concerts, graduation parties, retirement parties, etc, etc - as I know you all understand.

Now that we have started summer, I feel like I have time to write about my latest  review idea for my calculus class.  I started out with the grand plan of writing a calculus escape room...but that idea quickly went away as I discovered I had no real idea for writing a story about escaping something!  If you are interested in seeing a really great example of a fun escape room for your classroom, check out this one Calculus Escape Room...by my friend Jean Adams.

So, instead of an escape room, I just decided to come up with some challenges that students could work on completing.


First, I divided my students up into groups of 3 or 4.  I had eight groups in the classroom.  I started four groups with one challenge and four groups with another challenge.

Challenge #1 asked students to find the value of the derivative of nine functions at x = 1.

For example, you can see in the picture at the right...find the derivative of the function y = (x+4)/(3x-2) at x = 1.  The value is -14, so card 2 matches with card 9.  There are nine cards in this challenge and when the cards are matched correctly, a square is formed.








When the group felt like they were finished, they called me over and I checked their work.  It was a quick check, because I just memorized where each card went in the square based in the large numbers in the centers of the cards.

Challenge #2 was pretty quick and involved reviewing vocabulary.  Students were given a clue to a vocabulary word and a group of boxes to fill in.

Notice the shaded box...some of the boxes in each question were shaded.  Students used the letters in those boxes to unscramble a common phrase.  This was easy to check.

As groups finished these two challenges, I just switched them out so groups had something different to work on.

Students went on to work on other challenges other days.  I found it handy to have all of the challenges prepared on the first day, just in case some groups finished more quickly than others.

Other skills that were practiced in these challenges included:

3. implicit differentiation

4. curve sketching

5. Intermediate Value Theorem, Mean Value Theorem, Rolle's Theorem

6. volume

7. matching functions to their derivatives

8. u-substitution

9. limits

10. miscellaneous review

NOW...an 11th challenge is included - practice with position, velocity, and acceleration.

If you'd like to use this activity yourself - check it out here: 

A Scavenger Hunt in Your Seat (and a FREEBIE!)

I recently have been trying something new in my classroom - scavenger hunts that can be accomplished by each student in their seat.  No moving around the classroom...sometimes movement is good, but sometimes you just need students to do an activity where they stay in their seats :)

In this activity (sometimes called a circuit - thank you to Virge Cornelius for this idea), students are given a number of problems to do.  They start in the upper left hand corner with problem #1.  They work to complete problem number one.  After they have figured out the solution to problem #1, they look for the answer to that problem somewhere else on the page.  This becomes problem number two.

Students seem to enjoy these activities as they are self-checking.

Would you like to try this activity with your geometry class?  

You can download it for FREE from my TPT store here...

Mixed Angles Scavenger Hunt in your Seat

Love these and need more?  Try these!

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Playing Bingo in a 1:1 Math Class

There are days when a fun activity is necessary - kids need to practice specific skills, and they need a break from lecturing and practice worksheets.

My students love playing Bingo!  But, I don't like all the time that has to be spent making the bingo cards (it takes students forever to make their own) - or if I make them, it takes forever to make the cards and then laminate them for future use.

Lucky for me, one of my colleagues introduced me to the website Bingo Baker.

This website allows you to enter words and images into a bingo card. [Bingo Baker is freemium tool - it is free to use up to a certain point and then costs $14.95 for a lifetime membership - well worth it in my opinion!]

Here is the beginning of my Antiderivative Bingo Game.

Notice that I was able to add a graphic to the center space easily - I just dragged and dropped from my computer.  If you want to add something that is easily typed like cos x or 0, you just type it right into the square.  Unfortunately, Bingo Baker doesn't seem to have an equation editor.  However, you can get around this if you have an equation editor that you can save your equations as pictures.  Then you can drag and drop those into your card.

Now to the best part!

Bingo Baker will automatically generate different bingo cards for you!  You can give the class a link to follow and each student will get a different bingo card right on their device.

This is a link to see the screen students would get if they were going to play my St. Patrick's Day Calculus Bingo Game...St. Patrick's Day Calculus Bingo Card

As you can see, if students push generate card, they will get their own card pulled up right on their screen.

Then, I project the questions on the board.  For example, here is a first question for my St. Patrick's Game.

Then all a student has to do is touch the screen where they find the answer to this question.

If you are interested in any of my premade Bingo games, check out the links below...or have fun making your own bingo game!

Inlinkz Link Party

Math Teacher Christmas Giveaway!

Now that it is December, thoughts turn to preparations for Christmas.  We all get busier and busier!

I'd like to offer you a chance to win one of my TPT Store Bundles!

By entering this giveaway, you are subscribing to my email list; I email tips, freebies, and information about sales periodically. You are free to unsubscribe at any time.

Good luck!

Calculus Optimization Project - Popcorn Box

This is a great project to do on the day before Thanksgiving Break.  It works anytime, but it is really nice to do on a day when you need to keep the students' minds on math.

Materials Needed:

construction paper
scissors
rulers
tape
calculator
big bag of popcorn

I begin by having this on my board when students enter the classroom.

Students immediately want to know "what's that for" and "are we having a quiz?"  (Eye roll!)  But at least they are paying attention to their surroundings and I am generating interest in the day's lesson.

I have students choose a partner and then sign their name next to one of the (what will turn out to be) measurements on the board.

I explain to the students that we are going to make boxes out of their piece of construction paper.  They cut squares of equal size out of each corner of their sheet of construction paper.  Each group uses the measurement next to their name on the board in the front of the room.

After students cut the paper, they fold up the sides of the box and tape them in place.

Once their box is made, each group calculates the volume of their box.

I have each group write the volume that they calculated next to their names on the board.

Once all of the groups have written their volumes on the board, we look to see which measurements will give the maximum volume of the box.

Then we figure out, using algebra and the calculator, exactly where and what the maximum will be.  The construction paper that we use is 9 inches x 12 inches.  Students use these measurements to come up with a formula that will represent the volume of a box that can be formed if squares with sides of length x are cut out of the corners of the construction paper.  This graph is generated.

We talk about the graph and realize that for this particular situation, we only want to use the part of the graph between x = 0 and x = 4.5.  [squares larger than 4.5 cannot be cut out of the paper].

Of course, none of this actually involved any calculus.  I use this entire activity as an introduction to the idea that we can all start with a given constraint - in this case the piece of 9 x 12 construction paper - and generate different solutions to the problem - in this case make a box.  Which one is best? 

Then we talk about different types of optimization problem situations - I specifically bring up whether pop is in the most cost efficient container.  I actually have a coke "can" in the shape of a (sort of) sphere that Coke put out several years ago for Christmas.  Or, Dr. Pepper, made a special edition "can" in the shape of a football several years ago for the beginning of the football season.

After our discussion and calculator work, students get to fill their box with popcorn and eat!

Do you need more optimization problems?  Check out my Optimization Problems Notebook on Teachers Pay Teachers...Optimization Notebook

Another Way to Use Scavenger Hunts

My class loves a good scavenger hunt...you know the kind - you post problems all over the room - students start anywhere and work a problem, then find that answer posted somewhere in the room.  They continue to work problems until the end up back where they started.

But sometimes, you have a class you just don't want to let out of their seats.  Or maybe you want to hold everyone accountable for the work.

Fun First Day Math Activity - Algebra Review Using Clue

Last year I did a breakout game with my calculus class for beginning of the year review.  I will probably do that again this year to help them review some things for PreCalculus.  You can read about that here: Making a Breakout Game

But, this year I decided that I wanted to try something with my Geometry class too.

I have to thank Stephanie Howell for this idea.  I heard about it on the podcast Hacking Engagement - you can hear it too - Hacking Engagement Clue Game

So, here are the steps I went through to make this game.