Calculus Curve Sketching Activities and a FREEBIE!

It's that time of year in AP Calculus - teaching Curve Sketching and everything that goes along with it.  According to the new AP Calculus AB Guidelines, Unit 5 - Analytical Applications of Differentiation makes up between 15% and 18% of the AP Exam.  Unit 5 contains all of the information about Curve Sketching, so it is very important that students have a good handle on this topic.

Here are 5 activities that I use in my classroom for students to review all of the things!

1)  Two Truths and a Lie - Curve Sketching.  This is one of the best activities I do all year in calculus.  Students love it! In this activity, students are given an equation.  They then write 3 statements about the function.  Two are true and one is a lie.  These posters are hung around the room.  Students go through a gallery walk deciding which statements are true and which are lies.

2) Curve Sketching Color by Number - In this activity, students practice finding the characteristics of curves.  For example, where is the maximum...over what intervals is the function increasing...where is the inflection point, etc.  Even high school students love to color!



                                              


3) Line Them Up Activity - In this activity, students are given a set of cards.  Students begin with any card.  In the middle and bottom half of the card there is a question.  Students search for the answer to that question at the top of another card.  They then do the question on that card and so on.  The last card should have its answer at the top of the starting card.  There are two sets of cards included in this activity.


                                              

4) Writing About Curve Sketching - Having students write about curves and their important characteristics is very important because on the AP Test, students must justify their answer.  This means that the students need practice doing this!  In this activity, there are 5 writing prompts that students are asked to write about.


                                        

5) Finally - the Super Secret Number Puzzle.  Students are given a series of questions.  They write their answer in each blank.  When they are finished, they add up all of their answers.  This is the Super Secret Number.  If their super secret number adds up to my secret number, they probably did the questions correctly.  Add to the fun by posting the answer in a QR Code at the front of the room - students have to scan to see if they are right!


You made it all the way to the end of the post...how about a FREEBIE?  Check out this Quick Matching Curve Sketching Review Activity...

Curve Sketching FREEBIE!

Halloween Multiplication Color By Number

Halloween = awesome!  But, everyone needs a break from all of the sugar :)

You want to do something educational, and all the kids want to do is celebrate.

Try my Halloween Multiplication Color By Number.  In this packet, you will find two different pictures that students can use to practice their multiplication facts.  Perfect to hang for Halloween decorations!

If you are interested, click here to buy it now!

 

The Power of a Puzzle in the Math Classroom

I love reading about the puzzles that Math = Love shares on her blog.  I have tried a few of them in my class with awesome results!

Here is a shot of my students as they worked to solve the Equilateral Triangle Puzzle.

Not only do I enjoy using the suggestions that Math = Love has on her blog, I also enjoy supplying my students with other puzzles I find different places.

For example,

this one I found on amazon (Wooden Puzzle Brain Teaser)

As you can see, we have that one pesky piece that just won't fit in unless you get everything in exactly the right place!

But, my favorite puzzles are the ones that I put up on the front bulletin board.  These puzzles allow students to work together and have conversations with students they normally might not talk to.  I have had students stop in from the hallway during passing period to work on these puzzles.  Kids come by after school!

There are three types we did last year on the front bulletin board:

1) Fun word puzzles...

2) Crossword Puzzles - I really like the big format of these puzzles.  I found them on amazon. (BIG Crossword Puzzles)  

Sadly, I don't have a classroom picture of these big crossword puzzles, but I will be sure to take one this year and post it!

3)  Stick Together Sticker Puzzles - These were my favorite puzzles of the entire year.

Here is an example of one of the posters that we finished around Halloween.

Here is a video that one of my students made by taking a picture of our progress each day. {This one was one we did close to the beginning of the year.}

My favorite part was the conversations that students had with each other and with me while they were working on them.  Students who didn't normally talk to each other worked together.  Students were excited to come into the classroom to see the progress on the puzzle.  They talked endlessly about what they thought the picture would be in the end.  When we finished one puzzle, they begged for another one.

{If you would like to try one of these Stick Together Puzzles yourself, see their website...Let's Stick Together}

10 Fun Secondary Math FREEBIES!

Everyone can use a little something FREE sometime!

Check out these 10 Freebies from me and some of my best Secondary Math Friends. {Click on each picture in order to download that Freebie.}

1)  This one is from my store Teaching High School Math.  I believe that students should work on writing in math class to help the teacher to see if they understand the material.  I have several writing activities in my store, but here is a free one for the beginning of the year in your geometry class.  Student practice basic vocabulary.  They are given several diagrams along with words and symbols that must be used used to describe the diagrams in a paragraph.  Great for formative assessment!

2)  This one is from my friend Jean Adams at Flamingo Math.  If you teach calculus, you might be using some things from her calculus curriculum!  This would be a great first day activity for Calculus, PreCalculus, or Algebra 2 (there are 3 options!).  It really sets the tone that your class will be one in which students work :)

3) This is from Hayley at Activity After Math.  She's a math teacher, but this activity could be used in a lot of different classes.  I love the idea of practicing coordinate graphing by graphing the United States!  And...she has EVERY INDIVIDUAL STATE in her store...but this graph of the United States is a FREEBIE!

4) I know all of you Algebra Teachers get this question all the time...why do we have to flip the inequality sign when dividing by a negative??  Well Julie at Secondary Math Solutions will help you answer this question in this Discovery Activity.

5)  Then, after your students figure out why they have to flip the sign, they can practice solving and graphing inequalities with this No Prep Activity from Amy Alvis!

6) Here's another skill that students need to practice a lot with - Literal Equations.  Combine that with a Connect Four game = FUN!  This is from Audrey at Math by the Mountain.

7) Need something to review vocabulary before the big test?  Check out this Algebra Vocabulary Review from Rachael at Rise Over Run.  It contains 36 vocabulary words.  Six different game suggestions are included, or come up with your own!

8) Next up are some fun notes about Quadratic Functions.  These are in comic book style - what could be more fun than that?  Students can color them in or add their own doodles.  These are from Joan Kessler.

9)  Here's another geometry activity for when you get to right triangles.  A graphic organizer that students can use to help remember the 3 basic trig ratios.  In addition, there are practice problems included...BOOM...an entire lesson done!  This is from Mel at Secondary Math Shop.

10)  And, finally, back to a second Freebie from me!  This one is a great one for allowing your students to practice working with Similar Triangles.  It also incorporates Technology as students use their device to check their answers using QR Codes (check out my post on using QR Codes Using QR Codes in Math Class ).  

I hope you have found something you can use in your classroom!

Start Your Calculus Year Off Right - 5 Fun Limits Activities

Do you need some fun ways to have your students practice limits?

First up ...

Here is an activity that I created on Desmos - it's free for you to use with your students if you are interested.

Have you ever played the game Guess Who?  There are a lot of different versions out there...Pokemon, Disney, etc, etc.  But the general idea is you choose one of the given characters and keep that a secret from your opponent.  By asking one yes or no question at a time, your opponent has to guess which character you chose.  For example, they might ask does your character wear glasses?...Does your character have brown hair?...Is your character a girl?...

In this activity - known as a Polygraph Activity on Desmos - I have provided 12 graphs for your students.  As described above, each student chooses a secret graph.  Desmos magically assigns each student playing the game another student in the room.  Students type yes or no questions back and forth until finally they are able to guess their opponents graph.  One awesome thing about this is that you, as the teacher, can watch the students play on your screen...you can view the questions that are asked and how they are being answered.  Great formative assessment!

Here is a link to my game: Desmos Limits Game

Here are some other activities I have in my TPT store that your students can use to practice limits.

2)  Are you going digital?  Here are some digital task cards you can use to provide your students with practice using vocabulary and work out simple limit problems.

3)  Here is one of my favorite types of activities...A Scavenger Hunt!  Teachers post the 12 cards around the room.  Students begin with any card.  As they find the answer, they look for that card in another area of the room.  They continue in this manner until they return to the first card.  A fun way to practice that gets students out of their seats.

4) Mazes are always a fun thing for students to do.  Great for self-checking!  Here is one that students can use to practice limits.

5) Finally, here is the first in a series of Super Secret Number puzzles that you can use in calculus.  This one is, of course, about limits.  Students solve all of the problems and then add up the solutions.  This is the Super Secret Number.  Students check with me to see if they have the Super Secret Number correct.

I hope these activities help you get off to a great start this school year!

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

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