math through discovery

Thursday, August 30, 2018



This set of Related Rates Matching Cards is made up of
 eight related rate problems
 eight equations
 eight related rate equations
 eight solutions

Give each group of students 24 cards (eight related rate problems, eight equations, and eight related rate equations).  Students should read through the related rate problems and find the matching equation that could be used to solve the problems.  Then they should match the related rate equations that can be generated from the equation using implicit differentiation. 

Students should then solve each of the eight problems.  When they have solved the eight problems, distribute the eight solution cards so they can confirm their solutions.

This is a great activity if you are reviewing for a unit test on related rates or preparing for the final exam or for the AP exam.  It is appropriate for both AB and BC Calculus classes

Related-Rates-Matching-Cards

Friday, August 24, 2018


If you have two solid that have identical bases and height but one is a prism and one is a pyramid, students will often look at the two shapes and say that the pyramid will fit in the prism exactly twice.  Most students don't even think it could be three times. 

I have filled a square prism and square pyramid with water and the students are shocked that the pyramid fits in three times.  They can't figure out how that can work.

With this product you can show the students how the three pyramids fit into the square prism.  After students have seen this model, they never forget that the pyramid fits in the prism three times. 

Build-a-Model-Volume-of-a-Square-Prism-and-Volume-of-a-Square-Pyramid

Wednesday, August 22, 2018


As you are thinking about starting the new year in AB Calculus, BC Calculus or just a regular Calculus class you might want to check out this product.  

These five lessons are designed to be used in five 40 minute periods to introduce students to the 5 main topics they will be studying for the next year.  

1. Instantaneous Rate of Change
2. Behavior of a Function
3. Definite Integrals
4. Using Formulas to find Definite Integrals
5. Limits

Each lesson is designed to use the graphing calculator to building understanding for the five topics graphically, numerically, analytically, and verbally. Each lesson is designed to be completed in one regular class period of 40-50 minutes.

A two question assignment is also included.

Answers to all activities are included.

This is a great way to begin a study of calculus.



Jet-Tour-of-Calculus-Five-Days-of-Lessons-Bundled

This is a really fun activity to do with students. You take a given picture (run two-sided), cut it apart into 9 or 16 pieces, distribute one piece to each student, and then give students directions to either enlarge the square they just received, reduce the square they have just received, or distort the square they have just received.

After they have completed their new square the students use the codes on the back of their original square to reconstruct the cartoon.

This activity really helps students understand how enlargements, reductions, and distortions are achieved.

You can display the original and the new image on the wall of your classroom.

Making-an-Enlargement-Reduction-or-Distortion-of-a-Cartoon


These two products were designed to be used by students in both AB and BC calculus classes to review all the concepts they have learned over the year.  But a recent purchaser wrote that
  • I wanted to review Calculus. This was a great help! Thank you.
The product has had many positive reviews:

  • Nice Review
  • This is a great product!
  • Great exam recap.
  • I which I had found this a bit earlier in the year last year. My students love it, but wished they had it about a month earlier. I will be using it at the beginning of the second semester this coming year. Thanks !!!
  • Kids felt that this really helped them focus their study for the AP Exam. Got them thinking about what they need to do for given problem situations.
  • I am using this activity with my AP Calc AB class as we review for the AP exam. It has been very helpful in getting the students to really think about what they do when they see certain words. It brings the Calc AB concepts together in one activity, giving the students a great review sheet in the end.