Investigations where students discover the relationship between variables can help students build a deeper understanding of functions. Often these explorations are hands on and engaging lessons. They typically start with some sort of interesting video or question prompt such as "What makes for an exciting bungee jump?" or "Which cup will keep my coffee warm the longest?". I was prompted to think about my favourite investigations after seeing a post from Nat Banting on Twitter. Below are a collection of links and descriptions of my favourite secondary mathematics investigations.
I like the investigation above because they share several common features.
Do you have a favourite activity or resource for activities? Please let me know what it is.
I really like some of the questions found on the Openmiddle.com website. It is a great resource for questions that really get students thinking. They are often formatted so that there is a very low threshold for entry to the problem but they allow for enrichment and extensions. I created the problem below for a professional development session for Math 10 teachers. Students in the Math 10 course are near the following outcome in the yearly plan: AN03 Students will be expected to demonstrate an understanding of powers with integral and rational exponents.
Fill in the boxes with whole numbers 1 through 6, using each number at most once, so that the value of the expression is as large (or as small) as possible.
In order to verify that these were correct values, I wrote a short program in Python (see below) to check all of the 720 possible (6!) values. It was my personal Hour of Code activity. I`m just learning to use Python so my code could definitely be more efficient. If you can write some better code, let me know and I`ll post it here and give you credit.
largest = 0
smallest = 10000
for i in ValuesList:
for j in ValuesList:
for k in ValuesList:
for l in ValuesList:
for m in ValuesList:
for n in ValuesList:
if i!=j and i!=k and i!=l and i!=m and i!=n and j!=k and j!=l and j!=m and j!=n and k!=l and k!=m and k!=n and l!=m and l!=n and m!=n:
if z > largest:
largest = z
if z < smallest:
smallest = z
Update: I submitted this problem to the OpenMiddle.com website and it has been posted there.