This video was inspired from comments made in Dan Meyer’s My Opening Keynote for CUE 2014.
What questions do you have when you watch this video?
Ask students to write down their questions, I normally ask students to find at least 3. When I observe that most students have questions written, I ask them to share those questions with their neighbor. I then throw up a Microsoft Word document and start typing down questions students supply. Students from my classroom came up with all sorts of different questions, some we can easily answer and others that we can’t. I am looking for a key question or questions to start this lesson. If students do not ask one of these questions, I tell them that I hope I can answer most of the questions provided, but that I need them to consider one of these questions first.
Any of these type of questions will lead students down the inquiry I hope to explore with them.
- Is there a pattern
- What is changing from one frame to the next
- Is the pattern constant?
- Is this an Arithmetic Pattern?
- Is this a Geometric Pattern?
- How did you make a cube?
Once again, this video can create a few different paths of exploration. We can explore:
- Rules of Exponents
These are both excellent topics and students generate a lot of classroom discourse discussing each one.
- Patterns: Students will notice that I first make a square, each side the same length as the initial picture, and then a cube with each side the length of the number of cubes in the square. The cubing part is where most classes will struggle, many will just try to create a cube out of the preceding square.
- Rules of Exponents: This is what I designed this video for, in an attempt to create a visual representation of (x^a)^b = x^(a*b). Using the unifix cubes created a quick, easy way for students to quickly see and do the mathematical calculations. The powers I started with were easily recognizable visually: (x^2)^3. One thing my students start to see is how the base figures into all of this, we normally pause the video and use the SMARTBoard to draw lines to create the pattern of multiplying the base. For example on slide 3: we circle the bottom left 2 blocks, one stack represents 2^2, two stack represents 2^3, four stacks represent 2^4, etc.
- Frame 9: (4^2)^3 = 4096 => 4^6
- Frame 12: 5^2 = 25
- Frame 13: (5^2)^3 = 15625 => 5^6
- Patterns: I ask students to predict what a Step 4 figure would look like
- Rules of Powers: Have the students determine a third power and sketch what their figure would look like & how many blocks it would take to create it.