Inquiry Question 1: What information goes on the blank side of the cube?

Directions: 

Work in your groups to, collaboratively, decide what information should go on the blank side of the cube, following the steps laid out for you below. Then, collaboratively, compose a proof that provides a map of your thinking and a rationale for all the elements of your answer. Note, this proof must speak for itself. You will not be able to verbally explain your proof to the class. Rather, your classmates should be able to independently read/view your group's proof and be able to understand how you arrived at your proposed solution.

Materials Needed :

• Puzzle cube

• Collaborative group

• Paper

• Your brain

• Poster paper

DAY ONE

Step 2: Begin making observations (approx. time - 5 min)

What do your NOTICE about your cube? What information is on it? Where is that information located? What color is the information? It will be hard not to form hypotheses or inferences about what this information means. But try not to. Slow down and make sure you notice what is there first and you will be more successful next.

Jot down what you notice and the order in which you noticed it.

Make sure that you take at least 5 minutes for pure observation.

See my video below as an example:

Step 3: Turn your observations into hypotheses (approx. time - 20 min)

Start testing the meaning of what you noticed. Ask yourself, what is the relationship between different information on each side and use the guesses you make about those relationships help you to predict what might go on the blank side. 

For example, you may first guess that all the information in the top right corners of the cube sides have to be related to each other, or perhaps all the green information is related to each other. Maybe from there, you might notice all the red numbers are multiples of 4. Once you have developed these hypotheses, then you must TEST them to make sure that they hold true for all sides of the cube. If they do, then you are definitely onto something.

Jot down all of the questions you generated in your meet as you try to formulate hypotheses, all of the hypotheses that you tried out (even the ones that didn't work out), what your group did when it arrived at a dead end, and finally your solution. 

Make sure that you end when class time is up (I am guessing approximately 20 min). If you don't have a complete solution yet, don't worry. You can spend some time finishing up tomorrow.

See my video below showing what this step might look like: 

DAY TWO

We will begin with a quick check in as a whole class. 

Step 3 (cont'd): Turn your observations into hypotheses (approx. time - 10 min)

If your group still needs time to work towards a solution hypothesis, spend some time doing this before moving onto Step 5.

Watch the time for 10 minutes. When 10 minutes are up, move on to Step 5 - explaining as much of the solution as you were able to solve.

Step 4: Compose a proof, explaining your solution (approx. time - 35 min)

First, consider the PURPOSE of your proof - to verify the correctness of your solution, as you see it. In other words, the purpose of the proof is to give your solution credibility (to learn more about what a "proof" is and to see some examples follow the link) . Second, consider the AUDIENCE of your proof - your fellow classmates. It is important to recognize that they while they understand that the goal of this puzzle is to solve for a blank side, they may have chosen a different puzzle to solve, therefore you can't assume that they know anything about your puzzle. My tip: Start from the beginning with the most basic observations.

Create your proof (jamboard if online, poster if in class). As you compose you task will be to think about not just HOW to prove your solution, but also what is the best WAY to organize your information so that your classmates can best understand your proof. Remember, you will not be able to verbally explain your proof, rather it will have to stand on it's own. Things to consider:

• Use of visuals or no visuals

• Use of charts

• Use of if/then statements

• Use of arrows

• Use of bullet points or numbers

• Any other ideas for making your ideas clear and easily understood.

Make sure you the clock. You will have the remaining class time to finish this proof. Your proof will be due - in as complete form as possible - tomorrow. If online, please submit your Jamboard (sharing link) too Google Classroom.

DAY THREE

Sharing out of Proofs (approx. time - 15 min)

Today, spend the first 15 minutes of class viewing every group's proof - starting with other groups and then ending with your own.  As you view each Proof leave two comments underneath:

1. A comment that names a specific strength (must go beyond simplistic and empty comments like: "good job" or "nice") AND adds why that strength is a strength, 

2. A comment that either ask a question about their proof OR offer a suggestion for revision (please don't say anything like "it's hard to read," rather offer how they could fix it). 

When you have left the comments, then in this Google Doc generate a list of general principles that make for "effective" proofs and general principles that make for "ineffective" proofs.

Ranking Feedback (approx. time - 10 min)

Next meet back in your Breakout Groups. Together, review the feedback you received on your proof. As a group, decide on the comment that you found to be most helpful and the comment that you found to be least helpful. 

Share the comments in the collaborative Google Doc found on Google Classroom. Please post these comments anonymously - meaning do not call out your fellow classmates. Please also post a rationale for why the comment was or was not helpful. Please note you must be specific as to why you think of this comment is helpful or not helpful (you must go beyond "I don't agree with what they said."). 

Reflecting on the Process (approx. time - 25 min)

Now, for the most important part - reflection. What does this puzzle have to do with critical thinking skills? What about English? To begin making these connections, I would like you to consider the following questions. Please be thoughtful in your answers. Use complete sentences. Draw on evidence from your experience. Complete this, using this Google Doc.

1. Were all answers to the puzzle equally "right"? Why? - What made some answers more "right" or better than others? 

2. Were all proofs equally successful? Why - What principles, features, qualities made some proofs better than others? 

3. Consider the feedback you received from your peers on your proof. Now answer the following: What qualities made for feedback that was unhelpful? Feedback that was helpful? Explain.

4. Review all the "thinking notes" that your recorder generated and shared on Google Classroom. Review the proof that you wrote for this problem. Think about the proofs other groups created. Look at the columned notes you took about what made for effective/ineffective proofs. Now answer: What did it take - skills, questions, emotions, other things - to be successful in this activity? - How do you define success for this activity? Does it mean solving the puzzle or something else? 

Turn it in to Google Classroom upon completion