Increasing critical thinking in a class should be a goal of all teachers. The book Building Thinking Classrooms is an excellent read for any teacher (it says math, but the pedagogy strategies are good for any grade level or subject) who is trying to have their students do more thinking. Playing games that involve strategy can be a great way to engage students and to help students to practice communicating their strategy and thinking. One game I use for this is “Farkle.” Farkle is a dice game that uses 6 dice. Have students play in small groups, taking turns, and ask them to share their reasoning with the group for each move.

## Make “What is Your Strategy” Standard in Your Class

Critical thinking is an essential skill for students to develop, as it prepares them for success in academics and beyond. One effective way to cultivate critical thinking abilities in the classroom is by encouraging students to explain their strategies when solving problems or working on projects. This approach pushes students to analyze their thought processes, evaluate different perspectives, and refine their understanding of complex concepts.

My goal is that students naturally respond to questions with a critique, analyse, or strategy. I teach students about Depth of Knowledge (DOK) the first week of school and it is an ongoing conversation all year. I tell students that “because” is my favorite word. Even if the question is not a higher level question, we can potentially increase it by having students be in the habit of adding “because.”

## Key Benefits of Encouraging Students to Explain Their Strategies

**Organizing and Clarifying Thought Processes**: Requiring students to articulate their strategies enables them to break down complex ideas into simpler components, fostering enhanced critical thinking skills.**Promoting Self-Assessment**: When students explain their approaches, they evaluate their own understanding, helping them recognize and address gaps or misconceptions in their thinking.**Strengthening Justification and Reasoning**: Articulating strategies pushes students to develop logical arguments and consider alternative viewpoints, enhancing their critical thinking capabilities.**Encouraging Reflection and Refinement**: Sharing strategies allows students to identify areas for improvement, leading to more sophisticated approaches and deeper subject matter understanding.**Engaging with Diverse Perspectives**: In classrooms, students are exposed to their peers’ strategies, promoting critical thinking by encouraging them to consider multiple approaches and evaluate each one’s merits.**Fostering Responsiveness to Feedback**: As students receive feedback from teachers and classmates, they can recognize flaws in their thinking, prompting them to revise and improve their strategiesâ€”an essential component of critical thinking.**Enhancing Application and Transfer of Knowledge**: Explaining strategies often involves connecting concepts from different knowledge areas, requiring students to recognize relationships and apply information effectively to new situations.

## The Rules of Farkle

Farkle is a dice game where you roll 6 dice. You must score or you get a FARKLE. A Farkle earns you zero points for the round. Basic scoring is you get 50 points for a 5 and 100 points for 1. If you get 3 of a kind it scores the number times 100 (except three 1’s which get you 1000 points) so a three 4’s is 400 points. Get an extra four and you get an extra 400 points! A straight gets you 1500 points and three pairs is 750 points. You can keep rolling in a round as much as you want so long as you don’t Farkle. You MUST score at least 300 points in a round before you can quit the round.

## Is Farkle a Strategy Game?

My son dismissed the game saying it was just a game of luck. I argued there is an element of strategy to it. We sat together around my phone app discussing what I would choose to do and what he would choose to do. They did not always match. Discussing strategies is a good way to increase the DOK and thinking for students. Games are a fun way to get students into strategizing.

Alexis Gray and I played Farkle where we talked strategy not just point scoring. Farkle is a way for students to demonstrate strategic thinking with mathematical justification. Whether or not students calculate the actual probabilities they can understand some of the basic concepts such as rolling 4 die is a better probability of NOT getting a Farkle than 3 die.

## Farkle Templates

I prefer actual dice in the classroom if possible. I have dice at each student group in the supply caddies for students to play Farkle if they finish a task early. However, it is not always possible to use actual dice so I created a couple of Google versions of Farkle.

## Play Farkle

Not sure that using my template is the best place to start. Maybe using a mobile game or website is better for students to ENGAGE (From the 5 E’s lesson plan style) with the lesson. Give them a chance to develop some strategies. First, they need to play and learn the rules. I also like physical dice, so if you have those use those.

## Slides

The purpose of my Google Slides for Farkle is to give students a place to explain their STRATEGY and thinking for each round. Students can play with physical dice, virtual dice or I have a spreadsheet that simulates rolling Farkle dice.

### Feedback

One of my favorite reasons to use Google Slides is the feedback options. WHILE students are playing (or even after) the teacher or peers can view the Slides and insert feedback comments to help further the students THINKING and explaining.

Alternative Strategies

If you follow me you know I massively fangirl Jo Boaler, Stanford math professor, and author of the best book ever Mathematical Mindsets. One of the things she promotes is having students value different approaches and strategies. Have students share their Farkle Slides with a peer. Hopefully some comments such as “Interesting that you chose to only roll one die, I would have rolled both of the 5’s” are shared.

Teachers can also insert comments to help develop students thinking around not only their strategy but ask them to go deeper with their mathematical reasoning for their strategy.

## Not Checking Answers

One thing I like about activities such as this Farkle game is each student’s Slides are different. They have different numbers and different dice rolls. When students are doing the same problem they check each other’s answers. Low critical thinking. When students have different numbers then they must compare and contrast to how they strategized. Higher critical thinking.

## How To Use This

This would be fairly time consuming. One thing I advocate is having ONE thing at a time that you’re going back and forth with students on to help develop their critical thinking skills. Other activities I might have students doing is a Quia game or Desmos activity where the students are practicing probability where the computer gives the student immediate feedback. This frees up teacher time to offer students challenges like “How would you calculate the probability of a Farkle with 4 die?” and then follow it up with “but what if you had 5 die, how would that change the calculation?” There are actually a lot of things to consider in calculating a Farkle with a lot of die, so the “correct answer” would not necessarily be the goal. “Did you consider that a 2, 2, 2, 2 and a 2, 2, 2, # are both non Farkle rolls, how does that impact how you would do your calculation?” More important is the students strategy than their actual calculation of this math problem.

## Drag Scoring Die

A student rolls dice. Either physical dice or virtual dice. Notice along the top edge is virtual die to drag. For the scoring die the student will keep, they can drag this onto the gameboard.

Suggestion, that students take a picture or screenshot of their dice roll and place on the Slide. Chromebook users can use Control + Shift + Windows Switcher Key. What is awesome about Chromebooks is when a screenshot is taken a little pop up comes up giving the student the option to copy to clipboard. This makes it easy to paste right onto Google Slides.

## Duplicate Slides

Farkle requires multiple rounds of dice rolling, thus multiple strategies during the same round. (Farkle has 10 rounds.) For each subsequent dice roll the student should duplicate the slide and update the strategy box. (Remember Control A will select all, I find this useful for replacing the text from the previous slide.)

I also duplicated the scoring slide for each round, but it could easy be dragged to each round so the student can update it.

## The Answer is Always a Spreadsheet

Because I can not help myself from coding spreadsheets I created a spreadsheet that specifically generates 6 random numbers and allows the student to roll again for the purpose of Farkle.

### Farkle Menu

Notice in the template that next to the Help menu is a “Farkle Math” menu.

Students will choose to “Roll Dice” to get 6 random numbers.

*Note: The Google security screen is designed to be scary. You should definitely be wary of files you download off the Internet. I will, of course, tell you I am trustworthy and did not code anything malicious or anything that gives me access to your files (I would never do that.) Please review the Google blog for directions on how to authorize the script. You have to click on the tiny words “Advanced” and then the link that says “unsafe.” It is safe! Google is letting you know they did not review the code you are authorizing and they are not vouching for it. ONLY YOU have access to your files. *

### Delete Non Scoring Dice

On the app players tap the dice they DO want to keep. In my spreadsheet, you instead DELETE the dice you do NOT want to keep.

### Farkle Math Menu

To roll again, go back to the Farkle Math menu. Choose “Again roll.” In the row below, the deleted numbers will produce new numbers. To make it more clear in the menu what you are doing I went with the ungrammatical “Again Roll” instead of “Roll Again.”

In the case that the roll produces all scoring die, use “Roll Dice” to get a new roll of 6 numbers.

### Clear Dice

At the end of the round, choose “Clear Dice.” This clears out the spreadsheet and allows the player to “Roll Dice” again.

I was playing with the spreadsheet side by side with the Slides. Made it easy to roll and record my actions and strategy.

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