Student Learning Objective :
1. Develop deep problem solving skills, computational thinking, logical thinking. As they tackle logic problems with gradually increasing difficulty, students learn how to deduce more information from existing information, make deeper connections. They develop multiple strategies to solve the problems. These strategies help them solve harder problems. Hence it encourages the growth mindset.
2. Students lay the foundation of the concept of mathematical proof. They realize that making moves that they are sure of gets them to the solution more efficiently and faster than making guesses (Scoring system rewards fewer moves to get to solution). This also builds independent thinking, and ability to objectively critique your own work.
3. These skills are very useful in current science and business jobs such as programming, robotics, science research, business and data analytics, investing, banking, and business decision making.
Alignment with Common Core: Build Mathematical Practices laid out in Common Core
1. Make sense of problems and persevere in solving them.
2. Reason abstractly
3. Construct Viable Arguments and and critique the reasoning of others
7. Look for and make use of structure.
Link to App for Download : https://itunes.apple.com/us/app/logiccity-for-schools/id1016653802?mt=8
Step 1. Hook : Light up the city, get the best score
Teachers – Give students access to the problems via the app above (ipad / iphone needed) and the directions for students below. Let them try out a few puzzles. Give help in terms of what the rules are if needed (can be accessed by touching the ? on the top right in the app).
The main idea is to let the students play and discover (learn by doing) while facilitating through discussion and sharing of ideas and strategies across the students.
Students – You’ve discovered a lost city, with no people and no lights. Your mission is to bring lights and power back to the city. In order to do this, you have to solve some logic problems that open up the switches to light up the city. The more problems you solve, the more of the city you light up and the higher your score. The highest scorers get to be the mayor, head engineer, treasurer, lead architect, and judge of the city for a day (can substitute your own titles as desired)
Step 2. Discussion : How do you get a higher score ?
Teachers – Once the students have solved a few problems, ask them what influences their score in LogicCity, and how can they get a higher score ? The three things that affect it are:
1. Total number of puzzles solved.
2. The difficulty level of the puzzle solved (represented as the number of the puzzle on the initial buildings screen)
3. Using fewer moves to solve a puzzle.
This should incent the students to think harder and use fewer moves to solve problems. Also, they will try to tackle the harder problems hence building their deeper thinking skills.
After discussion, let the students solve more problems, and think about what strategies they are using for the next discussion.
Step 3: Independent Practice followed by Discussion : Building strategies to solve the problems, that enable solving harder problems
Teachers – Discuss what strategies the students are using to solve the problems. Several sample strategies to solve LogicCity puzzles are attached below (illustrated via the rules construct used in puzzles 26-70 in the app), in increasing order of difficulty. The harder strategies to solve problems will come up as the students attempt the harder problems. This is the core of the discussion, and may take multiple classes to discuss.
It is very useful and satisfying for the students to discover the strategies themselves as they play, or through discussion with each other.
It is also really fun to solve a few puzzles together as different students call out the next move and their reasoning behind it.
Note : To access these presentations, they have to be downloaded, and played on Keynote (mac presentation software). Please contact us if you would like a powerpoint version of these.
Strategy 1 : Line Sweeping (click the link below to download)
Strategy 2 : Intersection Sweeping (click the link below to download)
Strategy 3 : Parallel Sweeping (click the link below to download)
Strategy 4 : 3 of a Kind (click the link below to download)
For more strategies, contact us at firstname.lastname@example.org
It is very valuable to continue to solve harder puzzles as that is when the students truly encounter a challenge and the opportunity to develop the growth mindset.
The levels are unlocked so the students can progress at their own pace at their learning level and hence keeping them engaged. If they move too fast and can’t solve a problem, encourage them to go back and try a few easier problems, develop strategies and then go to the harder problems. It makes a huge difference to practice and build some strategies. They can often solve the harder problems once they do they equip themselves with problem solving strategies.
Step 4: Discussion with the class :
Was this fun ? What did you learn ? Were you surprised at the difficulty of the problems ? Were you surprised when you solved some of them ?
Key meta-learnings :
- Developing strategies while solving problems helps them solve harder problems. #WithMathICan. Hence, if they try, they can solve some very hard problems that initially seemed difficult – an important learning and method to encourage the growth mindset.
- Even though there is very little information laid out on the starting puzzle, all of the remaining parts of the board can be derived from the existing information. This is often true in situations where knowing a few things / setting a few rules / making a few critical choices will often define the remaining structure / outcome even if it is not immediately obvious.