Lesson Plan

# Building deep problem solving skills #WithMathICan

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 critique the reasoning of others 7. Look for and make use of structure.
Objectives

1. Students will be able to develop deep problem solving skills. As they tackle logic problems with gradually increasing difficulty,  they will learn not only through failure, but also be motivated to develop strategies to solve the problems. These strategies then help them tackle even harder problems. Hence they should come to the realization that they can actually solve really hard problems that indeed seemed too hard to solve without developing those strategies.

2. Students begin to lay the foundation of the concept of mathematical proof, as they come to realize that making moves that they are sure of gets them to the solution more efficiently and faster than making guesses (Fewer moves to get to solution rewards them with a higher score)

3. Students learn how you can derive a lot of additional information from existing information - a skill that is very useful in current science and business jobs such as programming, robotics, science research, architecture and business analytics, investing and decision making.

Subjects
Math
Science
Grades 5 – 12

#### 1 Hook : Light up the city, get the best score

Give students access to the problems via the app above (ipad / iphone needed) and the directions for students. 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.

Student Instructions

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 fewer the number of moves you take to solve the problems, 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.

#### 2 Discussion 1 : How do you get a higher score ?

Activity: Conversing

Once the students have solved a few problems, ask them what influences the score, 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 start to think harder and try to use fewer moves to solve problems, and to try to tackle the harder problems.

After discussion, let the students continue to solve a dew more problems, and think about what strategies are they using to solve the problems for the next discussion.

Student Instructions

Think about what leads to a higher total score in the game,   and hence what you can do to increase your score.

Start to think about what strategies you are using to solve the puzzles for discussion with the class.

#### 3 Independent Practice followed by Discussion : Building strategies to solve the problems, that enable solving harder problems

Teachers - several strategies that help solve the puzzles are available at the link above. To find them, go to the link, scroll down to Step 3, and find the documents attached under each of the strategies. The documents can be opened using Keynote (Mac presentation software). Press play once you open it for an animated demo of the strategy.

Note : The demo strategies assume the rule construct for puzzles 26-70 in the app. The more advanced strategies are needed as you do the more difficult puzzles.

For the learning to be most effective, let the students play with several puzzles in this section and self-discover the strategies and then create group discussions.

It is also really fun to put a device under the smart-board camera, and solve a few puzzles together as different students call out the next move and their reasoning behind it.

This is the longest section and may take several classes to get to discover all the strategies. The older students or the ones with prior experience with Sudoku may get there faster.

It is very valuable to continue to solve to the 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 faster if they so desire. 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 and they can often solve it the next time around, once equipped with the strategies.

Student Instructions

Solve the puzzles between levels 26-70. Think about the strategies you are using, and discuss with others. Think about what other strategies you can develop. Does developing the strategies help you solve harder problems ?

#### 4 Wrap Up : What did we learn ?

Activity: Conversing

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 :

1. Developing strategies to solve problems helps them solve harder problems. Hence, if they try, they can solve some very hard problems that otherwise seemed difficult - an important learning  and method to encourage the growth mindset.

2. 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.