3.3

• Problem Solving


  refers to mathematical tasks that have the potential to provide intellectual challenges for enhancing students' mathematical understanding and development
• Problem Solving


  is the act of defining a problem; determining the cause of the problem; identifying, prioritizing, and selecting alternatives for a solution, and implementing a solution.
• Polya's Four Step

  1. Understand the problem
  2. Devise a Plan
  3. Carry out the Plan
  4. Lok Back
• Understand the Problem


  Make sure you understand what the question is asking
• Devise the Plan


  This step involves figuring out a strategy to solve the problem.
• Carry out the Plan


  Once you have a plan, it's time to carry it out.
• Look Back


  After solving the problem, it's important to review your solution.
• George Polya


  a Hungarian-American mathematician. He is best known for his significant contributions to probability theory and his four-step approach to problem- solving, which he detailed in his book "How To Solve It". Pólya served as a professor of mathematics at ETH Zürich and later at Stanford University. His work continues to influence the field of mathematics and education today.
• Recreational Mathematics


  An umbrella term, referring to Mathematical puzzles and Mathematical games
• Recreational Mathematics


  • Involves puzzles, games, and challenges that involve mathematical concepts but are typically pursued for enjoyment rather than practical applications
  • Requires creative thinking, problem-solving skills, and a solid understanding of mathematical principles to solve
• Mathematical games


  • The players of the game may not need to use mathematics in order to play mathematical games
  • Can improve problem-solving skills, promote logical thinking, and enhance mathematical understanding in a fun and engaging way
  • Can foster creativity, increase engagement with math, and offer enjoyable learning opportunities for all ages
• Tangram


  A Chinese puzzle made by splitting a flat square into five triangles, a square, and a parallelogram capable of being recombined to create several pictures
• Tangram


  • An operation puzzle consisting of seven flat polygons, called tans, which are put together to form shapes
• Rubik's Cube


  A 3-D combination puzzle invented in 1974 by Hungarian sculptor and professor of architecture Ernő Rubik

  
• Rubik's Cube


  • Consists of 26 small cubes that rotate on a central axis; nine colored cube faces, in three rows of three each, form each side of the cube
  • When the cube is twisted out of its original arrangement, the player must then return it to the original configuration—one among 43 quintillion possible ones

  
• Magic Square


  A square which is divided into smaller squares and each smaller square usually contains distinct integers
• Magic Square


  • In a magic square, the sum of the n numbers in each row, column, and diagonal equals the same constant, known as the magic constant or magic sum
  • The integers in a magic square typically range from 1 to n^2
  • The magic constant M is calculated using the formula: M = n(n^2 + 1)/2
• 2048


  A single-player sliding title puzzle video game

  
• 2048


  • The game's objective is to slide numbered tiles on a grid to combine them to create a tile with the number 2048
  • One can continue to play the game after reaching the goal, creating tiles with larger numbers
  • It's played on a 4x4 grid, with numbered tiles, and at each stage, you slide tiles in any of the four directions of the screen (up, down, left, and right)
  • If two tiles of the same number fall onto one another, then they merge into a tile whose number is the sum of the tile's numbers

  
• Sudoku


  A popular form of number game

  
• Sudoku


  • In its simplest and most common configuration, sudoku consists of a 9 × 9 grid with numbers appearing in some of the squares
  • The object of the puzzle is to fill the remaining squares, using all the numbers 1–9 exactly once in each row, column, and the nine 3 × 3 subgrids
  • Each row should have numbers 1-9, no repeats
  • Each column should have numbers 1-9, no repeats
  • Each 3x3 quadrant should have numbers 1-9, no repeats

  
• American Howard Garns in 1979 invented sudoku as we know it, and published it originally as a puzzle in Dell Magazines with the name "Numbers in Place"

  
• Maki Kaji of Japan then published the grid in Nikoli, his puzzle company's magazine in 1984. He is the bestower of the modern name of sudoku, meaning "single numbers" in English