## Mathematics 11 Logical REasoning

Specific Curriculum Outcomes

**LR01**Analyze and prove conjectures, using**, to solve problems.***inductive and deductive reasoning***LR02**Analyze puzzles and games that involve**, using problem-solving strategies.***spatial reasoning****Spatial thinking, or reasoning, involves the location and movement of objects and ourselves, either mentally or physically, in space. ****This outcome is the same as G01 from Mathematics at Work 10*## Activities

**The Pentomino Farm Problem**- Use a full set of twelve pentominoes arranged as a fence to enclose a field. The rule used to join them is that they must touch along the full edge of a square and not just at the corners. What is the area of the largest field that you can build? What is the largest field area if you impose a constraint that either the field, the fence or both must be a rectangle?

**Swish from ThinkFun**- Swish is a spatial card game that challenges you to be the first to make matches, or “Swishes.” Swishes are made by stacking as few as two or as many as 12 cards so that every ball swishes into a hoop of the same color. The player with the most matches at the end of the game wins.

**Connect 4 video from Numberphile**- Connect-Four is a game in the Tic-Tac-Toe family; the object is to get four stones in a row horizontally, vertically or diagonally. There is a "gravity" rule: you can play only in the bottom-most unoccupied cell in a column. The video from Brady Haran talks about some of background on the game. James Allen has even written an entire book on the game and solved it with a computer program. You can also play connect 4 with alternate rules: don't let your opponent place four stones such that they make the four vertices of a rectangle.**Connect 3-4-5 Variation**- Players continue to place all of their discs until the board is filled. Then each player scores 3 points for each 3-in-a-row, 8 points for each 4-in-a-row and 15 points for each 5-in-a-row.**Connect 4 Rectangle Variation**- Play so that the winner is the first player to have four discs that make the corners of a rectangle with sides parallel to sides of the board.**Connect 4 Cooperative Variation**from Mathpickle.com - Play so that you LOSE the game if you create 3 in a row. If your opponent and you work together – can you fill the whole board with nobody losing?

**Skikaku Puzzles from Nikoli and Skikaku**- These puzzles (also known as Rectangles) are spatial puzzles with simple rules.

**Galaxy Puzzles by KrazyDad**- In these puzzles, you fill in the horizontal and vertical edges to form a galaxy shaped island around each circle, which represents the galactic center. The galaxy shapes must be rotationally (or 180°) symmetric. Each Galaxy puzzle has only one unique solution.

**The Two Doors Riddle from the movie Labyrinth**- You find yourself in a strange place with 2 doors. One door leads to death and the other to your destination. The doors are guarded by two guards. One of the guard always say truth while other always lies. You don't know which guard is which, nor what door leads to your destination... You can ask only one question to go out from there. What should you ask?