## Extended 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 2, 4, 6 Puzzle from Daniel Finkel**- The 2-4-6 Puzzle teaches an invaluable lesson about inductive reasoning, confirmation bias, and how “wrong” answers lead to deeper knowledge. It can be adapted with different rules for endless play options and difficulties.

**The Squareable Puzzle from Daniel Finkel**- A number is squareable if you can build a square out of precisely that many squares. Can you find all the numbers less than 30 that are squareable? Is there a pattern?

**Panda Squares from David Butler**- You have 16 square tiles, each made up of four small squares. These smaller squares are coloured either black or white. In fact, the 16 squares cover all possible colourings considering different orientations as different. Arrange the 16 tiles into a 4 by 4 square so that the colours match along the edges of tiles next to each other. There are lots of possible solutions.

**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?

**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 and Math in English**- 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.