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As scholars transition from elementary school math to high school math, it is important to provide them opportunities to use deductive reasoning. Scholars use inductive reasoning ( reasoning based on patterns) quite often in elementary school and are not exposed to the process of deductive reasoning. As scholars transition into high school math, It is important to be purposeful and meaningful in providing them opportunities to solve problems deductively. Deductive reasoning is the process of using general ideas to reach specific conclusions.
In logic, an inference is deductively valid if its conclusion follows logically from its premises. The process of deductive reasoning is used to solve problems in business, science research, policy (Law) and a wide range of other career fields.
Scholars need opportunities to utilize this particular skill set as it is important for success in high school math, college and career. Logic puzzles are a great way to practice the use of deductive reasoning. Here are a few of my favorite's. Credit goes to Jeff Wanko ( Professor of Education at the University of Miami).
Shikaku Puzzles
Shikaku Puzzles
In a Shikaku puzzle, your goal is to divide the entire puzzle (along the dotted lines) into rectangles—none of which overlap. Each circled number appears in exactly one of the rectangles and no rectangle in the solution can have more than one of the starting circled numbers in it.
The objective of the puzzle is to subdivide the entire region along the dotted lines into non-overlapping rectangles.
The three most important rules include:
The entire region is filled with rectangles.
Each rectangle contains exactly one circled number.
The circled number in each rectangle corresponds to the area of that rectangle.
Click the link below to download and view puzzles you can share with your class.
Hashiwokakero
Hashiwokakero
In a Hashiwokakero puzzle, schaolrs are to connect the circled numbers (or islands) with single or double-lane bridges. The bridges are either horizontal or vertical and cannot cross other bridges or islands. The number in each circle indicates the total number of bridges connected to that island. All islands must be inter-connected, that is, you must be able to travel between any two islands by using bridges and other islands.
In summary, the objective of Hashiwokakero puzzles, is to connect the circled numbers (islands) with line segments (bridges).
These important rules most be followed when completing the puzzles:
Bridges can be either single or double lanes.
Bridges are horizontal or vertical.
Bridges never cross other bridges or islands.
The number on each island matches the total number of bridges connected to that island.
All islands are inter-connected. That is, you must be able to travel between any two islands in a puzzle.
Click the link below to download and view puzzles you can share with your class.
Battleships
Battleships
Battleships puzzles are based on the classic board game of Battleships, except here you are trying to figure out the placement of a larger fleet of ships, based on some initial clues. In the standard 10 x 10 Battleships grid, your goal is to place the fleet of one battleship (four grid cells in length), two cruisers (three cells each), three destroyers (two cells each), and four submarines (one cell each).
The objective of Battleships puzzles is to place the full fleet of ships in the 10 x 10 grid.
Schaolrs must remember these important rules when playing Battleship puzzles:
The numbers along the perimeter indicate the number of ship pieces in the corresponding rows and columns.
Initial clues are given in the puzzle grid to indicate some of the ship pieces and/or water.
No two ships can touch each other, not even diagonally.
Click the link below to download and view puzzles you can share with your class.
Sashigane
Sashigane
In a Sashigane puzzle, your goal is to divide the entire puzzle (along the dotted lines) into L shapes, where the two legs of every L are each only one unit wide. Every square in the grid is part of an L and no squares are left over. It is also helpful to note here that sashigane is the Japanese word for a carpenter’s square—the large metal L that a carpenter uses to ensure a 90° angle.
The objective of Sashigane puzzles is to subdivide the entire region along the dotted lines into L shapes with legs that are one unit wide.
Scholars must adhere to these rules while playing the puzzle:
Circled numbers indicate the number of squares in an L that contains the circled number.
Circles indicate the location of the bend of an L that contains that circle.
Arrows are located at the end of a leg for an L and the arrow points toward the bend of the L.
Star Battle
Star Battle
In a Star Battle puzzle, your goal is to place stars in the grid in such a way that exactly one star appears in each row, column, and region. Stars must also be placed so that no two stars touch each other—not even diagonally.
The objective of Star Battle puzzles is to place stars in the grid.
Here are the rules:
One star appears in each row, column, and region.
No two stars can touch, not even diagonally.
Click the link below to download and view puzzles you can share with your class.
Ripple Effect
Ripple Effect
The objective of Ripple Effect puzzles, is to place numbers in the grid squares.
Scholars must make sure to follow these important rules:
Each region of n squares contains the numbers 1, 2, … , n.
In any row or column, if the same number (n) occurs more than once, there must be at least n squares between any two occurrences.
Click here to be directed to additional Ripple Effect puzzles to share with your classroom.
If you would like additional information on best practice's for implementation, please do not hesitate to reach out to tmartin2@apslearns.org.
" All APS Scholars will graduate as architects of their future, prepared to thrive in an ever-changing world."
-APS Vision
Reach out to the Math Department Via email if additional support is needed at math@apslearns.org
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