Mathematics 12
Integrated Unit - Numerical Puzzles and Logic Games
Note: This outcome should be developed throughout the course and not in isolation.
Note: This outcome should be developed throughout the course and not in isolation.
Mathematics 12 Pacing Guide - This pacing guide replaces the previous yearly plan. It has been updated to reflect removed outcomes and provide flexibility for responsive instruction.
Mathematics 12 Desmos Activity Collection - A collection of online student Desmos activities organized by unit.
LR01 - The emphasis of this outcome should NOT be on the successful completion of any puzzle or game but rather on analyzing numerical and logical reasoning and problem-solving strategies.
LR01 Students will be expected to analyze puzzles and games that involve numerical and logical reasoning, using problem-solving strategies.
(It is intended that this outcome be integrated throughout the course by using games and puzzles such as chess, sudoku, Nim, logic puzzles, magic squares, Kakuro, and cribbage.)
LR01.01 Determine, explain, and verify a strategy to solve a puzzle or to win a game; for example,
guess and check
look for a pattern
make a systematic list
draw or model
eliminate possibilities
simplify the original problem
work backward
develop alternative approaches
LR01.02 Identify and correct errors in a solution to a puzzle or in a strategy for winning a game.
LR01.03 Create a variation on a puzzle or a game, and describe a strategy for solving the puzzle or winning the game.
Additional Resources and Activities for LR01 (numerical and logical puzzles and games):
Numerical Puzzles
KenKen/Inkies - Fill in the blank squares so that each row and each column contain all of the digits 1 thru 4 (or whatever the size of the puzzle is). The heavy lines indicate areas (called cages) that contain groups of numbers that can be combined (in any order) to produce the result shown in the cage, with the indicated math operation. For example, 8× means you can multiply the values together to produce 8.
Thirty-One - Lay out the ace to six of each suit in a row, face up and not overlapping, one suit above another. You will have one column of four aces, a column of four twos, and so on—six columns in all. The first player flips a card upside down and says its number value. Players alternate, each time turning down one card, mentally adding its value to the running total, and saying the new sum out loud. The player who exactly reaches thirty-one, or who forces the next player to go over that sum, wins the game.
The Desert Trek Problem - Sara needs to trek from an oasis to a destination 10 miles away across a barren desert. The facts: Crossing one mile of desert requires using 1 gallon of water. Sara can only carry 6 gallons of water at a time from the water-abundant oasis where she begins. Sara can drop a water cache (of any amount of water from the supply she is carrying at that moment) at any of the nine stops along the route, and then pick up any part of the cache on a later trip. What's the minimum number of times Sara must leave the oasis in order to cross the entire 10 mile span of desert? This problem was from the Brilliant.org 100 Day Summer Challenge.
Logical Puzzles
Logical Games Desmos Activities
Skyscrapers Puzzles Desmos Activity - Students arrange buildings in a square grid to solve this puzzle.
Tents and Trees Puzzles Desmos Activity - Place tents on a grid, each one next to a tree. Numbers around the edge of the grid tell you how many tents appear in each row and column. A tent can only be found horizontally or vertically adjacent to a tree, and tents are never adjacent to each other, neither vertically, horizontally, nor diagonally. You can find a pdf handout of this puzzle at Sarah Carter's blog.
SET Desmos Activity - If students have never played SET before, this activity will help them learn how.
Wolves and Sheep Puzzle Desmos Activity - Place 5 wolves and 3 sheep on a 5x5 grid so that all the sheep are safe.
Pennies and Paperclip - Pennies and Paperclips is a two-player game played on a 4 by 4 checkerboard with a standard color pattern. One player, "Penny", gets two pennies as her pieces. The other player, "Clip", gets a pile of paperclips as his pieces. Penny places her two pennies on any two different squares on the board. Once the pennies are placed, Clip attempts to cover the remainder of the board with paperclips — with each paperclip being required to cover two adjacent squares. Paperclips are not allowed to overlap. If the remainder of the board can be covered with paperclips then Clip is declared the winner. If the remainder of the board cannot be covered with paperclips then Penny is the winner.
Nim and Drips - These games are Nim and its variations. Drips is a tablet and phone friendly version of Nim that helps you discover the winning strategy. You can play Nim with heaps of pennies or tooth picks. A Nim handout and a Mimio *.ink file. Another version of Nim "Circle of Pennies" but using counters in a circle.
Hex and Bridg-It - These are similar "connection" games. In Hex, players take turns claiming a single hexagon within the overall playing board (often an 11 x 11 hexagonal grid in the shape of a rhombus). The goal for each player is to form a connected path linking the opposing sides of the board marked by their colors, before their opponent connects his or her sides in a similar fashion. The first player to complete his or her connection wins the game. In Bridg-It, players attempt to make a continuous connected path of bridges from one side of the board to the opposite side while blocking their opponent from doing the same. A Hex handout and a Bridg-It handout.
Sudoku Printables - Here are thousands of free Sudoku puzzles to print. Each booklet of printable Sudoku contains eight puzzles, instructions, hints and answers.
Bridges (Hashiwokakero) Puzzles - Here are hundreds of free Bridges puzzles suitable for printing. In these puzzles, you connect the islands to form a network so that you can reach any island from any other island. The number on each island indicates the number of outgoing bridges. You may only connect islands horizontally or vertically, and you may use one or two bridges to connect islands, but no more than two. Each Bridge puzzle has only one unique solution, which you can find without guessing.
Logic Puzzles - A large collection of logic puzzles for play, both online and the old fashioned way with pencil and paper. The kind of puzzles here are most commonly referred to as "logic grid" puzzles. In each puzzle you are given a series of categories, and an equal number of options within each category. Each option is used once and only once. Your goal is to figure out which options are linked together based on a series of given clues. Each puzzle has only one unique solution, and each can be solved using simple logical processes (i.e. educated guesses are not required).
Dots and Boxes - To make one side of a box, click on any two dots next to each other (vertically or horizontally). If you complete a square it is yours, and you get a free turn.
Four in a Line - Called "Connect 4" by Hasbro. Play against computer or another human.
Tic-Tac-Toe - Play Tic-Tac-Toe against another player or the computer. Different board sizes and computer strength.
Towers of Hanoi - The object of the game is to move all the disks over to Tower 3 (drag and drop). But you cannot place a larger disk onto a smaller disk.