Resources for Planning - Working with Specific Puzzles
 
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Working with Specific Puzzles

WING 1
Cafeteria | Testing Lab | Assembly Line

WING 2
Lounge | Shipping | Vats

WING 3
Garden | Mine Shaft | Warehouse



WING 1        

Cafeteria

The goal of this group of puzzles is to feed the monsters by filling their plates with the correct portions of slop, drumsticks, sushi, and burgers. Players must study the relationships between the numerical portions of different foods on each tray, as well as the same food across all trays. To begin play on level one (Employee's Cafeteria), the player clicks the flashing dispensing button on the food machine and places the food that appears in the correct spot on a monster's tray. If the food is placed on the correct tray, the monster will respond favorably and that plate of food is locked into place. One light will go out on the plate counter. If the plate is incorrectly placed, the monster will respond negatively, and the food will be ejected from the tray and land in the correct place on another monster's tray. When this happens, three lights will go out on the plate counter. In order to successfully complete the first level of play, the player must place all plates of food correctly before all of the lights expire on the plate counter.

In subsequent puzzle levels, players choose the food item to be placed and adjust the numerical value of it.

  Math Discussion Terms
Proportion, equation, ratios, equivalent

Maryland Voluntary State Curriculum Alignment

Standard 6.0 Knowledge of Number Relationships and Computation/Arithmetic
Topic C Number Computation
Indicator 3 Analyze ratios, proportions, and percents

Grade 7:
Objective a-Determine Equivalent Ratios

Grade 8:
Objective c-Solve problems using proportional reasoning

Lesson Plans

GRADE 7 DETERMINE RATIOS LESSON PLAN

GRADE 8 PROPORTIONAL REASONING LESSON PLAN

GRADE 8 PROPORTIONAL APPLICATIONS LESSON PLAN

Student Graphic Organizer for Cafeteria Puzzles
 


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Testing Lab

The goal of this group of puzzles is to follow a recipe by combining the correct amounts of four different ingredients. The three measuring cups provided may not match the quantities specified in the recipe, so players must transfer the ingredients between measuring cups, sometimes in multiple combinations, to obtain the correct amounts to add to the mixture in the vat.

In Level 1, the recipe amounts are expressed as integers (liters), and the sum of all four ingredients in the recipe equals the total volume of the vat.

In Level 2, the recipe amounts are expressed as fractions of the total recipe, and the player must determine the correct amounts based on the total volume of the vat.

In Level 3, the amounts are expressed as integers (liters), and the sum of the four ingredients in the recipe is a multiple or fraction of the total volume of the vat. The player must scale the recipe to fill the vat with the correct proportion of each ingredient.

Players may also transfer ingredients from one measuring cup into another measuring cup, the vat, or the waste pipe. The waste pipe is a container into which players can empty a measuring cup when it contains an ingredient that they do not want to add to the vat. This allows players to finish working with one ingredient so they can dispense another or to pour out an ingredient that they no longer need. When the maximum capacity of the waste pipe has been reached, the player can no longer empty any measuring cup into the waste pipe.

A round of play is over when players have finished following the recipe and/or the vat is full. At the conclusion of a round of play, a graph will appear that indicates the percentage of the amount of the ingredient added by the player relative to the required amount.

  Math Discussion Terms
Fraction, whole number, common denominator, numerator, denominator, least common denomination, least common multiple, prime factors, numerical expression, algebraic expression, variable

Maryland Voluntary State Curriculum Alignment

Standard 1.0 Knowledge of Algebra, Patterns, and Functions
Topic B Expressions, Equations, and Inequalities
Indicator 1 Write and evaluate expressions

Grade 6:
Objective a - Add and subtract fractions and mixed numbers and express answers in simplest form
Objective b - Multiply fractions and mixed numbers and express in simplest form

Grade 7:
Objective b - Add, subtract, and multiply positive fractions and mixed numbers

Standard 6.0 Knowledge of Number Relationships and Computation/Arithmetic
Topic A Knowledge of Number and Place Value
Indicator 1 Apply knowledge of rational numbers and place value

Grade 6:
Objective c - Identify and determine equivalent forms of fractions as decimals, as percents, and as ratios
Grade 7:
Objective c - Determine equivalent forms of rational numbers expressed as fractions, decimal, percents, and ratios

Lesson Plans

GRADE 7 ALGEBRAIC EXPRESSIONS LESSON PLAN

GRADE 7 ADD, SUBTRACT, MULTIPLY FRACTIONS LESSON PLAN

Student Graphic Organizer for Lab Puzzle
 


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Assembly Line

The goal of this group of puzzles is to fill up the bins with the correct amount of regular and premium (starred) cans. In order to do this, the player must study the numerical relationships between the gears as well as the spaces between the placement of regular and premium (starred) cans on the conveyor belt.

When the player enters the room in level one of the game, the assembly line is running with two incorrect gears, and the trays of replacement gears are off-screen. The assembly line supervisor prompts the player to fix the problem. To examine the situation, the player can slow down or speed up the line or stop it entirely.

The player must click the STOP button to pause the assembly line and see the replacement gears on either side of the conveyor belt. The player must click and drag the gears that represent the correct ratio and put them in place. Each time the player clicks STOP and replaces gears, the assembly line resets. If either of the two gears is incorrect, the supervisor will tell the player that the machine is still broken. If the placement of both gears is correct, the supervisor will tell the player that things are working correctly.

Subsequent levels of play provide less visual cues to the player as to the placement of the regular and premium cans on the conveyor belt.

  Math Discussion Terms
Multiples, ratio, numerator, denominator, fraction

Maryland Voluntary State Curriculum Alignment

Standard 6.0 Knowledge of Number Relationships and Computation/Arithmetic
Topic C Number Computation
Indicator 3 Analyze ratios, proportions, and percents

Grade 6:
Objective a-Represent ratios in a variety of forms

Objective b-Use ratios and unit rates to solve problems

Grade 7:
Objective a-Determine Equivalent Ratios
Objective b- Determine and use rates, unit rates, and percents as ratios in the context of a problem

Lesson Plans

GRADE 6 RATIOS LESSON PLAN

GRADE 7 DETERMINE RATIOS LESSON PLAN

Student Graphic Organizer for Assembly Line
 


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WING 2        

Lounge

In the Lounge puzzles, players must use varied combinations of coins to obtain items from a vending machine. In the Employee Lounge and Managers' Lounge (Levels 1 and 2), the puzzle has two distinct parts, or phases, that follow each other in sequence. In the first phase, the player moves three coins, one at a time, from the stacks of coins and places them into the three coin slots on the machine. If the sum of the three coins equals the price of an item in the machine, the machine dispenses the snack. Players can also intuit the value of their coins by looking at the equations each combination equals.

In phase 2 of the Employee Lounge and Managers' Lounge, one of the vending machine items "electrifies" to signify that the player should place the correct amount of coins to dispense the item. If the player deposits the correct combination of coins, the item is dispensed and the door to the multi-pack bonus item is opened and visually highlighted with flashing lights. The vending machine displays new prices for the remaining items, all empty locations, and the multi-pack bonus item. One stack of coins is replaced with a stack of coins of another color. (Two of the colors remain the same.)

The Employee Lounge and Managers' Lounge Levels function the same with one exception:
  • In Level 1, players can deposit any combination of three coins, including three coins of the same color.
  • In Level 2, players cannot deposit three coins of the same color.
In the Executive Lounge (Level 3) of the Lounge puzzle, players are presented with a matrix of vending machine items and four coins that must add up to the item amount. A "scratch pad" on the right of the screen is available to help players figure out the coin combinations. Additionally, buttons at the end of each row and column of the matrix help the player determine moves. When the user fills a row or column with four coins that total the correct price of the item in the row or column, the button illuminates to indicate that the item can now be dispensed. To solve the puzzle, the player must correctly place the coins in each row and column, thus illuminating each button.

  Math Discussion Terms
Expression, variable, evaluate, value

Maryland Voluntary State Curriculum Alignment

Standard 1: Knowledge of Algebra, Patterns, and Functions
Topic B: Expressions, Equations, and Inequalities
Indicator 1: Write and evaluate expressions

Grade 7:
Objective b - Evaluate algebraic expressions

Lesson Plans

GRADE 7 EXPRESSIONS LESSON PLAN
 


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Shipping

In the Shipping puzzles, players are assigned to work on the loading dock where jars of Tasti-Pet pet food are received from the factory on pallets and prepared for shipment. The player's job is to label each pallet based on the arrangement of jars, which visually represents a mathematical equation. But first, the player must decipher a system of symbols that the monsters are using to represent numbers and mathematical operations.

To do this, players have to complete two tasks:
  1. Players first encounter a "hint" pallet that has a "hint" equation at the bottom of the pallet, showing the symbols that relate to the jars. They must then use this hint pallet to find out the other numbers and operators on the keypad, filling in equations that translate the symbols to numbers. Players click on a symbol and drag it to the correct place on the keypad.
    1. In Level 1, the symbols will not "stick" on the keypad if they are incorrect. In Level 2 and 3, all symbols players select will "stick," whether they are correct or not.
    2. Players can match 14 of the 15 keys; the 15th key is assumed to be correct, but the player must move it to the keypad before the game proceeds.
    3. In Level 1, the hint on the "hint" pallet contains a symbol for "=." In Level 2, this part of the hint is missing.
  2. After players have deciphered all of the symbols, they must then use the keypad to correctly identify the configurations of other pallets that arrive at the factory. They do this by clicking on the correct symbols in order and then clicking on the "enter" button on the keypad. They can also use the "clear" button to start over again; they can also drag individual symbols off of the keypad.

    If players enter an incorrect value of the equation related to a pallet, a siren sounds, the pallet disappears, and the foreman shows his great displeasure. If players enter a correct value for the pallet, the foreman pushes the pallet on its way.

    In Level 2, after placing all the symbols on the keypad, players must decide how to package the jars on the pallets, placing them in boxes that hold either ten jars (shown by a box with ten jars) or one jar (shown by a box with one jar). They do this by using the key pad to select how many boxes of each kind they need, clicking on the symbol for how many boxes of ten they need first and then clicking on the symbol for how many boxes of single jars they need. Note that players have to enter the symbol for zero if they do not need that kind of box.
  3. Level 3 provides another interesting challenge for players. At this level, each round of the puzzle will use a number system other than base - 10. Puzzles will be presented in base - 12, 9, 8, 6, 4, and 2.
  4. All pallet configurations will represent either an addition or a multiplication equation until the player has successfully completed one round of the puzzle. After a successful completion of one round, the "hint" pallet configurations may include any of the four operations (randomly selected) illustrated below.
    • Addition is represented as a single row of full jars, divided into two groups, with space between the two groupings. The numbers of jars in each of the two groups represent the addend. For example, the arrangement below represents 3 + 4 = 7.
    • Multiplication is represented as an array of full jars stacked in rows and columns. The number of rows represents the first factor in the equation (the multiplicand), and the number of columns represents the second factor (the multiplier). The total number of jars represents the product. For example, the arrangement below represents 3 x 4 = 12.
    • Subtraction is represented by a combination of empty and full jars in a single row. The jars are divided into two groups (empty and full), with space between the two groupings. The total number of jars on the pallet represents the minuend. The number of empty jars represents the subtrahend. The number of full jars represents the difference. (Minuend - Subtrahend = Difference) For example, the arrangement below represents 7 - 4 = 3.
    • Division is represented as an array of empty and full jars stacked in rows and columns, with space between each column. Each column contains either empty or full jars, but not both. The total number of jars on the pallet represents the dividend. The number of columns represents the divisor. The number of full jars represents the quotient. For example. The arrangement below represents 15 / 5 = 3.
  Math Discussion Terms
Addition Identity Property, constant, difference, equation, expression, Multiplication Identity Property, Multiplication Property of Zero, operation, product, quotient, sum, symbol, variable, decimal, expanded form, expression, digits, Mayan Number System, numeration system, order, position, Roman numerals, unique

Maryland Voluntary State Curriculum

Standard 6.0: Knowledge of Number Relationships and Computation/Arithmetic
Topic A: Knowledge of Number and Place Value
Indicator 1: Apply knowledge of rational numbers and place

Grade 7:
Objective a - Read, write, and represent whole numbers

Standard 1.0: Knowledge of Algebra, Patterns, and Functions
Topic B: Expressions, Equations, and Inequalities
Indicator 2: Identify, write, solve, and apply equations and inequalities

Grade 6:
Objective b - Determine the unknown in a linear equation

Lesson Plans

GRADE 7 REPRESENTING NUMBERS IN OTHER BASES LESSON PLAN

GRADE 6 SOLVING EQUATIONS LESSON PLAN
 


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Vats

The goal of this group of puzzles is to align the mixing arms of nine vats and the bridges, so that players can cross from a starting position to the vat on the bottom right. Along the way, players must avoid the green blobs that are trying to destroy them and collect as many of the ten dinosaur eggs as possible. And, as an additional challenge, each move the player makes creates a certain amount of pressure on the bridges; too much pressure will destroy them.

The vats are used to mix up Echidna's Tasti-Pet pet food. Each vat has tick marks at the top (as well as a number that tells players how many tick marks there are). These marks indicate how many moves it will take to rotate the arm of that vat a full 360 degrees. One arm might take 4 ticks to move around the vat; another might take 12.

The player controls how the arms move by putting a number in the remote control device that governs the movement of the arms. For example, if the player puts in a value of 6, the vat arm with 4 ticks will revolve one-and-a-half times, while the arm of the 12-tick vat will move only half way around its vat. All arms rotate in a clockwise direction.

The player can move from the bridge to an arm only when the arm is precisely aligned with the bridge. The player can collect dinosaur eggs only when they are on a mixing arm when it stops at the tick mark where an object is located. The player is destroyed by the monster when they both arrive at the same location on a bridge or arm. Bridges have five states of "damage," ranging from "undamaged" to "destroyed." When players begin a round, three bridges are in states of damage that range from 1 to 3; each move they make increases the pressure (which they can monitor on an on-screen meter), leading to the destruction of some (or all of the) bridges.

At levels 2 and 3, drawbridges replace bridges, increasing the difficulty. The player must calculate the input value that will get both arms of two adjacent vats to stop at the bridge at the same time. Unless the arms align, the bridge stays up, and the player can't advance. Drawbridges connect a few of the vats at level 2, and all of them at level 3.

The Vats puzzles explore algebraic concepts like variables, rates of change, balancing equations, and especially modular arithmetic. The greatest challenges are:
  1. Advancing arms to target positions with the minimum number of commands (arithmetic, modular arithmetic).
  2. Plotting the most efficient path through the vats (spatial reasoning).
  3. At levels 2 and 3, programming commands that will cause vats of different "periodicities" to align (variables, simultaneous equations).
  Math Discussion Terms
Sequence, function rule, term, function table, coefficient, constant, slope, ordered pair solution

Maryland Voluntary State Curriculum Alignment
Standard 1.0: Knowledge of Algebra, Patterns, and Functions
Topic B: Expressions, Equations, and Inequalities
Indicator 1: Write and evaluate expressions

Grade 8:
Objective a - Write an algebraic expression to represent unknown quantities

Algebra/Data Analysis Goal 1: The student will demonstrate the ability to investigate, interpret, and communicate solutions to mathematical and real-world problems using patterns, functions and algebra.
Expectation 1: The student will analyze a wide variety of patterns and functional relationships using the language of mathematics and appropriate technology.
Indicator 2: The student will represent patterns and/or functional relationships in a table, as a graph, and/or by mathematical expression.

Expectation 2: The student will model and interpret real-world situations using the language of mathematics and appropriate technology. Indicator 1: The student will determine the equation for a line, solve linear equations, and/or describe the solutions using numbers, symbols, and/or graphs.

Lesson Plans

GRADE 8 ALGEBRAIC EXPRESSIONS LESSON PLAN

GRADE 8 FUNCTION RULES LESSON PLAN
 


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WING 3        

Garden

The Garden puzzles help players acquire an understanding of the connection between area and perimeter. At each level, players must plant a series of five different specimens of sometimes nasty plants that can sometimes eat other vegetation. Each plant requires its own version of fencing, ranging from split rail to electrified fences. Players must create rectangular garden plots of specific areas for each plant, bounded by fences of specific lengths in accordance with a series of "work orders" prepared by upper management of the Tasti-Pet Food Factory. For example, if a work order requires a plot area of 20 units, bounded by a fence with a length of 18 units, then the player must mark out a 4 x 5 plot. Other size rectangles might satisfy the area or perimeter requirement, but only a 4 x 5 will satisfy both. The whole garden area is gridded, and the grid lines correspond with the units of fencing.

Players are further challenged by the need to be economical, because creating too large a plot or too small a plot has consequences:
  • If the area for a plot is too small, not all the available plants will be planted.
  • If the area is too large, weeds will invade the empty spaces, and consume the desirable plants.
  • If the perimeter is too small, fencing will be wasted (which makes for an unhappy boss).
  • If the perimeter is too large, there will be gaps in the fencing, and the plants will begin to escape (remember, these are monster plants).
There is one plot for each of the five pet food ingredients. The five plots must all fit into a larger garden area, but, in placing these plots in Levels 1 and 2, players must be careful to avoid enclosing a gnome. Gnomes that are fenced in at these two levels will eat all the crops within the plot.

In Level 1, the player has some flexibility in setting out the plots; Level 2 has fewer possible solutions. In Level 3, garden gnomes are not destructive, but take up the same amount of space (1 square per gnome). This level is more difficult because several of the target rectangles require the player to enclose some of the garden gnomes. For example, a target of 19 plants bounded by a fence of length 18 can be accomplished by drawing a 4 x 5 plot that encloses 1 gnome. While only some of the rectangles require the player to enclose gnomes, the player won't know which ones, and will have to reason much more carefully.

  Math Discussion Terms
Area, dimension, formula, length, perimeter, width

Maryland Voluntary State Curriculum Alignment

Standard: 3.0 Knowledge of Measurement
Topic: C Applications in Measurement
Indicator: 1. Estimate and apply measurement formulas

Grade 6:
Objective d- Determine missing dimension of a quadrilateral given the perimeter length
Objective e - Determine the missing dimension of rectangles

Lesson Plans

GRADE 6 AREA AND PERIMETER LESSON PLAN
 


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Mine Shaft

In this group of puzzles, the player's job is to test out security robots ("bots" for short) ... shaped figures on springs whose job it is to progress down a path and explode the wall that lies at the end of all the paths.

Each "bot" is the shape of a polygon, and its shape determines the way it will travel down a particular path. The number of sides of the polygonal robot indicates how many tiles the "bot" will move with each bounce. A triangle, for instance, indicates that the "bot" would bounce on every third floor tile. Players must place each polygonal robot on the 0 area of correct path (to the left side of the path). When the players push the button below each "bot," it bounces along to the right. Players also have to make sure their "bots" avoid obstacles, such as dynamite, bombs, electrified tiles, or some combination of all three. An obstacle will destroy the "bot." If one "bot" successfully completes each path, the wall on the right side is broken and the player earns a reward.

In Level 2 of the puzzle, there is an additional hazard: a warp. If a "bot" moves over a warp that is the same color as it is, the "bot" will descend or ascend to another path, so players have to take that into account if they want to reach the end of the path. (When a robot passes beneath a same-colored tile, it is transported up to the catwalk above. When a robot passes over a same-colored tile, it is transported down to the catwalk below.)

Level 3 adds an additional obstacle: holes in the path with a scissor lift below it. If a robot lands on a hole, it will fall onto the path below, where the scissor lift will "dump" the robot forward onto the next tile to the right of the scissor lift. The robot will then begin bouncing again at its normal interval. Therefore, landing on a hole effectively places the robot one catwalk down and offsets the numbers that the robot will land on by +1.

  Math Discussion Terms
Multiple, polygon, triangle, square, pentagon, hexagon, septagon, octagon, rule, table of values, graph, linear equation, rate of change, slope, y-intercept, segment, parallel

Maryland Voluntary State Curriculum Alignment

Standard 1.0 Knowledge of Algebra, Patterns, and Functions
Topic A Knowledge of Number and Place Value
Indicator 1 Apply knowledge of rational numbers and place value

Grade 6:
Objective b - Interpret and write a rule for a one-operation function table

Algebra/Data Analysis Goal 1: The student will demonstrate the ability to investigate, interpret, and communicate solutions to mathematical and real-world problems using patterns, functions and algebra.
Expectation 2: The student will model and interpret real-world situations using the language of mathematics and appropriate technology.
Indicator 1: The student will determine the equation for a line, solve linear equations, and/or describe the solutions using numbers, symbols, and/or graphs.

Grade 8:

Indicator 1 - The student will determine the equation for a line, solve linear equations, and/or describe the solutions using numbers, symbols and/or graphs

Lesson Plans

GRADE 6 MULTIPLES LESSON PLAN

GRADE 8 SLOPE LESSON PLAN
 


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Warehouse

Lately, the Tasti-Pet factory has been overrun with Mannegishi, pests of the highest order that can squeeze through even the smallest cracks in the wall and eat up the machinery, reducing it to an unworkable pile of wires and hunks of metal.

In this group of puzzles, players are challenged to use their knowledge of positive and negative numbers and vectors to work electrical devices called resonators in order to create electrical fields that will levitate Mannegishi into cages. Each resonator will transport Mannegishi a certain distance in a straight line, but resonators will only work in pairs.

They may be placed pointing in the same direction, and their power is the sum of the power of both resonators. For example, a resonator with a value of 3, paired with one with a resonator with a value of 2 will combine to move a Mannegishi 5 positions.

If resonators are paired in opposing directions, they work against one another, and the distance the Mannegishi moves will be the difference between the two amplitudes. If a resonator with the amplitude of 3 is pointing right, and one with the value of 2 is pointing left, they will move the Mannegishi one space to the right.

There are predetermined locations for where the resonators can be placed and a fixed set of resonators. The challenge is for players to create the right combination of resonator pairs to move the gremling along the path and into the cage.

In level 1, players must learn how the mechanisms work and how to manipulate the resonators. In level 2, players must first deduce the amplitude of the resonators before solving, and at level 3, a larger number of resonator values make the task more challenging.

  Math Discussion Terms
Difference, integer, negative, number line, positive, sum

Maryland Voluntary State Curriculum Alignment

Standard 6 Knowledge of Number Relationships and Computation/Arithmetic
Topic C Number Computation
Indicator 1 Analyze number relations and compute

Grade 7:
Objective a - Add, subtract, multiply, and divide integers

Lesson Plans

GRADE 7 ADDING INTEGERS LESSON PLAN

 
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