| 36 CLAIMS 1. The invention relates to an algorithm for an educational strategy game that removes learning barriers, fosters permanent learning by creating a positive learning climate, fun and competition, and enhances algorithmic thinking skills and intelligence, characterized in that it comprises: - The global climate crisis story (110) as a funny and competitive game theme, - Different puzzle shapes (131) such as square and rectangle that give a basic understanding of the subject, - Tip badges (120, 140, 160, 274) that provide the user and student with an insight in the subject, - Menu with the Start/Settings/Badges/Story/Tutorial options, - The screen with game levels and question numbers, where all questions except the intended one are locked with the gas mask icon, - The game board that provides solutions by dragging and dropping puzzle pieces and maintains the continuity of the scenario by presenting to the user carbon emission values and earned points, - A processor (260, 270) executing the equation Earned Points = ((120- t)/10)*Level Score if t<120, or Earned Points = Level Score if t>120 to calculate Earned Points, where t is the user’s process time. 2. A puzzle game according to Claim 1 or Claim 2, characterized in that, the intended mathematical concept is simulated as puzzle pieces. 3. A puzzle game according to Claim 2, wherein the concept is reduced into 2 simple rules where the equal edge lengths of pieces simulating the pieces of a puzzle are matched, resulting in a regular polygon, such as a rectangle. 37 A puzzle game according to any of the preceding claims, wherein it can be played interactively with friends and/or opponents on smart mobile devices, tablets and computers. A puzzle game according to any of the preceding claims, characterized in that it can be employed only as algebraic modeling tools without operation, if algebraic expressions (identities) being quadratic with 1 unknown, quadratic with 2 unknowns, cubic with 1 unknown and cubic with 2 unknowns (identities) are factorized and/or if the given two-term expressions are presented as products. A puzzle game according to any of the preceding claims, characterized in that the intended mathematical concept is illustrated by visual modeling without the use of its terms. A puzzle game according to any of the preceding claims, wherein the concept is reduced into two simple rules driven by the principles of a puzzle. A puzzle game according to any of the preceding claims, characterized in that it employs algebraic modeling as an enjoyable strategy function. |
TECHNICAL FIELD
The invention relates to an educational strategy game in the form of an algebraic magnet puzzle capable of removing, only via a specific narrative game, barriers in learning algebraic expressions and identities that students find most difficult, and fostering permanent learning by creating a positive learning climate, fun and competition.
PRIOR ART
Mathematics typically represents a lesson which many students and even adults have bias and fear against, leading to learning difficulties. Today, even the widespread use of dramatization activities fails to alter the serious and feared facade of mathematics. Although colorful designs foster development at preschool and primary school grades, supportive processes cannot sufficiently be researched or adapted for middle school and higher grades. Despite originally intended to render the problem-solving skills permanent, algebraic expressions, identities and factoring covered by the 8 th -grade mathematics curriculum represents a tough concept that many students find difficult and fail in at tests.
A review of digital and mobile apps related to algebraic expressions has revealed that they are mostly contest-like apps designed merely to test knowledge and speed along with conventional questions aimed at solving the equation and finding out the unknown. These apps would help the student to reinforce the previously gained understanding of the concept, however they have no aim of helping the already biased and aloof student love and learn mathematics.
Modeling algebraic expressions has been involved in the curriculum since 2006. However, textbooks do not offer more than illustrations. Such illustrations aimed at providing a concrete form of the concept fall short of this goal.
In some of the limited educational platforms, there are apps that achieve this function. However, what these apps offer is merely a digitized version of the conventional method of algebraic modeling as discussed in traditional textbooks and time-saving ready-made drawings, but they fail to render the learning process permanent and enjoyable.
Involved in an international mathematics exhibition is an app that produces the mathematical modeling of 3-D structures created on the screen and lists the higher underlying mathematical formulas when the structure has been set up. The app provides an awareness and insight in the concept, but does not provide a background for learning how those formulas were derived or could be solved.
DISCLOSURE
The development of mathematical thinking traditions of students should be supported with algebraic expressions and the ability to carry out operations therewith through correct operational experiences.
The invention is an educational supportive mathematical process capable of removing, only via a specific narrative game, barriers in learning algebraic expressions and identities that students find most difficult, and fostering permanent learning by creating a positive learning climate, fun and competition.
With its narrative theme about the global climate crisis and thanks to its strategy under which each problem solved serves as the solution of the encrypted codes in the climate station and where the points earned help to draw attention to global climate disasters faced by the human, promoting in turn the reduction of carbon emissions, the present invention also turns the app into a strategic mission.
The invention has been designed as an educational strategy game with its theme about the global climate crisis, which employs algebraic modeling as an enjoyable strategy function and reduces the whole concept into 2 simple rules driven by the principles of a puzzle.
The invention has been designed originally as a classroom tool and then transformed, upon positive feedback, into a box game before it was eventually deployed on the mobile platform.
Brief Description of Drawings
Embodiments of the present invention briefly summarized above and discussed in more detail below can be understood by reference to the accompanying drawings. In order to facilitate understanding, identical reference numerals have been used where possible to identify identical elements in the figures.
Figure- 1: Shows the initial part of the main algorithm.
Figure-2: shows the rest of Figure-1.
Figure-3: shows the rest of Figure-2.
Figure-4: shows the rest of Figure-3.
Figure-5: shows the algorithm Al querying whether it is a 3 -term linear identity with 1 unknown.
Figure-6: shows the algorithm A2 querying whether it is a 3-term quadratic identity with 2 unknowns.
Figure-7: shows the algorithm A3 querying whether it is the multiplication of two 2-term brackets with 1 unknown.
Figure-8: shows the algorithm A4 querying whether it is the multiplication of two 2-term brackets with 2 unknowns.
Figure-9: shows the algorithm A5 querying whether it is the multiplication of three 2-term brackets with 1 unknown.
Figure-10: shows the algorithm A6 querying whether it is the multiplication of two 2-term brackets with 2 unknowns.
Figure-11: shows the algorithm A7 querying whether it is a 4-term cubic identity with 1 unknown.
Figure-12: shows the algorithm A8 querying whether it is a 4-term cubic identity with 2 unknowns.
List of References
Main Algorithm
100. Start
110. Read the story of the game
111. Climate change is no longer a possibility, but the pure reality. The world is in the midst of an ecological crisis. There is no time left to waste. The 6th Great Mass extinction has already begun. The only way to save the world is to limit global warming to 1.5 degrees and switch to zero carbon emissions. A climate station project was launched through the efforts of scientists and several visionary investors. The atmospheric codes in the climate station were encrypted with an algebraic puzzle.
120. Earn 1 tip badge
130. Get familiar with the puzzle pieces
131. 1st task: Get familiar with the puzzle pieces to solve the passwords.
The name of the biggest puzzle is Xsquared (X 2 ), because the area of a square with an edge of X is called Xsquared. X.X= X 2
The 2nd puzzle is a rectangle and its name is X, because its area is equal to 1 ,X=X
The name of the smallest puzzle is 1 , because the area of a square with an edge of 1 is 1.1=1 2 =1
140. Earn 1 tip badge
150. Learn how to solve the algebraic puzzle at the climate station
151. Each number preceding an expression denotes the number of pieces you will use.
2nd task: Set up the puzzle and remember the 2 simple rules
1. Your pattern should be an exact rectangle or square
2. X should be juxtaposed with the edge of X, and 1 with the edge of 1.
If pieces are properly interlocked, the password box will open. Check the edges of puzzles and fill in the brackets.
160. Earn 1 tip badge
170. The menu screen with the Game Start/Settings/Badges/Story/Tutorial options is displayed
180. Run the Start button
200. Start 201. The screen with game levels and question numbers, where all questions except the intended one are locked with the gas mask icon is displayed
210. Open the next question
220. The game board and the algebraic code to be solved are displayed
221. The outer frame of the solution pops up for 10 seconds
230. Use the tip?
240. Is the code a 3 -term linear identity with 1 unknown?
241. Is the code a 3 -term quadratic identity with 1 unknown?
242. Is the code a multiplication of two 2-term brackets with 1 unknown?
243. Is the code a multiplication of two 2-term brackets with 2 unknowns?
244. Is the code a multiplication of three 2-term brackets with 1 unknown?
245. Is the code a multiplication of three 2-term brackets with 2 unknowns?
246. Is the code a 4-term cubic identity with 1 unknown?
247. Is the code a 4-term cubic identity with 2 unknowns?
250. Your process time=t
260. t<120
261. Your Earned Points=Level Score
270. Your Earned Points=((120-t)/10)*Level Score
271. The climate card shows the Earned Points, Time and Climate tasks.
272. The emission value on the game board is reduced by each point you have earned.
273. The last question of this level? 274. The level-end tip badge is displayed.
275. The last question of the game?
276. Proceed with the next level.
280. Display the last screen and points.
281. Select your climate house and avatar.
282. In the house, perform actions to the extent of the decrease you have achieved in the emission value.
283. Do an in-app purchase.
284. Do you have any non-used badges?
285. Would you like to purchase badges?
286. Request for a new random algebraic code.
287. Use your badges for new actions to decrease emission.
288. Contact with your neighbors, use your points, plan shared actions. Set up a clan.
289. The clan score applies to all members.
290. Is carbon emission reduced to zero?
291. You earned a 5X climate badge. You are now more powerful. Keep going.
292. Is carbon emission below 0?
293. You and your clan managed to reduce carbon emission below zero. Global warming has been stopped.
294. Keep improving the climate.
295. Continue the game with your avatar, you are now at a higher level where you will fight the climate enemies. 296. End
Algorithm Al querying whether it is a 3-term linear identity with 1 unknown
240. Is the code Al a 3-term linear identity with 1 unknown?
300. Drag and drop to the board biggest square puzzle pieces in a quantity equal to the coefficient of X squared.
301. Drag and drop to the board rectangular puzzle pieces in a quantity equal to the coefficient of X.
302. Drag and drop to the board smallest square puzzle pieces in a quantity equal to the constant.
303. Drag the puzzle pieces and interlock them to each other to create a puzzle. (Model the algebraic expression with algebra diamonds)
304. Does X match X and 1 match 1 ?
305. Is the resulting shape a regular rectangle?
306. Are pieces properly interlocked?
307. Go to the open password box and focus on the edge lengths of puzzles.
308. Count the number of Xs and 1 s along short and long edges of the resulting pattern and write the total count in brackets.
Algorithm A2 querying whether it is a 3-term quadratic identity with 2 unknowns
241. Is A2 a 3-term quadratic identity with 2 unknowns?
400. Drag and drop to the board biggest square puzzle pieces in a quantity equal to the coefficient of X squared.
401. Drag and drop to the board rectangular puzzle pieces in a quantity equal to the coefficient of XY.
402. Drag and drop to the board smallest square puzzle pieces in a quantity equal to the coefficient of Y squared.
403. Drag the puzzle pieces and interlock them to each other to create a puzzle. (Model the algebraic expression with algebra diamonds)
404. Does X match X and Y match Y?
405. Is the resulting shape a regular rectangle?
406. Are pieces properly interlocked?
407. Go to the open password box and focus on the edge lengths of puzzles.
408. Count the number of Xs and 1 s along short and long edges of the resulting pattern and write the total count in brackets.
Algorithm A3 querying whether it is the multiplication of two 2-term brackets with 1 unknown
242. Is it a multiplication of two 2-term brackets with 1 unknown?
500. Focus on the edge lengths of puzzles.
501. Use the biggest square puzzle for the length X.
502. Use rectangle puzzles for the constant in a quantity equal to its value.
503. Drag the puzzle pieces and interlock them to each other to create a puzzle. (Model the algebraic expression with algebra diamonds)
504. Do you have a L-shaped polygon now? 505. Complete the L polygon to a regular rectangle to finish the puzzle.
506. Does X match X and 1 match 1 ?
507. Are pieces properly interlocked?
508. Go to the open password box and focus on the surface area of each puzzle.
509. Write down the total count of X squared, X and 1 used in the resulting pattern.
Algorithm A4 querying whether it is the multiplication of two 2-term brackets with 2 unknowns
243. Is it a multiplication of two 2-term brackets with 2 unknowns?
600. Focus on the edge lengths of puzzles.
601. Use the biggest square puzzle for the length X.
602. Use the X* Y rectangular puzzle for Y.
603. Drag the puzzle pieces and interlock them to each other to create a puzzle. (Model the algebraic expression with algebra diamonds)
604. Do you have a L-shaped polygon now?
605. Complete the L object to a regular rectangle to finish the puzzle.
606. Does X match X and Y match Y?
607. Are pieces properly interlocked?
608. Go to the open password box and focus on the surface area of each puzzle.
609. Write down the total count of X squared, XY and Y squared used in the resulting pattern. Algorithm A5 querying whether it is the multiplication of three 2-term brackets with 1 unknown
244. Is it a multiplication of two 3 -term brackets with 1 unknown?
700. Watch the presentation slide for 3D puzzles, focusing on the length of puzzle edges.
701. Use the biggest cubic puzzle for the length X.
702. For the constant, use rectangular prism puzzles with edge size of 1 in a quantity equal to the constant’s value.
703. Drag the puzzle pieces and interlock them to each other to create a puzzle (model the algebraic expression with algebra diamonds).
704. Do you have a L-shaped object now?
705. Complete the L object to a regular cube to finish the puzzle.
706. Does X match X and 1 match 1 ?
707. Are pieces properly interlocked?
708. Go to the open password box and focus on the volume of each puzzle.
709. Write down the total count of X cubed, X squared, X and 1 volume units used in the resulting pattern.
Algorithm A6 querying whether it is the multiplication of two 2-term brackets with 2 unknowns
245. Is it a multiplication of two 2-term brackets with 2 unknowns?
800. Focus on the edge lengths of puzzles.
801. Use the biggest square puzzle for the length X. 802. Use the X* Y rectangular puzzle for Y.
803. Drag the puzzle pieces and interlock them to each other to create a puzzle. (Model the algebraic expression with algebra diamonds)
804. Do you have a L-shaped object now?
805. Complete the L object to a regular cube to finish the puzzle.
806. Does X match X and Y match Y?
807. Are pieces properly interlocked?
808. Go to the open password box and focus on the surface area of each puzzle.
809. Write down the total count of X squared, XY and Y squared used in the resulting pattern.
Algorithm A7 querying whether it is a 4-term cubic identity with 1 unknown
246. Is it a 4-term cubic identity with 1 unknown?
900. Watch the presentation slide for 3D puzzles, focusing on their volume.
901. Use biggest cubic puzzles in a quantity equal to the coefficient of X cubed.
902. Use square right prisms with a volume of X*X*1 in a quantity equal to the coefficient of X squared.
903. Use square right prisms with a volume of X* 1*1 in a quantity equal to the coefficient of X.
904. Use unit cubes with a volume of 1*1*1 (smallest cubic puzzle) in a quantity equal to the value of the constant.
905. Drag the puzzle pieces so that same surfaces are interlocked to each other to create a puzzle. (Model the algebraic expression with algebra diamonds) 906. Is the resulting object a regular cube?
907. Does X match X and 1 match 1 ?
908. Are pieces properly interlocked?
909. Go to the open password box and focus on the edge lengths of the resulting object.
910. Write down in brackets the total counts of widths, lengths and heights in the resulting pattern.
Algorithm A8 querying whether it is a 4-term cubic identity with 2 unknowns
247. Is it a 4-term cubic identity with 2 unknowns?
1000. Watch the presentation slide for 3D puzzles, focusing on their volume.
1001. Use biggest cubic puzzles in a quantity equal to the coefficient of X cubed.
1002. Use square right prisms with a volume of X*X*Y in a quantity equal to the coefficient of X to the power of 2* Y.
1003. Use square right prisms with a volume of X*Y*Y in a quantity equal to the coefficient of X*Y squared.
1004. Use the smallest cube with a volume of Y*Y*Y in a quantity equal to the coefficient of Y cubed.
1005. Drag the puzzle pieces so that same surfaces are interlocked to each other to create a puzzle. (Model the algebraic expression with algebra diamonds)
1006. Is the resulting object a regular cube?
1007. Does X match X and Y match Y?
1008. Are pieces properly interlocked? 1009. Go to the open password box and focus on the edge lengths of the resulting object.
1010. Write down in brackets the total counts of widths, lengths and heights in the resulting pattern.
DETAILED DESCRIPTION OF THE INVENTION
The game starts with a story, narrating the climate station project built to stop global climate disasters and global warming. The atmospheric codes in the station are encrypted with an algebraic puzzle. The operating principles of the station are actually the theme, but they are presented as the rule of the game rather than a mathematical concept. To save the world from global climate disasters, passwords should be solved, hence reducing carbon emissions. Not developing a learning barrier, the user figures out algebraic modeling by himself/herself only through applying, without questioning, the rules to achieve the goal of the strategic process. After a while, the user realizes that 3 -term quadratic identities represent the surface area and their factorized forms represent a surface area formula, and principally discovers the geometric meaning of algebraic expressions within the safe environment of the game.
By employing the game as an algebraic modeling tool without operation, the result of the operation can be found if quadratic algebraic expressions (identities) being quadratic with 1 unknown, quadratic with 2 unknowns, cubic with 1 unknown and cubic with 2 unknowns (identities) are factorized and/or if the given two-term expressions are presented as products. It is clear that titles will be intimidating for many students, however these terms are not used in the game.
The algebraic code appears and algebra diamonds are introduced as puzzle pieces. Where X, 1 and Y identify the edge, the edge X is matched by the length of X, the edge 1 by the length of 1 and the edge Y by the length of Y, hence the resulting shape will be a perfect rectangle. No further information is presented in the strategical narrative game.
There are 2 key codes: a) a 3 -term quadratic identity with 1 or 2 unknowns (perfect square or non -perfect square).
Puzzles moved to the game board by dragging and dropping form a regular rectangle, ensuring that the user peripherally carries out an algebraic modeling indeed. At the next stage, the user checks the edge lengths of the pattern and fills in the brackets opened in the password box. Indeed, the initial identity represents the surface area, and when the surface area formula is written, it means the user has done the factorizing. b) in case it appears in the form of a product of 2 -term bracketed expressions with 1 or 2 unknowns, the user is informed, without making any reference to the distributive property of multiplication, that brackets represent the lengths of edge , hence the user first forms the edges and then fills in the gaps, completing the puzzle to a regular rectangle. This time, the user counts the number of puzzle pieces and writes the total count in the password box.
Once the pattern is setup up and correct password is entered in the password box, earned score is calculated based on the user’s process time.
According to the climate crisis story of the game, average daily carbon emission of each individual on earth is 13,500 gr. This value is displayed on the game board. After moving to the next question, average emission is reduced by the previous score. As the process progresses, it is essential that the emissions zero or even drop below zero so that global warming can be stopped. In the case of cubic identities with 1 or 2 unknowns, 3-D cubes and prisms are combined on the same principle.
The main algorithm starts with step (100). In step (110), the user reads the story of the game and in step (111), the following text is displayed to the user: “Climate change is no longer a possibility, but the pure reality. The world is in the midst of an ecological crisis. There is no time left to waste. The 6th Great Mass extinction has already begun. The only way to save the world is to limit global warming to 1.5 degrees and switch to zero carbon emissions. A climate station project was launched through the efforts of scientists and several visionary investors. The atmospheric codes in the climate station were encrypted with an algebraic puzzle.” In step (120), the user earns 1 tip badge, then in step (130), the user gets familiar with the pieces of the puzzle and in step (131), the user is informed of the 1 st task and puzzles as follows: “1 st task: Get familiar with the puzzle pieces to solve the passwords. The name of the biggest puzzle is Xsquared (X 2 ), because the area of a square with an edge of X is called Xsquared. X.X= X 2 and the 2 nd puzzle is a rectangle. It is named as X because its surface area is 1 ,X=X”. With step (140), the user earns 1 tip badge, next in step (150), the user figures out how to draw an algebraic puzzle at the climate station, and then step (151) shows that the number preceding each expression denotes the number of pieces to be used and describes the 2 nd task as follows: “Set up the puzzle and remember the 2 simple rules”. 1. Your pattern should be an exact rectangle or square. 2. X should be juxtaposed with the edge of X, and 1 with the edge of 1. If pieces are properly interlocked, the password box will open and the user is instructed to check the edges of puzzles and fill in the brackets. In step (160), the user earns 1 tip badge, and then in step (170), the menu screen with the Game Start/Settings/Badges/Story /Tutorial options is displayed. With step (180), the Start button is run. The process starts with the step (200) and in step (201), the screen with game levels and question numbers, where all questions except the intended one are locked with the gas mask icon, is displayed. Then, in step (210), the user unlocks the next question and in step (220), the game board and the algebraic code to be solved are displayed. Then, in step (221), the outer frame of the solution pops up for 10 seconds. Step (230) asks the user whether to use the tip. If the user replies yes, the process returns to step (221) and proceeds with the steps starting with step (220).
If the user replies no, the user is asked, in step (240), whether the code is a 3 -term linear identity with 1 unknown. If the user replies yes to step (240), then Algorithm Al querying whether it is a 3 -term linear identity with 1 unknown runs, followed by step (250) showing the user’s process time=t. In step (260), the process checks if time denoted as t<l 20. If t<l 20, step (270) calculates the points the user has earned with the equation Your Earned Points=((120-t)/10)*Level Score. In step (271), the card shows the Earned Points, Time and Climate tasks to the user, and then in step (272), the emission value on the game board is reduced by each point user has earned. In step (273), the user is asked if that is the last question of the level, and if the user replies no, the process returns to step (220) to repeat the subsequent steps. If user replies yes, step (274) displays the level-end tip badge, and then step (275) asks the user if that is the last question of the game. If user replies no, the process proceeds with the next step starting with step (276) and then returns to step (200) to repeat the subsequent steps. If user replies yes to step (275), the process proceeds with step (280) to display the last screen and score to the user. In step (281), the user is instructed to select a climate house and avatar, and then in step (282), the user performs in the house actions to the extent of the decrease that the user has achieved in the emission value. Then, in step (284), the user is asked if (s)he has any nonused badges, and if the user replies no, the process proceeds with step (285) to ask the user whether (s)he wants to purchase badges. If the user replies no, a new random algebraic code is requested in step (286), and then the process returns to step (240) to proceed accordingly. If user replies yes to step (284), the process proceeds with step (287) where the user utilizes his/her badges for new actions to decrease emission. In step (288), the user is instructed to contact with his/her neighbors, redeem the points, plan shared actions and set up a clan. Then, in step (289), the clan score applies to all members. Then, in step (290), the user is asked whether the carbon emission was reduced to zero. If user replies no, the process returns to step (285). If user replies yes, the process proceeds with step (291) to report “You earned a 5X climate badge. You are now more powerful. Keep going.”. Then, step (292) asks the user whether the carbon emission was reduced below zero. If user replies no, the process returns to step (285). If user replies yes, the process proceeds with step (293) to report “You and your clan managed to reduce carbon emission below zero. Global warming has been stopped.” In step (294), the user is instructed “keep improving the climate”. Then, step (295) reports “Continue the game with your avatar, you are now at a higher level where you will fight the climate enemies”, and finally the algorithm ends with step (296).
If the user has replied no to step (240), the process proceeds with step (241) to ask the user whether the code is a 3 -term quadratic identity with 1 unknown. If the user replies yes to step (241), the Algorithm A2 querying whether it is a 3 -term quadratic identity with 3 unknowns is executed. Then, step (250) shows the process time = t, And in step (260), the process checks if time denoted as t<120. If t<120, step (270) calculates the points the user has earned with the equation Your Earned Points=((120-t)/10)*Level Score. In step (271), the card shows the Earned Points, Time and Climate tasks to the user, and then in step (272), the emission value on the game board is reduced by each point user has earned. In step (273), the user is asked if that is the last question of the level, and if the user replies no, the process returns to step (220) to repeat the subsequent steps. If user replies yes, step (274) displays the level-end tip badge, and then step (275) asks the user if that is the last question of the game. If user replies no, the process proceeds with the next step starting with step (276) and then returns to step (200) to repeat the subsequent steps. If user replies yes to step (275), the process proceeds to display the last screen and score to the user. In step (281), the user is instructed to select a climate house and avatar, and then in step (282), the user performs in the house actions to the extent of the decrease that the user has achieved in the emission value. Then, in step (284), the user is asked if (s)he has any non-used badges, and if the user replies no, the process proceeds with step (285) to ask the user whether (s)he wants to purchase badges. If the user replies no, a new random algebraic code is requested in step (286), and then the process returns to step (240) to proceed accordingly. If user replies yes to step (284), the process proceeds with step (287) where the user utilizes his/her badges for new actions to decrease emission. In step (288), the user is instructed to contact with his/her neighbors, redeem the points, plan shared actions and set up a clan. Then, in step (289), the clan score applies to all members. Then, in step (290), the user is asked whether the carbon emission was reduced to zero. If user replies no, the process returns to step (285). If user replies yes, the process proceeds with step (291) to report “You earned a 5X climate badge. You are now more powerful. Keep going.”. Then, step (292) asks the user whether the carbon emission was reduced below 0. If user replies no, the process returns to step (285). If user replies yes, the process proceeds with step (293) to report “You and your clan managed to reduce carbon emission below zero. Global warming has been stopped.” In step (294), the user is instructed “keep improving the climate”. Then, step (295) reports “Continue the game with your avatar, you are now at a higher level where you will fight the climate enemies”, and finally the algorithm ends with step (296).
If the user has replied no to step (241), step (242) asks the user whether the code is a multiplication of two 2-term brackets with 1 unknown, and If the user replies yes to step (242), the Algorithm A3 querying whether it is the multiplication of two 2- term parentheses with 2 unknowns is executed. Then, step (250) shows the user’s process time=t and in step (260), the process checks if time denoted as t<120. If t<120, step (270) calculates the points the user has earned with the equation Your Earned Points=((120-t)/10)*Level Score. In step (271), the card shows the Earned Points, Time and Climate tasks to the user, and then in step (272), the emission value on the game board is reduced by each point user has earned. In step (273), the user is asked if that is the last question of the level, and if the user replies no, the process returns to step (220) to repeat the subsequent steps. If user replies yes, step (274) displays the level-end tip badge, and then step (275) asks the user if that is the last question of the game. If user replies no, the process proceeds with the next step starting with step (276) and then returns to step (200) to repeat the subsequent steps. If user replies yes to step (275), the process proceeds with step (280) to display the last screen and score to the user. In step (281), the user is instructed to select a climate house and avatar, and then in step (282), the user performs in the house actions to the extent of the decrease that the user has achieved in the emission value. Then, in step (284), the user is asked if (s)he has any non-used badges, and if the user replies no, the process proceeds with step (285) to ask the user whether (s)he wants to purchase badges. If the user replies no, a new random algebraic code is requested in step (286), and then the process returns to step (240) to proceed accordingly. If user replies yes to step (284), the process proceeds with step (287) where the user utilizes his/her badges for new actions to decrease emission. In step (288), the user is instructed to contact with his/her neighbors, redeem the points, plan shared actions and set up a clan. Then, in step (289), the clan score applies to all members. Then, in step (290), the user is asked whether the carbon emission was reduced to zero. If user replies no, the process returns to step (285). If user replies yes, the process proceeds with step (291) to report “You earned a 5X climate badge. You are now more powerful. Keep going.”. Then, step (292) asks the user whether the carbon emission was reduced below 0. If user replies no, the process returns to step (285). If user replies yes, the process proceeds with step (293) to report “You and your clan managed to reduce carbon emission below zero. Global warming has been stopped.” In step (294), the user is instructed “keep improving the climate”. Then, step (295) reports “Continue the game with your avatar, you are now at a higher level where you will fight the climate enemies”, and finally the algorithm ends with step (296).
If the user has replied no to step (242), the process proceeds with step (243) to ask the user whether it is the multiplication of two 2 -term brackets with 2 unknowns, and if the user replies yes to step (243), the Algorithm A4 querying whether it is the multiplication of two 2-term parentheses with 2 unknowns is executed. Then, step (250) shows the user’s process time=t and in step (260), the process checks if time denoted as t<l 20. If t<l 20, step (270) calculates the points the user has earned with the equation Your Earned Points=((120-t)/10)*Level Score. In step (271), the card shows the Earned Points, Time and Climate tasks to the user, and then in step (272), the emission value on the game board is reduced by each point user has earned. In step (273), the user is asked if that is the last question of the level, and if the user replies no, the process returns to step (220) to repeat the subsequent steps. If user replies yes, step (274) displays the level-end tip badge, and then step (275) asks the user if that is the last question of the game. If user replies no, the process proceeds with the next step starting with step (276) and then returns to step (200) to repeat the subsequent steps. If user replies yes to step (275), the process proceeds with step (280) to display the last screen and score to the user. In step (281), the user is instructed to select a climate house and avatar, and then in step (282), the user performs in the house actions to the extent of the decrease that the user has achieved in the emission value. Then, in step (284), the user is asked if (s)he has any nonused badges, and if the user replies no, the process proceeds with step (285) to ask the user whether (s)he wants to purchase badges. If the user replies no, a new random algebraic code is requested in step (286), and then the process returns to step (240) to proceed accordingly. If user replies yes to step (284), the process proceeds with step (287) where the user utilizes his/her badges for new actions to decrease emission. In step (288), the user is instructed to contact with his/her neighbors, redeem the points, plan shared actions and set up a clan. Then, in step (289), the clan score applies to all members. Then, in step (290), the user is asked whether the carbon emission was reduced to zero. If user replies no, the process returns to step (285). If user replies yes, the process proceeds with step (291) to report “You earned a 5X climate badge. You are now more powerful. Keep going.”. Then, step (292) asks the user whether the carbon emission was reduced below 0. If user replies no, the process returns to step (285). If user replies yes, the process proceeds with step (293) to report “You and your clan managed to reduce carbon emission below zero. Global warming has been stopped.” In step (294), the user is instructed “keep improving the climate”. Then, step (295) reports “Continue the game with your avatar, you are now at a higher level where you will fight the climate enemies”, and finally the algorithm ends with step (296).
If the user has replied no to step (243), step (244) asks the user whether the code is a multiplication of three 2-term brackets with 1 unknown and if the user replies yes to step (244), the Algorithm A5 querying whether it is the multiplication of three 2- term parentheses with 1 unknown is executed. Then, step (250) shows the user’s process time=t and in step (260), the process checks if time denoted as t<l . If t<l 20, step (270) calculates the points the user has earned with the equation Your Earned Points=((120-t)/10)*Level Score. In step (271), the card shows the Earned Points, Time and Climate tasks to the user, and then in step (272), the emission value on the game board is reduced by each point user has earned. In step (273), the user is asked if that is the last question of the level, and if the user replies no, the process returns to step (220) to repeat the subsequent steps. If user replies yes, step (274) displays the level-end tip badge, and then step (275) asks the user if that is the last question of the game. If user replies no, the process proceeds with the next step starting with step (276) and then returns to step (200) to repeat the subsequent steps. If user replies yes to step (275), the process proceeds with step (280) to display the last screen and score to the user. In step (281), the user is instructed to select a climate house and avatar, and then in step (282), the user performs in the house actions to the extent of the decrease that the user has achieved in the emission value. Then, in step (284), the user is asked if (s)he has any non-used badges, and if the user replies no, the process proceeds with step (285) to ask the user whether (s)he wants to purchase badges. If the user replies no, a new random algebraic code is requested in step (286), and then the process returns to step (240) to proceed accordingly. If user replies yes to step (284), the process proceeds with step (287) where the user utilizes his/her badges for new actions to decrease emission. In step (288), the user is instructed to contact with his/her neighbors, redeem the points, plan shared actions and set up a clan. Then, in step (289), the clan score applies to all members. Then, in step (290), the user is asked whether the carbon emission was reduced to zero. If user replies no, the process returns to step (285). If user replies yes, the process proceeds with step (291) to report “You earned a 5X climate badge. You are now more powerful. Keep going.”. Then, step (292) asks the user whether the carbon emission was reduced below 0. If user replies no, the process returns to step (285). If user replies yes, the process proceeds with step (293) to report “You and your clan managed to reduce carbon emission below zero. Global warming has been stopped.” In step (294), the user is instructed “keep improving the climate”. Then, step (295) reports “Continue the game with your avatar, you are now at a higher level where you will fight the climate enemies”, and finally the algorithm ends with step (296).
If the user has replied no to step (244), step (245) asks the user whether the code is a multiplication of two 2-term brackets with 2 unknowns, and if the user replies yes to step (245), the Algorithm A6 querying whether it is the multiplication of two 2- term parentheses with 2 unknowns is executed. Then, step (250) shows the user’s process time=t and in step (260), the process checks if time denoted as t<120. If t<120, step (270) calculates the points the user has earned with the equation Your Earned Points=((120-t)/10)*Level Score. In step (271), the card shows the Earned Points, Time and Climate tasks to the user, and then in step (272), the emission value on the game board is reduced by each point user has earned. In step (273), the user is asked if that is the last question of the level, and if the user replies no, the process returns to step (275) to repeat the subsequent steps. If user replies yes, step (274) displays the level-end tip badge, and then step (27) asks the user if that is the last question of the game. If user replies no, the process proceeds with the next step starting with step (276) and then returns to step (200) to repeat the subsequent steps. If user replies yes to step (275), the process proceeds with step (280) to display the last screen and score to the user. In step (281), the user is instructed to select a climate house and avatar, and then in step (282), the user performs in the house actions to the extent of the decrease that the user has achieved in the emission value. Then, in step (284), the user is asked if (s)he has any non-used badges, and if the user replies no, the process proceeds with step (285) to ask the user whether (s)he wants to purchase badges. If the user replies no, a new random algebraic code is requested in step (286), and then the process returns to step (240) to proceed accordingly. If user replies yes to step (284), the process proceeds with step (287) where the user utilizes his/her badges for new actions to decrease emission. In step (288), the user is instructed to contact with his/her neighbors, redeem the points, plan shared actions and set up a clan. Then, in step (289), the clan score applies to all members. Then, in step (290), the user is asked whether the carbon emission was reduced to zero. If user replies no, the process returns to step (285). If user replies yes, the process proceeds with step (291) to report “You earned a 5X climate badge. You are now more powerful. Keep going.”. Then, step (292) asks the user whether the carbon emission was reduced below 0. If user replies no, the process returns to step (285). If user replies yes, the process proceeds with step (293) to report “You and your clan managed to reduce carbon emission below zero. Global warming has been stopped.” In step (294), the user is instructed “keep improving the climate”. Then, step (295) reports “Continue the game with your avatar, you are now at a higher level where you will fight the climate enemies”, and finally the algorithm ends with step (296).
If the user replies no to step (245), the process proceeds with step (246) to ask the user whether the code is a 4-term cubic identity with 1 unknown, and if the user replies yes to step (246), the Algorithm A7 querying whether it is a 4-term cubic identity with 1 unknown is executed. Then, step (250) shows the user’s process time=t and in step (260), the process checks if time denoted as t<120. If t<120, step (270) calculates the points the user has earned with the equation Your Earned Points=((120-t)/10)*Level Score. In step (271), the card shows the Earned Points, Time and Climate tasks to the user, and then in step (272), the emission value on the game board is reduced by each point user has earned. In step (273), the user is asked if that is the last question of the level, and if the user replies no, the process returns to step (220) to repeat the subsequent steps. If user replies yes, step (274) displays the level-end tip badge, and then step (275) asks the user if that is the last question of the game. If user replies no, the process proceeds with the next step starting with step (276) and then returns to step (200) to repeat the subsequent steps. If user replies yes to step (275), the process proceeds with step (280) to display the last screen and score to the user. In step (281), the user is instructed to select a climate house and avatar, and then in step (282), the user performs in the house actions to the extent of the decrease that the user has achieved in the emission value. Then, in step (284), the user is asked if (s)he has any non-used badges, and if the user replies no, the process proceeds with step (285) to ask the user whether (s)he wants to purchase badges. If the user replies no, a new random algebraic code is requested in step (286), and then the process returns to step (240) to proceed accordingly. If user replies yes to step (284), the process proceeds with step (287) where the user utilizes his/her badges for new actions to decrease emission. In step (288), the user is instructed to contact with his/her neighbors, redeem the points, plan shared actions and set up a clan. Then, in step (289), the clan score applies to all members. Then, in step (290), the user is asked whether the carbon emission was reduced to zero. If user replies no, the process returns to step (285). If user replies yes, the process proceeds with step (291) to report “You earned a 5X climate badge. You are now more powerful. Keep going.”. Then, step (292) asks the user whether the carbon emission was reduced below 0. If user replies no, the process returns to step (285). If user replies yes, the process proceeds with step (293) to report “You and your clan managed to reduce carbon emission below zero. Global warming has been stopped.” In step (294), the user is instructed “keep improving the climate”. Then, step (295) reports “Continue the game with your avatar, you are now at a higher level where you will fight the climate enemies”, and finally the algorithm ends with step (296).
If the user replies no to step (246), the process proceeds with step (247) to ask the user whether the code is a 4-term cubic identity with 2 unknowns, and if the user replies yes to step (247), the Algorithm A8 querying whether it is a 4-term cubic identity with 3 unknowns is executed. Then, step (250) shows the user’s process time=t and in step (260), the process checks if time denoted as t<l 20. If t<120, step (270) calculates the points the user has earned with the equation Your Earned Points=((120-t)/10)*Level Score. In step (271), the card shows the Earned Points, Time and Climate tasks to the user, and then in step (272), the emission value on the game board is reduced by each point user has earned. In step (273), the user is asked if that is the last question of the level, and if the user replies no, the process returns to step (220) to repeat the subsequent steps. If user replies yes, step (274) displays the level-end tip badge, and then step (275) asks the user if that is the last question of the game. If user replies no, the process proceeds with the next step starting with step (276) and then returns to step (200) to repeat the subsequent steps. If user replies yes to step (275), the process proceeds with step (280) to display the last screen and score to the user. In step (281), the user is instructed to select a climate house and avatar, and then in step (282), the user performs in the house actions to the extent of the decrease that the user has achieved in the emission value. Then, in step (284), the user is asked if (s)he has any non-used badges, and if the user replies no, the process proceeds with step (285) to ask the user whether (s)he wants to purchase badges. If the user replies no, a new random algebraic code is requested in step (286), and then the process returns to step (240) to proceed accordingly. If user replies yes to step (284), the process proceeds with step (287) where the user utilizes his/her badges for new actions to decrease emission. In step (288), the user is instructed to contact with his/her neighbors, redeem the points, plan shared actions and set up a clan. Then, in step (289), the clan score applies to all members. Then, in step (290), the user is asked whether the carbon emission was reduced to zero. If user replies no, the process returns to step (285). If user replies yes, the process proceeds with step (291) to report “You earned a 5X climate badge. You are now more powerful. Keep going.”. Then, step (292) asks the user whether the carbon emission was reduced below 0. If user replies no, the process returns to step (285). If user replies yes, the process proceeds with step (293) to report “You and your clan managed to reduce carbon emission below zero. Global warming has been stopped.” In step (294), the user is instructed “keep improving the climate”. Then, step (295) reports “Continue the game with your avatar, you are now at a higher level where you will fight the climate enemies”, and finally the algorithm ends with step (296). Algorithm Al querying whether it is a 3-term linear identity with 1 unknown
When the user replies yes to step (240) in the main algorithm, the Algorithm Al querying whether it is a 3-term linear identity with 1 unknown is activated. In step
(300) of the algorithm Al, the user drags and drops to the board biggest square puzzles pieces in a quantity equal to the coefficient of X squared, and then in step
(301), the user drags and drops to the board rectangular puzzles pieces in a quantity equal to the coefficient of X. In step (302), the user drags and drops to the board smallest square puzzle pieces in a quantity equal to the constant, and in step (303), the user drags the puzzle pieces and interlock them to each other to create a puzzle (model the algebraic expression with algebra diamonds). Then, step (304) asks the user whether X matches X and 1 matches 1. When user replies no to step (304), the process returns to step (303). When user replies yes to step (304), the process proceeds with step (305) in which the user is asked whether the resulting shape is a regular rectangle. When user replies no to step (305), the process returns to step (303). When user replies yes to step (305), step (306) asks the user whether the pieces are properly interlocked, and if the user replies no, the process returns to step (303). When user replies yes to step (306), the process proceeds with step (307) in which the user is instructed to “go to the open password box and focus on the edge lengths of puzzles”, And then the process proceeds with step (308) in which the user is instructed to count the number of Xs and 1 s along short and long edges of the resulting pattern and write the total count in brackets. With this, algorithm Al ends.
Algorithm A2 querying whether it is a 3-term quadratic identity with 2 unknowns
When the user replies yes to step (241) in the main algorithm, the Algorithm A2 querying whether it is a 3 -term quadratic identity with 2 unknowns is activated. In step (400) of the algorithm A2, the user drags and drops to the board biggest square puzzles pieces in a quantity equal to the coefficient of X squared, and then in step (401), the user drags and drops to the board rectangular puzzles pieces in a quantity equal to the coefficient of X. In step (402), the user drags and drops to the board smallest square puzzle pieces in a quantity equal to the coefficient of Y squared, and in step (403), the user drags the puzzle pieces and interlock them to each other to create a puzzle (model the algebraic expression with algebra diamonds). Then, step (404) asks the user whether X matches X and Y matches Y. When user replies no to step (404), the process returns to step (403). When user replies yes to step (404), the process proceeds with step (405) in which the user is asked whether the resulting shape is a regular rectangle. When user replies no to step (405), the process returns to step (403). When user replies yes to step (405), step (406) asks the user whether the pieces are properly interlocked, and if the user replies no, the process returns to step (403). When user replies yes to step (406), the process proceeds with step (407) in which the user is instructed to “go to the open password box and focus on the edge lengths of puzzles”, And then the process proceeds with step (408) in which the user is instructed to count the number of Xs and 1 s along short and long edges of the resulting pattern and write the total count in brackets. With this, algorithm A2 ends.
Algorithm A3 querying whether it is the multiplication of two 2-term brackets with 1 unknown
When the user replies yes to step (242) in the main algorithm, the Algorithm A3 querying whether it is the multiplication of two 2-term brackets with 1 unknown is activated. In step (500) of the algorithm A3, the user is instructed to “focus on the edge lengths of puzzles”, then step (501) instructs the user to use the biggest square puzzle for the length X, and step (502) instructs the user to use rectangle puzzles for the constant in a quantity equal to its value. Step (503) instructs the user to “drag the puzzle pieces and interlock them to each other to create a puzzle” (model the algebraic expression with algebra diamonds), and then step (504) asks the user whether a L-shaped polygon was then formed. When user replies no to step (504), the process returns to step (242). When user replies yes to step (504), the process proceeds with step (505) to instruct the user to complete the L polygon to a regular rectangle to finish the puzzle. In step (506), the user is asked whether X matches X and 1 matches 1, and if the user replies no to step (506), the process returns to step (503). When user replies yes to step (506), the process proceeds with step (507). With this step, the user is asked if the pieces are properly interlocked. When user replies no to step (507), the process returns to step (503). When user replies yes to step (507), the process proceeds with step (508) to instruct the user to go to the open password box and focus on the surface area of each puzzle. Then, the process proceeds with step (509) in which the user is instructed to write down the total count of X squared, X and 1 used in the resulting pattern. With this, algorithm A3 ends.
Algorithm A4 querying whether it is the multiplication of two 2-term parentheses with 2 unknowns
When the user replies yes to step (243) in the main algorithm, the Algorithm A4 querying whether it is the multiplication of two 2-term brackets with 2 unknowns is activated. In step (600) of the algorithm A4, the user is instructed to “focus on the edge lengths of puzzles”, then step (601) instructs the user to use the biggest square puzzle for the length X, and step (602) instructs the user to use the X* Y rectangular puzzle for Y. Step (603) instructs the user to “drag the puzzle pieces and interlock them to each other to create a puzzle” (model the algebraic expression with algebra diamonds), and then step (604) asks the user whether a L-shaped polygon was then formed. When user replies no to step (504), the process returns to step (243). When user replies yes to step (604), the process proceeds with step (505) to instruct the user to complete the L object to a regular rectangle to finish the puzzle. In step (606), the user is asked whether X matches X and Y matches Y, and if the user replies no to step (606), the process returns to step (603). When user replies yes to step (606), the process proceeds with step (607). With this step, the user is asked if the pieces are properly interlocked. When user replies no to step (607), the process returns to step (603). When user replies yes to step (607), the process proceeds with step (608) to instruct the user to go to the open password box and focus on the surface area of each puzzle. Then, the process proceeds with step (609) in which the user is instructed to write down the total count of X squared, XY and Y squared used in the resulting pattern. With this, algorithm A4 ends.
Algorithm A5 querying whether it is the multiplication of three 2-term brackets with 1 unknown
When the user replies yes to step (244) in the main algorithm, the Algorithm A5 querying whether it is the multiplication of three 2-term brackets with 1 unknown is activated. In step (700) of the algorithm A5, the user is instructed to “watch the presentation slide for 3D puzzles, focusing on the length of puzzle edges”, then step
(701) instructs the user to use the biggest cubic puzzle for the length X, and step
(702) instructs the user to use rectangular prism puzzles with edge size of 1 for the constant in a quantity equal to the constant’s value. Step (703) instructs the user to “drag the puzzle pieces and interlock them to each other to create a puzzle” (model the algebraic expression with algebra diamonds), and then step (704) asks the user whether a L-shaped object was then formed. When user replies no to step (704), the process returns to step (244). When user replies yes to step (704), the process proceeds with step (705) to instruct the user to complete the L object to a regular cube to finish the puzzle. In step (706), the user is asked whether X matches X and 1 matches 1 , and if the user replies no to step (706), the process returns to step (703). When user replies yes to step (706), the process proceeds with step (707). With this step, the user is asked if the pieces are properly interlocked. When user replies no to step (707), the process returns to step (703). When user replies yes to step (707), the process proceeds with step (708) to instruct the user to go to the open password box and focus on the volume of each puzzle. Then, the process proceeds with step (709) in which the user is instructed to write down the total count of X cubed, X squared, X and 1 volume units used in the resulting pattern. With this, algorithm A5 ends.
Algorithm A6 querying whether it is the multiplication of two 2-term brackets with 2 unknowns
When the user replies yes to step (245) in the main algorithm, the Algorithm A6 querying whether it is the multiplication of two 2-term brackets with 2 unknowns is activated. In step (800) of the algorithm A6, the user is instructed to “focus on the edge lengths of puzzles”, then step (801) instructs the user to use the biggest square puzzle for the length X, and step (802) instructs the user to use the X* Y rectangular puzzle for Y. Step (803) instructs the user to “drag the puzzle pieces and interlock them to each other to create a puzzle” (model the algebraic expression with algebra diamonds), and then step (804) asks the user whether a L -shaped object was then formed. When user replies no to step (804), the process returns to step (245). When user replies yes to step (804), the process proceeds with step (805) to instruct the user to complete the L object to a regular cube to finish the puzzle. In step (806), the user is asked whether X matches X and Y matches Y, and if the user replies no to step (806), the process returns to step (803). When user replies yes to step (806), the process proceeds with step (807). With this step, the user is asked if the pieces are properly interlocked. When user replies no to step (807), the process returns to step (803). When user replies yes to step (707), the process proceeds with step (808) to instruct the user to go to the open password box and focus on the surface area of each puzzle. Then, the process proceeds with step (809) in which the user is instructed to write down the total count of X squared, XY and Y squared used in the resulting pattern. With this, algorithm A6 ends.
Algorithm A7 querying whether it is a 4-term cubic identity with 1 unknown
When the user replies yes to step (246) in the main algorithm, the Algorithm A7 querying whether it is a 4-term cubic identity with 1 unknown is activated. In step (900) of the algorithm A7, the user is instructed to “watch the presentation slide for 3D puzzles, focusing on their volume”. Then, step (901) instructs the user to use biggest cubic puzzles in a quantity equal to the coefficient of X cubed. Then, step (902) instructs the user to use square right prisms with a volume of X*X*1 in a quantity equal to the coefficient of X squared, and step (903) instructs the user to use square right prisms with a volume of X* 1 * 1 in a quantity equal to the coefficient of X. Then, step (904) instructs the user to use unit cubes with a volume of 1*1*1 (smallest cubic puzzle) in a quantity equal to the value of the constant. Step (905) instructs the user to “drag the puzzle pieces and interlock them to each other to create a puzzle” (model the algebraic expression with algebra diamonds), and then step (906) asks the user whether the resulting object is a regular cube. When user replies no to step (906), the process returns to step (246). When user replies yes to step (906), the process proceeds with step (907) to ask the user whether X matches X and 1 matches 1. When user replies no to step (907), the process returns to step (905). When user replies yes to step (907), the process proceeds with step (908) in which the user is asked if the pieces are properly interlocked. When user replies no to step (908), the process returns to step (905). When user replies yes to step (908), the process proceeds with step (909) to instruct the user to go to the open password box and focus on the edge lengths of the resulting object. Then, in step (910), the user is asked to write down in brackets the total counts of widths, lengths and heights in the resulting pattern, and algorithm A7 ends.
Algorithm A8 querying whether it is a 4-term cubic identity with 2 unknowns
When the user replies yes to step (247) in the main algorithm, the Algorithm A8 querying whether it is a 4-term cubic identity with 2 unknowns is activated. In step (1000) of the algorithm A8, the user is instructed to “watch the presentation slide for 3D puzzles, focusing on their volume”. Then, step (1001) instructs the user to use biggest cubic puzzles in a quantity equal to the coefficient of X cubed. Then, step (1002) instructs the user to use square right prisms with a volume of X*X* Y in a quantity equal to the coefficient of X to the power of 2* Y, and step (1003) instructs the user to use square right prisms with a volume of X*Y*Y in a quantity equal to the coefficient of X*Y squared. Then, step (1004) instructs the user to use the smallest cube with a volume of Y*Y*Y in a quantity equal to the coefficient of Y cubed. Then, step (1005) instructs the user to “drag the puzzle pieces and interlock them to each other to create a puzzle” (model the algebraic expression with algebra diamonds), and then step (1006) asks the user whether the resulting object is a regular cube. When user replies no to step (1006), the process returns to step (247). When user replies yes to step (1006), the process proceeds with step (1007) to ask the user whether X matches X and Y matches Y. When user replies no to step (1007), the process returns to step (1005). When user replies yes to step (1007), the process proceeds with step (1008) in which the user is asked if the pieces are properly interlocked. When user replies no to step (1008), the process returns to step (1005). When user replies yes to step (1008), the process proceeds with step (1009) to instruct the user to go to the open password box and focus on the edge lengths of the resulting object. Then, in step (1010), the user is asked to write down in brackets the total counts of widths, lengths and heights in the resulting pattern, and algorithm A8 ends.