Reflecting on the Analog Design Process

I have enjoyed this analog design process. What started as a seed idea has grown and morphed into something kids could use to learn and improve their math skills. What works best for me is time to marinate and iterate. 


After processing the feedback from peers and my professor, one issue kept me thinking...the drawing cards seemed random, complicated, and almost frustrating - why not give every player a complete set of numeral cards and a set of operations? Then, the idea of levels began to develop. This helped me think through how to tier the game for different learners. THEN...today, in fact...after looking closely at different instructions (most specifically Catan, Jr) and feedback from my professor, I decided it needs to have a narrative. Nothing that changes the purpose and goal but fills it out more, adding muscle to the skeleton. Instead of three levels with only easier to harder concepts - they will build something specific - magical, of course. Level I is restoring a small village, with each design target tied to a task for restoring. Level II will be restoring a palace. And Level III will be a city. I'm designing/building everything in Canva to have a digital copy. All will be exported and then printed for playing. I would not change much about my process... primarily because I typically work with one idea leading to another leading to another, and then when I see it in my head, I take a deep dive into the details. 


Game Title: Equation Architects

(Narrative I'm playing with) 

In a world where equations are the key to unlocking power, magical places have fallen into ruin, and only those who can master the Order of Operations can rebuild them. Your mission as an Equation Architect is to use your math skills to design influential blueprints to bring these magical places back to life. For each round, you may build a bridge, tower, or garden by solving mathematical challenges. Can you design and solve the equations to rebuild these magical places? Only the greatest Equation Architect can succeed!


Subject Area: Upper Elementary/Early Middle School Math focusing on the order of operations (PEMDAS) and mathematical operations.

  • Procedural Knowledge: Players apply the order of operations (procedure) to construct valid equations. Players will use the PEMDAS rule set to construct valid equations accurately through a process-based approach. 
  • Conceptual Knowledge: Players will develop an understanding of how operations interact (addition, subtraction, multiplication, division, exponents, parentheses) within the order of operations. They will also practice and develop problem-solving skills by analyzing and evaluating both their own problems and those of other players.


Learning Objectives: 

  • Higher-Order Objective 1: Students will use the order of operations, including exponents and parentheses, to create equations that match or come close to a target number. 
    • Goal: Students should be proficient at using more advanced math operations, such as exponents and parentheses while following the correct order of operations. 
    • Activities: During the game, students will receive number and operation cards to create an equation that matches a target number. They will need to use the correct order of operations and include parentheses and exponents if necessary. 
    • Success: Students are successful when they can consistently build correct, complex equations that are close to or match the target number. 
  • Higher-Order Objective 2: Learners will evaluate and analyze peer-generated equations to check for accuracy in applying the order of operations and offer helpful feedback as needed. 
    • Goal: Students will analyze the work of their peers to develop evaluative skills and a deep understanding of the order of operations. 
    • Activities: After each round, students will review a peer's equation, check for mistakes in applying PEMDAS, offer suggestions for improvement, or validate their solution. 
    • Success is evident when students can accurately identify errors or affirm correctness in their peer's equations and explain their reasoning clearly. 
  • Lower-Order Objective: Learners will identify and correctly use basic mathematical operations (+, -, x, ÷) within equations. 
    • Goal: The goal is for students to perform basic arithmetic operations within equations correctly. 
    • Activities: During the Inspection rounds of the game, students will perform basic arithmetic operations from a written equation. 
    • Success is shown when students can reliably apply basic operations to create simple, correct equations.


Summary and Overview: In Equation Architects, players play the role of the math "architects," using their skills to build and solve equations that follow the order of operations (PEMDAS) and match or get close to a Design Target. The game is designed to be both competitive and collaborative. Players compete against each other to score points. Players also have the opportunity to collaborate and give feedback on equations. Players use their numeral and operation cards for Construction rounds to create an equation that matches or comes close to a Design Target. After three Construction rounds, players enter an Inspection round, where they solve a pre-made equation. The game continues through alternating phases of Construction and Inspection, with the winner being the player with the highest score. One game is nine rounds. 


The game reinforces understanding of the order of operations, number manipulation, and calculation. Students construct/create accurate mathematical expressions using the order of operations. The goal is to collect points based on accuracy, speed, and complexity of building the equations. 


Primary Core Dynamic is puzzle solving/solution. Players must figure out how to arrange their building block cards (numerals and operation cards) to build an equation that equals (or comes close to) the design target. This requires applying both computational skills and the order of operations to compute accurately. 


Main Mechanics: 

  • Building Blocks: Each player starts with a set of Building Block cards. These cards include whole numbers (0-10), mathematical operations (+, -, x, ÷) for Level I, adding parentheses for Level II, and exponents for Level III. 
  • Design Target: Using the design target set of cards, a player begins the game by drawing a design target card. There are three decks of Design Targets, one deck for each level. The higher the level, the more choices of targets that would require more complex equations. 
  • Draft the Blueprint: Players use their Building Block cards to construct equations using the correct order of operations (PEMDAS—parentheses, exponents, multiplication, division, addition, subtraction) to solve (or get as close as possible) to the design target. How close to the design target varies at each level. 
  • Checking the Blueprint:  Once a player has completed their equation, other players check the equation or judge for accuracy (correct order of operations and calculation). If the equation is accurate, the player scores points based on how many cards they used (complexity of equation) and the accuracy of the solution. If their equation is incorrect, they lose points.
  • Blueprint Inspection: Three rounds in the game (total of nine) are solving a pre-made equation. 
  • Win: The player with the most points after a set number of rounds wins the game.


Materials: This card game has scorecards and documents to work out problems. I've included a visual I've created for my rule book. This shows examples of the various materials 




Core Loop: 

1. Players a Design Target card, then build equations with Building Blocks using PEMDAS to match or get as close to a Design Target.

2. Players submit their equations, and points are awarded based on accuracy and complexity. 

3. In alternating rounds, players solve pre-made equations. 


Explicit Rules:

  • Players must explicitly follow PEMDAS when building equations.
  • Clear rules about when to draw target cards, construct equations, and submit solutions give players a structured path for decision-making.
  • Explicit rules about how points are awarded. 


Implicit Rules:

  • Players decide how and when to use complex operations like exponents and parentheses for higher scores.
  • Players choose how they interact with other players, whether focusing solely on their equations or observing and potentially challenging others.


Peer responses

One piece of feedback from a peer concerned speed. This was extremely helpful to consider, and ultimately, I omitted speed as a requirement for the game. Another piece of feedback was from my professor. Adding the narrative elevated the game. 

  • Level I: Restoring a Village
  • Level II: Building a Castle 
  • Level III: Designing a City


All the feedback has been helpful. I'm excited to see the game evolve and become.