## DRAGONBOX ALGEBRA 5+ overview

*DragonBox Algebra 5+*cleverly and gradually reveals that the player is learning math concepts. The game starts as a drag-and-drop card game but gradually increases in complexity and reveals its core mechanics to be derived from algebraic equations. Since this process is gradual and takes place over 200 levels (one to four hours of play), the player is gracefully introduced to aspects of mathematics that could initially be intimidating or confusing. In the science domain, research has shown that taking this “content first” approach without jargon or symbols develops improved conceptual understanding. As a result, the game is effective in getting students to understand the basic mechanics of cancelling numbers to “solve” an equation and maintaining equal value on both sides of an equation. While never directly attaching play to mathematics terminology or outlining precisely the mathematical operations happening in the game,

*DragonBox*serves as an effective method of introducing algebraic equations, especially to students not yet “ready” for algebra or struggling with algebra. In fact, by the end of the game, play looks strikingly similar to what one would see on an algebra worksheet.

## Experience breakdown

## LESSON PLAN OVERVIEW

*DragonBox* is one of the best examples of merging game rules with learning content. Consequently, when a player learns the rules of *DragonBox*, she is also learning some of the core rules and principles of algebra. This activity tries to leverage that by having students ostensibly describe and document the rules of the game and then convert those rules into a description of the basics of algebra.

During play, students document the rules of the game (e.g. light and dark versions of the same cards can be combined to form hurricanes). They should be as comprehensive and articulate as possible, acting like technical writers for the game's manual.

After they've drafted their manual, students convert this technical documentation into excerpts from an algebra textbook.

This activity is designed to coincide with players' first experience with the game, so that they believe themselves initially to just be documenting the game's rules and then later realize they have been simultaneously documenting mathematical rules.

## Learning Objectives

- Use the order of operations to simplify/solve equations with the least number of steps possible.
- Accurately simplify and solve for a single variable using the properties of real numbers under a given operation.

## LESSON STEPS

- Students begin
*DragonBox*and document any rules they observe. Make sure students are documenting the rules as precisely and thoroughly as possible. To provide context and guidance, have them consider themselves to be writing instruction manuals for the game. - Once students see the game start to convert the cards into mathematical numbers, variables, and operations, offer them a new task: converting their documentation (and future documentation) into explanations of algebraic rules. To provide this with some extra guidance and context, have students write this documentation in the form of algebra textbook examples.

- As an extension, students can share the rules they created in small groups and compile the best entries into one comprehensive mini-textbook, or the best examples could be showcased to the class, discussed, and compiled until students decide on a final list of algebraic rules covered in
*DragonBox*.

- What is the default operation linking all cards?
- What do you think the light and dark versions of cards represent? What is the mathematical term for that?
- What do you think the line between the two sides of the screen represents?
- What do you observe when you move a card over to the box’s side of the screen?
- Why when you add a card to one side do you have to add cards on the other side? What property does that represent?
- What does it mean that something is labeled “useless” after you finish a round? How do you prevent a card from being determined useless?
- Why can you eliminate a die with the value “1” when it is connected to another card?
- Why were you able to eliminate a fraction with two equal cards (one on top and the other on bottom) in the same fraction?
- When there’s a box at the bottom of the fraction, what strategy do you use to eliminate it?

## standards

### Common Core - Mathematics

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**Expressions & equations**

**Grade 6: Apply and extend previous understandings of arithmetic to algebraic expressions.**

CCSS.Math.Content.6.EE.A.2 Write, read, and evaluate expressions in which letters stand for numbers.CCSS.Math.Content.6.EE.A.3 Apply the properties of operations to generate equivalent expressions. For example, apply the distributive property to the expression 3 (2 + x) to produce the equivalent expression 6 + 3x; apply the distributive property to the expression 24x + 18y to produce the equivalent expression 6 (4x + 3y); apply properties of operations to y + y + y to produce the equivalent expression 3y.CCSS.Math.Content.6.EE.A.4 Identify when two expressions are equivalent (i.e., when the two expressions name the same number regardless of which value is substituted into them).For example, the expressions y + y + y and 3y are equivalent because they name the same number regardless of which number y stands for.

**Grade 6: Reason about and solve one-variable equations and inequalities.**

CCSS.Math.Content.6.EE.B.5 Understand solving an equation or inequality as a process of answering a question: which values from a specified set, if any, make the equation or inequality true? Use substitution to determine whether a given number in a specified set makes an equation or inequality true.

CCSS.Math.Content.6.EE.B.8 Write an inequality of the form x > c or x < c to represent a constraint or condition in a real-world or mathematical problem. Recognize that inequalities of the form x > c or x < c have infinitely many solutions; represent solutions of such inequalities on number line diagrams.

**Grade 7: Use properties of operations to generate equivalent expressions.**

CCSS.Math.Content.7.EE.A.1 Apply properties of operations as strategies to add, subtract, factor, and expand linear expressions with rational coefficients.

CCSS.Math.Content.7.EE.A.2 Understand that rewriting an expression in different forms in a problem context can shed light on the problem and how the quantities in it are related. For example, a + 0.05a = 1.05a means that “increase by 5%” is the same as “multiply by 1.05.”

**Grade 8: Analyze and solve linear equations and pairs of simultaneous linear equations.**CCSS.Math.Content.8.EE.C.7 Solve linear equations in one variable.

CCSS.Math.Content.8.EE.C.8 Analyze and solve pairs of simultaneous linear equations.