Empowering Students in Math
Innovative Learning Tools
Karon Stewart, LLC. We believe in making mathematics accessible and enjoyable. Edutainment. Our flagship product, The Linear Algebra Game, offers engaging ways to grasp complex concepts in linear algebra.
About The Linear Algebra Game
Instructions
The Linear Algebra Game Deck (54 Cards)
🌟 OBJECTIVE
Make connections between different representations of the same mathematical relationship by matching:
- Equation
- Narrative (word problem)
- Ordered Pair(s)
- Graph
- Table
Play by matching 2, 3, 4, or all 5 representations. The more complete the match, the more points you earn!
🎮 GAME SETUP
Deck Composition (54 cards):
- 10 Equation cards
- 10 Narrative cards
- 10 Ordered Pair cards
- 10 Graph cards
- 10 Table cards
- 4 Wild Cards (can be used as any card type)
Players: 1 to 4
Ages: Middle school and up
Play Time: 10–30 minutes
🤖 HOW TO PLAY
For 2–4 Players
1. Shuffle all cards and deal 7 to each player.
2. Place the remaining cards face down as the draw pile.
3. Turn one card face up to start the discard pile.
On your turn:
- Draw one card (from draw or discard pile)
- Make or add to a match if possible:
- At least two cards must match (e.g., equation + table)
- Up to 5-card full match
- Play one match per turn OR add to an existing one
- Discard one card to end your turn
Wild Cards: Use to fill in for any card type (limit: one per match). Replace later if the actual card is drawn.
End of Game:
- First player to make 3 full matches (5 cards each) wins
- OR when draw pile is empty: highest total score wins
Scoring:
- 2-card match = 1 point
- 3-card match = 2 points
- 4-card match = 3 points
- 5-card match = 5 points
Of course, you can always make up your own games, especially if you are familiar with games like Spades, Pitty-pat, Solitaire, and Go fish.
Standards
Illinois State standards
Students grasp the concept of a function as a rule that assigns to each input exactly one output. They understand that functions describe situations where one quantity determines another. They can translate among representations and partial representations of functions (noting that tabular and graphical representation may be partial representations), and they describe how aspects of the function are reflected in the different representations. (Illinois State Board of Education, 2021)
Grades 6–8 Expectations:
In grades 6–8 each and every student should–
- represent, analyze, and generalize a variety of patterns with tables, graphs, words, and, when possible, symbolic rules;
- relate and compare different forms of representation for a relationship;
- identify functions as linear or nonlinear and contrast their properties from tables, graphs, or equations. (National Council of Teachers of Mathematics, 2000)
References
Illinois State Board of Education. (2021). Illinois learning standards for mathematics. https://www.isbe.net/Pages/Illinois-Learning-Standards.aspxNational Council of Teachers of Mathematics. Principles and Standards for School Mathematics: Algebra. Reston, VA: NCTM, 2000. https://www.nctm.org/standards-and-positions/principles-and-standards/algebra/.
“Wait... x − 10 and 10 − x? Mistake or Masterpiece?”
Sometimes a mistake is just math’s way of saying, “Let’s dig deeper.”
When we printed our game deck, we accidentally included both x − 10 = y and 10 − x = y. At first, we thought, “Oops! That’s a duplicate with a twist.” But then… 💡
These two cards aren’t mistakes—they’re mirror images with meaning.
📏 They look similar.
📉 They graph differently.
🎯 They tell very different stories about how numbers move and grow.
So we decided to keep both. Why?
Because 10 − x flips the story. What happens when the input increases? In one, the output grows. In the other, the output shrinks.
We call this our “X-tra Card”—the perfect teachable moment hiding in plain sight. It’s a bonus that reminds us:
“In math, even your missteps can take you somewhere brilliant.”
🧠 LESSON 1: “Tale of Two Equations: Compare & Contrast”
Objective: Students will understand the difference between x − 10 = y and 10 − x = y by comparing inputs, outputs, and graphs.
Activity:
- Give students a T-chart for both equations with x = 0, 5, 10, 15.
- Have them plot both on the same coordinate plane.
- Ask:
- Which graph goes up? Which one goes down?
- Are they reflections of each other? Across which line?
- What do you notice about their outputs when x = 10?
- Which graph goes up? Which one goes down?
Wrap-Up:
These equations aren’t the same—they mirror each other across the line x = 10. One is decreasing, the other is increasing. It's a great lead-in to symmetry and inverse thinking.
🧠 LESSON 2: “Expression Switch: What Does Order Do?”
Objective: Students will explore how the position of x changes the result and what that means for expressions and real-world problems.
Real-Life Setup:
- Say: “You have $x and spend $10.” → x − 10
- Then flip: “You had $10 but spent $x.” → 10 − x
Activity:
- Write word problems for both.
- Ask: “Can you end up with the same amount of money in both? When?”
- Try with different values for x.
Discussion Prompt:
- How does switching the order change what happens?
- Does one expression always give a negative result? When?
Takeaway:
Order matters in subtraction. The story changes with the structure.
🧠 LESSON 3: “Negative Numbers: Enter Stage Left”
Objective: Introduce negative numbers using the difference between x − 10 and 10 − x.
Hook:
Use a number line or thermometer. Ask:
“If it’s 10 degrees and it drops by x, what happens?”
“If it’s x degrees and you drop to 10, what happens?”
Activity:
- Plug in x = 7, x = 10, x = 13 into both expressions.
- Highlight where negative numbers appear.
- Have students use visuals:
- Number lines
- Temperature charts
- Elevation (above and below sea level)
- Number lines
Final Reflection:
- Ask: “Which expression always turns negative when x gets big?”
- Discuss: “How can we predict when a number will be negative?”
Coming Soon - Pictures of students Playing the game.