Fortnite Formula Remix: Mixing the Perfect Shield Potion

Materials Needed

• Pencil and paper or a digital whiteboard
• Calculator
• Optional: colored water, measuring cups, or small containers to model mixtures
• Fortnite-themed “Shield Potion” problem cards, created by the teacher or learner

Learning Objectives

By the end of this 15-minute lesson, the learner will be able to:

• Rearrange a formula to isolate a quantity of interest.
• Use the formula Amount of solute = concentration × total volume to solve mixture problems.
• Explain how the rearranged formula helps determine an unknown amount in a mixture.

Success Criteria

I can:

• Identify the quantity that needs to be isolated.
• Perform the same inverse operation on both sides of an equation.
• Substitute values into a formula and label my answer.
• Check whether my answer is reasonable for the Fortnite mixture scenario.

Introduction: Bell Work and Hook — 3 Minutes

Bell Work: Reinforce Prior Knowledge

Complete these questions independently:

1. Solve for x: 3x = 18.
2. Solve for v: 12 = 4v.
3. If a shield potion is 25% concentrated and there are 100 mL of potion, how many milliliters are the active shield ingredient?

Quick answers: 1) x = 6; 2) v = 3; 3) 25 mL.

Hook

Tell the learner: “Your Fortnite squad has collected two types of shield potion. You need to create a custom potion with a specific strength. The formula is ready—but one of the quantities is missing. Can you remix the formula to find it?”

State the target: “Today, I can rearrange formulas and use them to solve mixture problems.”

Body: Gradual Release of Responsibility — 10 Minutes

I Do: Teacher or Adult Models — 4 Minutes

Introduce the basic mixture formula:

A = cV

• A = amount of active ingredient, or solute
• c = concentration written as a decimal
• V = total volume of the mixture

Explain: “The formula tells us that the amount of shield ingredient equals the concentration multiplied by the total volume.”

Rearranging to Isolate Volume

Suppose we know the amount of active ingredient and the concentration, but we need to find the total volume.

1. Start with the formula: A = cV.
2. Since V is multiplied by c, divide both sides by c.
3. Write the rearranged formula: V = A ÷ c or V = A/c.

Example: A shield potion contains 30 mL of active ingredient and has a concentration of 25%.

Convert 25% to a decimal: 25% = 0.25.

V = A/c = 30 ÷ 0.25 = 120 mL

The potion mixture has a total volume of 120 mL.

Modeling a Mixture Equation

If two potions are mixed, the total active ingredient from both potions equals the active ingredient in the final mixture:

c₁V₁ + c₂V₂ = c_f(V₁ + V₂)

This equation means:

• Active ingredient in Potion 1
• plus active ingredient in Potion 2
• equals active ingredient in the final mixture.

We Do: Solve Together — 4 Minutes

Squad Challenge: A player mixes a 20% shield potion with a 50% shield potion to create 200 mL of a 35% shield potion. How many milliliters of each potion are needed?

Let x represent the amount of 20% potion. Then the amount of 50% potion is 200 − x.

Build the mixture equation together:

0.20x + 0.50(200 − x) = 0.35(200)

Guide the learner through the steps:

1. Distribute: 0.20x + 100 − 0.50x = 70.
2. Combine like terms: −0.30x + 100 = 70.
3. Subtract 100 from both sides: −0.30x = −30.
4. Divide by −0.30: x = 100.

Therefore, use 100 mL of the 20% potion and:

200 − 100 = 100 mL

Use 100 mL of the 50% potion.

Quick Check

Ask: “Does the answer make sense?”

• The target concentration, 35%, is halfway between 20% and 50%.
• Therefore, equal amounts of the two potions should work.
• 100 mL + 100 mL = 200 mL.

You Do: Independent Fortnite Mission — 2 Minutes

Choose one challenge.

Mission A: Formula Rearrangement

A potion has 45 mL of active ingredient and a concentration of 30%. Rearrange and use the formula A = cV to find the total volume.

Mission B: Mixture Challenge

You need 300 mL of a 40% shield potion. You have a 20% potion and a 60% potion. How many milliliters of each should you mix?

Expected work for Mission B:

Let x be the amount of 20% potion. Then the amount of 60% potion is 300 − x.

0.20x + 0.60(300 − x) = 0.40(300)

Answer: 150 mL of the 20% potion and 150 mL of the 60% potion.

Conclusion: Debrief and Exit Check — 2 Minutes

Recap

Ask the learner to complete these statements aloud or in writing:

• “To isolate a variable, I use the __________ operation on both sides.”
• “The mixture formula is __________.”
• “A concentration must be written as a __________ when used in calculations.”

Expected responses: inverse; A = cV; decimal.

Exit Ticket

Rearrange A = cV to isolate c. Then find the concentration of a potion containing 24 mL of active ingredient in 80 mL of total mixture.

Answer:

c = A/V = 24/80 = 0.30 = 30%

Assessment Plan

Formative Assessment

• Check bell work for understanding of solving one-step equations.
• Ask the learner to explain why division isolates a variable in A = cV.
• Use the “Does the answer make sense?” check during the mixture example.
• Listen for correct use of terms such as concentration, volume, active ingredient, and isolate.

Summative Assessment

The learner demonstrates mastery by completing the exit ticket and showing:

• The correct rearrangement of the formula.
• Accurate substitution of values.
• Correct calculations and units.
• A reasonable interpretation of the answer.

Differentiation and Adaptations

Scaffolds for Support

• Provide a formula mat: A = cV, V = A/c, and c = A/V.
• Use colored symbols: one color for concentration, one for volume, and one for active ingredient.
• Allow the learner to model the problem with measuring cups or colored water.
• Provide the first algebraic step and ask the learner to complete the remaining steps.

Extensions

• Ask the learner to create an original Fortnite potion mixture problem with a different target concentration.
• Have the learner solve for an unknown concentration using c = A/V.
• Challenge the learner to explain why a target concentration must fall between the concentrations of the two starting potions.

Choice and Real-World Connection

The learner may rename the context using another interest, such as mixing paint colors, sports drinks, cleaning solutions, or crafting materials. The same formulas and reasoning apply whenever different-strength solutions are combined.