Mia's Math Expedition

Treat this like an expedition, not a test. Work without opening the answers. If a station feels foggy, write what you know and move on. An honest question mark gives us useful information.

1. Station 1: Build and solve an equation

   Mia has $5$ kg of hay. She buys $x$ bags of $\frac23$ kg each and finishes with $17$ kg.

   1. Write an equation.
   2. Solve for $x$, showing each operation on both sides.
   3. Check by substitution.
   equation → equivalent operations → check →
2. Station 2: Negative-coefficient inequality

   A tank starts at $18$ L and loses $3$ L each hour. Let $h=$ elapsed hours. Find when it contains at most $6$ L.

   1. Write an inequality.
   2. Solve it and show where the sign reverses.
   3. Interpret the solution beginning, “After at least...”
   model → isolate → divide by a negative → interpret →

3. Station 3: Arithmetic sequence

   A plan decreases the number of jumps each day: $72,65,58,51,\ldots$

   1. Calculate $d$.
   2. Write an explicit formula for $a_n$.
   3. Calculate $a_{10}$.
   difference → formula → substitute →
4. Station 4: Geometric sequence

   An image is repeatedly compressed: $640,320,160,80,\ldots$ kilobytes.

   1. Calculate $r$.
   2. Write an explicit formula.
   3. Calculate $a_7$.
   ratio → formula → substitute →
5. Station 5: Inverse proportion

   A fixed hay supply feeds $4$ horses for $15$ days.

   1. Choose DIRECT or INVERSE proportion.
   2. Calculate the constant horse-days.
   3. Calculate how long it feeds $6$ horses.
   relationship → constant product → days →

6. Station 6: Angle relationships
   1. Calculate $x$ and name the relationship.
   2. Calculate $y$ and name the relationship.
   relationship → equation → calculate →
7. Station 7: Triangle congruence
   1. Choose SSS, SAS, ASA, AAS, or not enough information.
   2. Match vertices $A,B,C$ with $D,E,F$.
   3. Name the side corresponding to $BC$.
   matching marks → rule → corresponding parts →
8. Station 8: Similar triangles
   1. Write a proportion.
   2. Calculate $x$.
   3. Calculate the scale factor from small to large.
   match sides → proportion → solve → scale factor →
9. Station 9: Area and perimeter
   1. Calculate the L-shape's area.
   2. Calculate its perimeter by tracing the outside.
   3. Calculate fencing cost at €7.50/m.
   outer - removed → trace → cost →

10. Station 10: Slope and rate

    A battery graph uses $x=$ hours and $y=$ battery level in percent. It passes through $(2,84)$ and $(6,60)$.

    1. Choose INCREASES or DECREASES.
    2. Calculate $\Delta y$ in percentage points.
    3. Calculate $\Delta x$ in hours.
    4. Calculate the slope with units.
    5. Interpret the rate in a sentence.
    6. Answer YES or NO: convert it to a percentage gradient? Explain.
    direction → Δy → Δx → divide → units → meaning →
11. Station 11: Simple interest

    Mia deposits €800 at $3\%$ simple interest per year for $2.5$ years.

    1. Convert the rate to a decimal.
    2. Calculate interest using $I=Prt$.
    3. Calculate the total amount.
    decimal → interest → total →
12. Station 12: Linear equation

    An art account starts with €40 and grows by €6 each week. Let $x=$ weeks and $y=$ euros.

    1. State $m$ with units.
    2. State $b$ with units.
    3. Write $y=mx+b$.
    4. Calculate the balance after $8$ weeks.
    5. Write the coordinate point for part (d).
    rate → start → equation → substitute → point →