White River: Slope \(= \frac{100-60}{4-2} = \frac{40}{2} = 20\).
White River \(y\)-int: \(60 = 20(2) + b \implies b = 20\).
White River Eq: \(C = 20m + 20\)
Credit: 0.75 pt for Wabash equation; 0.75 pt for White River equation with work.
Part B Solution & Rubric: 1.5 Pts
System Equated: \(15m + 30 = 20m + 20\)
Solve for \(m\): \(30 - 20 = 20m - 15m \implies 10 = 5m \implies \mathbf{m = 2}\text{ months}\)
Solve for Cost: \(C = 15(2) + 30 = \mathbf{\$60}\)
Final: 2 months, Cost = $60
Credit: 1 pt for setting equations equal and solving for \(m=2\); 0.5 pt for calculating cost \(\$60\).
ILEARN Scoring Note: If a student identifies Month 2 and $60 directly from inspecting the White River table and checking Wabash Rec, award full credit if clear check is shown.
Indiana ILEARN Math Assessment • Teacher Solutions Guide Page 1 of 2
Teacher Answer Key & Rubric
Comprehensive Analysis
ITEM 4 GEOMETRY AND MEASUREMENT (IAS 8.GM.6, 8.GM.8)
3 Points Max
Part A Solution & Rubric: 1.5 Pts
Distance formula: \(d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2}\)
Differences: \(\Delta x = 5 - (-3) = 8\); \(\Delta y = -2 - 4 = -6\)
Calculation: \(d^2 = 8^2 + (-6)^2 = 64 + 36 = 100\)
Final Distance: \(d = \sqrt{100} = 10\) units
Credit: 0.75 pt for correct \(\Delta x, \Delta y\); 0.75 pt for calculating \(d = 10\).
Part B Solution & Rubric: 1.5 Pts
Find Radius: \(r^2 + h^2 = s^2 \implies r^2 + 8^2 = 10^2\)
\(r^2 + 64 = 100 \implies r^2 = 36 \implies \mathbf{r = 6\text{ ft}}\)
Cone Volume: \(V = \frac{1}{3}\pi r^2 h = \frac{1}{3}\pi (6^2)(8)\)
Final Volume: \(V = 96\pi\text{ ft}^3\) (or \(\approx 301.6\text{ ft}^3\))
Credit: 0.75 pt for \(r = 6\text{ ft}\); 0.75 pt for volume formula & result.
Common Misconception: Using the slant height \(10\) in the volume formula instead of height \(8\), or using cylinder volume formula without \(\frac{1}{3}\).
ITEM 5 DATA ANALYSIS & STATISTICS (IAS 8.DSP.1, 8.DSP.3)
3 Points Max
Part A Solution & Rubric: 1 Pt
1. Joint Relative Freq: \(\frac{18}{100} = \mathbf{18\%}\) (or 0.18)
2. Conditional Relative Freq: \(\frac{18}{60} = \frac{3}{10} = \mathbf{30\%}\) (or 0.30)
Credit: 0.5 pt for 18%; 0.5 pt for 30%.
Part B Solution & Rubric: 2 Pts
Athletes in STEM: \(\frac{18}{60} = 30\%\)
Non-Athletes in STEM: \(\frac{12}{40} = 30\%\)
Conclusion: No evidence of association. The rate of STEM participation is identical (\(30\%\)) regardless of sport participation.
Credit: 1 pt for calculating both conditional rates; 1 pt for concluding no association based on evidence.
ILEARN High-Yield Skill: Many students confuse joint relative frequency (out of the grand total of 100) with conditional relative frequency (out of the subtotal row of 60). Emphasize reading the denominator!
ILEARN Diagnostic Performance Matrix & Cut Scores Indiana Dept of Education Scale Alignment
Below Proficiency
0 – 6 Pts
Needs foundational reteaching on rational vs irrational and basic equations.
Approaching
7 – 10 Pts
Understands procedures but makes errors with exponents or 3D geometry formulas.
At Proficiency
11 – 13 Pts
Meets Indiana grade-level standards. Solid grasp of algebra and data interpretation.
Above Proficiency
14 – 15 Pts
Demonstrates sophisticated mathematical communication and multi-step reasoning.
Next Steps: Strand 1-2 Focus: Number line irrational placement drills • Strand 3 Focus: Comparing tables to linear functions • Strand 4-5 Focus: 3D geometry flashcards & two-way relative frequency interpretation
Indiana ILEARN Math Assessment • Teacher Solutions Guide Page 2 of 2
