3. Solution: \(x = \mathbf{7}\)
Correct Answer:
x = 7
6
7.RP.A.2b
A recipe uses 3 cups of water for every 2 cups of milk. Write an equation relating water (\(w\)) to milk (\(m\)).
Teacher Solution & Steps:
Find constant ratio: \(\frac{\text{water}}{\text{milk}} = \frac{3}{2} = 1.5\)
Equation format: \(w = k \times m\)
Substitute constant: \(w = 1.5m\) or \(w = \frac{3}{2}m\)
Correct Answer:
w = 1.5m
Grade 8 Math Intervention Screener ANSWER KEY Page 2 of 4
Answer Key
7
7.RP.A.3
A family dinner at a restaurant costs $50.00. If you want to leave a 15% tip, what is the total cost including tip?
Teacher Solution & Steps:
1. Find Tip value: \(15\% \text{ of } \$50 = 0.15 \times 50 = \mathbf{\$7.50}\)
2. Add to bill: \(\$50.00 + \$7.50 = \mathbf{\$57.50}\)
Alternative: \(1.15 \times 50 = \mathbf{\$57.50}\)
Correct Answer:
$ 57.50
8
8.EE.A.1
Simplify and write as a single integer: \(\frac{5^6}{5^4}\)
Teacher Solution & Steps:
1. Exponent Division Rule: Subtract the exponents.
\(\frac{5^6}{5^4} = 5^{(6 - 4)} = \mathbf{5^2}\)
2. Solve exponent: \(5 \times 5 = \mathbf{25}\).
Correct Answer:
25
9
8.EE.B.5
A straight proportional line passes through \((0,0)\) and \((4, 12)\). What is the slope of this line?
Teacher Solution & Steps:
Calculate Slope (rate of change): \(m = \frac{\text{Change in } y}{\text{Change in } x}\)
\(m = \frac{12 - 0}{4 - 0} = \frac{12}{4}\)
Simplify division: \(12 \div 4 = \mathbf{3}\).
Correct Answer:
m = 3
Grade 8 Math Intervention Screener ANSWER KEY Page 3 of 4
Answer Key
10
8.EE.C.7b
Solve the linear equation for \(x\): 4x + 3 = 2x + 11
Teacher Solution & Steps:
1. Subtract \(2x\) from both sides: \(2x + 3 = 11\)
2. Subtract 3 from both sides: \(2x = 8\)
3. Divide by 2: \(\frac{2x}{2} = \frac{8}{2} \rightarrow \mathbf{x = 4}\)
Correct Answer:
x = 4
11
8.G.B.7
A right-angled triangle has leg measurements of 6 centimeters and 8 centimeters. What is the length of the hypotenuse?
Teacher Solution & Steps:
1. Formula: \(a^2 + b^2 = c^2\)
2. Substitute legs: \(6^2 + 8^2 = c^2 \rightarrow 36 + 64 = c^2\)
3. Solve for c: \(100 = c^2 \rightarrow c = \sqrt{100} = \mathbf{10}\) cm.
Correct Answer:
10 cm
12
8.F.A.3
Consider the linear function represented by: \(y = 3x - 4\). What is the value of \(y\) when \(x = 5\)?
Teacher Solution & Steps:
1. Substitute \(x = 5\) into linear equation:
\(y = 3(5) - 4\)
2. Solve: \(y = 15 - 4 \rightarrow y = \mathbf{11}\).
Correct Answer:
y = 11
What next?
Record final student scores on the Placement Guide & Class Data Tracker to establish Tier 2 or Tier 3 candidacy.
Grade 8 Math Intervention Screener ANSWER KEY Page 4 of 4
| Q10 (8.EE.7), Q11 (8.G.7), Q12 (8.F.3) | • Solves variables on both sides: \(4x + 3 = 2x + 11 \rightarrow \mathbf{x = 4}\). |
| • Pythagorean theorem: \(6^2 + 8^2 = c^2 \rightarrow c = \mathbf{10}\) cm. |
| • Substitutes into function: \(3(5) - 4 = \mathbf{11}\). | Tier 2: Minor algebraic manipulation errors; arithmetic errors in squaring/square-roots. |
| Tier 3: Combines terms across equal sign incorrectly (\(4x + 2x = 6x\)); adds sides directly for triangle hypotenuse (\(6 + 8 = 14\) cm). |
Tier 1: Core 20 - 24 pts
Candidacy: Excellent conceptual foundation. Solid readiness for variables on both sides, slope metrics, Pythagorean theorem, and general functions.
Action: Place in standard 8th-grade core mathematics with regular curriculum enrichment.
Tier 2: Targeted 12 - 19 pts
Candidacy: Deficits in exponents, slope interpretations, or equations with multiple steps. Needs small-group conceptual reinforcement.
Action: Small group (3-5 students) targeting negative variables, exponent rules, and linear ratios 2-3x weekly.
Tier 3: Intensive 0 - 11 pts
Candidacy: Significant conceptual gaps spanning elementary fractions division, basic rates, percentage equations, and one-step equations.
Action: High-frequency daily intervention (1-on-1 or max 3 students) using physical algebra tiles, coordinate maps, and double number lines.
Grade 8 Math Intervention Screener Placement Guide Page 1 of 2
Class Recording Sheet
Data Recording Instructions: Award 2 pts for correct work & answer, 1 pt for partial correctness (e.g., correct work but calculation error), and 0 pts for incorrect response. Use vertical columns to track class-wide standard deficiencies.
| Student Name | Q1
6.NS.1 | Q2
6.EE.7 | Q3
6.RP.3 | Q4
7.NS.2 | Q5
7.EE.4 | Q6
7.RP.2 | Q7
7.RP.3 | Q8
8.EE.1 | Q9
8.EE.5 | Q10
8.EE.7 | Q11
8.G.7 | Q12
8.F.3 | Score
Max 24 | Placement
Tier 1 / 2 / 3 |
| --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- |
| e.g., Jane Doe | 2 | 2 | 2 | 1 | 2 | 2 | 2 | 1 | 2 | 0 | 1 | 0 | 17 | Tier 2 |
| 1. ___________________________ | | | | | | | | | | | | | | |
| 2. ___________________________ | | | | | | | | | | | | | | |
| 3. ___________________________ | | | | | | | | | | | | | | |
| 4. ___________________________ | | | | | | | | | | | | | | |
| 5. ___________________________ | | | | | | | | | | | | | | |
| 6. ___________________________ | | | | | | | | | | | | | | |
| 7. ___________________________ | | | | | | | | | | | | | | |
| 8. ___________________________ | | | | | | | | | | | | | | |
| 9. ___________________________ | | | | | | | | | | | | | | |
| 10. __________________________ | | | | | | | | | | | | | | |
| 11. __________________________ | | | | | | | | | | | | | | |
| 12. __________________________ | | | | | | | | | | | | | | |
Next Steps for Small Groups: Map identical student errors (e.g., adding leg lengths directly for Q11 or multiplying bases for Q8) directly into custom 10-minute targeted mini-lessons before core math instruction begins.
Grade 8 Math Intervention Screener Placement Guide Page 2 of 2
