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8th Grade Math Diagnostic Screener • Lesson • Lenny.com
8th Grade Math Diagnostic Screener A comprehensive 8th-grade math screener diagnostic tool designed to identify students for Tier 2 and Tier 3 interventions. Includes a 4-page student booklet, a matching step-by-step answer key, and an instructional rubric, placement guide, and class data tracker spanning 6th, 7th, and 8th-grade standards.
B Bennington
Math Screener Student Booklet
A 4-page print-ready math screener for 8th-grade students. Contains 12 targeted, open-response diagnostic tasks spanning 6th-grade rational division and equations, 7th-grade signed integers and ratio scaling, and 8th-grade slope, multi-step equations, exponent rules, and the Pythagorean theorem to identify Tier 2 and Tier 3 candidates in 20-25 minutes.
Math Screener Answer Key
A 4-page print-ready teacher answer key that matches the student booklet exactly. Features completed step-by-step mathematical work, visual models, final answers in high-contrast red font, and quick diagnostic pointers for rapid screening of all 12 questions.
Math Screener Placement Guide
A 2-page guide for teachers containing a diagnostic rubric with common error analysis, a structured Tier Placement Guide (with clear cut-offs for Tier 1, 2, and 3), and a clean printable class data tracker spanning 6th, 7th, and 8th-grade standards.
8th Grade Math Diagnostic Screener A comprehensive 8th-grade math screener diagnostic tool designed to identify students for Tier 2 and Tier 3 interventions. Includes a 4-page student booklet, a matching step-by-step answer key, and an instructional rubric, placement guide, and class data tracker spanning 6th, 7th, and 8th-grade standards.
B Bennington
Math Screener Student Booklet Part I: 6th Grade Foundations
8th Grade Math Screener
Session Time: 20-25 min
Focus: 6th, 7th, & 8th Grade Core
Student Name
Date
Teacher / Class
Directions: Solve each problem below. Show all of your calculations, drawings, or algebraic steps in the workspaces. Do your best on each question!
1
Dividing Fractions (Reciprocals)
6.NS.A.1
How many \(\frac{1}{6}\)-cup servings of yogurt can you get out of a larger tub containing \(\frac{2}{3}\) cup of yogurt?
Show Your Work:
Final Answer:
servings
2
Solving Single-Step Equations
6.EE.B.7
Solve the algebraic equation for the variable \(x\). Show the step you used to isolate the variable. x - 2.5 = 7.5
Show Your Step:
Value of x:
x =
3
Calculating Percent of a Quantity
6.RP.A.3c
A survey of 60 students showed that 35% of them play soccer. How many of those surveyed students play soccer?
Show Your Work:
Final Answer:
students
Grade 8 Math Intervention Screener Page 1 of 4
Part II: 7th Grade Equations & Proportions
Student Name: _______________________
4
Operations with Negative Rational Numbers
7.NS.A.2
Evaluate the rational expression below. Remember to follow the correct order of operations: -15 ÷ (-3) + (-4) × 2
Show Your Steps:
Final Value:
5
Solving Two-Step Algebraic Equations
7.EE.B.4a
Solve the algebraic equation for \(x\). Show the steps you use to isolate the variable. 3x - 5 = 16
Show Your Steps:
Value of x:
x =
6
Writing Proportional Equations
7.RP.A.2b
A bakery recipe uses 3 cups of water for every 2 cups of milk. Write a proportional equation that relates the cups of water (\(w\)) to cups of milk (\(m\)).
Show Your Thinking (Use ratios or tables):
Equation:
w =
Grade 8 Math Intervention Screener Page 2 of 4
Part III: Percents, Exponents, & Slopes
Student Name: _______________________
7
Multi-Step Percent Problems (Tax & Tip)
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 of the dinner including tip?
Show Your Work:
Total Cost:
$
8
Laws of Integer Exponents
8.EE.A.1
Simplify the exponential expression below. Write your final answer as a single, standard integer (not an exponent): \[\frac{5^6}{5^4}\]
Show Your Steps (Explain exponent laws used):
Final Value:
9
Graph Proportions & Unit Slope
8.EE.B.5
A straight proportional line passes through the origin \((0,0)\) and the point \((4, 12)\) on a coordinate graph. What is the slope of this line?
Show Your Steps (Slope Formula or Ratio):
Slope (m):
m =
Grade 8 Math Intervention Screener Page 3 of 4
Part IV: Multi-Step Equations & Geometry
Student Name: _______________________
10
Equations with Variables on Both Sides
8.EE.C.7b
Solve the linear equation for \(x\). Show each step you take to isolate the variable. 4x + 3 = 2x + 11
Show Your Algebraic Steps:
Value of x:
x =
11
Applying Pythagorean Theorem
8.G.B.7
A right-angled triangle has leg measurements of 6 centimeters and 8 centimeters. What is the length of the hypotenuse, in centimeters?
Show Your Steps (Pythagorean formula):
Hypotenuse:
cm
12
Linear Functions & Evaluations
8.F.A.3
Consider the linear function represented by: \(y = 3x - 4\). What is the value of \(y\) when \(x = 5\)?
Show Your Work:
Value of y:
y =
How do you feel about this diagnostic?
Confident
OK
Needed Help
Grade 8 Math Intervention Screener Page 4 of 4
Math Screener Answer Key Teacher Resource • Answer Key
8th Grade Math Screener
Session Time: 20-25 min
Grade 8 Entry Diagnostic
Scoring Guidelines: Correct answers are shown in red with full algebraic and conceptual steps. Award 1 point for correct final value and 1 point for complete work (total 2 points per problem). Max Score: 24 points.
1
Dividing Fractions (Reciprocals)
6.NS.A.1
How many \(\frac{1}{6}\)-cup servings of yogurt can you get out of a larger tub containing \(\frac{2}{3}\) cup of yogurt?
Teacher Solution & Steps:
Divide cup quantities: \(\frac{2}{3} \div \frac{1}{6}\)
Multiply by reciprocal: \(\frac{2}{3} \times \frac{6}{1} = \frac{12}{3}\)
Simplify division: \(12 \div 3 = \mathbf{4}\) servings.
Correct Answer:
4 servings
2
Solving Single-Step Equations
6.EE.B.7
Solve the algebraic equation for the variable \(x\): x - 2.5 = 7.5
Teacher Solution & Steps:
Add 2.5 to both sides to isolate \(x\):
\(x - 2.5 + 2.5 = 7.5 + 2.5\)
Solve: \(x = \mathbf{10}\)
Correct Answer:
x = 10
3
Calculating Percent of a Quantity
6.RP.A.3c
A survey of 60 students showed that 35% of them play soccer. How many of those surveyed students play soccer?
Teacher Solution & Steps:
Convert percent to decimal: \(35\% = 0.35\)
Multiply: \(0.35 \times 60\)
Calculate: \(35 \times 6 = 210 \rightarrow 0.35 \times 60 = \mathbf{21}\) students.
Correct Answer:
21 students
Grade 8 Math Intervention Screener ANSWER KEY Page 1 of 4
Part II: 7th Grade Equations & Proportions Keys
Answer Key
4
Operations with Negative Rational Numbers
7.NS.A.2
Evaluate: -15 ÷ (-3) + (-4) × 2
Teacher Solution & Steps:
1. Division: \(-15 \div (-3) = \mathbf{5}\)
2. Multiplication: \(-4 \times 2 = \mathbf{-8}\)
3. Sum: \(5 + (-8) = \mathbf{-3}\)
Correct Answer:
-3
5
Solving Two-Step Algebraic Equations
7.EE.B.4a
Solve the equation for \(x\): 3x - 5 = 16
Teacher Solution & Steps:
1. Add 5 to both sides: \(3x - 5 + 5 = 16 + 5 \rightarrow \mathbf{3x = 21}\)
2. Divide by 3: \(\frac{3x}{3} = \frac{21}{3}\)
Math Screener Placement Guide Teacher Diagnostic Manual • Grade 8 Entry
Instructional Rubric & Placement Guide
8th Grade Screening Suite
12-Question Diagnostic Edition
Part I: Diagnostic Rubric & Error Analysis
Concept Cluster & Standards Proficient Performance Indicator Common Misconceptions (Tier 2/3 Signs) Cluster 1: 6th Grade Foundations Q1 (6.NS.1), Q2 (6.EE.7), Q3 (6.RP.3) • Divides fractions: \(\frac{2}{3} \div \frac{1}{6} = \mathbf{4}\) servings. • Isolates one-step decimal variable: \(x = \mathbf{10}\). • Calculates percentage quantity: \(35\% \text{ of } 60 = \mathbf{21}\) students. Tier 2: Multiplies instead of dividing fractions (\(\frac{2}{18} = \frac{1}{9}\)); minor percentage decimal error. Tier 3: Subtracts decimals incorrectly (\(x = 7.5 - 2.5 = 5\)); calculates 35% as raw subtractor or is unable to process basic fractions. Cluster 2: 7th Grade Foundations Q4 (7.NS.2), Q5 (7.EE.4), Q6 (7.RP.2) • Multi-step sign arithmetic: \(-15 \div (-3) + (-4) \times 2 = \mathbf{-3}\). • Solves two-step equation: \(3x - 5 = 16 \rightarrow \mathbf{x = 7}\). • Writes water-to-milk proportional line: \(\mathbf{w = 1.5m}\). Tier 2: Double-negative sign errors on division or product; swaps ratio inputs backward (\(w = \frac{2}{3}m\)). Tier 3: Thinks \(-15 \div (-3) = -5\); uses incorrect inverse operations on equation (\(3x = 11 \rightarrow x = 3.66\)). Cluster 3: Percents, Exponents, & Slopes Q7 (7.RP.3), Q8 (8.EE.1), Q9 (8.EE.5) • Multi-step percent: \(50.00 + 7.50 = \mathbf{\$57.50}\). • Division rule of exponents: \(\frac{5^6}{5^4} = 5^2 = \mathbf{25}\). • Calculates graph slope: \(m = \frac{12-0}{4-0} = \mathbf{3}\). Tier 2: Divides exponents instead of subtracting (\(5^{(6/4)}\)); finds discount/tip (\$7.50) but forgets to add to total. Tier 3: Multiplies bases for exponent (\(5^2 = 10\)); swaps slope coordinates (\(m = \frac{4}{12} = \frac{1}{3}\)). Cluster 4: Advanced 8th Grade
3. Solution: \(x = \mathbf{7}\)
Writing Proportional Equations 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 \(w = \frac{3}{2}m\)
Grade 8 Math Intervention Screener ANSWER KEY Page 2 of 4
Part III: Percents, Exponents, & Slopes Keys
Multi-Step Percent Problems (Tax & Tip) 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: \(1.15 \times 50 = \mathbf{\$57.50}\)
Laws of Integer Exponents 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: \(5 \times 5 = \mathbf{25}\).
Graph Proportions & Unit Slope 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: \(12 \div 4 = \mathbf{3}\).
Grade 8 Math Intervention Screener ANSWER KEY Page 3 of 4
Part IV: Advanced 8th Grade Keys
Equations with Variables on Both Sides 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: \(\frac{2x}{2} = \frac{8}{2} \rightarrow \mathbf{x = 4}\)
Applying Pythagorean Theorem 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.
Linear Functions & Evaluations 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:
2. Solve: \(y = 15 - 4 \rightarrow y = \mathbf{11}\).
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).
Part II: Placement Thresholds (Max Score: 24 Points) 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
Part III: Classroom Data Tracker (Grade 8 Screener) 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
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
