Math Milestone Diagnostic Screener
Diagnostic Assessment
Math Milestone Screener
Grades 3–8 Comprehensive Calculation & Problem-Solving Inventory
30 Questions Total
5 Problems / Grade Band
Student Name:
Date:
Grade Level:
Section 1: Grade 3 Standards (Whole Number Operations, Basic Fractions & Arrays)
Target Score: _____ / 5
1
Multi-Digit Subtraction with Regrouping
3.NBT.A.2
Calculate the exact difference: \( 742 - 389 \)
Answer:
2
Multiplication & Array Reasoning
3.OA.A.3
A baker arranges cookies in \( 8 \) rows with \( 7 \) cookies in each row. How many cookies are there in total?
Answer:
3
Fraction Models & Comparison
3.NF.A.3
Which fraction is greater: \( \frac{3}{4} \) or \( \frac{3}{8} \)? Explain or show how you know using identical whole units.
Answer:
4
Division as Equal Sharing
3.OA.A.2
Find the quotient: \( 56 \div 8 \)
Answer:
5
Two-Step Real-World Word Problem
3.OA.D.8
Maya had \( \$50 \). She bought \( 4 \) notebooks for \( \$6 \) each. How much money does Maya have left?
Answer:
Math Milestone Diagnostic Screener Grade Band: 3rd Grade Page 1 of 7
Diagnostic Screener
Grade 4 Mathematics
Student:
Section 2: Grade 4 Standards (Multi-Digit Operations, Factors, Fraction Addition & Decimals)
Target Score: _____ / 5
6
Multi-Digit Multiplication
4.NBT.B.5
Calculate the product: \( 47 \times 36 \)
Answer:
7
Long Division with Remainder
4.NBT.B.6
Find the quotient and remainder: \( 583 \div 4 \)
Answer:
8
Fractions: Adding Like Denominators
4.NF.B.3c
Solve and write your answer as a mixed number: \( 2\frac{3}{8} + 1\frac{7}{8} \)
Answer:
9
Decimal Notation & Addition
4.NF.C.6
Add the decimals: \( 3.45 + 0.8 \)
Answer:
10
Multi-Step Geometry Word Problem
4.MD.A.3
A rectangular garden has a length of \( 14\text{ ft} \) and a width of \( 9\text{ ft} \). Find both the perimeter and the area of the garden.
P: ______ A: ______
Math Milestone Diagnostic Screener Grade Band: 4th Grade Page 2 of 7
Diagnostic Screener
Grade 5 Mathematics
Student:
Section 3: Grade 5 Standards (Unlike Fraction Operations, Decimal Multiplication, Order of Ops & Volume)
Target Score: _____ / 5
11
Fractions with Unlike Denominators
5.NF.A.1
Compute and simplify to lowest terms: \( \frac{5}{6} - \frac{3}{8} \)
Answer:
12
Multi-Digit Decimal Multiplication
5.NBT.B.7
Calculate the product: \( 4.25 \times 3.6 \)
Answer:
13
Order of Operations & Grouping
5.OA.A.1
Evaluate the numerical expression: \( [24 - (3 + 5)] \times 2 + 9 \)
Answer:
14
Volume of Rectangular Prisms
5.MD.C.5
A storage container has length \( 12\text{ cm} \), width \( 7.5\text{ cm} \), and height \( 6\text{ cm} \). What is its total volume?
Answer:
15
Fraction Word Problem (Division / Unit Fractions)
5.NF.B.7c
A chef has \( 6 \) pounds of flour. Each batch of bread requires \( \frac{1}{3} \) pound of flour. How many full batches of bread can the chef bake?
Answer:
Math Milestone Diagnostic Screener Grade Band: 5th Grade Page 3 of 7
Diagnostic Screener
Grade 6 Mathematics
Student:
Section 4: Grade 6 Standards (Ratios & Rates, Fraction Division, Integers, Algebraic Equations)
Target Score: _____ / 5
16
Fraction Division
6.NS.A.1
Divide and simplify to lowest terms: \( \frac{4}{5} \div \frac{2}{3} \)
Answer:
17
Unit Rates & Proportions
6.RP.A.2
A car travels \( 260\text{ miles} \) on \( 8\text{ gallons} \) of fuel. What is the unit rate in miles per gallon?
Answer:
18
Integers & Absolute Value
6.NS.C.7
Evaluate the expression: \( |-18| - |-7| + (-4) \)
Answer:
19
One-Step Algebraic Equations
6.EE.B.7
Solve for \( x \): \( 3.5x = 28 \)
Answer:
20
Real-World Statistical Measures
6.SP.B.5c
A student scored \( 84, 92, 78, 90, \text{ and } 86 \) on five science quizzes. Calculate the mean (average) score.
Answer:
Math Milestone Diagnostic Screener Grade Band: 6th Grade Page 4 of 7
Diagnostic Screener
Grade 7 Mathematics
Student:
Section 5: Grade 7 Standards (Rational Number Ops, Percent Problems, Two-Step Equations & Probability)
Target Score: _____ / 5
21
Rational Numbers & Sign Rules
7.NS.A.2
Evaluate: \( -\frac{3}{4} \times (-16) - 19 \)
Answer:
22
Solving Two-Step Linear Equations
7.EE.B.4a
Solve for \( m \): \( -4m + 15 = -25 \)
Answer:
23
Multi-Step Percent Word Problem (Discount & Tax)
7.RP.A.3
A jacket originally priced at \( \$80 \) is on sale for \( 25\% \) off. A sales tax of \( 8\% \) is added to the sale price. What is the final cost?
Answer:
24
Geometry: Area of Circles
7.G.B.4
A circular rug has a radius of \( 7\text{ feet} \). Find its area. (Use \( \pi \approx \frac{22}{7} \) or \( 3.14 \))
Answer:
25
Compound Probability
7.SP.C.8
A bag has \( 4 \) blue marbles and \( 6 \) red marbles. If you pick one marble, replace it, and pick a second marble, what is the probability of picking red both times?
Answer:
Math Milestone Diagnostic Screener Grade Band: 7th Grade Page 5 of 7
Diagnostic Screener
Grade 8 Mathematics
Student:
Section 6: Grade 8 Standards (Exponents, Scientific Notation, Multi-Step Equations, Pythagorean Theorem, Linear Models)
Target Score: _____ / 5
26
Scientific Notation & Exponent Properties
8.EE.A.4
Simplify and write in standard scientific notation: \( \frac{4.8 \times 10^8}{1.6 \times 10^3} \)
Answer:
27
Multi-Step Equations (Variables on Both Sides)
8.EE.C.7b
Solve for \( x \): \( 5(x - 2) = 2x + 11 \)
Answer:
28
Pythagorean Theorem Application
8.G.B.7
A \( 13\text{-foot} \) ladder leans against a vertical wall. The base of the ladder is \( 5\text{ feet} \) away from the wall. How high up the wall does the ladder reach?
Answer:
29
System of Linear Equations
8.EE.C.8b
Solve the system of equations for \( (x, y) \):
\( y = 2x - 1 \)
\( 3x + y = 14 \)
\( x = \text{___}, y = \text{___} \)
30
Linear Modeling & Comparative Rates
8.F.B.4
Gym Plan A costs \( \$30 \) registration plus \( \$25/\text{month} \). Gym Plan B costs \( \$0 \) registration plus \( \$30/\text{month} \). At how many months will both gym plans cost the exact same amount?
Answer:
Math Milestone Diagnostic Screener Grade Band: 8th Grade Page 6 of 7
Teacher & Diagnostic Protocol
Diagnostic Screener Tracking Rubric
Performance Profiling, Grade-Band Mastery & RTI Intervention Placement
Total Score: _____ / 30
Instructional Level: Grade _____
Grade-Band Performance Matrix
| Grade Band | Items | Target Domain Focus | Score | Mastery Status |
|---|
| Grade 3 | 1–5 | Multi-digit subtraction, arrays, basic fractions, 2-step ops | ___ / 5 | 4–5: Mastered |
| Grade 4 | 6–10 | 2-digit mult, long division, like fractions, decimals, area/perim | ___ / 5 | 4–5: Mastered |
| Grade 5 | 11–15 | Unlike fractions, decimal mult, order of ops, prism volume | ___ / 5 | 4–5: Mastered |
| Grade 6 | 16–20 | Fraction division, unit rates, integers/abs value, 1-step eqns | ___ / 5 | 4–5: Mastered |
| Grade 7 | 21–25 | Rational number arithmetic, 2-step eqns, multi-step %, circles | ___ / 5 | 4–5: Mastered |
| Grade 8 | 26–30 | Scientific notation, variables both sides, Pythagorean, systems | ___ / 5 | 4–5: Mastered |
Tier 1: At / Above Level
24–30 Points (80–100%)
Strong foundational calculation and multi-step reasoning across all primary and middle school benchmarks. Ready for grade-level core curriculum and algebraic extension.
Action: Enrichment / On-level pacing
Tier 2: Targeted Support
16–23 Points (53–77%)
Gaps identified in specific grade transitions (commonly fractions in G5 or rational operations in G7). Needs targeted small-group reteaching on flagged bands.
Action: Small group intervention 2x/week
Tier 3: Intensive Support
0–15 Points (<52%)
Significant breakdown in prerequisite arithmetic fluency or conceptual comprehension prior to Grade 5. Immediate foundational intervention required.
Action: High-frequency intensive intervention
Diagnostic Notes & Instructional Action Plan
Identified Strengths & Fluency:
Priority Skill Gaps / Misconceptions:
Evaluator Signature: ___________________________________ Next Progress Review Date: ___________________
Math Milestone Diagnostic Screener Teacher Diagnostic Protocol Page 7 of 7
Math Milestone Answer Key
Teacher Reference & Solutions
Diagnostic Screener Answer Key
Grades 3 & 4 Detailed Solutions, Scoring Standards & Misconception Analysis
Scoring: 1 pt per correct item
Page 1: Questions 1–10
Grade 3 Benchmark Solutions (Items 1–5) 5 Points Total
1
Correct Answer: 353 3.NBT.A.2
Work: \( 742 - 389 = (700 - 300) + (30 - 80) + (12 - 9) = 353 \) with regrouping from hundreds and tens.
Common Misconception: Subtracting smaller digit from larger without regrouping (e.g., \( 742 - 389 \rightarrow 457 \)).
2
Correct Answer: 56 cookies 3.OA.A.3
Work: Equal groups calculation: \( 8 \times 7 = 56 \) total cookies.
Common Misconception: Adding dimensions instead of multiplying (\( 8 + 7 = 15 \)) or skip counting error.
3
Correct Answer: \frac{3}{4} (or \( \frac{3}{4} > \frac{3}{8} \)) 3.NF.A.3
Work: With equal numerators (\( 3 \)), fourths are larger pieces than eighths (\( \frac{3}{4} = \frac{6}{8} > \frac{3}{8} \)).
Common Misconception: Believing \( \frac{3}{8} \) is larger simply because 8 is greater than 4.
4
Correct Answer: 7 3.OA.A.2
Work: Division as inverse of multiplication: \( 56 \div 8 = 7 \) because \( 8 \times 7 = 56 \).
5
Correct Answer: $26 3.OA.D.8
Work: Step 1: \( 4 \times \$6 = \$24 \) spent. Step 2: \( \$50 - \$24 = \$26 \) remaining.
Common Misconception: Stopping after step 1 (\( \$24 \)) or adding \( \$50 + \$24 \).
Grade 4 Benchmark Solutions (Items 6–10) 5 Points Total
6
Correct Answer: 1,692 4.NBT.B.5
Work: \( 47 \times 6 = 282 \); \( 47 \times 30 = 1410 \); \( 282 + 1410 = 1,692 \).
Common Misconception: Forgetting placeholder zero in tens place yielding \( 282 + 141 = 423 \).
7
Correct Answer: 145 R 3 (or \( 145.75 \) / \( 145\frac{3}{4} \)) 4.NBT.B.6
Work: \( 583 \div 4 = 145 \) with remainder \( 3 \) (\( 145 \times 4 = 580 \); \( 583 - 580 = 3 \)).
8
Correct Answer: 4\frac{2}{8} or 4\frac{1}{4} (\( \frac{34}{8} \)) 4.NF.B.3c
Work: \( (2 + 1) + (\frac{3}{8} + \frac{7}{8}) = 3 + \frac{10}{8} = 3 + 1\frac{2}{8} = 4\frac{2}{8} = 4\frac{1}{4} \).
Common Misconception: Adding denominators to get \( 3\frac{10}{16} \).
9
Correct Answer: 4.25 4.NF.C.6
