Math Spark Diagnostic

Section C: Fractions & Decimals Arithmetic

Q7

\(\frac{2}{3} + \frac{1}{4}\) \(\frac{11}{12}\)

LCD = 12. Equivalents: \(\frac{8}{12} + \frac{3}{12} = \frac{11}{12}\).

Grading: 10 pts: Correct simplified sum with common denominator shown. 5 pts: Conceptual common denominator but math error.

Q8

Half of \(\frac{3}{4}\) cup brown sugar \(\frac{3}{8}\) cup

Calculation: \(\frac{3}{4} \times \frac{1}{2} = \frac{3 \times 1}{4 \times 2} = \frac{3}{8}\).

Grading: 10 pts: \(\frac{3}{8}\) with multiplication steps. 5 pts: Set up correctly but calculated incorrect denominator/numerator.

Q9

14.85 + 7.3 22.15

Requires vertical alignment: \(14.85 + 7.30 = 22.15\).

Grading: 10 pts: 22.15 with decimals aligned. 5 pts: Correct addition but misaligned digits (getting 15.58).

Q10

1.25 ÷ 5 0.25

Long division: \(1.25 \div 5\). Aligning decimal upwards yields \(0.25\) (not \(2.5\) or \(25\)).

Grading: 10 pts: 0.25 with proper long division shown. 5 pts: Correct digits (25) but decimal error.

D

Section D: Level 5 Geometry Extension

Q11

Coordinate plotting for Point A (2, 3)

Point A is plotted 2 units right on the x-axis and 3 units up on the y-axis.

Grading: 10 pts: Identifies (2, 3). 5 pts: Reverses coordinates (writes (3, 2)).

Q12

Rectangular prism volume: 5 cm × 3 cm × 4 cm 60 cm3

Formula: \(V = l \times w \times h = 5 \times 3 \times 4 = 15 \times 4 = 60\).

Grading: 10 pts: 60 with complete multiplication shown. 6 pts: Correct formula setup but calculation error.

Grade 6 Math Diagnostic Readiness Suite — Answer Key Page 2 of 3

Teacher Resource Continued... Section E Solutions & Summary

E

Section E: Level 6 Core Readiness

Q13

Ratio: 3 blue marbles to 8 total

A: 3 to 8 B: 3:8 C: 3/8

Critical transition to ratios. Student must add blue (3) + red (5) to find the correct total of 8.

Grading: 10 pts: All 3 representations correct. 5 pts: Wrote 3 to 5 (a part-to-part ratio instead of part-to-whole).

Q14

Unit rate: 120 miles in 2 hours 60 mph  or  60 miles/hour

Calculation: \(\frac{120 \text{ miles}}{2 \text{ hours}} = 60 \text{ miles/hour}\).

Grading: 10 pts: 60 with division setup. 5 pts: Division is set up but calculated incorrectly.

Q15

Scenario Integers (Climbing & Diving)

A: +150 (or 150) B: -40

Introduces positive and negative numbers. Below sea level represents a negative integer.

Grading: 10 pts: Both integers correct. 5 pts: Only one integer correct (or missed the negative sign).

Q16

Evaluate \(3x - 5\) when \(x = 4\) 7

Substitution steps: \(3(4) - 5 = 12 - 5 = 7\).

Grading: 10 pts: 7 with substitution steps shown. 5 pts: Correct substitution but missed final subtraction (e.g. gets 12).

Q17

Solve equation \(p + 8 = 15\) p = 7

Subtracting 8 from both sides of the equation isolates the variable: \(p = 15 - 8 = 7\).

Grading: 10 pts: p = 7 with variable isolation shown. 6 pts: Mental solution without showing algebraic steps.

📊 Quick Diagnostic Scaling

140 - 170 Points Exceeding Prereq Readiness

100 - 130 Points Target Level (Pacing Recommended)

Below 100 Points Requires Core Remediation

Grade 6 Math Diagnostic Readiness Suite — Answer Key Page 3 of 3

Grade 6 Math Diagnostic Readiness Suite — Skill Tracker Page 1 of 2

Student Tracking Grid Continued... Classroom Performance Matrix

2. Student Mastery Tracking Grid (17 Questions)

Mark check (✓) if correct; circle question number if student requires intervention.

📈 Core Remediation Strategy Plan

• If students miss Q1–Q3: Conduct a 15-minute sequence review on PEMDAS brackets and variable patterns.
• If students miss Q4–Q6: Provide sliding decimal multiplier visual cards to practice powers-of-10 placement.
• If students miss Q7–Q10: Set up a small-group visual fraction-strip workspace to reinforce LCD equivalence.
• If students miss Q11–Q12: Use building-block manipulation activities to build a base for 3D coordinate graphing.
• If students miss Q13–Q17: Dedicate the first core 6th-grade math week to ratio representations and simple algebraic balance equations.

Grade 6 Math Diagnostic Readiness Suite — Skill Tracker Page 2 of 2