| 2 pts |
| 7 | 12 supports, |
| 0 ft left (none) | \( 9\frac{3}{5} \div \frac{4}{5} = \frac{48}{5} \div \frac{4}{5} = \frac{48}{4} = 12 \) complete supports exactly. Remainder is \(0\text{ ft}\). (2 pts for 12 supports, 1 pt for recognizing zero remainder). | 3 pts |
Baseline Screener Teacher Scoring & Diagnostic Protocol • Part 1 Page 1 of 2
Baseline Screener: Scoring Guide • Part 2
Domains 3 & 4 Master Key
DOMAINS 3 & 4: INTEGERS & NUMERICAL REASONING (15 Points Total) CCSS: 6.NS.C.5, 6.NS.C.7, 6.EE.A.1, 6.NS.B.4
| Item | Correct Answer | Scoring Breakdown & Criteria | Points |
|---|---|---|---|
| 8 | A=-3.5, B=2.5, C=-1, D=4 | 0.5 pt per correct point. Point A halfway between -3 and -4; B halfway between 2 and 3; C on -1; D on 4. | 2 pts |
| 9 | a) < b) = c) < d) < | 0.5 pt each. Note c: \( | -9.5 |
| 10 | -213 m; Distance below sea surface | 1 pt for \(-145 - 68 = -213\text{ m}\). 1 pt for explaining absolute value \( | -213 |
| 11 | a) 64 b) 8/27 | 1 pt for \(4 \times 4 \times 4 = 64\). 1 pt for \( \frac{2 \times 2 \times 2}{3 \times 3 \times 3} = \frac{8}{27} \). | 2 pts |
| 12 | Value = 14 | Steps: \(2^4 = 16 \rightarrow (16-7) = 9 \rightarrow 3 \times 9 = 27 \rightarrow 27 \div 3 = 9 \rightarrow 5 + 9 = 14\). (1 pt exponent/parenthesis, 1 pt left-to-right operations). | 2 pts |
| 13 | GCF = 21; | ||
| 21(2 + 3) | 0.5 pt for identifying \(\text{GCF}=21\). 1 pt for expressing as \(21(2+3)\). (Accept \(7(6+9)\) or \(3(14+21)\) for 0.5 partial credit if non-greatest factor). | 1.5 pts | |
| 14 | Sometimes true; | ||
| Valid counterexample | 0.5 pt for "Sometimes". 1 pt for valid counterexample (e.g., dividing by an improper fraction like \(8 \div \frac{4}{2} = 4 < 8\) or dividing negative numbers). | 1.5 pts |
DIAGNOSTIC ERROR ANALYSIS & MISCONCEPTION MATRIX
Intervention Prescription
| Common Student Error | Underlying Mathematical Misconception | Targeted Instructional Remedy |
|---|---|---|
| Answer 598.0 in Item 2 | Counts decimal places only in one factor rather than total decimal places across factors (\(1 + 2 = 3\)). | Area model decomposition & fraction conversion (\(\frac{184}{10} \times \frac{325}{100} = \frac{59800}{1000}\)). |
| Inverts first fraction in Item 6 | Rote memorization of "flip" without understanding divisor represents group size ("how many groups of divisor fit in dividend"). | Measurement division storytelling and bar models before re-introducing reciprocal algorithm. |
| Claims \(-14 > -8\) in Item 9 | Applies whole number magnitude rules to negative values without spatial reference to zero. | Vertical thermometer number lines and debt/asset analogies (more negative is further from zero to the left). |
| Multiplies base by exponent (\(4^3 = 12\)) | Confuses repeated addition (multiplication) with repeated multiplication (exponentiation). | Expanded form scaffolding: require student to write out \(4 \times 4 \times 4\) before evaluating product. |
Baseline Screener Teacher Scoring & Diagnostic Protocol • Part 2 Page 2 of 2
b) \(|-24|\) \(|-19|\)
1 pt per symbol
7. Elevation Difference 2 pts
A desert basin is at \(-86\text{ m}\). A mountain ridge rises to \(412\text{ m}\). Find the elevation difference between them.
Difference:
8. Order of Operations 2 pts
Evaluate: \( 3^3 - 2 \times (14 - 8) + 5 \)
Answer:
6th Grade Mathematics Bi-Weekly Monitoring • Form B Page 2 of 3
Recurring Progress Monitor • Form C
Score ____ / 16 pts
Name:
Date:
Administered: Weeks 6–7
1. Decimal Computation 2 pts
Evaluate: \( 73.48 - 29.85 + 18.7 \)
Ans:
2. Decimal Multiplication 2 pts
Compute: \( 19.2 \times 4.5 \)
Ans:
3. Decimal Division 2 pts
Divide: \( 67.2 \div 2.1 \)
Ans:
4. Fraction Division 2 pts
Solve: \( \frac{7}{8} \div \frac{1}{4} \)
Ans:
5. Mixed Fraction Division 2 pts
Solve: \( 3\frac{1}{3} \div 1\frac{2}{3} \)
Ans:
6. Integers & Exponents 6 pts
a) \(-6.5\) \(-6.2\)
b) \( 2^4 + (21 - 3^2) \div 4 = \)
Color the bar up to your score on each check!
Mastery Benchmark (80%)
%
Baseline Week 1
%
Probe A Weeks 2–3
%
Probe B Weeks 4–5
%
Probe C Weeks 6–7
Personal Math Goal: Reach 80%+ on Probe C My Reflection: I improved most in:
6th Grade Mathematics Bi-Weekly Monitoring • Form C & Progress Graph Page 3 of 3
ROI = (Score_Latest − Score_Baseline) ÷ Weeks_Elapsed
Expected Core Growth: +0.50 to +0.75 pt/wk Targeted Intervention ROI: +1.00+ pt/wk
PROGRESS MONITORING DECISION RULES (AFTER PROBE C) Dual-Discrepancy Standard
Trajectory: Mastered
Data: Score \(\ge 13/16\) (80%+) on two consecutive probes, \(\text{ROI} \ge 0.75\).
Action: Fade intervention; return to Tier 1 core instruction with bi-monthly check.
Trajectory: Progressing
Data: Score 10–12/16 (60–79%) with positive growth (\(\text{ROI} \ge 0.5\)).
Action: Maintain current Tier 2 small group focus for 3 additional monitoring cycles.
Trajectory: Flat / At Risk
Data: Score \(< 10/16\) (<60%) or stagnant \(\text{ROI} < 0.35\).
Action: Intensify to Tier 3 (reduce group to 1:3 ratio, increase to 4x weekly, switch tools).
TARGETED SKILL INTERVENTION MENU
Concrete-Representational-Abstract (CRA)
Decimal Multi-Digit Computation
Use 10x10 base-ten grids to model hundredths products. Pair long division with money/base-ten currency manipulatives to preserve place value understanding before paper algorithms.
Fraction & Rational Division
Begin every intervention session with fraction strip or Cuisenaire rod measurement scenarios ("How many \(\frac{1}{4}\) rods fit into \(\frac{3}{2}\)?"). Avoid naked algorithm until student verbally justifies the reciprocal relationship.
Integers & Elevation/Value
Utilize vertical thermometer charts and two-color counter zero-pair models. Emphasize that absolute value measures scalar distance from zero on a number line, which is always non-negative.
Order of Operations & Powers
Implement the "Pyramid of Operations" visual organizer (grouping \(\rightarrow\) exponents \(\rightarrow\) multiplication/division from left to right \(\rightarrow\) addition/subtraction). Have students physically highlight operations before calculating.
Bi-Weekly Progress Monitoring Teacher Guide • MTSS Decision Rules Page 2 of 2
