Rational Operations Review Worksheet
Name:
7th Grade Math • Assessment Day Warm-Up
Date: Class:
10 Minutes Calculator OFF
Do Now: Rational Number Operations Review
Assessment Habits:
1. Determine the sign before solving. • 2. Show your calculations. • 3. Check that your answer makes sense.
1
7.NS.A.2
Complete each statement with positive or negative:
a. Negative \(\times\) Negative \(=\)
b. Positive \(\div\) Negative \(=\)
2
7.NS.A.2.d
What is the decimal equivalent of \(-\frac{3}{8}\)?
A. \(-0.38\)
B. \(-0.375\)
C. \(0.375\)
D. \(-2.\overline{6}\)
3
7.NS.A.2
Evaluate each expression. Show at least 2–3 calculation steps in the workspace provided.
Part A: \(-2.4 \times 3.5\)
Answer:
Part B: \(-\frac{3}{4} \div \frac{1}{2}\)
Answer:
4
7.NS.A.3
A research submarine descends at a constant rate of \(12.5\text{ meters per minute}\) for \(4\text{ minutes}\), and then rises \(8\text{ meters}\).
1. Expression:
2. Solve (show your calculations):
Final Answer (include units):
5
7.NS.A.2
A student evaluated the expression below and made an error:
\(-24 \div (-6) = -4\)
Student Claim: "The quotient is negative because both numbers in the expression are negative."
1. Identify the mistake: What did the student misunderstand?
2. Correct solution: \(-24 \div (-6) =\)
Standard Focus: 7.NS.A.2 • 7.NS.A.3 • Calculator OFF
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Rational Operations Answer Key
Teacher Diagnostic Key & Guide 7th Grade Math • Assessment Day Warm-Up
Do Now: Rational Number Operations • Answer Key
Pre-Assessment Activation • Focus Standards: 7.NS.A.2, 7.NS.A.3 • Calculator OFF • 10 Minutes
Quick-Scan Answer Matrix Target Time: 10 min | 5 Questions
| # | Standard | Correct Answer | Key Misconception Flag |
|---|
| 1 | 7.NS.A.2 | a. positive • b. negative | Conflating addition signs (\(- + - = -\)) with multiplication |
| 2 | 7.NS.A.2.d | B. \(-0.375\) | Writing digits directly (\(-0.38\)) or dropping negative |
| 3 | 7.NS.A.2 | Part A: \(-8.4\) • Part B: \(-\frac{3}{2}\) or \(-1\frac{1}{2}\) | Miscounting decimal places; multiplying without reciprocal |
| 4 | 7.NS.A.3 | \((-12.5)(4) + 8 = -42\text{ meters}\) | Omitting units; adding all values (\(58\text{ m}\)); subtracting rise |
| 5 | 7.NS.A.2 | Mistake: applied addition sign rule; Ans: \(+4\) | Believing "two negatives always make a negative" |
Question 1 • Sign Rules Review (7.NS.A.2)
Fast Confidence Builder
Part a: Negative \(\times\) Negative \(=\) positive
Multiplying by a negative reverses direction on the number line. Reversing twice yields a positive product.
Part b: Positive \(\div\) Negative \(=\) negative
Dividing numbers with different signs always yields a negative quotient: \(\frac{+a}{-b} = -\frac{a}{b}\).
Question 2 • Fraction to Decimal Conversion (7.NS.A.2.d)
Multiple Choice • Key: B
Division Algorithm Steps:
\(3.000 \div 8\)
\(3.0 \div 8 = 0.3\) (remainder \(0.6\))
\(0.60 \div 8 = 0.07\) (remainder \(0.04\))
\(0.040 \div 8 = 0.005\) (remainder \(0\))
Attach negative sign: \(\mathbf{-0.375}\)
Misconception Analysis:
- A (\(-0.38\)): Concatenating numerator and denominator without dividing.
- B (\(-0.375\)): Correct terminating decimal.
- C (\(0.375\)): Dropped negative sign during long division.
- D (\(-2.\overline{6}\)): Inverted fraction \(8 \div 3\) instead of \(3 \div 8\).
Question 3 • Rational Number Operations (7.NS.A.2) • Expanded Workspace
Procedural Fluency • 2–3 Calculation Steps
Part A: \(-2.4 \times 3.5\) \(-8.4\)
Step 1: Multiply absolute values: \(24 \times 35 = 840\)
Step 2: Count decimal places: 1 in \(2.4\) + 1 in \(3.5\) = 2 decimal places \(\rightarrow 8.40\)
Step 3: Apply sign: \((\text{neg}) \times (\text{pos}) = \mathbf{-8.4}\)
Look-for: Student places decimal point 2 places from right, not 1.
Part B: \(-\frac{3}{4} \div \frac{1}{2}\) \(-\frac{3}{2}\) or \(-1\frac{1}{2}\)
Step 1: Multiply by reciprocal of divisor: \(-\frac{3}{4} \times \frac{2}{1}\)
Step 2: Multiply numerators & denominators: \(-\frac{6}{4}\)
Step 3: Simplify: \(-\frac{3}{2}\) or \(-1\frac{1}{2}\) or \(-1.5\)
Look-for: Inverting the second fraction (\(\frac{1}{2} \to \frac{2}{1}\)), not the first.
Rational Number Operations • Pre-Assessment Warm-Up
PAGE 1 OF 2 • TEACHER ANSWER KEY
Teacher Diagnostic Key & Guide Section 2: Deep Dives & Pre-Assessment Protocol
Questions 4 & 5 Solutions • Assessment Day Protocol
Question 4 • Streamlined Submarine Problem (7.NS.A.3)
Expression & Calculation • Units Required
1. Expression:
\((-12.5)(4) + 8\) or \(-(12.5 \times 4) + 8\)
Descent represents a negative rate (\(-12.5\text{ m/min}\)), and rising represents positive addition (\(+8\text{ m}\)).
2. Solution & Final Answer:
\(-12.5 \times 4 = -50\)
\(-50 + 8 = -42\)
Answer: \(-42\text{ meters}\) (or \(42\text{ meters below surface}\))
Scoring & Habit Check: Ensure students include the unit (meters or m). If a student writes \(58\text{ m}\), they added the magnitudes ignoring direction. If they wrote \(-58\text{ m}\), they subtracted the ascent instead of adding.
Question 5 • Streamlined Error Analysis (7.NS.A.2)
Quick Mistake Diagnosis + Correct Solution
1. Identify the Mistake:
The student confused the addition sign rule with the division sign rule. When dividing two numbers with the same sign (two negatives), the quotient is always positive.
2. Correct Solution:
\(-24 \div (-6) = +4\) (or \(4\))
Inverse check: \(4 \times (-6) = -24\), confirming the quotient must be positive.
Pre-Assessment Warm-Up: 10-Minute Confidence & Habit Protocol
Immediate Test Prep
1 Min 0:00 – 1:30: Launch
- • Read the 3 Assessment Habits aloud together.
- • Set a 7-minute timer for silent, independent solving.
- • Calculators completely put away.
2 Min 1:30 – 7:30: Fast Laps
Lap 1 (Signs & Decimals): Check Q1 and Q2. Point to the sign rule for any student marking \(C\) on Q2.
Lap 2 (Workspaces): Ensure students show decimal multiplication alignment on Q3A and reciprocal flip on Q3B.
3 Min 7:30 – 10:00: Rapid Stamp
- • Stamp Q4: Reiterate \(-50 + 8 = -42\text{ m}\). Emphasize putting units on the exam.
- • Stamp Q5: Choral repeat: "Same signs divide to positive." Transition to test immediately with high confidence.
Rational Number Operations • Pre-Assessment Warm-Up
PAGE 2 OF 2 • TEACHER ANSWER KEY
