Signed Fraction Smash

4

Phase 4: Independent Mastery (15 min)

Students transition to Sections B & C independently. Circulate with a green highlighter to mark correct signs first, encouraging instant reinforcement. Use targeted pull-out table for Tier 3 students.

Diagnostic Misconception Analysis & Target Interventions

Tier 3 Support / Scaffolds

• Provide a color-coded Sign Rule Bookmark with \( (-) \times (-) = (+) \) highlighted in green.
• Require students to highlight negative signs with a yellow marker before beginning calculation.
• Use factor trees or pre-printed multiplication charts to support students who struggle with GCFs.

Extension & Depth

• Challenge with 3-factor expressions: \( \left(-\frac{2}{3}\right) \times \left(-\frac{3}{5}\right) \times \left(-\frac{5}{8}\right) \).
• Introduce mixed numbers: require conversion to improper fractions first before applying sign rule.
• Ask students to create their own real-world stock market or temperature scenario involving signed fractions.

Formative Exit Assessment Prompt

Final 4 Minutes

Ask every student to solve on a slip: \( \left(-\frac{5}{6}\right) \times \left(-\frac{9}{10}\right) \).
Check 1: Did they write \(+\)? • Check 2: Did they cross-cancel \(5\) & \(10\) (to \(1\) and \(2\)), and \(9\) & \(6\) (to \(3\) and \(2\))? • Correct: \( +\frac{3}{4} \).

Signed Fraction Intervention Lesson Plan • Tier 2/3 Guide Page 2 of 2

Final Position:

9. Stock Loss Recovery: An investor tracks an asset that loses \( -\frac{5}{2} \) dollars per share. If a fund manager liquidates \( \frac{4}{15} \) of a share, what is the total change in value?

Value Change:

Self-Check Reflection: Circle your confidence level with multiplying signed fractions:

1. Need More Help 2. Getting There 3. I Got This!

Signed Fraction Action Worksheet Page 2 of 2

Alert: Watch for students leaving answer as \(+\frac{30}{300}\) unreduced.

5. \( \frac{7}{8} \times \left(-\frac{16}{21}\right) \) \( -\frac{2}{3} \)

Sign: \( (+) \times (-) = (-) \).
Cross-cancel: \( 7 \) & \( 21 \rightarrow 1 \) & \( 3 \); \( 8 \) & \( 16 \rightarrow 1 \) & \( 2 \).
Multiply: \( -\frac{1 \times 2}{1 \times 3} = \mathbf{-\frac{2}{3}} \).

Alert: Ensure negative sign is not dropped during cross-cancel.

6. \( (-6) \times \left(-\frac{2}{9}\right) \) \( +\frac{4}{3} \text{ or } 1\frac{1}{3} \)

Rewrite: \( -\frac{6}{1} \times \left(-\frac{2}{9}\right) \). Sign: \( (-) \times (-) = (+) \).
Cross-cancel: \( 6 \) & \( 9 \) by factor \( 3 \rightarrow 2 \) & \( 3 \).
Multiply: \( +\frac{2 \times 2}{1 \times 3} = \mathbf{+\frac{4}{3} \text{ or } 1\frac{1}{3}} \).

Alert: Students who don't write \(6/1\) often multiply bottom by 6!

7. \( \left(-\frac{3}{10}\right) \times \frac{5}{18} \) \( -\frac{1}{12} \)

Sign: \( (-) \times (+) = (-) \).
Cross-cancel: \( 3 \) & \( 18 \rightarrow 1 \) & \( 6 \); \( 5 \) & \( 10 \rightarrow 1 \) & \( 2 \).
Multiply: \( -\frac{1 \times 1}{2 \times 6} = \mathbf{-\frac{1}{12}} \).

Alert: Common arithmetic slip is writing denominator as \(2 + 6 = 8\).

4 Part 4: Real-World Scenarios Solutions (2 pts each)

Contextual Interpretation

8. Deep-Sea Drone Descent \( -\frac{1}{2} \text{ km} \text{ (or } 0.5 \text{ km below sea level)} \)

Set up expression: \( \text{Rate} \times \text{Time} = \left(-\frac{3}{4}\right) \times \frac{2}{3} \).
Sign check: Negative rate \(\times\) positive time = negative position relative to surface.
Work: Cross-cancel \(3\) and \(3\) (\(\rightarrow 1\)), \(2\) and \(4\) (\(\rightarrow 1\) and \(2\)). Result = \( -\frac{1}{2} \) km.

9. Stock Loss Recovery Calculation \( -\$\frac{2}{3} \text{ (or a loss of } 67\text{ cents)} \)

Set up expression: \( \left(-\frac{5}{2}\right) \times \frac{4}{15} \).
Sign check: \( (-) \times (+) = (-) \).
Work: Cross-cancel \(5\) and \(15\) (\(\div 5 \rightarrow 1\) and \(3\)); \(2\) and \(4\) (\(\div 2 \rightarrow 1\) and \(2\)). Result = \( -\frac{2}{3} \) dollars.

Remediation Next-Steps Guide

If student scores 0–2 on Part 1: Halt fraction multiplication. Re-teach sign rules using 2-color counters or number line vectors before moving forward.
If student scores 0–2 on Part 2: Student lacks cross-canceling fluency. Pair with a multiplication table and enforce the factor-matching routine.

Signed Fraction Action Master Key Page 2 of 2

Triple Threat Practice • Master Answer Key Tier 2/3 Extension Key

Page 2 Record

Player 1 Scratch Zone Record Tile # & Work

Tile #: ___ Sign: [   ]

Tile #: ___ Sign: [   ]

Tile #: ___ Sign: [   ]

Player 2 Scratch Zone Record Tile # & Work

Tile #: ___ Sign: [   ]

Tile #: ___ Sign: [   ]

Tile #: ___ Sign: [   ]

Referee Verification Station (Partner checks this ONLY after partner states their answer!) Self-Checking Station

#1 \( +\frac{2}{5} \)

#2 \( -\frac{3}{5} \)

#3 \( +\frac{2}{5} \)

#4 \( +\frac{3}{2} \text{ or } 1\frac{1}{2} \)

#5 \( -\frac{1}{4} \)

#6 \( +\frac{1}{6} \)

#7 \( -\frac{1}{2} \)

#8 \( +\frac{1}{6} \)

#9 \( -\frac{2}{5} \)

#10 \( +\frac{1}{4} \)

#11 \( -6 \)

#12 \( +\frac{1}{10} \)

#13 \( -\frac{1}{6} \)

#14 \( +\frac{1}{6} \)

#15 \( -\frac{1}{4} \)

#16 \( +\frac{3}{10} \)

Signed Fraction Duel Game • Record & Verification Intervention Station Activity