Fraction Fusion Worksheet
Fraction Fusion
Drafting Lab • Visual Models & Scaffolded Thinking
Grade 8 Math MODULE 04
Name:
Date:
Period:
Score:
Protocol: 1. Find LCD • 2. Scale Numerators • 3. Add & Apply Integer Rules • 4. Simplify completely
1 Core Construction & Visual Tape Models
Use the scaffold hints and visual models to find the common denominator.
01 LCD: _____
\( \frac{2}{3} + \frac{1}{6} \)
Visual Partition Tape: Shade combined sixths
\( \frac{2}{3}=\frac{4}{6} \)
\( \frac{1}{6} \)
Total:
Hint: 6 is a multiple of 3. Multiply \( \frac{2}{3} \) by \( \frac{2}{2} \) to get sixths!
Answer:
02 LCD: _____
\( \frac{3}{8} + \frac{5}{12} \)
Common 24-Unit Partition:
\( \frac{3}{8} \times \frac{3}{3} = \frac{9}{24} \)
\( \frac{5}{12} \times \frac{2}{2} = \frac{10}{24} \)
Hint: Multiples of 12: 12, 24, 36... The smallest that 8 divides is 24.
Answer:
03 LCD: _____
\( \frac{4}{7} + \frac{2}{5} \)
Hint: 7 and 5 are prime! Multiply them directly: \(7 \times 5 = 35\).
Answer:
04 LCD: _____
\( \frac{7}{15} + \frac{3}{10} \)
Hint: Count multiples of 15: 15, 30... 30 works for 10 and 15!
Answer:
2 Signed Rationals & Number Line Models
Use integer sign scaffolds to determine whether the sum is positive or negative.
05 LCD: 12
\( -\frac{3}{4} + \frac{5}{6} \)
Vector: Start at \(-\frac{9}{12}\), move right \(+\frac{10}{12}\)
0
-\(\frac{9}{12}\)
+\(\frac{1}{12}\)
Hint: Numerators: \(-9 + 10 = +1\). Since \(10 > 9\), answer is positive!
Answer:
06 LCD: _____
\( \frac{2}{9} + \left(-\frac{5}{12}\right) \)
Hint: LCD is 36. Numerators: \(8 + (-15)\). Since \(|-15| > 8\), sum is negative!
Answer:
07 LCD: _____
\( -\frac{7}{10} + \left(-\frac{4}{15}\right) \)
Hint: Two negatives? Add absolute values and attach the negative sign!
Answer:
08 LCD: _____
\( -\frac{5}{8} + \frac{11}{16} \)
Hint: 16 is divisible by 8! Only scale \( -\frac{5}{8} \) by \( \frac{2}{2} \).
Answer:
Fraction Fusion • 8th Grade Mathematics Turn over for Part 3, 4 & 5 Page 1 of 2
Part II: Mixed Assembly & Blueprint Schematics
Real-World Dimensions, Multi-Term Sums & Scaffolded Engineering
Name:
3 Mixed Numbers & Multi-Term Sums
Use the scaffold tips to regroup improper fractions.
09 Mixed Number
\( 2\frac{1}{3} + 3\frac{3}{4} \)
Scaffold: Whole: \(2+3=5\). Fractions: \(\frac{13}{12} = 1\frac{1}{12}\). Combine \(5 + 1\frac{1}{12}\)!
Answer:
10 Signed Mixed
\( 4\frac{5}{8} + \left(-1\frac{1}{6}\right) \)
Scaffold: Adding negative is subtracting: \(4\frac{15}{24} - 1\frac{4}{24}\). Subtract wholes & fractions!
Answer:
11 Negative Mixed
\( -3\frac{2}{5} + \left(-2\frac{7}{10}\right) \)
Scaffold: Negative outside: \( -(3\frac{4}{10} + 2\frac{7}{10}) \). Regroup \( \frac{11}{10} \) carefully!
Answer:
12 Three Fractions
\( \frac{1}{2} + \frac{2}{3} + \frac{3}{4} \)
Scaffold: Common multiple for all 3: {2, 3, 4}. LCD is 12! Convert all three fractions.
Answer:
4 Blueprint Applications & Schematics
Use the schematics and step prompts to compute totals.
Structural 13 Architectural Support Truss
Calculate total perimeter \(P\) of the support truss. Express as a simplified mixed number with units.
Guide: \(P = 3\frac{3}{8} + 2\frac{5}{6} + 4\frac{1}{4}\). Common denominator for 8, 6, and 4 is 24.
3⅜ m 2⅚ m 4¼ m
P =
m
Fluids 14 Hydraulic Arm Fluid Reservoir
Mix \(\frac{7}{12}\) L of lubricant with \(\frac{9}{16}\) L of hydraulic blend. Find total volume \(V\).
Guide: List multiples of 16 (16, 32, 48...) to find LCM of 12 and 16. Convert to 48ths.
Fluid Fill Levels:
⁷⁄₁₂ L
⁹⁄₁₆ L
V =
L
5 Quality Control: Error Analysis & Visual Proof
Inspect & Correct
Inspector Report 15: A technician claimed: \( \frac{3}{5} + \frac{2}{7} = \frac{3+2}{5+7} = \frac{5}{12} \).
Visual Magnitude Check: Compare starting fraction vs. claimed sum
Start: \( \frac{3}{5} = 60\% \)
Claim: \( \frac{5}{12} \approx 41.7\% \)
Explain why this proves Marcus is wrong:
Correct Computation:
Correct Sum:
Fraction Fusion • 8th Grade Mathematics Completed Blueprint Verification Page 2 of 2
Fraction Fusion Answer Key
Fraction Fusion
Answer Key
Teacher Instructional Guide, Visual Solutions & Scaffold Support
Standard 8.NS.A / 7.NS.A 20 PTS TOTAL
Scaffold Tier 1 (Visuals): Prompt: "Count shaded sub-units to see common partition size."
Scaffold Tier 2 (LCD): Prompt: "List multiples of larger denominator until divisible."
Scaffold Tier 3 (Signs): Prompt: "Which magnitude is greater? The sum inherits that sign."
1 Part 1: Unlike Denominators & Visual Tape Solutions
4 Problems • 4 Points
01 LCD = 6
\( \frac{2}{3} + \frac{1}{6} \)
Key Model: 4 sixths + 1 sixth = 5 sixths
Shaded:
\( \frac{4}{6} + \frac{1}{6} = \frac{5}{6} \) (5 of 6 shaded)
Student shades 5 parts Ans: \( \frac{5}{6} \)
02 LCD = 24
\( \frac{3}{8} + \frac{5}{12} \)
24-Unit Partition Sum: \( \frac{3 \times 3}{24} = \frac{9}{24} \) & \( \frac{5 \times 2}{24} = \frac{10}{24} \) \( \frac{9}{24} + \frac{10}{24} = \frac{19}{24} \)
19 is prime Ans: \( \frac{19}{24} \)
03 LCD = 35
\( \frac{4}{7} + \frac{2}{5} \)
\( \frac{4 \times 5}{35} + \frac{2 \times 7}{35} = \frac{20}{35} + \frac{14}{35} = \frac{34}{35} \)
Coprime denominators Ans: \( \frac{34}{35} \)
04 LCD = 30
\( \frac{7}{15} + \frac{3}{10} \)
\( \frac{7 \times 2}{30} + \frac{3 \times 3}{30} = \frac{14}{30} + \frac{9}{30} = \frac{23}{30} \)
23 is prime Ans: \( \frac{23}{30} \)
2 Part 2: Signed Rational Numbers & Vector Solutions
4 Problems • 4 Points
05 LCD = 12
\( -\frac{3}{4} + \frac{5}{6} \)
Vector: \(-\frac{9}{12} \xrightarrow{+ \frac{10}{12}} +\frac{1}{12}\)
Positive result Ans: \( \frac{1}{12} \)
06 LCD = 36
\( \frac{2}{9} + \left(-\frac{5}{12}\right) \)
\( \frac{8}{36} + \left(-\frac{15}{36}\right) = \frac{8 - 15}{36} = -\frac{7}{36} \)
\(|-15| > 8 \rightarrow -\) Ans: \( -\frac{7}{36} \)
07 LCD = 30
\( -\frac{7}{10} + \left(-\frac{4}{15}\right) \)
\( -\frac{21}{30} + \left(-\frac{8}{30}\right) = \frac{-21 - 8}{30} = -\frac{29}{30} \)
Both negative addends Ans: \( -\frac{29}{30} \)
08 LCD = 16
\( -\frac{5}{8} + \frac{11}{16} \)
\( -\frac{10}{16} + \frac{11}{16} = \frac{-10 + 11}{16} = \frac{1}{16} \)
Only scale first term Ans: \( \frac{1}{16} \)
Fraction Fusion Teacher Guide • Page 1 Visual Solutions See Reverse for Parts 3, 4 & 5 Page 1 of 2
