Fraction Strategy Anchor Chart Fraction Strategy Anchor Chart
Computation with Unlike Denominators • IEP Goal Support
Goal Mastery Target 80% Accuracy (4/5)
The 4-Step "LEAP" Strategy
L Step 1
List Multiples
Find the Least Common Denominator (LCD) by listing multiples.
3: 3, 6, 9, 12 12 , 16
E Step 2
Equivalent Forms
Multiply numerator & denominator by the same number.
\(\frac{2 \times 4}{3 \times 4} = \frac{8}{12}\)
A Step 3
Add / Subtract
Operate numerators only! Keep the denominator same.
\(\frac{8}{12} + \frac{3}{12} = \frac{11}{12}\)
P Step 4
Polish / Simplify
Divide by common factors or convert improper fractions.
\(\frac{6 \div 3}{9 \div 3} = \frac{2}{3}\)
Modeled Worked Examples
Addition Example \(\frac{1}{2} + \frac{2}{5}\)
Denominators are 2 and 5 . LCD = 10 .
Convert both to denominator of 10:
\(\frac{1 \times 5}{2 \times 5} = \frac{5}{10}\) \(\frac{2 \times 2}{5 \times 2} = \frac{4}{10}\)
Add numerators: \(\frac{5 + 4}{10} = \frac{9}{10}\)
Final answer is in simplest form: \(\frac{9}{10}\)
Subtraction Example \(\frac{5}{6} - \frac{1}{3}\)
Denominators are 6 and 3 . LCD = 6 .
Convert \(\frac{1}{3}\) (since 6 is already the denominator of \(\frac{5}{6}\)):
\(\frac{1 \times 2}{3 \times 2} = \frac{2}{6}\)
Subtract numerators: \(\frac{5 - 2}{6} = \frac{3}{6}\)
Simplify \(\frac{3 \div 3}{6 \div 3} = \) \(\frac{1}{2}\)
Denominator Danger Zone!
NEVER Do This:
\(\frac{1}{3} + \frac{1}{4} \neq \frac{1 + 1}{3 + 4} = \frac{2}{7}\)
Never add or subtract bottom numbers!
ALWAYS Do This:
\(\frac{4}{12} + \frac{3}{12} = \frac{4 + 3}{12} = \frac{7}{12}\)
Make denominators match first, then keep them!
Student Independent Self-Monitoring Checklist Use on every problem before writing your final answer!
1. Found common denominator
2. Multiplied top and bottom
3. Kept denominator identical
4. Simplified final fraction
Fraction Operations Toolkit • Instructional Anchor Chart Page 1 of 1
Faded Strategy Practice Worksheet Faded Strategy Practice Worksheet
Adding & Subtracting Fractions with Unlike Denominators • Gradual Release
Name:
Date:
1 Level 1: Full Strategy Scaffold (Step-by-Step Prompts) Follow each guided step
1. Compute: \(\frac{1}{4} + \frac{2}{3}\)
Denominators: 4 and 3
Step 1: Multiples
4: 4, 8, ___, 16
3: 3, 6, 9, ___
LCD = ______
Step 2: Equivalent
\(\frac{1 \times \square}{4 \times \square} = \frac{\square}{12}\)
\(\frac{2 \times \square}{3 \times \square} = \frac{\square}{12}\)
Step 3 & 4: Add
\(\frac{\square}{12} + \frac{\square}{12} = \frac{\square}{12}\)
Ans:
2. Compute: \(\frac{5}{6} - \frac{1}{2}\)
Denominators: 6 and 2
Step 1: Multiples
6: 6, 12, 18
2: 2, 4, ___, 8
LCD = ______
Step 2: Equivalent
\(\frac{5}{6} = \frac{5}{6}\)
\(\frac{1 \times \square}{2 \times \square} = \frac{\square}{6}\)
Step 3 & 4: Subtract
\(\frac{5}{6} - \frac{\square}{6} = \frac{\square}{6} = \frac{\square}{\square}\)
Ans:
2 Level 2: Partial Prompting (Faded Guidance) Write LCD and show your steps
3. Compute: \(\frac{3}{8} + \frac{1}{4}\) LCD: ______
Simplified
Ans:
4. Compute: \(\frac{4}{5} - \frac{3}{10}\) LCD: ______
Simplified
Ans:
Fraction Operations Toolkit • Faded Strategy Practice (Scaffolded) Page 1 of 2
Faded Strategy Practice Worksheet
Level 3: Independent Strategy Execution • IEP Goal Assessment
Name:
Date:
3 Level 3: Independent Practice (Unprompted Work)
Use your taught strategies independently. Show all computation steps in the boxes below.
Prompt Level Independent
5. Compute: \(\frac{2}{3} + \frac{1}{5}\)
Workspace (Show all steps):
Simplified
Ans:
6. Compute: \(\frac{7}{8} - \frac{1}{2}\)
Workspace (Show all steps):
Simplified
Ans:
7. Compute: \(\frac{5}{6} - \frac{3}{4}\)
Workspace (Show all steps):
Simplified
Ans:
8. Compute: \(\frac{3}{10} + \frac{2}{5}\)
Progress Monitoring Probes Tracker Progress Monitoring Probes
Fraction Computation (Unlike Denominators) • Probes 1 & 2
Student:
Target: ≥80% (4/5)
Probe 1 Date:
\(\frac{1}{3} + \frac{2}{5}\) LCD: ___
Ans:
\(\frac{3}{4} - \frac{1}{6}\) LCD: ___
Ans:
\(\frac{2}{7} + \frac{1}{2}\) LCD: ___
Ans:
\(\frac{7}{10} - \frac{2}{5}\) LCD: ___
Ans:
\(\frac{3}{8} + \frac{1}{3}\) LCD: ___
Ans:
Score: ____ / 5 (____%) Met (≥80%): [ ] Y [ ] N
Prompt: [ ] Ind [ ] Cue Error: [ ] LCD [ ] Equiv [ ] Fact
Probe 2 Date:
\(\frac{2}{3} - \frac{1}{4}\) LCD: ___
Ans:
\(\frac{1}{6} + \frac{3}{8}\) LCD: ___
Ans:
\(\frac{4}{5} - \frac{1}{2}\) LCD: ___
Ans:
\(\frac{3}{10} + \frac{1}{2}\) LCD: ___
Ans:
\(\frac{5}{6} - \frac{2}{3}\) LCD: ___
Ans:
Score: ____ / 5 (____%) Met (≥80%): [ ] Y [ ] N
Prompt: [ ] Ind [ ] Cue Error: [ ] LCD [ ] Equiv [ ] Fact
Fraction Operations Toolkit • Progress Monitoring Assessment Suite Page 1 of 2
Progress Monitoring Probes & Log
Fraction Computation • Probes 3 & 4 + Cumulative Tracker
Student:
Target: ≥80% (4/5)
Probe 3 Date:
\(\frac{1}{2} + \frac{3}{7}\) LCD: ___
Ans:
\(\frac{5}{8} - \frac{1}{4}\) LCD: ___
Ans:
\(\frac{2}{9} + \frac{1}{3}\) LCD: ___
Ans:
\(\frac{7}{12} - \frac{1}{3}\) LCD: ___
Ans:
\(\frac{3}{5} + \frac{1}{4}\) LCD: ___
Ans:
Score: ____ / 5 (____%) Met: [ ] Y [ ] N
Probe 4 Date:
\(\frac{3}{4} - \frac{2}{5}\) LCD: ___
Ans:
\(\frac{1}{6} + \frac{2}{3}\) LCD: ___
Ans:
\(\frac{5}{6} - \frac{1}{2}\) LCD: ___
Computation Scoring Guide Teacher Key KEY
Scoring Guide & Solutions
Faded Practice Worksheet Solutions • Levels 1, 2, and 3
Teacher Administration IEP Goal Master Key
Level 1: Full Scaffold Solutions
Problem 1: \(\frac{1}{4} + \frac{2}{3}\) Answer: \(\frac{11}{12}\)
Step 1 (LCD): Multiples of 4 (4, 8, 12) & 3 (3, 6, 9, 12). LCD = 12 .
Step 2 (Equiv): \(\frac{1 \times 3}{4 \times 3} = \frac{3}{12}\) and \(\frac{2 \times 4}{3 \times 4} = \frac{8}{12}\)
Step 3 (Add): \(\frac{3}{12} + \frac{8}{12} = \frac{11}{12}\)
Step 4 (Simplify): \(\frac{11}{12}\) is in simplest form (11 is prime).
Problem 2: \(\frac{5}{6} - \frac{1}{2}\) Answer: \(\frac{1}{3}\) (\(\frac{2}{6}\))
Step 1 (LCD): Multiples of 6 (6, 12) & 2 (2, 4, 6). LCD = 6 .
Step 2 (Equiv): \(\frac{5}{6} = \frac{5}{6}\) and \(\frac{1 \times 3}{2 \times 3} = \frac{3}{6}\)
Step 3 (Subtract): \(\frac{5}{6} - \frac{3}{6} = \frac{2}{6}\)
Step 4 (Simplify): Divide by 2: \(\frac{2 \div 2}{6 \div 2} = \mathbf{\frac{1}{3}}\)
Level 2: Partial Prompting Solutions
Problem 3: \(\frac{3}{8} + \frac{1}{4}\) Answer: \(\frac{5}{8}\)
LCD: 8. Only convert second fraction.
Work: \(\frac{3}{8} + \frac{1 \times 2}{4 \times 2} = \frac{3}{8} + \frac{2}{8} = \frac{5}{8}\)
Notes: Common error is multiplying both fractions to get 32. Accept \(\frac{20}{32}\) if simplified to \(\frac{5}{8}\).
Problem 4: \(\frac{4}{5} - \frac{3}{10}\) Answer: \(\frac{1}{2}\) (\(\frac{5}{10}\))
LCD: 10. Convert first fraction.
Work: \(\frac{4 \times 2}{5 \times 2} - \frac{3}{10} = \frac{8}{10} - \frac{3}{10} = \frac{5}{10}\)
Simplify: \(\frac{5 \div 5}{10 \div 5} = \mathbf{\frac{1}{2}}\). Full credit requires simplest form.
Level 3: Independent Practice Solutions (Problems 5-8)
Problem 5: \(\frac{2}{3} + \frac{1}{5}\) \(\frac{13}{15}\)
LCD: 15. \(\frac{10}{15} + \frac{3}{15} = \frac{13}{15}\). Prime numerator; cannot simplify.
Problem 6: \(\frac{7}{8} - \frac{1}{2}\) \(\frac{3}{8}\)
LCD: 8. \(\frac{7}{8} - \frac{4}{8} = \frac{3}{8}\). Simplest form.
Problem 7: \(\frac{5}{6} - \frac{3}{4}\) \(\frac{1}{12}\)
