Misconception Alert: Students stopping at \(3\frac{22}{15}\). Remediation Prompt: "Look at \(\frac{22}{15}\). Is that more than 1 whole? How many whole groups of 15 are in 22? Where does that extra whole go?"
Mixed Number Fusion • Teacher Answer Key (Page 1 of 2) Confidential • For Educator Use Only
Independent Practice & Application Solutions
TOTAL POINTS: 15 PTS
1 pt for correct equivalent fractions, 1 pt for final simplified sum
3 \(3\frac{1}{6} + 4\frac{2}{3}\)
LCD = 6
Rewrite: \(3\frac{1}{6} + 4\frac{4}{6}\)
Wholes: \(3 + 4 = 7\)
Fractions: \(\frac{1}{6} + \frac{4}{6} = \frac{5}{6}\)
No regrouping needed (\(\frac{5}{6} < 1\))
Answer: \(7\frac{5}{6}\)
4 \(2\frac{3}{8} + 1\frac{3}{4}\)
LCD = 8
Rewrite: \(2\frac{3}{8} + 1\frac{6}{8}\)
Wholes: \(2 + 1 = 3\), Fractions: \(\frac{9}{8}\)
Regroup: \(\frac{9}{8} = 1\frac{1}{8}\)
Sum: \(3 + 1\frac{1}{8} = 4\frac{1}{8}\)
Answer: \(4\frac{1}{8}\)
5 \(4\frac{5}{6} + 3\frac{1}{4}\)
LCD = 12
Rewrite: \(4\frac{10}{12} + 3\frac{3}{12}\)
Wholes: \(4 + 3 = 7\), Fractions: \(\frac{13}{12}\)
Regroup: \(\frac{13}{12} = 1\frac{1}{12}\)
Sum: \(7 + 1\frac{1}{12} = 8\frac{1}{12}\)
Answer: \(8\frac{1}{12}\)
6 \(5\frac{2}{5} + 2\frac{7}{10}\)
LCD = 10
Rewrite: \(5\frac{4}{10} + 2\frac{7}{10}\)
Wholes: \(5 + 2 = 7\), Fractions: \(\frac{11}{10}\)
Regroup: \(\frac{11}{10} = 1\frac{1}{10}\)
Sum: \(7 + 1\frac{1}{10} = 8\frac{1}{10}\)
Answer: \(8\frac{1}{10}\)
Full Solution
Calculations (2 pts):
Equation: \(3\frac{3}{4} + 2\frac{2}{3}\)
LCD of 4 and 3 is 12
\(3\frac{3 \times 3}{4 \times 3} = 3\frac{9}{12}\)
\(2\frac{2 \times 4}{3 \times 4} = 2\frac{8}{12}\)
Sum: \(5\frac{17}{12}\) → Regroup: \(5 + 1\frac{5}{12} = \mathbf{6\frac{5}{12}}\)
Sentence Answer with Units (1 pt):
"The total length of the ramp is \(6\frac{5}{12}\) feet."
Check: Did student include the units ("feet")? Look for unit omission.
Diagnostic Next Steps Matrix Targeted Interventions
Score: 0 – 7 pts (Tier 3) Struggling with LCD or adds straight across. Use visual fraction bars or pattern blocks to model equivalence before mixed numbers.
Score: 8 – 11 pts (Tier 2) Finds LCD successfully but leaves answers like \(3\frac{22}{15}\). Provide mini-whiteboard drill on renaming improper fractions only.
Score: 12 – 15 pts (Mastery) Demonstrates fluency. Advance to subtracting mixed numbers with borrowing/regrouping (e.g., \(5\frac{1}{4} - 2\frac{2}{3}\)).
Mixed Number Fusion • Teacher Answer Key (Page 2 of 2) Intervention Pacing Guide • Formative Assessment Ready
