A focused Grade 5 learning session for Subtracting Fractions with Unlike Denominators using visual models, worked examples, strategy guidance, and a short mastery check.
Student goal: I can subtract fractions with unlike denominators.
Subtracting Fractions with Unlike Denominators is the Grade 5 skill of students subtract fractions with unlike denominators by first rewriting them with a common denominator. They handle cases involving regrouping and apply the strategy to measurement and real-world problems.
Strong understanding comes from naming what the numbers, shapes, units, or data values represent, then showing the idea with a model or clear steps before solving.
The key to this topic is understanding the structure behind the work, not just following a rule. Students should be able to talk through what is happening, point to a model, and explain why the answer makes sense.
Question: Bar shows 8 parts, 5 shaded. Remove 2 parts. \(\frac{5}{8} - \frac{2}{8} = ?\)
How the model helps: Same denominator: \(5 - 2 = 3\) parts remaining. Answer: \(\frac{3}{8}\).
Question: Circle divided into 6 parts, 5 shaded (blue). Remove \(\frac{1}{6}\). What is \(\frac{5}{6} - \frac{1}{6}\)?
Answer: \(\frac{4}{6} = \frac{2}{3}\)
Question: Bar shows 10 parts, 9 shaded. Remove \(\frac{1}{5}\) of the whole. \(\frac{9}{10} - \frac{1}{5} = ?\)
Answer: \(\frac{7}{10}\)
Question: Recipe needs \(\frac{3}{4}\) cup flour. Maria used \(\frac{1}{6}\) cup. How much more needed?
Answer: \(\frac{7}{12}\) cups
Why it works: LCD = 12. \(\frac{3}{4} = \frac{9}{12}\); \(\frac{1}{6} = \frac{2}{12}\). \(\frac{9}{12} - \frac{2}{12} = \frac{7}{12}\).
Subtracting Fractions with Unlike Denominators gets easier when students read the model, track what each number means, and explain why the answer fits the situation.
Keep the whole consistent, show equal parts clearly, and explain what the fraction means.
Use scratch paper. The explanation matters more than simply seeing whether the choice is correct.
Subtract: \(\frac{7}{9} - \frac{2}{3}\)
Answer C: \(\frac{1}{9}\)
Use ninths: \(\frac{2}{3}=\frac{6}{9}\). Then \(\frac{7}{9}-\frac{6}{9}=\frac{1}{9}\).
Subtract: \(\frac{5}{6} - \frac{1}{4}\)
Answer A: \(\frac{7}{12}\)
LCD = 12. \(\frac{5}{6} = \frac{10}{12}\); \(\frac{1}{4} = \frac{3}{12}\). \(\frac{10}{12} - \frac{3}{12} = \frac{7}{12}\).
Bar shows 8 parts, 5 shaded. Remove 2 parts. \(\frac{5}{8} - \frac{2}{8} = ?\)
Answer A: \(\frac{3}{8}\)
Same denominator: \(5 - 2 = 3\) parts remaining. Answer: \(\frac{3}{8}\).
Subtract: \(\frac{7}{8} - \frac{1}{3}\)
Answer B: \(\frac{13}{24}\)
LCD = 24. \(\frac{7}{8} = \frac{21}{24}\); \(\frac{1}{3} = \frac{8}{24}\). \(\frac{21}{24} - \frac{8}{24} = \frac{13}{24}\).
Recipe needs \(\frac{3}{4}\) cup flour. Maria used \(\frac{1}{6}\) cup. How much more needed?
Answer D: \(\frac{7}{12}\) cups
LCD = 12. \(\frac{3}{4} = \frac{9}{12}\); \(\frac{1}{6} = \frac{2}{12}\). \(\frac{9}{12} - \frac{2}{12} = \frac{7}{12}\).
Number line: Start at \(\frac{9}{10}\). Back by \(\frac{3}{10}\). Where do you land?
Answer B: \(\frac{6}{10}\)
\(\frac{9}{10} - \frac{3}{10} = \frac{6}{10}\).
Simplify: \(\frac{9}{12} - \frac{3}{12}\)
Answer D: \(\frac{1}{2}\)
\(\frac{9}{12} - \frac{3}{12} = \frac{6}{12}\), which simplifies to \(\frac{1}{2}\).
Subtract: \(\frac{4}{5} - \frac{1}{2}\)
Answer C: \(\frac{3}{10}\)
Use tenths: \(\frac{4}{5}=\frac{8}{10}\) and \(\frac{1}{2}=\frac{5}{10}\). Then \(\frac{8}{10}-\frac{5}{10}=\frac{3}{10}\).
Pizza has 8 slices. Ben eats \(\frac{3}{8}\), sister eats \(\frac{1}{4}\). How much remains?
Answer A: \(\frac{3}{8}\)
Together eaten: \(\frac{3}{8} + \frac{2}{8} = \frac{5}{8}\). Remaining: \(1 - \frac{5}{8} = \frac{3}{8}\).
Subtract: \(\frac{4}{5} - \frac{2}{3}\)
Answer A: \(\frac{2}{15}\)
LCD = 15. \(\frac{4}{5} = \frac{12}{15}\); \(\frac{2}{3} = \frac{10}{15}\). \(\frac{12}{15} - \frac{10}{15} = \frac{2}{15}\).
Circle divided into 6 parts, 5 shaded (blue). Remove \(\frac{1}{6}\). What is \(\frac{5}{6} - \frac{1}{6}\)?
Answer A: \(\frac{4}{6} = \frac{2}{3}\)
\(\frac{5}{6} - \frac{1}{6} = \frac{4}{6}\), simplifies to \(\frac{2}{3}\).
