A focused Grade 5 learning session for Finding Common Denominators using visual models, worked examples, strategy guidance, and a short mastery check.
Student goal: I can find common denominators for fractions.
Finding Common Denominators is the Grade 5 skill of students find common denominators by identifying common multiples. They understand that equivalent fractions can be created by multiplying the numerator and denominator by the same number, preparing for addition and subtraction of unlike fractions.
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: Complete the table showing multiples. Which number is the least common denominator for \(\frac{1}{6}\) and \(\frac{1}{8}\)?
| Denom. | Mult 1 | Mult 2 | Mult 3 | Mult 4 |
|---|---|---|---|---|
| 6 | 6 | 12 | 18 | 24 |
| 8 | 8 | 16 | 24 | 32 |
How the model helps: From the table, 24 appears in both rows. The least common denominator is 24.
Question: Rewrite \(\frac{2}{3}\) and \(\frac{3}{5}\) with a common denominator.
| Original | New Fraction |
|---|---|
| \(\frac{2}{3}\) | \(\frac{?}{15}\) |
| \(\frac{3}{5}\) | \(\frac{?}{15}\) |
Answer: \(\frac{10}{15}\) and \(\frac{9}{15}\)
Question: The two fraction bars show \(\frac{1}{2}\) and \(\frac{1}{4}\) aligned side by side. What is the common denominator?
Answer: 4
Question: A recipe calls for \(\frac{1}{3}\) cup of oil and \(\frac{1}{2}\) cup of water. To measure both together, what common denominator would you use?
Answer: 6
Why it works: Common denominator for 3 and 2 is 6. \(\frac{1}{3} = \frac{2}{6}\) and \(\frac{1}{2} = \frac{3}{6}\).
Finding Common Denominators gets easier when students read the model, track what each number means, and explain why the answer fits the situation.
Understand the structure first, then solve, check, and explain why the answer makes sense.
Use scratch paper. The explanation matters more than simply seeing whether the choice is correct.
What is a common denominator for \(\frac{1}{3}\) and \(\frac{1}{4}\)?
Answer B: 12
Multiples of 3: 3, 6, 9, 12, \ldots{} Multiples of 4: 4, 8, 12, \ldots{} The least common multiple is 12, which is a common denominator.
Which number is a common denominator for \(\frac{2}{5}\) and \(\frac{3}{4}\)?
Answer A: 20
Multiples of 5: 5, 10, 15, 20, \ldots{} Multiples of 4: 4, 8, 12, 16, 20, \ldots{} The least common denominator is 20.
Complete the table showing multiples. Which number is the least common denominator for \(\frac{1}{6}\) and \(\frac{1}{8}\)?
Answer D: 24
From the table, 24 appears in both rows. The least common denominator is 24.
Rewrite \(\frac{1}{3}\) and \(\frac{1}{4}\) with a common denominator of 12.
Answer A: \(\frac{4}{12}\) and \(\frac{3}{12}\)
\(\frac{1}{3} = \frac{1 \times 4}{3 \times 4} = \frac{4}{12}\) and \(\frac{1}{4} = \frac{1 \times 3}{4 \times 3} = \frac{3}{12}\).
List the first four multiples of 7.
Answer D: 7, 14, 21, 28
Multiples of 7 are found by multiplying 7 by 1, 2, 3, 4: \(7 \times 1 = 7\), \(7 \times 2 = 14\), \(7 \times 3 = 21\), \(7 \times 4 = 28\).
Which is the least common denominator for \(\frac{5}{6}\) and \(\frac{1}{4}\)?
Answer B: 12
Multiples of 6: 6, 12, 18, \ldots{} Multiples of 4: 4, 8, 12, \ldots{} The LCD is 12.
Compare the fractions \(\frac{2}{5}\) and \(\frac{1}{3}\) by finding a common denominator. Which statement is true?
Answer B: \(\frac{2}{5} > \frac{1}{3}\)
Common denominator is 15. \(\frac{2}{5} = \frac{6}{15}\) and \(\frac{1}{3} = \frac{5}{15}\). Since \(6 > 5\), \(\frac{2}{5} > \frac{1}{3}\).
Marcus has \(\frac{1}{2}\) of a pizza. Sofia has \(\frac{1}{3}\) of a pizza. To compare their amounts, which denominator should they use?
Answer D: 6
A common denominator for \(\frac{1}{2}\) and \(\frac{1}{3}\) is 6. \(\frac{1}{2} = \frac{3}{6}\) and \(\frac{1}{3} = \frac{2}{6}\).
Rewrite \(\frac{2}{3}\) and \(\frac{3}{5}\) with a common denominator.
Answer A: \(\frac{10}{15}\) and \(\frac{9}{15}\)
\(\frac{2}{3} = \frac{2 \times 5}{3 \times 5} = \frac{10}{15}\) and \(\frac{3}{5} = \frac{3 \times 3}{5 \times 3} = \frac{9}{15}\).
What is the least common multiple of 4 and 6?
Answer D: 12
Multiples of 4: 4, 8, 12, \ldots{} Multiples of 6: 6, 12, 18, \ldots{} The LCM is 12.
The two fraction bars show \(\frac{1}{2}\) and \(\frac{1}{4}\) aligned side by side. What is the common denominator?
Answer B: 4
The bar for \(\frac{1}{2}\) divides into 2 parts; the bar for \(\frac{1}{4}\) divides into 4 parts. Common denominator is 4.
