Different Denominator Teacher Guide Grade 4 • Fraction Faceoff • Lesson 1
Different Denominator Teacher Guide
Standard: 4.NF.A.2
Time: 55–60 Minutes
Learning Objective
Students will compare two fractions with different denominators using visual fraction bars, benchmark fractions (\(0, \frac{1}{2}, 1\)), and common denominators, recording results with \(<\), \(>\), or \(=\).
Materials
• Fraction strips / area models
• Independent Practice (2 pp.)
• Homework (1 p.) & Exit Ticket
Lesson Pacing & Facilitation Script
1. Warm-Up: Same-Whole Check 8 mins
Draw two different-sized rectangles on the board. Ask: "If I shade \(\frac{1}{2}\) of a small pizza and \(\frac{1}{2}\) of a giant pizza, are they equal?" Reinforce that fraction comparisons are only valid when both fractions refer to the same whole .
2. Mini-Lesson: Three Strategies for Different Denominators 17 mins
Strategy A — Benchmark \(\frac{1}{2}\): Compare \(\frac{3}{8}\) and \(\frac{5}{6}\). Since \(\frac{3}{8} < \frac{4}{8} (\frac{1}{2})\) and \(\frac{5}{6} > \frac{3}{6} (\frac{1}{2})\), \(\frac{3}{8} < \frac{5}{6}\).Strategy B — Visual Fraction Bars: Align equal-length bars for \(\frac{2}{3}\) and \(\frac{3}{4}\) to see \(\frac{3}{4}\) extends farther.Strategy C — Common Denominator: Multiply numerator & denominator to create equivalent fractions: \(\frac{2}{3} = \frac{8}{12}\) and \(\frac{3}{4} = \frac{9}{12}\), so \(\frac{2}{3} < \frac{3}{4}\).
3. Independent Practice & Small-Group Check 20 mins
Distribute Different Denominator Independent Practice . Circulate and ask: "How did you know whether \(\frac{3}{5}\) is greater or less than \(\frac{1}{2}\)?" Pull students struggling with equivalent fractions for a quick 5-minute model-drawing huddle.
4. Closure & Exit Ticket 10 mins
Have students share one benchmark shortcut they used today, then complete the Different Denominator Exit Ticket independently.
Common Misconceptions
Whole-Number Bias: Thinking \(\frac{3}{8} > \frac{2}{3}\) because \(3 > 2\) and \(8 > 3\). Counter with equal-length fraction bars.Changing Only the Denominator: Writing \(\frac{2}{3} = \frac{2}{12}\) instead of multiplying both top and bottom by \(4\).
Differentiation
Support: Provide laminated fraction strips and a \(\frac{1}{2}\)-benchmark reference mat (e.g., \(\frac{2}{4}, \frac{3}{6}, \frac{4}{8}, \frac{5}{10}\)).Extend: Challenge early finishers to order three fractions (\(\frac{3}{4}, \frac{5}{8}, \frac{2}{3}\)) from least to greatest.
Lesson 1 • Teacher Reference
Complete Answer Keys
Independent Practice Answer Key
Part 1: Shade & Compare
1. \(\frac{2}{3} > \frac{3}{6}\) (or \(\frac{4}{6} > \frac{3}{6}\))
2. \(\frac{3}{4} > \frac{5}{8}\) (\(\frac{6}{8} > \frac{5}{8}\))
3. \(\frac{2}{5} < \frac{1}{2}\) (\(\frac{4}{10} < \frac{5}{10}\))
Part 2: Benchmark \(\frac{1}{2}\) Sort
Less than \(\frac{1}{2}\): \(\frac{2}{5}, \frac{3}{8}, \frac{1}{4}\)
Greater than \(\frac{1}{2}\): \(\frac{5}{6}, \frac{4}{6}, \frac{7}{10}\)
Part 3: Common Denominators
4. \(\frac{2}{3} = \frac{8}{12}\) and \(\frac{3}{4} = \frac{9}{12} \rightarrow \frac{2}{3} < \frac{3}{4}\)
5. \(\frac{3}{5} = \frac{6}{10}\) and \(\frac{7}{10} = \frac{7}{10} \rightarrow \frac{3}{5} < \frac{7}{10}\)
6. \(\frac{5}{6} = \frac{10}{12}\) and \(\frac{3}{4} = \frac{9}{12} \rightarrow \frac{5}{6} > \frac{3}{4}\)
7. \(\frac{1}{3} = \frac{4}{12}\) and \(\frac{4}{12} = \frac{4}{12} \rightarrow \frac{1}{3} = \frac{4}{12}\)
Part 4: Word Problem
8. Maya walked farther. \(\frac{3}{4} = \frac{9}{12}\) and \(\frac{2}{3} = \frac{8}{12}\), so \(\frac{3}{4} > \frac{2}{3}\).
Homework Answer Key
Part 1: Model & Compare
1. \(\frac{1}{2} < \frac{2}{3}\) (\(\frac{3}{6} < \frac{4}{6}\))
2. \(\frac{3}{4} > \frac{2}{5}\) (\(\frac{15}{20} > \frac{8}{20}\))
Part 2: Compare Using <, >, or =
3. \(\frac{3}{8} < \frac{2}{4}\) | 4. \(\frac{4}{5} > \frac{7}{10}\)
5. \(\frac{2}{6} = \frac{1}{3}\) | 6. \(\frac{5}{8} < \frac{3}{4}\)
Part 3: Word Problem
7. Leo read more. \(\frac{5}{6} > \frac{1}{2}\), while \(\frac{3}{8} < \frac{1}{2}\) (or \(\frac{5}{6} = \frac{20}{24}\) and \(\frac{3}{8} = \frac{9}{24}\)).
Part 4: Explain Your Thinking
8. Sample: \(\frac{4}{10}\) is less than \(\frac{1}{2}\) (\(\frac{5}{10}\)), and \(\frac{2}{3}\) is greater than \(\frac{1}{2}\), so \(\frac{4}{10} < \frac{2}{3}\).
Exit Ticket Answer Key & Quick Rubric
1. \(\frac{3}{4} > \frac{5}{8}\) (equivalent: \(\frac{6}{8} > \frac{5}{8}\)) | 2. \(\frac{2}{5} < \frac{2}{3}\) (or \(\frac{6}{15} < \frac{10}{15}\))
3. Choice B (\(\frac{4}{6}\)) is greater than \(\frac{1}{2}\).
4. Carlos ate more. \(\frac{2}{3} = \frac{8}{12}\) and \(\frac{5}{12}\) stays \(\frac{5}{12}\), so \(\frac{2}{3} > \frac{5}{12}\).
Mastery Check: 3–4 correct = Ready for Lesson 2 | 0–2 correct = Reteach with fraction strips.
Different Denominator Independent Practice Lesson 1 • Independent Practice
Different Denominator Duel
Name: ________________________
Date: _______________
Part 1: Shade the Fraction Bars & Compare
Shade each bar to show the fraction. Then write < , > , or = in the circle.
1. Compare \(\frac{2}{3}\) and \(\frac{3}{6}\)
\(\frac{2}{3}\) \(\frac{3}{6}\)
\(\frac{2}{3}\)
\(\frac{3}{6}\)
2. Compare \(\frac{3}{4}\) and \(\frac{5}{8}\)
\(\frac{3}{4}\) \(\frac{5}{8}\)
\(\frac{3}{4}\)
\(\frac{5}{8}\)
3. Compare \(\frac{2}{5}\) and \(\frac{1}{2}\)
\(\frac{2}{5}\) \(\frac{1}{2}\)
\(\frac{2}{5}\)
\(\frac{1}{2}\)
Part 2: Benchmark \(\frac{1}{2}\) Sort
Sort each fraction from the box into the correct column: \(\frac{2}{5}, \quad \frac{5}{6}, \quad \frac{3}{8}, \quad \frac{4}{6}, \quad \frac{1}{4}, \quad \frac{7}{10}\)
Less than \(\frac{1}{2}\)
Greater than \(\frac{1}{2}\)
Lesson 1 • Independent Practice (Page 2)
Name: ________________________
Part 3: Compare Using Common Denominators
Rewrite one or both fractions so they have the same denominator. Show your equivalent fractions, then write < , > , or = .
\(\frac{2}{3}\) \(\frac{3}{4}\)
(use 12)
\(\frac{3}{5}\) \(\frac{7}{10}\)
(use 10)
\(\frac{5}{6}\) \(\frac{3}{4}\)
(use 12)
\(\frac{1}{3}\) \(\frac{4}{12}\)
(use 12)
Part 4: Real-World Fraction Duel
8. Maya walked \(\frac{3}{4}\) of a mile to the park. Her brother Noah walked \(\frac{2}{3}\) of a mile to the library. Who walked farther? Show your work using a model or common denominators, and write a sentence to explain your answer.
Different Denominator Homework Lesson 1 • Homework
Different Denominator Practice
Name: ________________________
Date: _______________
Part 1: Shade & Compare
Shade the fraction bars to compare. Write < , > , or = in each circle.
\(\frac{1}{2}\) \(\frac{2}{3}\)
\(\frac{3}{4}\) \(\frac{2}{5}\)
Part 2: Compare Using Benchmarks or Common Denominators
Write < , > , or = in each circle. Use the space below each problem to show your work.
\(\frac{3}{8}\) \(\frac{2}{4}\)
\(\frac{4}{5}\) \(\frac{7}{10}\)
\(\frac{2}{6}\) \(\frac{1}{3}\)
\(\frac{5}{8}\) \(\frac{3}{4}\)
7. Word Problem: Leo read \(\frac{5}{6}\) of his book. Sam read \(\frac{3}{8}\) of the same book. Who read more of the book? Show how you know.
8. Explain Your Thinking: How can you use the benchmark \(\frac{1}{2}\) to compare \(\frac{4}{10}\) and \(\frac{2}{3}\) without drawing a picture?
Different Denominator Exit Ticket Lesson 1 • Quick Check
Different Denominator Exit Ticket
Name: ________________________
Date: _______________
Compare the Fractions
Write < , > , or = in each circle. Show your work below each problem.
\(\frac{3}{4}\) \(\frac{5}{8}\)
\(\frac{2}{5}\) \(\frac{2}{3}\)
3. Which fraction is greater than \(\frac{1}{2}\) ? Circle the letter of the correct answer.
A. \(\frac{3}{8}\)
B. \(\frac{4}{6}\)
C. \(\frac{2}{5}\)
D. \(\frac{4}{10}\)
4. Carlos ate \(\frac{2}{3}\) of a granola bar. Elena ate \(\frac{5}{12}\) of the same-sized granola bar. Who ate more? Show your work to prove your answer.
Unit Fraction Teacher Guide Grade 4 • Fraction Faceoff • Lesson 2
Unit Fraction Teacher Guide
Standard: 4.NF.A.2
Time: 55–60 Minutes
Learning Objective
Students will compare unit fractions (\(\frac{1}{a}\) and \(\frac{1}{b}\)) by reasoning about the size of equal parts, discovering that a larger denominator creates smaller pieces.
Materials
• Equal paper strips for folding
• Independent Practice (2 pp.)
• Homework (1 p.) & Exit Ticket
Lesson Pacing & Facilitation Script
1. Warm-Up: The Giant Cookie Debate 8 mins
Ask: "Would you rather share 1 giant cookie equally with 2 friends (\(\frac{1}{2}\)) or with 8 friends (\(\frac{1}{8}\))? Why?" Connect students' real-life intuition ("more people = smaller slice") directly to unit fractions.
2. Mini-Lesson: Paper-Strip Folding & The Inverse Rule 17 mins
Hands-On Discovery: Give each student 3 identical paper strips. Fold into \(\frac{1}{2}\), \(\frac{1}{4}\), and \(\frac{1}{8}\). Line them up side by side.Key Generalization: When the numerator is \(1\), we are looking at one piece . The larger the denominator, the more pieces the whole is cut into, so each piece is smaller : \(\frac{1}{2} > \frac{1}{4} > \frac{1}{8}\).Number Line Check: Plot \(\frac{1}{3}\) and \(\frac{1}{6}\) on two stacked \(0\text{–}1\) number lines to verify \(\frac{1}{3}\) is farther from \(0\).
3. Independent Practice & Conferring 20 mins
Students complete Unit Fraction Independent Practice . Prompt students to use the language: "Both fractions have 1 piece, and sixths are larger than tenths because the whole is cut into fewer pieces."
4. Closure & Exit Ticket 10 mins
Have students order \(\frac{1}{10}, \frac{1}{3}, \frac{1}{5}\) on mini-whiteboards from least to greatest, then complete the Unit Fraction Exit Ticket .
Common Misconceptions
"Bigger Number = Bigger Fraction": Students assume \(\frac{1}{12} > \frac{1}{4}\) because \(12 > 4\). Always anchor back to sharing a whole into \(12\) vs. \(4\) equal parts.Unequal Wholes: Drawing a longer bar for \(\frac{1}{8}\) than \(\frac{1}{4}\). Remind students to align start and end points.
Differentiation
Support: Keep folded paper strips on desks as a tactile reference during independent work.Extend: Ask students to find a unit fraction that sits between \(\frac{1}{4}\) and \(\frac{1}{2}\) (e.g., \(\frac{1}{3}\)).
Lesson 2 • Teacher Reference
Complete Answer Keys
Independent Practice Answer Key
Part 1: Shade & Compare
1. \(\frac{1}{3} > \frac{1}{6}\) (1 of 3 parts is larger than 1 of 6 parts)
2. \(\frac{1}{8} < \frac{1}{4}\) (1 of 8 parts is smaller than 1 of 4 parts)
3. \(\frac{1}{2} > \frac{1}{5}\)
Part 2: Number Line & Ordering
4. \(\frac{1}{4}\) is farther from \(0\) than \(\frac{1}{8}\), so \(\frac{1}{4} > \frac{1}{8}\).
5. Least to greatest: \(\frac{1}{10}, \frac{1}{6}, \frac{1}{4}, \frac{1}{2}\)
Part 3: Fast Unit Comparisons
6. \(\frac{1}{5} > \frac{1}{9}\) | 7. \(\frac{1}{12} < \frac{1}{7}\)
8. \(\frac{1}{3} > \frac{1}{4}\) | 9. \(\frac{1}{6} = \frac{1}{6}\)
Part 4: Word Problem
10. Jada got the larger piece. \(\frac{1}{4} > \frac{1}{6}\) because cutting a sandwich into 4 equal pieces makes larger pieces than cutting it into 6 equal pieces.
Homework Answer Key
Part 1: Shade & Compare
1. \(\frac{1}{3} > \frac{1}{5}\) | 2. \(\frac{1}{6} < \frac{1}{2}\)
Part 2: Compare Unit Fractions
3. \(\frac{1}{8} < \frac{1}{4}\) | 4. \(\frac{1}{3} > \frac{1}{10}\)
5. \(\frac{1}{12} < \frac{1}{5}\) | 6. \(\frac{1}{7} > \frac{1}{9}\)
Part 3: Word Problem
7. Mia walked farther. \(\frac{1}{3} > \frac{1}{5}\) because thirds are larger parts of a mile than fifths.
Part 4: Explain Your Thinking
8. Sample: A larger denominator means the whole is divided into more equal pieces, so each piece (\(\frac{1}{10}\)) is smaller than \(\frac{1}{4}\).
Exit Ticket Answer Key & Quick Rubric
1. \(\frac{1}{4} > \frac{1}{10}\) | 2. \(\frac{1}{8} < \frac{1}{3}\)
3. Choice C (\(\frac{1}{3}\)) is the greatest unit fraction.
4. Liam's ribbon is longer because \(\frac{1}{5} > \frac{1}{8}\) (fifths are larger than eighths).
Mastery Check: 3–4 correct = Ready for Lesson 3 | 0–2 correct = Reteach with paper-folding strips.
Unit Fraction Independent Practice Lesson 2 • Independent Practice
Unit Fraction Showdown
Name: ________________________
Date: _______________
Part 1: Shade One Equal Piece & Compare
Shade 1 piece of each bar to show the unit fraction. Write < , > , or = in the circle.
1. Compare \(\frac{1}{3}\) and \(\frac{1}{6}\)
\(\frac{1}{3}\) \(\frac{1}{6}\)
\(\frac{1}{3}\)
\(\frac{1}{6}\)
2. Compare \(\frac{1}{8}\) and \(\frac{1}{4}\)
\(\frac{1}{8}\) \(\frac{1}{4}\)
\(\frac{1}{8}\)
\(\frac{1}{4}\)
3. Compare \(\frac{1}{2}\) and \(\frac{1}{5}\)
\(\frac{1}{2}\) \(\frac{1}{5}\)
\(\frac{1}{2}\)
\(\frac{1}{5}\)
Part 2: Number Line Check & Ordering
4. Label \(\frac{1}{4}\) on the top number line and \(\frac{1}{8}\) on the bottom number line. Circle the greater fraction.
0
1
0
1
Lesson 2 • Independent Practice (Page 2)
Name: ________________________
5. Order these unit fractions from least to greatest : \(\quad \frac{1}{4}, \quad \frac{1}{10}, \quad \frac{1}{2}, \quad \frac{1}{6}\)
Part 3: Compare Unit Fractions
Write < , > , or = in each circle. Think about piece size!
\(\frac{1}{5}\) \(\frac{1}{9}\)
\(\frac{1}{12}\) \(\frac{1}{7}\)
\(\frac{1}{3}\) \(\frac{1}{4}\)
\(\frac{1}{6}\) \(\frac{1}{6}\)
Part 4: Real-World Unit Fraction Problem
10. Jada and Tyler bought two identical sub sandwiches. Jada cut hers into 4 equal pieces and ate 1 piece (\(\frac{1}{4}\)). Tyler cut his into 6 equal pieces and ate 1 piece (\(\frac{1}{6}\)). Who ate the larger piece? Draw a model and explain why.
Unit Fraction Homework Lesson 2 • Homework
Unit Fraction Practice
Name: ________________________
Date: _______________
Part 1: Shade & Compare
Shade 1 piece of each bar. Write < , > , or = in each circle.
\(\frac{1}{3}\) \(\frac{1}{5}\)
\(\frac{1}{6}\) \(\frac{1}{2}\)
Part 2: Compare Unit Fractions
Write < , > , or = in each circle.
\(\frac{1}{8}\) \(\frac{1}{4}\)
\(\frac{1}{3}\) \(\frac{1}{10}\)
\(\frac{1}{12}\) \(\frac{1}{5}\)
\(\frac{1}{7}\) \(\frac{1}{9}\)
7. Word Problem: Mia ran \(\frac{1}{3}\) of a mile. Ben ran \(\frac{1}{5}\) of a mile. Who ran farther? Explain how you know.
8. Explain Your Thinking: Why is \(\frac{1}{10}\) smaller than \(\frac{1}{4}\) even though \(10\) is greater than \(4\)?
Unit Fraction Exit Ticket Lesson 2 • Quick Check
Unit Fraction Exit Ticket
Name: ________________________
Date: _______________
Compare the Unit Fractions
Write < , > , or = in each circle.
\(\frac{1}{4}\) \(\frac{1}{10}\)
\(\frac{1}{8}\) \(\frac{1}{3}\)
3. Which unit fraction is the greatest ? Circle the letter of the correct answer.
A. \(\frac{1}{12}\)
B. \(\frac{1}{6}\)
C. \(\frac{1}{3}\)
D. \(\frac{1}{9}\)
4. Liam cut a ribbon into pieces that are each \(\frac{1}{5}\) of a yard long. Ava cut her ribbon into pieces that are each \(\frac{1}{8}\) of a yard long. Whose piece is longer? Explain using what you know about unit fractions.
Same Numerator Teacher Guide Grade 4 • Fraction Faceoff • Lesson 3
Same Numerator Teacher Guide
Standard: 4.NF.A.2
Time: 55–60 Minutes
Learning Objective
Students will compare two fractions with the same numerator (e.g., \(\frac{3}{5}\) and \(\frac{3}{8}\)) by reasoning that when the number of pieces is equal, the fraction with the smaller denominator has larger pieces.
Materials
• Fraction bars / circles
• Independent Practice (2 pp.)
• Homework (1 p.) & Exit Ticket
Lesson Pacing & Facilitation Script
1. Warm-Up: Connect to Unit Fractions 8 mins
Review Lesson 2: "Which is greater, \(\frac{1}{4}\) or \(\frac{1}{6}\)?" Then ask: "Now what if you get 3 of those pieces: \(\frac{3}{4}\) vs. \(\frac{3}{6}\)?" Have students turn and talk before revealing the visual model.
2. Mini-Lesson: Same Count, Different Size 17 mins
Visual Proof: Shade \(\frac{3}{5}\) and \(\frac{3}{8}\) on equal-length fraction bars. Point out that both have 3 shaded pieces .Sentence Frame: "Both fractions have ___ pieces. Since fifths are larger than eighths, 3 fifths is greater than 3 eighths (\(\frac{3}{5} > \frac{3}{8}\))." Missing-Piece Bonus: Briefly note that \(\frac{4}{5}\) and \(\frac{4}{6}\) are both 1 piece away from a whole—and since \(\frac{1}{6}\) is smaller than \(\frac{1}{5}\), \(\frac{4}{5}\) is missing a bigger piece? Wait: \(\frac{5}{6}\) vs \(\frac{4}{5}\) is different; for \(\frac{4}{5}\) vs \(\frac{4}{6}\), same numerator directly tells us \(\frac{4}{5} > \frac{4}{6}\)!
3. Independent Practice & Conferring 20 mins
Students complete Same Numerator Independent Practice . Listen for students explaining piece size rather than reciting a memorized "opposite rule."
4. Closure & Exit Ticket 10 mins
Ask a volunteer to explain why \(\frac{2}{3} > \frac{2}{9}\) without drawing a picture, then administer the Same Numerator Exit Ticket .
Common Misconceptions
Overgeneralizing "Smaller Denominator = Bigger": Remind students this shortcut ONLY works when the numerators are the same (same number of pieces).Whole-Number Thinking: Thinking \(\frac{3}{10} > \frac{3}{4}\) because \(10 > 4\).
Differentiation
Support: Provide the sentence frame: "Both have ___ pieces. ___ are larger than ___, so ___ > ___." Extend: Have students order \(\frac{4}{12}, \frac{4}{5}, \frac{4}{8}, \frac{4}{6}\) from greatest to least and justify.
Lesson 3 • Teacher Reference
Complete Answer Keys
Independent Practice Answer Key
Part 1: Shade & Compare
1. \(\frac{2}{3} > \frac{2}{6}\) (both have 2 pieces; thirds are larger than sixths)
2. \(\frac{3}{8} < \frac{3}{4}\) (both have 3 pieces; eighths are smaller than fourths)
3. \(\frac{4}{5} > \frac{4}{10}\)
Part 2: Ordering Same Numerators
4. Greatest to least: \(\frac{3}{4}, \frac{3}{6}, \frac{3}{8}, \frac{3}{10}\)
Part 3: Fast Same-Numerator Comparisons
5. \(\frac{2}{5} > \frac{2}{9}\) | 6. \(\frac{5}{12} < \frac{5}{6}\)
7. \(\frac{4}{7} > \frac{4}{9}\) | 8. \(\frac{3}{5} = \frac{3}{5}\)
Part 4: Word Problem
9. Priya used more flour. \(\frac{3}{4} > \frac{3}{8}\) because both recipes use 3 pieces, and fourths are larger than eighths.
Homework Answer Key
Part 1: Shade & Compare
1. \(\frac{2}{4} > \frac{2}{8}\) | 2. \(\frac{3}{6} < \frac{3}{5}\)
Part 2: Compare Fractions
3. \(\frac{4}{6} > \frac{4}{10}\) | 4. \(\frac{2}{7} < \frac{2}{3}\)
5. \(\frac{5}{8} > \frac{5}{12}\) | 6. \(\frac{3}{4} > \frac{3}{5}\)
Part 3: Word Problem
7. Marcus painted more. \(\frac{2}{3} > \frac{2}{5}\) because thirds are larger parts than fifths.
Part 4: Explain Your Thinking
8. Sample: Both fractions have 4 shaded parts, and sixths are larger pieces than tenths, so \(\frac{4}{6} > \frac{4}{10}\).
Exit Ticket Answer Key & Quick Rubric
1. \(\frac{3}{5} > \frac{3}{10}\) | 2. \(\frac{2}{9} < \frac{2}{4}\)
3. Choice B (\(\frac{4}{5}\)) is the greatest fraction.
4. Sofia drank more. \(\frac{3}{4} > \frac{3}{6}\) because both drank 3 pieces of a bottle, and fourths are larger than sixths.
Mastery Check: 3–4 correct = Ready for Lesson 4 | 0–2 correct = Reteach with fraction bars.
Same Numerator Independent Practice Lesson 3 • Independent Practice
Same Numerator Clash
Name: ________________________
Date: _______________
Part 1: Shade the Fraction Bars & Compare
Shade each bar to show the fraction. Write < , > , or = in the circle.
1. Compare \(\frac{2}{3}\) and \(\frac{2}{6}\)
\(\frac{2}{3}\) \(\frac{2}{6}\)
\(\frac{2}{3}\)
\(\frac{2}{6}\)
2. Compare \(\frac{3}{8}\) and \(\frac{3}{4}\)
\(\frac{3}{8}\) \(\frac{3}{4}\)
\(\frac{3}{8}\)
\(\frac{3}{4}\)
3. Compare \(\frac{4}{5}\) and \(\frac{4}{10}\)
\(\frac{4}{5}\) \(\frac{4}{10}\)
\(\frac{4}{5}\)
\(\frac{4}{10}\)
Part 2: Order Same-Numerator Fractions
4. Order these fractions from greatest to least : \(\quad \frac{3}{8}, \quad \frac{3}{4}, \quad \frac{3}{10}, \quad \frac{3}{6}\)
Lesson 3 • Independent Practice (Page 2)
Name: ________________________
Part 3: Compare Fractions with the Same Numerator
Write < , > , or = in each circle. Compare the size of the pieces!
\(\frac{2}{5}\) \(\frac{2}{9}\)
\(\frac{5}{12}\) \(\frac{5}{6}\)
\(\frac{4}{7}\) \(\frac{4}{9}\)
\(\frac{3}{5}\) \(\frac{3}{5}\)
Part 4: Real-World Same Numerator Problem
9. Priya used \(\frac{3}{4}\) cup of flour to make pancakes. Her dad used \(\frac{3}{8}\) cup of flour to make waffles. Who used more flour? Explain your answer using piece sizes.
Same Numerator Homework Lesson 3 • Homework
Same Numerator Practice
Name: ________________________
Date: _______________
Part 1: Shade & Compare
Shade each bar to show the fraction. Write < , > , or = in each circle.
\(\frac{2}{4}\) \(\frac{2}{8}\)
\(\frac{3}{6}\) \(\frac{3}{5}\)
Part 2: Compare Same-Numerator Fractions
Write < , > , or = in each circle.
\(\frac{4}{6}\) \(\frac{4}{10}\)
\(\frac{2}{7}\) \(\frac{2}{3}\)
\(\frac{5}{8}\) \(\frac{5}{12}\)
\(\frac{3}{4}\) \(\frac{3}{5}\)
7. Word Problem: Marcus painted \(\frac{2}{3}\) of a fence. Chloe painted \(\frac{2}{5}\) of an identical fence. Who painted more? Explain how you know.
8. Explain Your Thinking: Both \(\frac{4}{6}\) and \(\frac{4}{10}\) have a numerator of 4. How do you know which fraction is greater?
Same Numerator Exit Ticket Lesson 3 • Quick Check
Same Numerator Exit Ticket
Name: ________________________
Date: _______________
Compare Fractions with the Same Numerator
Write < , > , or = in each circle.
\(\frac{3}{5}\) \(\frac{3}{10}\)
\(\frac{2}{9}\) \(\frac{2}{4}\)
3. Which fraction is the greatest ? Circle the letter of the correct answer.
A. \(\frac{4}{12}\)
B. \(\frac{4}{5}\)
C. \(\frac{4}{8}\)
D. \(\frac{4}{10}\)
4. Sofia drank \(\frac{3}{4}\) of a bottle of water. Her brother drank \(\frac{3}{6}\) of an identical bottle. Who drank more water? Explain your thinking.
Mixed Fraction Teacher Guide Grade 4 • Fraction Faceoff • Lesson 4
Mixed Fraction Teacher Guide
Standard: 4.NF.A.2
Time: 55–60 Minutes
Learning Objective
Students will select and apply the most efficient strategy—unit fractions, same numerator, benchmark \(\frac{1}{2}\), or common denominators—to compare and order mixed sets of fractions and critique mathematical reasoning.
Materials
• Strategy Anchor Chart
• Independent Practice (2 pp.)
• Homework (1 p.) & Exit Ticket
Lesson Pacing & Facilitation Script
1. Warm-Up: Strategy Spotlight 8 mins
Write 3 pairs on the board: (A) \(\frac{1}{7}\) vs \(\frac{1}{4}\), (B) \(\frac{3}{5}\) vs \(\frac{3}{8}\), (C) \(\frac{2}{3}\) vs \(\frac{5}{8}\). Ask: "Which pair can you solve in under 3 seconds, and what strategy did you use?"
2. Mini-Lesson: Building the Comparison Toolkit 15 mins
Step 1 — Check for Unit Fractions: Both numerators are \(1\)? Larger denominator = smaller piece.Step 2 — Check for Same Numerator: Same number of pieces? Smaller denominator = larger pieces.Step 3 — Check Benchmark \(\frac{1}{2}\) or \(1\): Is one less than \(\frac{1}{2}\) and the other greater than \(\frac{1}{2}\)?Step 4 — Common Denominator: If none of the shortcuts apply (e.g., \(\frac{2}{3}\) vs \(\frac{3}{4}\)), make equivalent fractions.
3. Independent Practice & Error Analysis 22 mins
Students complete Mixed Fraction Independent Practice . Encourage them to name their chosen strategy before calculating. Review the Error Analysis problem (#9) as a whole class if time allows.
4. Closure & Summative Exit Ticket 10 mins
Administer the Mixed Fraction Exit Ticket to assess mastery across all four comparison types.
Common Misconceptions
Forcing Common Denominators Every Time: Students multiply \(7 \times 9 = 63\) for \(\frac{3}{7}\) vs \(\frac{3}{9}\) instead of using Same Numerator reasoning.Mixing Up Ordering Direction: Confusing "least to greatest" with "greatest to least."
Differentiation
Support: Allow students to keep a 4-strategy checklist card on their desk to guide strategy choice.Extend: Ask students to create their own comparison pair for each of the 4 strategies and trade with a partner.
Lesson 4 • Teacher Reference
Complete Answer Keys
Independent Practice Answer Key
Part 1: Mixed Comparison Arena
1. \(\frac{1}{9} < \frac{1}{4}\) (Unit Fraction)
2. \(\frac{3}{5} > \frac{3}{10}\) (Same Numerator)
3. \(\frac{2}{5} < \frac{5}{6}\) (Benchmark \(\frac{1}{2}\))
4. \(\frac{3}{4} > \frac{5}{8}\) (Common Denominator: \(\frac{6}{8} > \frac{5}{8}\))
5. \(\frac{4}{7} > \frac{4}{12}\) (Same Numerator)
6. \(\frac{2}{3} = \frac{4}{6}\) (Common Denominator)
Part 2: Order Three Fractions
7. Least to greatest: \(\frac{1}{4}, \frac{3}{8}, \frac{2}{3}\)
8. Greatest to least: \(\frac{5}{6}, \frac{3}{5}, \frac{2}{5}\)
Part 3: Error Analysis
9. Jordan is incorrect. Both \(\frac{4}{6}\) and \(\frac{4}{10}\) have 4 pieces, and sixths are larger than tenths, so \(\frac{4}{6} > \frac{4}{10}\).
Part 4: Multi-Step Word Problem
10. Elena (\(\frac{5}{6}\)) > Leo (\(\frac{2}{3} = \frac{4}{6}\)) > Noah (\(\frac{3}{8} < \frac{1}{2}\)). Elena walked the farthest.
Homework Answer Key
Part 1: Mixed Comparisons
1. \(\frac{1}{6} > \frac{1}{12}\) | 2. \(\frac{5}{8} > \frac{5}{10}\)
3. \(\frac{3}{10} < \frac{3}{4}\) | 4. \(\frac{2}{3} < \frac{5}{6}\)
5. \(\frac{3}{6} = \frac{1}{2}\) | 6. \(\frac{4}{5} > \frac{3}{8}\)
Part 2: Word Problem
7. Coach Lee's team drank more. \(\frac{5}{8} > \frac{1}{2}\) while \(\frac{2}{5} < \frac{1}{2}\).
Part 3: Strategy Choice
8. Sample: Use Same Numerator for \(\frac{3}{5}\) vs \(\frac{3}{9}\) because both have 3 pieces and fifths are larger than ninths—no common denominator needed.
Exit Ticket Answer Key & Unit Mastery Rubric
1. \(\frac{1}{8} < \frac{1}{5}\) | 2. \(\frac{4}{7} > \frac{4}{10}\) | 3. \(\frac{3}{4} > \frac{5}{8}\)
4. Choice C (\(\frac{1}{3} < \frac{2}{5} < \frac{3}{4}\)) is ordered from least to greatest.
5. Maya is correct. \(\frac{2}{3} = \frac{8}{12}\) and \(\frac{5}{6} = \frac{10}{12}\), or \(\frac{2}{3}\) is \(\frac{1}{3}\) away from 1 while \(\frac{5}{6}\) is only \(\frac{1}{6}\) away from 1, so \(\frac{5}{6} > \frac{2}{3}\).
Unit Mastery: 4–5 correct = Mastered 4.NF.A.2 | 0–3 correct = Target specific strategy from Lessons 1–3.
Mixed Fraction Independent Practice Lesson 4 • Independent Practice
Mixed Fraction Championship
Name: ________________________
Date: _______________
Your 4-Strategy Comparison Toolkit
1. Unit Fraction: Smaller denom = bigger piece
2. Same Numerator: Compare piece sizes
3. Benchmark \(\frac{1}{2}\): Compare each to \(\frac{1}{2}\)
4. Common Denom: Make equivalent fractions
Part 1: Mixed Comparison Arena
Write < , > , or = in each circle. On the line, name the strategy you used and show work if needed.
\(\frac{1}{9}\) \(\frac{1}{4}\)
\(\frac{3}{5}\) \(\frac{3}{10}\)
\(\frac{2}{5}\) \(\frac{5}{6}\)
\(\frac{3}{4}\) \(\frac{5}{8}\)
\(\frac{4}{7}\) \(\frac{4}{12}\)
\(\frac{2}{3}\) \(\frac{4}{6}\)
Lesson 4 • Independent Practice (Page 2)
Name: ________________________
Part 2: Order Mixed Fractions
7. Order from least to greatest : \(\quad \frac{2}{3}, \quad \frac{1}{4}, \quad \frac{3}{8}\)
8. Order from greatest to least : \(\quad \frac{2}{5}, \quad \frac{5}{6}, \quad \frac{3}{5}\)
Part 3: Championship Error Analysis
9. Jordan wrote \(\frac{4}{10} > \frac{4}{6}\) because \(10\) is greater than \(6\). Is Jordan correct? Explain why or why not.
Part 4: Multi-Step Word Problem
10. Three friends ran on a track. Elena ran \(\frac{5}{6}\) of a mile, Leo ran \(\frac{2}{3}\) of a mile, and Noah ran \(\frac{3}{8}\) of a mile. Who ran the farthest? Show your work.
Mixed Fraction Homework Lesson 4 • Homework
Mixed Fraction Practice
Name: ________________________
Date: _______________
Part 1: Choose Your Strategy & Compare
Write < , > , or = in each circle. Show work below when needed.
\(\frac{1}{6}\) \(\frac{1}{12}\)
\(\frac{5}{8}\) \(\frac{5}{10}\)
\(\frac{3}{10}\) \(\frac{3}{4}\)
\(\frac{2}{3}\) \(\frac{5}{6}\)
\(\frac{3}{6}\) \(\frac{1}{2}\)
\(\frac{4}{5}\) \(\frac{3}{8}\)
7. Word Problem: Coach Lee's team drank \(\frac{5}{8}\) of a water cooler. Coach Park's team drank \(\frac{2}{5}\) of an identical cooler. Which team drank more? Show how you know.
8. Strategy Choice: Which strategy is fastest for comparing \(\frac{3}{5}\) and \(\frac{3}{9}\), and why?
Mixed Fraction Exit Ticket Lesson 4 • Summative Quick Check
Mixed Fraction Exit Ticket
Name: ________________________
Date: _______________
Compare Using Any Strategy
Write < , > , or = in each circle.
\(\frac{1}{8}\) \(\frac{1}{5}\)
\(\frac{4}{7}\) \(\frac{4}{10}\)
\(\frac{3}{4}\) \(\frac{5}{8}\)
4. Which list shows the fractions in order from least to greatest ? Circle the letter.
A. \(\quad \frac{3}{4}, \quad \frac{2}{5}, \quad \frac{1}{3}\)
B. \(\quad \frac{2}{5}, \quad \frac{1}{3}, \quad \frac{3}{4}\)
C. \(\quad \frac{1}{3}, \quad \frac{2}{5}, \quad \frac{3}{4}\)
D. \(\quad \frac{1}{3}, \quad \frac{3}{4}, \quad \frac{2}{5}\)
5. Maya says \(\frac{5}{6} > \frac{2}{3}\). Do you agree or disagree? Use a model, benchmark, or equivalent fractions to prove your answer.
