Learning target: Students will generate equivalent fractions and compare two fractions with unlike denominators, explaining the relationship with a model or strategy aligned to 5.NR.3.2.

Materials: Fraction strips, paper and pencils for drawings, a projected number line, and the teacher’s comparison examples.

Retrieve prerequisite knowledge: ask students to write an equivalent fraction for 1/2 with denominator 4 and explain how they know. Expected answer: 2/4, because the numerator and denominator were both multiplied by 2, so the fraction’s value stays the same. If students change only the denominator, briefly model multiplying both parts by the same number and have them try again. State the learning target and success criteria: make equivalent fractions with a common denominator, compare the numerators, and use a model or strategy to justify the comparison.

Guided practice, I do (10 minutes): Display 2/3 and 3/4 with fraction strips. Think aloud as you rename both fractions in twelfths: 2/3 = 8/12 and 3/4 = 9/12. Align the strips to show the same whole and compare the lengths; conclude 2/3 < 3/4 because 8 twelfths is less than 9 twelfths. Label numerator and denominator on a displayed fraction, and show equivalent with the matching lengths and equal values. Ask, “What must stay the same when we make an equivalent fraction?”

Collaborative practice, we do (15 minutes): Partners use fraction strips or a drawn number line to compare 1/2 and 3/8. Ask them to make the units alike, record the equivalents, and explain their reasoning to a partner. Expected reasoning: 1/2 = 4/8, and 4/8 > 3/8, so 1/2 > 3/8. Hinge question: “Which is greater, 1/2 or 3/8, and what common unit proves it?” Look for 4/8 > 3/8 and a model or explanation that compares equal-sized parts. If students compare denominators alone or say 3/8 is greater because 8 is greater than 2, revoice the error, align the strips, and ask them to compare the lengths and then the eighths. Recheck the same idea with 2/3 and 3/4: students should identify twelfths and show 8/12 < 9/12.

Independent practice, you do (12 minutes): Students compare 5/6 and 3/4, choosing fraction strips or a drawn number line. Expected result: 5/6 = 10/12 and 3/4 = 9/12, so 5/6 > 3/4. Require the equivalent fractions and a model or written explanation. Provide the choice of representation to support access while keeping the comparison and justification independent.

Transition and vocabulary check (3 minutes): Have students return materials and point to the numerator and denominator in 3/4; ask them to say what equivalent means using 1/2 = 2/4 as an example. Classroom language objective: explain a fraction comparison orally and in writing using numerator, denominator, equivalent, and a comparison statement. Partners rehearse, “___ is greater than/less than ___ because ___ and ___ are equivalent fractions with denominator ___.” Listen for accurate vocabulary and a reason tied to equal-sized parts.

Exit ticket (5 minutes): Compare 2/3 and 3/5. Show equivalent fractions with a common denominator and include a bar model, fraction strip sketch, or number-line representation. Expected result: 2/3 = 10/15 and 3/5 = 9/15, so 2/3 > 3/5. Collect the work as evidence of the target.

Consolidate (5 minutes): Invite students to explain how using common-sized parts made the comparison fair. Reinforce that equivalent fractions name the same amount and that comparing numerators is useful only after the fractions refer to equal-sized parts. Use the exit-ticket models and explanations to decide whether to begin the next lesson with another common-unit comparison or a brief reteach.

Homework: none

IEP: Provide fraction strips and number lines throughout; read comparison prompts aloud, present multi-step work one step at a time, and allow extended time on the exit ticket.

ESOL: For the four students at WIDA levels 2–3, use a labeled visual for numerator, denominator, and equivalent, with a matching fraction-strip example. Offer optional Spanish or Korean vocabulary resources without making a classmate responsible for translation. Build in partner oral rehearsal with the comparison frame from the lesson, then check for accurate use of the vocabulary and a reason connected to the model.

504: Seat the student near the board and build a brief movement break into independent practice before returning to the comparison task.

Gifted: Offer a real-world distance comparison, such as comparing 7/8 mile with 5/6 mile walked on two trail routes. Ask students to justify the comparison using both common denominators and a benchmark or number-line strategy, and explain which strategy is more efficient.

Evidence: Use the exit ticket comparing 2/3 and 3/5 to check whether students generate equivalent fractions with a common denominator, state the correct relationship, and justify it with a representation. Look for 10/15 and 9/15, 2/3 > 3/5, and a model that represents equal-sized parts. If the common denominator or comparison is incorrect, give actionable feedback by asking the student to represent both fractions in fifteenths, then recheck with 1/2 and 3/10.