Fractions as Numbers

Overview

In Lesson 7 of the “Build, Model, Solve” unit, students revisit unit fractions, equivalence, and comparison from Grade 3 using concrete and visual models. They then extend this understanding by generating equivalent fractions and comparing fractions with different numerators and denominators.

Learning intentions

Students will be able to:

• Explain how fractions name equal parts of the same whole.
• Generate equivalent fractions using visual models and multiplication.
• Compare fractions with different numerators and denominators.
• Justify comparisons using fraction strips, number lines, or benchmark fractions.

Success criteria

• I can show that two fractions are equivalent even when their parts differ in number and size.
• I can create an equivalent fraction by multiplying the numerator and denominator by the same number.
• I can compare fractions that refer to the same whole using <, >, or =.
• I can explain my reasoning with a model, equation, or benchmark such as one-half.

Curriculum links

• Number and Operations—Fractions: explain and generate equivalent fractions using visual fraction models.
• Number and Operations—Fractions: compare fractions with different numerators and denominators and record comparisons using symbols.
• Mathematical Practices: model with mathematics, use appropriate tools strategically, and construct viable arguments.
• Grade 3 review: understand unit fractions, fractions on number lines, and fractions as numbers.

Lesson structure (60 minutes)

1. 0–7 min · Hook and retrieval. Display a rectangle divided into fourths with two parts shaded, alongside the same rectangle divided into eighths with four parts shaded, using the opening comparison slide. Ask, “Which fraction is greater: 2/4 or 4/8? How do you know?” Students make a silent choice, discuss with a partner, and share a model or explanation. Record several ideas without confirming the answer immediately.

2. 7–17 min · Direct teach: equivalent fractions. Use the equivalent fractions teaching slides and a large fraction strip to model 1/2 = 2/4 = 4/8. Emphasize that the whole stays the same, the number of parts increases, and each part becomes smaller. Connect the model to multiplying both numerator and denominator by the same number. Students build the examples with fraction strips and explain what changes and what stays the same.

3. 17–30 min · Partner investigation. Give each pair fraction strips, a number line from 0 to 1, pattern blocks, and paper-folding materials. Display the investigation directions on the partner investigation instructions. Students represent pairs such as 1/2 and 3/6, 2/3 and 4/6, and 3/4 and 6/8. They record one visual model and one equation for each pair on the fraction models and equivalence worksheet. Circulate and ask, “How does your model prove the fractions are the same size?”

4. 30–42 min · Compare different fractions. Model a comparison such as 3/4 and 5/8 by locating both fractions on the same number line or converting 3/4 to 6/8. Then model a benchmark comparison such as 3/8 and 1/2. Students use their materials to compare 2/3 and 3/5, 5/6 and 3/4, and 4/10 and 1/2. They write a symbol and a justification on the worksheet. Reinforce that comparisons are valid only when the fractions refer to the same whole.

5. 42–53 min · Independent application. Students complete the remaining problems on the fraction models and equivalence worksheet independently. Tasks include generating equivalent fractions, identifying a missing numerator or denominator, comparing fractions, and explaining one comparison with a drawing, number line, common denominator, or benchmark. Pause midway for a quick check: students hold up one finger for “I used a model,” two for “I used an equivalent fraction,” or three for “I used a benchmark.”

6. 53–60 min · Discussion and exit check. Revisit the opening comparison with the synthesis and exit prompt slides. Students explain why 2/4 and 4/8 are equal and complete an individual exit response: “Compare 3/6 and 2/3. Write <, >, or =, and prove your answer with a model or explanation.” Collect responses to identify students ready for the next lesson and students needing additional modeling.

Resources

• the fraction equivalence and comparison slide deck
• the fraction models and equivalence worksheet
• Fraction strips labeled from 0 to 1
• Blank number lines from 0 to 1
• Pattern blocks or paper fraction shapes
• Plain paper for folding
• Colored pencils or crayons
• Document camera or interactive display
• Pencils and math notebooks

Assessment

• Listen for whether students explain that the whole remains constant and both numerator and denominator are multiplied by the same factor.
• Check partner models and worksheet justifications for accurate equivalence, comparison symbols, and use of a common whole.
• Use the exit response to sort students into: secure, developing, or needing a small-group reteach with fraction strips.

Differentiation

• Support students with pre-labeled fraction strips, color-coded numerator and denominator examples, and a number line marked at fourths and eighths. Provide sentence starters such as “These fractions are equivalent because…” and “___ is greater than ___ because…”
• For students needing additional support, limit initial comparisons to fractions with related denominators, such as fourths and eighths, and model each step with one concrete representation.
• Provide EAL support through gestures, visual models, and repeated language for “same whole,” “equal parts,” “equivalent,” “numerator,” and “denominator.” Pair students strategically for mathematical talk.
• Challenge early finishers to find two different ways to prove whether 5/6 is greater than 7/9, then explain which method is most efficient.