Shape and Density

This worksheet is designed for students in Grades 7 and 8 to build a deep, conceptual understanding of density as an intrinsic property of matter. Through quantitative problems and explanation-based prompts, learners explore how density remains constant despite changes in shape, cutting, or uniform scaling, while also examining how buoyancy depends on volume displacement rather than material alone.

Learning Goals

• Density Invariance (Gr. 7-8): Understand that density does not change when an object is reshaped, cut into pieces, or scaled uniformly.
• Mass-Volume Scaling: Reason mathematically about how mass and volume increase or decrease proportionally in scaled objects (e.g., spheres of different radii).
• Buoyancy & Displacement: Apply density comparisons to predict floating or sinking and explain cases like steel boats floating due to displaced water.
• Percent Above Water Reasoning: Relate the fraction of an object’s volume above water to density ratios using proportional thinking.
• Scientific Justification: Support conclusions with clear mathematical reasoning and written explanations.

Instructional Benefits

• Teacher-Created Resource: Designed by educators to align with middle school physical science, chemistry, and math standards.
• Concept-Focused Practice: Emphasizes why density stays the same and how shape influences buoyancy without changing density.
• Integrated Math & Science: Reinforces geometric scaling, ratios, and proportional reasoning within authentic science contexts.
• Explanation-Driven Questions: Encourages students to justify answers quantitatively, strengthening scientific communication skills.
• Flexible Use: Ideal for science lessons, cross-curricular math integration, small groups, enrichment, assessment preparation, homework, or homeschool instruction.

This Shape and Density worksheet helps students move beyond memorization to a true understanding of material properties and buoyancy. By analyzing reshaped objects, scaled solids, and floating scenarios, learners strengthen quantitative reasoning, geometric insight, and scientific explanation-key skills for success in advanced physical science and chemistry topics.

This worksheet is part of our Density collection.