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Scale Factors Questions for Teachers
A question bank built for middle-school and lower-secondary geometry, covering similar shapes, dilations, enlargements and reductions, and linear, area and volume scale factors. Built for Years 7-10 (Grades 6-10) and aligned to how scale factors are taught across the Australian Curriculum and US state standards.
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What's Included in the Scale Factors Question Bank?
🔥Progressive Difficulty Levels
Progressive Difficulty Levels
🌍 Targeted Practice
Targeted Practice
💡Conceptual Understanding
Conceptual Understanding
Practice Questions
Practice Questions
Questions move from finding a scale factor between two similar shapes through to multi-step problems on dilations, area scale factor and volume scale factor. Each level builds on the last so students reach the harder reasoning questions ready, not cold.
Engaging Exercises
Engaging Exercises
Targeted practice on the sub-skills that trip students up: identifying corresponding sides on similar figures, applying a linear scale factor to a missing length, squaring the scale factor for area, cubing it for volume, and interpreting scale on maps and scale drawings.
Differentiated Questions
Differentiated Questions
Questions are written to draw out the reasoning, not just the answer. Students explain why the area scale factor is the square of the linear scale factor, when to enlarge versus reduce, and how a scale of 1 cm to 5 km translates to real distance.
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What is covered in the scale factors question bank?
Linear, Area and Volume Scale Factors
Similar Shapes and Dilations
Scale Drawings, Maps and Real-World Problems
Students work through the three scale factors most commonly tested in middle-school and lower-secondary geometry: the linear scale factor (LSF) for lengths and perimeters, the area scale factor (LSF squared) for two-dimensional figures, and the volume scale factor (LSF cubed) for three-dimensional solids. Questions move from straight calculation to multi-step problems where students apply the right scale factor to the right dimension.
A set of questions on similar shapes and dilations, including identifying corresponding sides on similar triangles and quadrilaterals, finding a missing side using a given scale factor, and describing a dilation by its centre and scale factor. The questions build the proportional reasoning students rely on later in trigonometry and coordinate geometry.
Word problems on scale drawings, floor plans, maps and scale models. Students convert between scaled and real measurements (for example, a map scale of 1 cm to 5 km, or a model car at a scale of 1:24), reason about whether to enlarge or reduce, and check their answers against the original dimensions. These questions show students where scale factors show up outside the maths classroom.
Explore the full range of questions and strengthen your students' understanding of scale factors with Tutero's question bank