Question

summative assessment
designing a scaled school playground blueprint
statement of inquiry:
proportional relationships and transformations model real - world spaces and change.

your task
you are an architect designing a new school playground. you will create a scaled blueprint,
prove similarity using dilation, and analyze one feature using slope.
part 1: playground design & scale drawing

• choose at least 4 playground features (slide, swings, court, ramp, path, etc.).

peirce’s playground is approximately 120 meters by 50 meters.

• choose a scale (must choose one of these scales)
• 1 cm = 4 m → draw 30 cm × 12.5 cm
• 1 cm = 3 m → draw 40 cm × 16.7 cm
• 1 cm = 2.5 m → draw 48 cm × 20 cm
• create a scaled blueprint with ruler and labels.
• include a title, scale key, and all measurements.

part 2: dilation & similarity (separate sheet of paper or section of your
poster)

• select one playground feature.
• examples: a slide, basketball hoop height, merry - go - round
• a feature of the park you may like to have two of, a larger and smaller

version for the lower grades.

• create a dilated version using a scale factor and center of dilation.
• prove similarity using corresponding sides and angles.
• write a short similarity justification.
• how do you know they are similar? are their angles congruent? is the

quotient of their sides the same?

Explanation:

The problem involves creating a scaled blueprint (scale drawing), using dilation (a transformation in geometry) to create similar figures, and analyzing slope. These concepts are central to Geometry (subfield of Mathematics), as scale drawings, dilations, similarity, and slope are key topics in Geometry. The task requires applying geometric principles to model a real - world space (the playground) through scale, transformations, and slope analysis.

Answer:

Mathematics - Geometry