Objective: Students will identify geometric features (circles, sectors, symmetry) in a clock face, connect fractional and angle relationships to time measurement, estimate and calculate angles between clock hands at different times, and explore how art and math intersect in mechanical design.
Look: What shapes do you notice in the design? What patterns or symmetries do you see? How might math have helped the artist make this clock work and look beautiful?
Student Task:
Sketch the clock face in their notebooks. Label the geometric features they notice, such as circle, radius, diameter, center, Roman numerals, symmetry lines. Math Vocabulary: Circle, radius, diameter, sector, symmetry, fraction, angle, ratio.
Write: Prompts – If a clock face is a circle (360°), what fraction of the circle does each hour mark represent? How many degrees apart are the hour marks? What about the minute marks? At 3:00, what’s the angle between the hands? What about 2:20? How could you design a new clock face with a different pattern or proportion
Share: What patterns or relationships did you discover about time and angles? How did your group visualize or calculate your question? How does symmetry or proportion make the clock beautiful and functional?
Math Extension Options
Fractions of Time: Express times as fractions of a full rotation (e.g., 15 minutes = ¼ turn).
Ratios and Speed: Explore how gear ratios in a clock control the movement of the hands.
Design Challenge: Create a 12-sided clock instead of a circular one. How would that change the angles?
History Link: Research how mathematical precision evolved in clockmaking over time.
Standard: M.7.G.A.1 Solve problems involving scale drawings of geometric figures, including computing actual lengths and areas from a scale drawing and reproducing a scale drawing at a different scale.