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PlayOwl

Mathematics · Grade 7

Scale Drawings and Geometric Constructions

Learners treat a scale as a proportional relationship: they find actual lengths and areas from maps, plans and models, explain why areas grow by the square of the scale factor, and redraw a figure at a new scale. They then reason about constructing triangles: which three lengths can meet, why the angles always add to 180°, and which sets of measurements give exactly one triangle, more than one, or none.

  • 4 lessons
  • About 95 minutes
  • Scale drawings and triangles check: 11 questions
  • Ways to answer: fill in the blanks, choose an answer, type a fraction, match pairs, type a number and place on a number line
See plans Included with Family, Teacher and School plans. Open in PlayOwl

What learners will discover

  • Use a scale or scale factor to find actual lengths from a scale drawing and drawing lengths from actual lengths, including scales written with different units.
  • Compute actual areas from a scale drawing, explaining why areas are multiplied by the square of the scale factor, and redraw a figure at a different scale.
  • Use the triangle inequality to decide whether three lengths form a triangle and to find the possible lengths of a third side.
  • Use the 180° angle sum and the given conditions to decide whether measurements determine exactly one triangle, more than one triangle or no triangle.

Lessons

  1. Scales and actual lengths 9 steps5 practiceabout 22 min
  2. Areas and redrawing at a new scale 9 steps5 practiceabout 24 min
  3. Which three lengths make a triangle? 9 steps4 practiceabout 22 min
  4. Angles and how many triangles 9 steps5 practiceabout 27 min
  5. Scale drawings and triangles check 11 questions at the end

Keep exploring

Games to practice with

  • Number-Line HopHelp the frog hop to the right number — from counting to negative fractions.
  • Ratio KitchenScale recipes, fill ratio tables and find the better buy.
  • Coordinate CourierDrive the parcel van to the right address on the coordinate grid.

More 7th grade math

Guide for grown-ups