RockLicker · Grade 6 · Lesson 4 of 5

How Steep Is This Map?

Convert map scale into horizontal distance and calculate a simplified average gradient.

  • Grade 6
  • 50 minutes
  • Worksheet + teacher guidance
Back to Grade 6

What you will learn

Average gradient is elevation change divided by horizontal distance. It summarizes the interval considered; it does not describe every local slope along a route.

Words to use

  • scale: map-to-ground relationship
  • horizontal distance: plan-view distance
  • gradient: rise divided by run

Evidence for this lesson

Imaginary map scale 1:10,000. A: elevation 100 to 140 m across 2 cm. B: same elevation change across 5 cm. Measurements are horizontal map distances, not trail lengths.

Use the supplied record as written; do not invent missing results.

Work through the activity

  1. 10 min · Convert scaleAt 1:10,000, explain that 1 cm on the map represents 100 m on the ground. Keep map and ground units separate.
  2. 15 min · Calculate distancesConvert 2 cm and 5 cm into ground distances. Both example slopes rise from 100 to 140 m.
  3. 15 min · Calculate gradientsDivide the 40 m rise by each horizontal distance and multiply by 100 for percent. Compare the average slopes.
  4. 10 min · Explain limitsIdentify the steeper average and explain why average gradient does not establish trail length, local hazards or safe access.
RockLicker
GRADE 6 · LESSON 4

How Steep Is This Map?

Draw on the printed sheet or write, type or dictate your response.
Draw on the printed sheet or write, type or dictate your response.
Draw on the printed sheet or write, type or dictate your response.
Draw on the printed sheet or write, type or dictate your response.

Responses stay in this open page only. Print before closing or changing pages; no student record is stored online.

Check your understanding

A 40 m rise over 200 m horizontal distance is …

Teacher & family guide · answers and assessment

Grade 6 · How Steep Is This Map?

Learning goal: Convert map scale into horizontal distance and calculate a simplified average gradient.

Expected responses

  1. 100 m: 10,000 cm equals 100 m.
  2. A: 200 m; B: 500 m.
  3. A: 40/200 = 0.20 = 20%; B: 40/500 = 0.08 = 8%.
  4. A has the steeper average; local slope changes, route condition and actual walking distance remain unknown.

Understanding check: 20%. 40 divided by 200 is 0.20, or 20%. This is not an angle in degrees.

Watch for this misconception

A 20% gradient is not a 20-degree angle; percent and degrees are different measures.

Assess the evidence

Look for the observations, calculation or explanation named in the learning goal. Accept accurate drawings and dictated responses. Use the expected responses to discuss reasoning; a correct guess without explanation is a starting point for another conversation.

Adapt and extend

Read prompts aloud, enlarge print or let a partner record the learner’s explanation. Calculate the gradient if the same 40 m rise occurs over 400 m.