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Hiking Maps: Distance and Elevation Estimates worksheet preview

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Hiking Maps: Distance and Elevation Estimates

Estimate irrational trail measurements, compare signed elevation changes, locate values on number lines, and estimate expressions involving π².

Grade 8MathInteractive · Printable

Aligned to8.NS.A.2

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What’s included

  • Single worksheet
  • Auto-graded online
  • 1 Common Core standard
  • Printable answer key
  • 14 questions
  • Classroom-ready

Details

Format
Interactive · Printable
Grade
Grade 8
Subject
Math
Question types
Fill in the blank, Multiple choice, Circle the answer, Short answer

About this worksheet

What students practice

  • Students use rational bounds to estimate and compare irrational measurements.
  • Students locate positive and negative irrational numbers on number lines.
  • Students estimate expressions involving square roots and π².

How to use

Assign after introducing square-root estimates. Have students use the provided bounds without a calculator and show supporting calculations on separate paper.

Curriculum

Common Core standard covered

8.NS.A.2

Estimate irrational numbers with rational ones to compare them, place them on a number line, and estimate expressions like pi squared.

Preview

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Name Date

Hiking Maps: Distance and Elevation Estimates

Use rational estimates to check trail distances, signed changes, and map calculations.

Check the Trail Measurements

Use squares and rational bounds to estimate each measurement. Treat the square-root measurements as exact.

1.
A trail map lists a route length of √47 kilometers. Which interval contains this length?
Route Estimate Checks
NumberSquare
6.744.89
6.846.24
6.947.61
749
  • A. Between 6.7 and 6.8 kilometers.
  • B. Between 6.8 and 6.9 kilometers.
  • C. Between 6.9 and 7.0 kilometers.
  • D. Between 7.0 and 7.1 kilometers.
2.
Another route is √61 kilometers long. Use 7.81² = 60.9961 and 7.82² = 61.1524.

Estimate its length to the nearest tenth:   km

3.
A connector trail is √33 kilometers long. Select every rational estimate that is shorter than the exact trail length. Use 5.744 < √33 < 5.745.

5.7 km23/4 km5.8 km5.74 km

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