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Ski Resort: Lift Lines and Snowfall Estimates worksheet preview

Worksheet

Ski Resort: Lift Lines and Snowfall Estimates

Estimate irrational values using ski resort snowfall records and lift-line models, then compare values and locate them on number lines.

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 irrational numbers.
  • Students compare irrational values and locate them on number lines.
  • Students estimate expressions involving square roots and pi.

How to use

Have students work without a calculator and use nearby squares to justify estimates. Review the final explanation together.

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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Ski Resort: Lift Lines and Snowfall Estimates

Use rational estimates to locate, compare, and interpret irrational values.

Bound the Recorded Values

Work without a calculator. Use nearby perfect squares or square the decimal bounds. All square roots mean the nonnegative square root.

1.
A snowfall model gives a depth of √58 inches. Between which consecutive whole numbers does this depth lie?

  < √58 <  

2.
A lift-line model gives a wait of √118 minutes. Which pair of bounds is correct?
  • A. 10.8 < √118 < 10.9
  • B. 10.9 < √118 < 11.0
  • C. 11.8 < √118 < 11.9
  • D. 10.7 < √118 < 10.8
3.
A snow-depth calculation gives √7 inches. Use 2.64² = 6.9696 and 2.65² = 7.0225 to estimate √7 to the nearest hundredth.

Estimated depth:   inches

4.
For a lift wait of √92 minutes, which calculation establishes that the wait is between 9.5 and 9.6 minutes?
  • A. 9.5² = 90.25 and 9.6² = 92.16.
  • B. 9.4² = 88.36 and 9.5² = 90.25.
  • C. 9² = 81 and 10² = 100.
  • D. 9.6² = 92.16 and 9.7² = 94.09.

Locate and Compare

Use rational benchmarks to locate the resort's modeled values. Each marked interval on a number line represents 0.1 unit.

5.
A snowfall estimate is √43 inches. Between which adjacent marks should it be placed?66.16.26.36.46.56.66.76.86.97
  • A. Between 6.3 and 6.4.
  • B. Between 6.4 and 6.5.
  • C. Between 6.6 and 6.7.
  • D. Between 6.5 and 6.6.
6.
The signed difference between a modeled snowfall total and the seasonal average is −√19 inches. Write the two adjacent marks that surround this value, smaller first.−5−4.9−4.8−4.7−4.6−4.5−4.4−4.3−4.2−4.1−4

  < −√19 <  

7.
Four modeled lift waits, in minutes, are π, √15, 3.9, and √16.2. Which list orders them from least to greatest?
  • A. π < √15 < √16.2 < 3.9
  • B. √15 < π < 3.9 < √16.2
  • C. π < √15 < 3.9 < √16.2
  • D. π < 3.9 < √15 < √16.2
8.
A modeled snowfall depth is √26 inches. Select every rational depth that is greater than √26 inches.

5.09 inches5.1 inches5 inches5.2 inches

Use Estimates to Make Decisions

Apply rational estimates to the resort reports. Round only as directed.

9.
The morning snowfall model gives √82 inches. The resort posts depths to the nearest tenth. Use 9.05² = 81.9025 and 9.06² = 82.0836.

What depth should the resort post?   inches

10.
Noor can choose the Pine lift, with a modeled wait of √150 minutes, or the Summit lift, with a wait of 12.3 minutes. Which comparison is correct?
  • A. The Pine wait is shorter because √150 < 12.0.
  • B. The Pine wait is shorter because √150 < 12.3.
  • C. The Summit wait is shorter because √150 > 12.3.
  • D. The waits are equal because √150 = 12.3.
11.
A resort planning spreadsheet includes the expression π². Use 3.14 as a rational approximation for π, then square that approximation.

Estimate π² to the nearest hundredth:  

12.
A snowfall model predicts √37 inches during each of two equal storm periods. Estimate the combined depth, 2√37, to the nearest tenth. You may use 6.08² = 36.9664 and 6.09² = 37.0881.

Combined depth:   inches

13.
Eli's modeled lift wait is √170 minutes. He wants a time allowance that is at least this long. His timer accepts only multiples of 0.1 minute. Use 13² = 169 and 13.1² = 171.61.

What is the smallest time allowance he can enter?   minutes

14.
A snowfall model gives a depth of √(49 + 36) inches. Sam writes, “√(49 + 36) = √49 + √36 = 13 inches.” Explain why Sam's method is incorrect. Use consecutive whole-number bounds to show why 13 inches is not a reasonable estimate.

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