Selecting Tools and Techniques to Solve Problems(TEKS.Math.7.1.C)
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Texas 7th Grade Math › Selecting Tools and Techniques to Solve Problems(TEKS.Math.7.1.C)
A circular garden has a diameter of 9.85 meters. You need its circumference using $\pi \approx 3.14$ and must round to the nearest tenth. Which tool/technique is most efficient and accurate?
Mental math
Paper and pencil computation
Calculator
Spreadsheet
Explanation
Multiplying a decimal by $\pi$ requires precision and careful rounding; a calculator is fastest and least error-prone. Mental math risks accuracy, paper-and-pencil is slower and more error-prone, and a spreadsheet is overkill for one calculation.
Without finding exact decimals, decide which is greater: 11/12 or 7/8. Which tool/technique is most efficient and accurate?
Mental math using fraction comparison
Graphing calculator
Spreadsheet
Paper and pencil long division to convert to decimals
Explanation
Use quick mental cross-multiplication: $11 \times 8 = 88$ and $7 \times 12 = 84$, so 11/12 is greater. Calculators, spreadsheets, or long division are slower and unnecessary.
You want to quickly check if five items priced 3.99, 7.49, 1.89, 12.59, and 0.79 will cost less than 30 dollars before tax. Which tool/technique is most efficient and accurate for this quick decision?
Calculator to compute the exact total
Estimation using compatible numbers
Paper and pencil exact column addition
Spreadsheet
Explanation
Estimation is best for a quick check: 3.99 ≈ 4, 7.49 ≈ 7.5, 1.89 ≈ 2, 12.59 ≈ 12.5, 0.79 ≈ 0.8; sum ≈ 26.8, which is under 30. Exact calculator or paper-and-pencil is slower than needed, and a spreadsheet is overkill.
Solve the equation $3(2x - 5) = 27$. Which tool/technique is most efficient and accurate?
Mental math guess-and-check
Estimation only
Graphing calculator
Paper and pencil algebraic steps
Explanation
Algebraic steps are clearest and reliable: $3(2x-5)=27 \Rightarrow 6x-15=27 \Rightarrow 6x=42 \Rightarrow x=7$. Guess-and-check and estimation are inefficient or not exact; a graphing calculator is unnecessary for this linear equation.
Your science lab recorded 30 temperature readings with one decimal place (for example: 19.6, 20.1, 18.9, 21.3, ...). You need the mean and median and to find any values above 22.0. Which tool/technique is most efficient and accurate?
Hand calculator only
Spreadsheet
Mental math
Paper and pencil list and tally
Explanation
A spreadsheet efficiently computes mean, sorts to find the median, and filters values over 22.0 with minimal error. A hand calculator is tedious and error-prone for many numbers, mental math is impractical, and paper lists are slow.