Selecting Tools and Techniques to Solve Problems(TEKS.Math.6.1.C)
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Texas 6th Grade Math › Selecting Tools and Techniques to Solve Problems(TEKS.Math.6.1.C)
A student needs the exact total cost for 8 items priced 3.49, 7.95, 12.59, 4.39, 9.75, 6.88, 2.49, and 5.27, plus 8.25% sales tax. Which tool would be most appropriate to get an accurate answer efficiently?
Mental math
Estimation
Calculator
Paper and pencil
Explanation
This requires adding many decimals and then applying a percentage for tax. High accuracy is needed, and a calculator reduces place-value and computation errors compared with mental math or paper/pencil.
You are planning to buy tiles to cover a room that is 12.4 feet by 9.8 feet. Each tile covers about 1 square foot. You only need a quick number to order enough boxes (you will round up later). Which technique would give the most useful answer quickly?
Calculator
Estimation
Mental math
Manipulatives
Explanation
Estimation is best because only an approximate count is needed. Round 12.4 to 12 and 9.8 to 10 to estimate about 120 tiles. A calculator or paper calculation gives unnecessary precision; manipulatives are not needed.
To reconcile a checkbook, find the exact value of $23.8 + 7.64 + 19.07 - 8.5$, and your teacher asks you to show your setup aligning decimals. Which tool is most appropriate?
Mental math
Calculator
Manipulatives
Paper and pencil
Explanation
Paper and pencil let you line up decimals, record steps, and check place value for an exact total. Mental math risks place-value mistakes; a calculator gives an answer but does not show your setup; manipulatives are not relevant.
What is $0.25 \times 48$? Which technique would be most efficient?
Mental math
Paper and pencil
Calculator
Manipulatives
Explanation
\$0.25$ is one-fourth, so a quarter of 48 is 12. Mental math is quick and reliable here; paper/pencil or a calculator is unnecessary, and manipulatives are not needed.
Your teacher asks you to model and compare $1\frac{3}{4}$ and \$1.6$ using physical pieces to see which is greater. Which tool would be most appropriate?
Paper and pencil
Calculator
Manipulatives
Estimation
Explanation
The task is to model the quantities, so manipulatives (e.g., fraction/decimal tiles or number line strips) are most appropriate. A calculator compares numbers but does not create a physical model; estimation may be misleading; pencil sketches are less direct than using actual pieces.