Mathematical Process Standards>Applying Mathematics to Everyday Life and Work(TEKS.Math.7.1.A)
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Texas 7th Grade Math › Mathematical Process Standards>Applying Mathematics to Everyday Life and Work(TEKS.Math.7.1.A)
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.
A fundraiser sold 350 bars at \$2 each toward a \$1500 goal.
What is the first step to determine how much more money is needed to reach the goal?
Multiply 350 by 2
Subtract 350 from 1500
Divide 1500 by 2
Add 350 and 1500
Explanation
First compute the amount raised in dollars: $350 \times 2 = 700$. Then compare to the goal by calculating $1500 - 700$. Subtracting 350 from 1500 mixes units (bars vs. dollars), and the other options do not set up the needed comparison.
A cell phone plan costs 40 per month plus 0.12 per text over 300 texts. Alex sent 520 texts this month. Which expression gives Alex's total bill for the month?
40 + 0.12(520 - 300)
40 + 0.12(520)
0.12(520 - 300)
40 + (520 - 300)/0.12
Explanation
Monthly fee 40 plus overage: 0.12 per text for (520 − 300) = 220 extra texts, so total is 40 + 0.12(520 − 300). Choice B charges for all 520 texts. Choice C omits the fixed 40. Choice D divides by 0.12 instead of multiplying.
Which equation matches this table? x: -2, 0, 1, 3; y: -1, 3, 5, 9
$y = 2x + 3$
$y = 3x + 2$
$y = 2x - 3$
$y = -2x + 3$
Explanation
When $x=0$, $y=3$, so $b=3$. From $x=0$ to $x=1$, $y$ increases from 3 to 5, a change of 2, so $m=2$. The matching equation is $y=2x+3$. The other choices change the slope or intercept.
Which equation matches this table? x: -2, 0, 2, 6; y: 7, 4, 1, -5
$y = 1.5x + 4$
$y = -x + 4$
$y = -1.5x + 4$
$y = -1.5x - 4$
Explanation
When $x=0$, $y=4$, so $b=4$. From $x=-2$ to $x=0$, $y$ changes from 7 to 4 (down 3) while $x$ increases by 2, so $m=\frac{-3}{2}=-1.5$. Thus $y=-1.5x+4$.
A ride-share app charges a base fee of 2.50 plus 1.80 per mile. Jen's trip was 12 miles. Which equation correctly models the total cost $C$ of this trip?
$C = 1.80(12)$
$C = 2.50 + 1.80(12)$
$C = 2.50 + 1.80 + 12$
$C = 2.50(12) + 1.80$
Explanation
Base fee 2.50 plus mileage: 1.80 per mile for 12 miles, so $C = 2.50 + 1.80(12)$. Choice A omits the base fee. Choice C adds 12 instead of multiplying by the rate. Choice D multiplies the base fee by miles, which is incorrect.
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.
A water tank holds 800 liters. It currently has 275 liters. A pump adds 12 liters per minute.
Which calculation best checks whether running the pump for 44 minutes will fill the tank?
$275 + 44$
$800 - 275 \div 12$
$275 + 12 \times 44$
$800 \times 44 - 12$
Explanation
To check reasonableness, model the final amount after 44 minutes: $275 + 12 \times 44$. If this is at least 800, the time is reasonable. The other options do not represent adding 12 liters each minute to the current amount.
Which table matches $y = 2x - 6$?
x: 0, 3, 6, 9; y: -4, 2, 8, 14
x: 0, 3, 6, 9; y: -6, -12, -18, -24
x: 0, 3, 6, 9; y: 6, 12, 18, 24
x: 0, 3, 6, 9; y: -6, 0, 6, 12
Explanation
At $x=0$, $y=-6$ sets $b=-6$. Slope $m=2$ means each increase of 3 in $x$ raises $y$ by 6. The table with $y: -6, 0, 6, 12$ matches $y=2x-6$.
An online shop sells notebooks for 3.25 each and charges a one-time shipping fee of 6.50 per order. Maya buys 8 notebooks. What is the total cost?
$3.25 + 8 + 6.50$
$3.25 \times 8$
\$32.50$
$6.50(3.25 + 8)$
Explanation
Item cost: 3.25 each for 8 notebooks gives 3.25 × 8 = 26. Add shipping 6.50 once: 26 + 6.50 = 32.50. Choice A adds instead of multiplying. Choice B omits shipping. Choice D multiplies shipping by the sum, which is not how fees work.