Mathematical Process Standards
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Texas 6th Grade Math › Mathematical Process Standards
A class trip costs 180 dollars. The class has 24 dollars saved but must pay a one-time 12-dollar materials fee before selling bracelets. They will sell bracelets for 6 dollars each. How many bracelets are needed to reach the goal?
What is the first calculation you should do to plan the solution?
$180 \div 6$
$24 + 12$
$180 - 6$
$180 - 24 + 12$
Explanation
Analyze: Goal $=180$, current savings $=24$, one-time fee $=12$ reduces savings, each bracelet adds $6$. Plan: First find the remaining amount needed after accounting for savings and the fee: $180 - 24 + 12 = 168$. Then determine bracelets: $168 \div 6 = 28$. Determine solution: $28$ bracelets. Justify: The sequence mirrors the situation (apply fee and savings before dividing by price per bracelet). Evaluate: Check total: $24 - 12 + 6\times 28 = 12 + 168 = 180$, exactly the goal, so reasonable.
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.
Words: Three-fourths of a class of 24 students passed the test. Which representation shows the same relationship?
Words: One-fourth of the class passed, which is 6 students.
Symbols: $\frac{3}{4} \times 24 = 18$
Diagram: A bar divided into 4 equal parts with 1 part shaded to show those who passed.
Graph: A line $y=1.25x$ with the point (24, 18) highlighted.
Explanation
Taking three-fourths of 24 gives $\frac{3}{4}\times 24=18$, so 18 students passed. The other choices mismatch the proportion or show a different relationship.
Jake claims that $\frac{3}{4}$ is greater than $\frac{7}{8}$ because 3 and 4 are smaller numbers than 7 and 8. How would you correctly explain which fraction is larger?
Smaller numbers make smaller fractions, so $\frac{3}{4}$ is smaller than $\frac{7}{8}$ because 3 < 7 and 4 < 8.
You cannot compare fractions with different denominators, so there is no way to tell without long decimals.
Rewrite with a common denominator: $\frac{3}{4} = \frac{6}{8}$ and $\frac{7}{8}$ stays the same. With the same denominator, compare numerators: $6 < 7$, so $\frac{3}{4} < \frac{7}{8}$.
$\frac{3}{4}$ is close to 1 and $\frac{7}{8}$ is not, so $\frac{3}{4}$ must be larger.
Explanation
Comparing fractions is valid by using a common denominator. Convert $\frac{3}{4}$ to $\frac{6}{8}$ and compare it to $\frac{7}{8}$. Because both fractions have denominator 8, the one with the greater numerator is larger. Since $6 < 7$, $\frac{6}{8} < \frac{7}{8}$, so $\frac{3}{4} < \frac{7}{8}$.
A bike shop recorded helmets sold by size in one day: small 7, medium 12, large 9, extra-large 2.
What representation would best organize this data to quickly compare sizes and compute the total sold?
A frequency table with columns for size and number sold, plus a row for the total
A sentence describing the sizes and numbers in one long list
A collage of helmet drawings without counts
One bar showing only the total number of helmets sold
Explanation
A frequency table organizes each size with its count and allows adding a total, making comparisons and calculations clear. The other options are incomplete or do not support analysis.
Consider these two procedures: 1) Finding 10% of a number. 2) Dividing the number by 10. How are these two mathematical ideas related?
Both decrease numbers by 10 each time.
Finding 10% of a number is the same as dividing the number by 10.
Finding 10% is the same as subtracting 10 from the number.
Dividing by 10 is the same as taking 10% more.
Explanation
Because 10% equals $\frac{1}{10}$, finding 10% of a number means multiplying by $\frac{1}{10}$, which is equivalent to dividing by 10. Recognizing percent–fraction equivalences builds mental math flexibility (e.g., 10% is divide by 10).
A community cleanup is making snack bags. Each of the 96 volunteers gets 1 granola bar, and each of the 7 team leaders needs 2 bars. Boxes contain 18 bars. What expression should you calculate first to find the total number of bars needed before dividing by 18?
$96 + 7 + 2$
$96 \times (7 + 2)$
$96 + 2 \times 7$
$(96 + 7) \times 2$
Explanation
You need the total bars required: 96 bars for volunteers plus 2 bars per team leader, so $96 + 2 \times 7$. The other choices either add everything, group incorrectly, or double the entire group.
Mina recorded the high temperature each day for 7 days.
To show how the temperature changed over the week, which representation is best?
A pie chart of the seven temperatures
A line graph with time on the horizontal axis and temperature on the vertical axis
An unordered list of the temperatures
A two-column table with days and temperatures in no particular order
Explanation
A line graph is designed to display how a quantity changes over time, making trends easy to see. The other formats do not clearly communicate change across days.
A delivery driver gets paid $12 per hour plus $0.50 per mile driven. Last Saturday, the driver worked 6.5 hours and drove 120 miles. Which expression gives the driver's pay in dollars for that day?
$12 \times 6.5 + 0.50 \times 120$
$12(6.5 + 120) + 0.50$
$12 \times 6.5 \times 0.50 \times 120$
$12 \times 6.5 + 0.50 \times (6.5 + 120)$
Explanation
Hourly earnings are $12 \times 6.5$ and mileage pay is $0.50 \times 120$. Add those to get the total. The other options mix hours with miles or multiply everything together, which does not match the pay rules.
Consider these two ideas: 1) Subtracting $b$ from $a$. 2) Adding the opposite of $b$ to $a$. How are these ideas related?
$a - b$ equals $a + (-b)$.
$a - b$ equals $(-a) + b$.
Subtracting always makes a number smaller, but adding the opposite always makes it larger.
They are only equal when $a$ and $b$ are positive integers.
Explanation
Subtraction is defined as adding the additive inverse: $a - b = a + (-b)$. Understanding this connection unifies subtraction and addition of integers and supports consistent strategies with signed numbers.