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Flashcards: Functions Describing a Relationship Between Two Quantities: CCSS.Math.Content.HSF-BF.A.1

Sally wants to buy a new computer for next year. The computer that she has her eye on costs $\$1\textup,216$ $\displaystyle \$1\textup,216$. Sally works as a dog walker and gets paid $\$8$ $\displaystyle \$8$ an hour. If Sally works eight hours every week, how many weeks of work will it take for her to earn enough money to buy the new computer?

Sally will need to work $\displaystyle 21$ weeks.

Sally will need to work $\displaystyle 17$ weeks.

Sally will need to work $\displaystyle 20$ weeks.

Sally will need to work $\displaystyle 19$ weeks.

Sally will need to work $\displaystyle 15$ weeks.

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Flashcards: Functions Describing a Relationship Between Two Quantities: CCSS.Math.Content.HSF-BF.A.1

Sally will need to work $\displaystyle 21$ weeks.

Sally will need to work $\displaystyle 17$ weeks.

Sally will need to work $\displaystyle 20$ weeks.

Sally will need to work $\displaystyle 19$ weeks.

Sally will need to work $\displaystyle 15$ weeks.

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Flashcards: Functions Describing a Relationship Between Two Quantities: CCSS.Math.Content.HSF-BF.A.1

Your answer:

Sally will need to work $\displaystyle 21$ weeks.

Your answer:

Sally will need to work $\displaystyle 17$ weeks.

Your answer:

Sally will need to work $\displaystyle 20$ weeks.

Your answer:

Sally will need to work $\displaystyle 15$ weeks.

Correct answer:

Sally will need to work $\displaystyle 19$ weeks.

Explanation:

This question is testing one's ability to recognize functions in everyday situations and build the mathematical model that shows the relationship between two quantities. A question such as this requires examination into the behavior between the quantities, whether it be explicit expression, a recursive process, or a multi-step calculation. It also requires the use of algebraic operations to solve the question at hand and then build a function that models the relationship.

For the purpose of Common Core Standards, writing a function which describes a relationship falls within the Cluster A of build a function that models a relationship between two quantities concept (CCSS.Math.content.HSF.BF.A). Questions in this cluster depend heavily of building an understanding between real life situations as seen through a mathematical perspective.

Knowing the standard and the concept for which it relates to, we can now do the step-by-step process to solve the problem in question.

Step 1: Identify what the question is asking for.

Step 2: Identify what is given/known from the question.

Step 3: Using algebraic methods creating function to describe relationship.

Step 4: Answer the question.

Following the steps listed above for this particular problem is as follows.

Step 1: Identify what the question is asking for.

How many weeks will Sally need to work to earn enough money to buy the new computer?

Step 2: Identify what is given/known from the question.

The computer costs $\$1\textup,216$ $\displaystyle \$1\textup,216$

Sally earns $\$$8/hour$ $\displaystyle \$$8/hour$

Sally works $\displaystyle $8 hours/week$

Step 3: Using algebraic methods creating function to describe relationship.

$\\ \textup{Cost of Computer}=\$1216 \\ \textup{Wage}= \$8\cdot \textup{hours} \\ \textup{Weekly Hours Worked}=8 \\ \textup{Cost of Computer}=\textup{Wage}\times \textup{Weekly Hours Worked}\times \textup{Weeks Worked}$ $\displaystyle \\ \textup{Cost of Computer}=\$1216 \\ \textup{Wage}= \$8\cdot \textup{hours} \\ \textup{Weekly Hours Worked}=8 \\ \textup{Cost of Computer}=\textup{Wage}\times \textup{Weekly Hours Worked}\times \textup{Weeks Worked}$

Step 4: Answer the question.

From this model, substitute in the known values and solve for the weeks worked to answer the question.

$\\ \textup{Cost of Computer}=\textup{Wage}\times \textup{Weekly Hours Worked}\times \textup{Weeks Worked} \\ \$1216=\$8\times 8\times \textup{Weeks Worked} \\ \$1216=\$64 \times \textup{Weeks Worked}$ $\displaystyle \\ \textup{Cost of Computer}=\textup{Wage}\times \textup{Weekly Hours Worked}\times \textup{Weeks Worked} \\ \$1216=\$8\times 8\times \textup{Weeks Worked} \\ \$1216=\$64 \times \textup{Weeks Worked}$

Using algebraic operations divide by 64 on both sides to calculate the number of weeks Sally will need to work.

$\\ \frac{\$1216}{\$64}=\textup{Weeks Worked} \\ \\ 19=\textup{Weeks Worked}$ $\displaystyle \\ \frac{\$1216}{\$64}=\textup{Weeks Worked} \\ \\ 19=\textup{Weeks Worked}$

Flashcards: Functions Describing a Relationship Between Two Quantities: CCSS.Math.Content.HSF-BF.A.1

Jane wants to buy a new backpack for next year. The backpack that she has her eye on costs $\$112$ $\displaystyle \$112$. Jane works as a car washer and gets paid $\$4$ $\displaystyle \$4$ an hour. If Jane works $\displaystyle 3$ hours every week, how many weeks of work will it take for her to earn enough money to buy the new backpack?

Jane will need to work $\displaystyle 8$ weeks to buy the new backpack.

Jane will need to work $\displaystyle 9$ weeks to buy the new backpack.

Jane will need to work $\displaystyle 10$ weeks to buy the new backpack.

Jane will need to work $\displaystyle 12$ weeks to buy the new backpack.

Jane will need to work $\displaystyle 11$ weeks to buy the new backpack.

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Flashcards: Functions Describing a Relationship Between Two Quantities: CCSS.Math.Content.HSF-BF.A.1

Your answer:

Jane will need to work $\displaystyle 8$ weeks to buy the new backpack.

Your answer:

Jane will need to work $\displaystyle 9$ weeks to buy the new backpack.

Your answer:

Jane will need to work $\displaystyle 12$ weeks to buy the new backpack.

Your answer:

Jane will need to work $\displaystyle 11$ weeks to buy the new backpack.

Correct answer:

Jane will need to work $\displaystyle 10$ weeks to buy the new backpack.

Explanation:

For the purpose of Common Core Standards, writing a function which describes a relationship falls within the Cluster A of build a function that models a relationship between two quantities concept (CCSS.MATH.CONTENT.HSF.BF.A). Questions in this cluster depend heavily of building an understanding between real life situations as seen through a mathematical perspective.

Knowing the standard and the concept for which it relates to, we can now do the step-by-step process to solve the problem in question.

Step 1: Identify what the question is asking for.

Step 2: Identify what is given/known from the question.

Step 3: Using algebraic methods creating function to describe relationship.

Step 4: Answer the question.

Following the steps listed above for this particular problem is as follows.

Step 1: Identify what the question is asking for.

How many weeks will Jane need to work to earn enough money to buy the new backpack?

Step 2: Identify what is given/known from the question.

The backpack costs $\$112$ $\displaystyle \$112$

Jane earns $\$$4/hour$ $\displaystyle \$$4/hour$

Jane works $\displaystyle $3 hours/week$

Step 3: Using algebraic methods creating function to describe relationship.

$\\ \textup{Cost of Backpack}=\$112 \\ \textup{Wage}= \$4\cdot \textup{hours} \\ \textup{Weekly Hours Worked}=3 \\ \textup{Cost of Backpack}=\textup{Wage}\times \textup{Weekly Hours Worked}\times \textup{Weeks Worked}$ $\displaystyle \\ \textup{Cost of Backpack}=\$112 \\ \textup{Wage}= \$4\cdot \textup{hours} \\ \textup{Weekly Hours Worked}=3 \\ \textup{Cost of Backpack}=\textup{Wage}\times \textup{Weekly Hours Worked}\times \textup{Weeks Worked}$

Step 4: Answer the question.

From this model, substitute in the known values and solve for the weeks worked to answer the question.

$\\ \textup{Cost of Backpack}=\textup{Wage}\times \textup{Weekly Hours Worked}\times \textup{Weeks Worked} \\ \$112=\$4\times 3\times \textup{Weeks Worked} \\ \$112=\$12 \times \textup{Weeks Worked}$ $\displaystyle \\ \textup{Cost of Backpack}=\textup{Wage}\times \textup{Weekly Hours Worked}\times \textup{Weeks Worked} \\ \$112=\$4\times 3\times \textup{Weeks Worked} \\ \$112=\$12 \times \textup{Weeks Worked}$

Using algebraic operations divide by 12 on both sides to calculate the number of weeks Jane will need to work.

$\\ \frac{\$112}{\$12}=\textup{Weeks Worked} \\ \\ 9.\overline{3}=\textup{Weeks Worked}\\ \\10=\textup{Weeks Worked}$ $\displaystyle \\ \frac{\$112}{\$12}=\textup{Weeks Worked} \\ \\ 9.\overline{3}=\textup{Weeks Worked}\\ \\10=\textup{Weeks Worked}$

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Flashcards: Functions Describing a Relationship Between Two Quantities: CCSS.Math.Content.HSF-BF.A.1

All Common Core: High School - Functions Resources

Flashcards: Functions Describing a Relationship Between Two Quantities: CCSS.Math.Content.HSF-BF.A.1

Flashcards: Functions Describing a Relationship Between Two Quantities: CCSS.Math.Content.HSF-BF.A.1

Flashcards: Functions Describing a Relationship Between Two Quantities: CCSS.Math.Content.HSF-BF.A.1

Flashcards: Functions Describing a Relationship Between Two Quantities: CCSS.Math.Content.HSF-BF.A.1

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