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All Common Core: High School - Functions Resources

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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 $\$1\textup,216$ . Sally works as a dog walker and gets paid $\$8$ 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 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 weeks.

Your answer:

Sally will need to work weeks.

Your answer:

Sally will need to work weeks.

Your answer:

Sally will need to work weeks.

Correct answer:

Sally will need to work 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 $\$1\textup,216$

Sally earns $\$$8/hour$

Sally works $8 hours/week

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

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

Step 4: Answer the question.

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

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

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

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

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 $\$112$ . Jane works as a car washer and gets paid $\$4$ an hour. If Jane works 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 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 weeks to buy the new backpack.

Your answer:

Jane will need to work weeks to buy the new backpack.

Your answer:

Jane will need to work weeks to buy the new backpack.

Your answer:

Jane will need to work weeks to buy the new backpack.

Correct answer:

Jane will need to work 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 $\$112$

Jane earns $\$$4/hour$

Jane works $3 hours/week

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

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

Step 4: Answer the question.

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

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

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

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

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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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