Aufmann et al - Mathematical Excursions 4/e

1. –/5 points MathSuccess1 2.1.001. My Notes

This exercise will reduce math anxiety and reveal content relevance.
Math Mindset Modules prepare students for challenging math topics with interactive and reflective exercises on relevant topics.

What Is Growth Mindset?

Watch the following video about Growth Mindset vs. Fixed Mindset.

Passion Over Approval

One of the key differences between the two mindsets is the idea of seeking approval. Those with a fixed mindset compare themselves against others when it comes to their ability and intelligence. They put high value on their grades because, to them, grades prove their intelligence. Being at the top of the class makes them feel smart, and they see good grades as a result of their natural intelligence. On the other hand, having others perform better than them causes them to feel inferior. In addition, if they try their hardest and still do not perform as well as others, they are more likely to give up.

If someone with a growth mindset is outperformed by their peers, they understand that it was likely because they need to put more work into their studies. They ask themselves how they can do better next time. There is nothing hard work cannot fix when it comes to their ability and knowledge. If they perform well, they know it reflects their effort, not their intelligence.

Comparing Growth and Fixed Mindsets in Math and Stats Class

The following accordion sections describe how you can approach challenges in your math and stats classes with a fixed mindset and growth mindset.

Encountering Challenging Questions ▲

Scenario: You are working through an exam prep test and you encounter a word problem. You attempt the problem and it takes you a good chunk of time. You check an answer key and discover you got it wrong.

Fixed Mindset: You give up on the problem or ask a classmate for their solution to see how they got their answer. You also put the question in a search engine and find the full solution online.

Growth Mindset: You review your work and compare your steps with similar problems from class. You move on to other questions and return to the word problem later. You cover up your previous attempt and try again. If you are still stuck, you consult a classmate on a step, but not the entire process.
"You Lost Me..." ▲

Scenario: Your instructor is presenting a concept, and halfway through the lecture, you find that you are completely lost.

Fixed Mindset: You shut down and give up on the lecture. Your immediate thought is that the instructor is not explaining it well, but you do not ask questions. You may ask a classmate for their notes after class, but for the rest of your lecture, you sit there and let your attention drift.

Growth Mindset: You immediately ask your instructor questions about what confused you. You keep working through the lecture in hopes that something is explained in a different way later on. If you end up being lost at the end of the lecture, you make an appointment to go to your instructor's office hours.
X Marks the Spot ▲

Scenario: You get your exam back and you see that you got a 60%. You thought you knew—really, really knew—the material going into it. Many questions have red Xs, and there are comments written next to the incorrect questions.

Fixed Mindset: You figure you thought you knew it and it is clear you were not smart enough. You put the test in your desk drawer and never speak of it again.

Growth Mindset: You bring your exam home and rework the questions you got incorrect. For questions you are stumped on, you make an appointment with your instructor during their office hours and ask clarifying questions about where you went wrong.

If you are worried that you have a fixed mindset, remember that the most important lesson is that mindsets can change. Approaching challenges and criticism from a different angle can help you learn from mistakes and reach higher levels of success.

Multiple-Choice Questions

Note that some questions are opinion-based that could be answered a variety of ways and others have specific right or wrong answers.

(a)

According to a Growth Mindset, how should you react to receiving a low grade on an assessment?

Use answer keys to rework test questions you got wrong. Find solutions to tough homework problems using search engines or phone apps. Feel threatened by those that get a higher grade than you. Forget about looking over an exam since you didn't understand it the first time.

(b)

How would you describe your mindset about math?

Growth Mindset Fixed Mindset Somewhere in the middle

(c)

How do you feel about the following statement? "Some people are just better at math than others."

Strongly agree Agree Disagree Strongly Disagree

(d)

How confident are you walking into a math classroom?

Very confident Confident Somewhat confident Not Confident

(e)

What are some aspects of growth mindset you can focus on this semester? (Select all that apply.)

Approaching challenges as opportunities Asking questions when stuck Not comparing myself to others Persisting when working on difficult questions Reworking incorrect questions on exams and homework

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2. –/1 points AufExc4 1.3.010. My Notes

This exercise will build student confidence and growth mindset.
Read It links are available as a learning tool under each question so students can quickly jump to the corresponding section of the eTextbook.

Use Polya's four-step problem-solving strategy and the problem-solving procedures presented in this lesson to solve the following exercise.

A frog is at the bottom of a 19-foot well. Each time the frog leaps it moves up 3 feet. If the frog has not reached the top of the well, then the frog slides back 1 foot before it is ready to make another leap. How many leaps will the frog need to escape the well?

leaps

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3. –/1 points AufExc4 7.5.015. My Notes

This exercise will build student confidence and growth mindset.
Students get just-in-time learning support with Watch It videos that contain narrated and closed-captioned videos walking students through the proper steps to solve a similar problem.

Find the volume of a cube whose side measures 2.5 in. (Round your answer to three decimal places.)

in³

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4. –/1 points AufExc4 13.IR1.012. My Notes

This exercise will build student confidence and growth mindset.
Chapter-level integrated review (IR) content covers prerequisite algebra skills relevant to the topics in each chapter.

Find the ordered-pair solution of

y = 3x − 6

corresponding to

x = 6.

(x, y) =

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5. –/26 points AufExc4 9.Lab.001. My Notes

Question Part

Points

Submissions Used

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This exercise will engage students in the learning process.
Responsive Labs provide learners with opportunities to think about and use the mathematics they are learning in various ways outside of the classroom by providing a real-life application that adapts to the data that students have provided.

Overview

Recipes often indicate a specific number of servings. In this project, you will scale ingredient amounts to make more servings than a recipe indicates and consider the overall results of scaling a recipe.

Part 1

Find a recipe, in a cookbook or online, that requires at least four ingredients and makes four servings.

If the recipe has more than four ingredients, select four to be your primary ingredients. These will be referred to as ingredient 1, ingredient 2, ingredient 3, and ingredient 4 in this project.

Enter your primary ingredients in the following table. (For example, if you have 2 cups of flour, enter "flour" as the Name of the ingredient, "2" as the Amount, and "cups" as the Unit.)

	Name	Amount	Unit
Ingredient 1
Ingredient 2
Ingredient 3
Ingredient 4

Part 2

Scale all ingredients so that there will be ten servings instead of four. Enter the new amounts of your primary ingredients

	Amount	Unit
Ingredient 1		Same as in part 1
Ingredient 2		Same as in part 1
Ingredient 3		Same as in part 1
Ingredient 4		Same as in part 1

Part 3

Scale all ingredients so that there will be fifteen servings instead of four. Do this by starting with the four-serving recipe. Enter the new amounts of your primary ingredients.

	Amount	Unit
Ingredient 1		Same as in part 1
Ingredient 2		Same as in part 1
Ingredient 3		Same as in part 1
Ingredient 4		Same as in part 1

Part 4

Again, scale all ingredients so that there will be fifteen servings instead of four. Now, do this by starting with the ten-serving recipe. Enter the new amounts of your primary ingredients.

	Amount	Unit
Ingredient 1		Same as in part 1
Ingredient 2		Same as in part 1
Ingredient 3		Same as in part 1
Ingredient 4		Same as in part 1

Part 5

Are your answers in Parts 3 and 4 equal? Why or why not?

This answer has not been graded yet.

Think about the additional supplies involved (not just the ingredients) to make your recipe. Does everything involved with the recipe scale proportionately when the number of servings increases?

Include specific examples in your explanation.

This answer has not been graded yet.

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6. –/4 points AufExc4 11.3.EX.001. My Notes

This exercise will engage students in the learning process.
Excursions from each end-of-section in the textbook are available in WebAssign to relate concepts to contemporary applications.

Car Leases
Leasing a car may result in lower monthly car payments. The primary reason for this is that at the end of the lease term, you do not own the car. Ownership of the car reverts to the dealer, who can then sell it as a used car and realize the profit from the sale.

The value of the car at the end of the lease term is called the residual value of the car. The residual value of a car is frequently based on a percent of the manufacturer's suggested retail price (MSRP) and normally varies between 40% and 60% of the MSRP, depending on the type of lease.

For instance, suppose the MSRP of a car is $18,500 and the residual value is 45% of the MSRP. Then

Residual value	=	0.45 · 18,500
	=	8325.

The residual value is $8325. This is the amount the dealer thinks the car will be worth at the end of the lease period. The person leasing the car, the lessee, usually has the option of purchasing the car at that price at the end of the lease.

In addition to the residual value of the car, the monthly lease payment for a car takes into consideration net capitalized cost, the money factor, average monthly finance charge, and average monthly depreciation. Each of these terms is defined below.

Net capitalized cost

=

negotiated price − down payment − trade-in value

Money factor

=

annual interest rate

24

Average monthly finance charge

=

(net capitalized cost + residual value) × money factor

Average monthly depreciation

=

net capitalized cost − residual value

term of the lease in months

Using these definitions, we have the following formula for a monthly lease payment.

Here is an example of calculating a monthly lease payment for a car.

The director of human resources for a company decides to lease a car for 30 months. Suppose the annual interest rate is 8.4%, the negotiated price is $29,500, there is no trade-in, and the down payment is $5000. Find the monthly lease payment. Assume that the residual value is 55% of the MSRP of $33,400.

Solution

Net capitalized cost

=

negotiated price − down payment − trade-in value

=

29,500 − 5000 − 0 = 24,500

Residual value

=

0.55(33,400) = 18,370

Money factor

=

Annual interest rate

24

=

0.084

24

= 0.0035

Average monthly finance charge	=	(net capitalized cost + residual value) × money factor
	=	(24,500 + 18,370) × 0.0035
	≈	150.05

Average monthly depreciation

=

net capitalized cost − residual value

term of the lease in months

=

24,500 − 18,370

30

≈

204.33

Monthly lease payment	=	average monthly finance charge + average monthly depreciation
	=	150.05 + 204.33
	=	354.38

The monthly lease payment is $354.38.

Explore the animation below then answer the question.

Suppose you decide to obtain a 4-year lease for a car and negotiate a selling price of $28,614, including license fees. The trade-in value of your old car is $3350. If you make a down payment of $2500, the money factor is 0.0027, and the residual value is $15,000, find each of the following.

(a) The net capitalized cost
$

(b) The average monthly finance charge (Round your answer to the nearest cent.)
$

(c) The average monthly depreciation
$

(d) The monthly lease payment (Round your answer to the nearest cent.)
$

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7. 0/1 points | Previous Answers AufExc4 11.1.004. My Notes

This exercise will develop conceptual understanding.
Learn It modules address your students' knowledge gaps with just-in-time instruction. Learn Its provide targeted instruction and practice on that topic using narrative, videos, and tutorials all in one place. If the topic is still too challenging, students can choose to continue learning through associated prerequisite Learn Its.

Calculate the simple interest earned. Round to the nearest cent.

P = $2300, r = 6%, t = 1 year

$

138.00

Suggested tutorial: Learn It: Calculate Simple Interest and Future Value.

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8. –/1 points AufExc4 12.5.029.MI. My Notes

This exercise will develop conceptual understanding.
Master It tutorials are an optional student-help tool available within select questions for just-in-time support. Students can use the tutorial to guide them through the problem-solving process step-by-step using different numbers.

Three cards are dealt from a shuffled standard deck of playing cards.

What is the probability that the three cards dealt are, in order, an ace, a face card, and a 10? (A face card is a jack, queen, or king.)

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9. –/5 points AufExc4 6.5.057.MI.SA. My Notes

This exercise will develop conceptual understanding.
Master It tutorials—Standalone are embedded, step-by-step tutorials used to help students understand each step required to solve the problem, before inputting their final answer.

This question has several parts that must be completed sequentially. If you skip a part of the question, you will not receive any points for the skipped part, and you will not be able to come back to the skipped part.

To determine whether a given base ten number is divisible by 13, multiply the ones digit of the given number by 4. Find the sum of this multiple of 4 and the number formed by omitting the ones digit from the given number. If necessary, repeat this procedure until you obtain a small final sum.

If the final sum is divisible by 13, then the given number is divisible by 13.

If the final sum is not divisible by 13, then the given number is not divisible by 13.

Use the above divisibility test for 13 to determine whether the given number is divisible by 13.

97

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Aufmann et al - Mathematical Excursions 4/e (Homework)

Current Score : 0 / 45

Due : Sunday, January 27, 2030 00:00 EST

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Assignment Scoring

What Is Growth Mindset?

Overview

Part 1

Part 2

Part 3

Part 4

Part 5

WebAssign

Welcome, demo@demo

Aufmann et al - Mathematical Excursions 4/e (Homework)

Current Score : 0 / 45

Due : Sunday, January 27, 2030 00:00 EST

Last Saved : n/a Saving... ()

Instructions

Assignment Submission

Assignment Scoring

What Is Growth Mindset?

Overview

Part 1

Part 2

Part 3

Part 4

Part 5