1.3.3: Exercise 1.3

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MAKING CONNECTIONS TO THE COLLABORATION

(1) Which of the following was one of the main mathematical ideas of the collaboration?

(i) The human population is quickly growing.

(ii) It is important to take time to make sense of large numbers because they occur in many important situations.

(iii) The world population in the year 1 CE was approximately 200 million people.

(iv) There is not much difference between a million and a billion.

DEVELOPING SKILLS AND UNDERSTANDING

(2) Which of the following statements is true?

(i) A trillion is 10¹⁰.

(ii) A trillion is 10 billion.

(iii) A trillion is 100 billion.

(iv) A trillion is 1,000 billion.

(3) Refer back to the table in Question 1 of Collaboration 1.2. One of your classmates estimates the doubling time to be 500 years in 1000 CE. Does that answer seem reasonable? Meaning, does that number fit in with the numbers you see in your table? Write one or two sentences supporting your statement. Use the Writing Principle.

(4) There are many types of investments. Putting money into a savings account or an individual retirement account are two examples of investments.

Some types of investments earn interest based on a percentage rate. People often estimate the doubling time of investments to predict how much money the investment will be worth in the future. An investment that earns 5% interest will double in value about every 14 years. Use this information to complete the missing values in the table below for $7,500 invested at 5% interest. Fill in the missing values in the table.

Year	Value of Investment
2020	$7,500
(i)	$15,000
(ii)	$30,000
2062	(iii)

(5) Which of the following is the best estimate for the amount of time it would take the investment in Question 4 to reach a hundred thousand dollars?

(i) Less than 40 years

(ii) Between 40 and 60 years

(iii) Between 60 and 80 years

(iv) More than 80 years

MAKING CONNECTIONS ACROSS THE COURSE

Exercise 1.1 explained the purpose of each exercise section. Refer back to that information to answer the following questions.

(6) The first section of every assignment is called “Making Connections to the Collaboration.” The purpose of this section is to

(i) help you identify and remember the important mathematical ideas of the collaboration.

(ii) help you make a personal connection to the material in the collaboration.

(iii) help you review all the work you did in the collaboration.

(7) Which of the following are ways to use the “Developing Skills and Understanding” section to support your learning? There may be more than one correct answer.

(i) To earn points to improve your grade.

(ii) This section is not important unless you did not understand the work in the collaboration.

(iii) To assess how well you understand the new material from the collaboration.

(iv) To review information from previous collaborations.

(8) Why do you rate yourself in the ”After Preparation” surveys? There may be more than one correct answer.

(i) So you can show the instructor how much you know.

(ii) To honestly assess if you are ready for the next collaboration.

(iii) To get the best rating in the collaboration.

(iv) So you know what is expected in the next collaboration.

After Exercise 1.2 (survey)

Self-Regulated Learning: Reflect

It is not enough to complete the rating in the “After Preparation” surveys. First, you should use the rating to get ready for your next lesson. If your rating is a 3 or below, you should get help with the material before class. Remember, your instructor is going to assume that you are confident with the material and will not take class time to answer questions about it. If you need help, you should see your instructor or a tutor. You might also consider setting up a study group with classmates so you can help each other.

Second, you should use this rating to help you get better at self-assessment. Just like any other skill, being good at self-assessment takes practice. If you rate yourself as confident but then find that you are not prepared for class, you are not doing a good job of self-assessment. In this case, it is a good idea to talk to your instructor or a tutor about how you can do a better job of assessing yourself and preparing for class.

Self-regulating your learning includes looking back and reflecting on what you understand.

Use the following descriptions to rate yourself:

5—I am extremely confident I can do this task.

4—I am somewhat confident I can do this task.

3—I am not sure how confident I am.

2—I am not very confident I can do this task.

1—I am definitely not confident I can do this task.

Skill or Concept: I can …	Rating from 1 to 5
double values in contextual situations.
identify place value to the trillions.
read a table of numbers.
add and subtract numbers.

After Preparation 1.2, you rated your confidence in applying these same mathematical skills. (Please review your ratings from Preparation 1.2). After applying these skills in this assignment, has your confidence in your ability to successfully apply these skills changed? If so, why?

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