OSU Math Worksheet

10 math questions on one assignment and 9 on the other. On practice assignment 13B you don’t need to do question 10.

Foundations of Mathematical Reasoning Version 3.0 (2020)
Student Pages
Practice Assignment 13.B
The Resource Algebraic Terminology contains the following information:
Formulas are a type of algebraic equation. You have probably seen algebraic equations
in previous math classes. For example:
𝑦=𝑥+3
Each side of this equation is called an algebra expression.
expression
⏞
𝑦
expression
= ⏞
𝑥+3
So “𝑥 + 3” is an expression and “𝑦” is an expression. The equal sign indicates that the
two expressions are equal, thus forming an algebraic equation.
Therefore, an algebraic equation must have an equal sign with expressions on each
side.
Expression = Expression
[Note that 𝑦 = 𝑥 + 3 is exactly the same as 𝑥 + 3 = 𝑦].
An equation defines a sequence of calculations, often using algebra to shorten the
information. In the example above, this sequence is:
1. Start with 𝑥.
2. Add three to 𝑥.
3. The result is 𝑦.
Notice how much shorter 𝑦 = 𝑥 + 3 is than the three listed steps.
The word formula is usually used to express important and non-changing relationships,
especially in contexts such as science, business, medicine, sports, or statistics. For
example, the formula for the area of a rectangle is 𝐴 = 𝐿 ∙ 𝑊.
This is a formula because the relationship between area and the length and width of a
rectangle is always the same.
An example of an equation would be if you had a job in which you make $12 per hour.
This relationship could be written algebraically as 𝑃 = 12ℎ where 𝑃 is your pay in
dollars, and ℎ is the number of hours you work. If you get a raise, the relationship would
change. You also might call the equation a model because it models a situation using
mathematics.
Copyright © 2020, The Charles A. Dana Center at The University of Texas at Austin
Foundations of Mathematical Reasoning Version 3.0 (2020)
Student Pages
Calculation sequence
Question 1: Refer to the information above to answer the following question.
𝑥
The equation 𝑦 = 4 − 5 represents which sequence of calculations?
1)
a)
Start with 𝑥, subtract 5, divide the result by 4.
b)
Start with 𝑥, divide by 4, subtract 5 from the result.
c)
Start with 𝑥, divide by 4, subtract the result from 5.
Repaying a loan
Questions 2–5: Lenders such as banks, credit unions, and mortgage companies make
loans. The person receiving the loan usually pays the loan off in small payments over a
long period of time. The lender earns money by charging interest, which is based on a
percent of the amount that is borrowed. There are different types of interest. Short-term
loans are often calculated using the formula for simple interest. The total amount repaid
is based on the value of the original loan, called the principal, and the interest. The
formula for the total dollars needed to repay the loan, with interest, is found using the
formula
𝐴 =𝑃+𝑃∙𝑟∙𝑡
or
𝐴 = 𝑃(1 + 𝑟 ∙ 𝑡)
where
•
𝐴 is the amount (total principal plus interest) required to repay the loan
•
𝑃 is the amount borrowed, the principal
•
𝑟 is the annual interest rate, quoted as a percent, but used as a decimal
•
𝑡 is the time, in years (so six months would be 1/2 year)
2)
Suppose you get a loan of $5,000 at an annual interest rate of 4.25%. Use the
given information to write the formula for the total amount to be repaid in 𝑡 years.
3)
Make a table of values that shows the payoff amount (𝐴) for 4 months, 6 months, 1
year, 3 years, and 6 years.
𝒕 (years)
𝑨 ($)
0
4 months
6 months
Copyright © 2020, The Charles A. Dana Center at The University of Texas at Austin
Foundations of Mathematical Reasoning Version 3.0 (2020)
Student Pages
𝒕 (years)
𝑨 ($)
1 year
3 years
6 years
4)
How can these two formulas both represent simple interest? Write a brief
explanation.
𝐴 =𝑃+𝑃∙𝑟∙𝑡
or
𝐴 = 𝑃(1 + 𝑟 ∙ 𝑡)
Making connections across the course
Questions 5–9: The tuition at a daycare center is based on family income. A reduced
tuition has a subsidy. There are three levels of tuition:
•
Full subsidy—the family does not pay any tuition
•
Partial subsidy—the family pays part of the tuition
•
No subsidy—the family pays the full tuition
The data for the daycare center for each age level are given below. For example, the
center receives full subsidies for 17 children in the class with 3-year-olds. Answer the
questions below. Round to the nearest whole percent.
Partial
Subsidy
Full Subsidy
No Subsidy
3-year-olds
17
13
8
4-year-olds
22
14
15
5-year-olds
15
16
11
Total
5)
Complete the last column and last row in the table above.
Copyright © 2020, The Charles A. Dana Center at The University of Texas at Austin
Total
Foundations of Mathematical Reasoning Version 3.0 (2020)
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6)
What percent of 3-year-olds received a full or partial subsidy? Round to the
nearest percent.
7)
What percent of those who receive no subsidy are 5 years old? Round to the
nearest percent.
8)
What percent of the students are 3 years old?
9)
The daycare center’s income for one term comes from federal funding for the
subsidy and the tuition paid by families based on the formula below. Find the total
income of the center.
𝐼 = 1,530𝐹 + 1,750𝑃 + 1,875𝑁
where
𝐼 = total income
𝐹 = number of children receiving a full subsidy
𝑃 = number of children receiving a partial subsidy
𝑁 = number of children receiving no subsidy
The following problem should be printed out, completed, and placed in your
binder.
Mathematical formulas
10) Search the web for mathematical formulas. Record two formulas (e.g., compound
interest) that you have not yet used in this course. Tell what each variable
represents and give an occupation that might use this formula.
Copyright © 2020, The Charles A. Dana Center at The University of Texas at Austin
Foundations of Mathematical Reasoning Version 3.0 (2020)
Student Pages
Practice Assignment 12.D
Questions 1–4: In Practice Assignment 12. C, you compared the price of renting a Ford
Fiesta to renting a Chevy Sonic for 1,500 mile road trip. It turns out, that the advertised
mpg for new cars is based on a speed of 55 mph. As speed increases above 55 mph,
the efficiency reduces dramatically.1
1)
•
3% less efficient at 60 mph
•
17% less efficient at 70 mph
Compare the efficiency of a Ford Fiesta (37 mpg highway) versus a Chevy Sonic
(24 mpg highway) at speeds of 55 mph, 60 mph, and 70 mph. Round to the
nearest tenth.
55
mph
Fiesta
37
mpg
Sonic
34
mpg
60
mph
70
mph
2)
If gasoline costs $3.10 per gallon, how much money would you save by driving 60
mph versus 70 mph on the trip of 1,500 miles in the Fiesta?
3)
If gasoline costs $3.10 per gallon, how much money would you save by driving 60
mph versus 70 mph on the trip of 1,500 miles in the Sonic?
4)
How much longer, to the nearest minute, would it take to travel 300 miles at 60
mph versus 70 mph?
5)
Now back to Jenna and her decision to rent a car or drive her own car.
Write to Jenna, explaining how she can decide if it is better to drive her own car or
to get a rental. Your explanation should include information about what factors
affect the cost of driving and why.
1
MPG for Speed. (n.d.). Speed kills MPG. Retrieved June, 20, 2020, from http://www.mpgforspeed.com.
Copyright © 2020, The Charles A. Dana Center at The University of Texas at Austin
Foundations of Mathematical Reasoning Version 3.0 (2020)
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6)
Find the cost per year of some activity or item that you pay for at least twice a
week on average. For example, buying a cup of coffee or energy drink,
downloading music, going to a movie, paying a babysitter, riding a bus, etc.
Explain your work.
Questions 7–9: The National Center for Children in Poverty (NCCP) posted the
following information in 2020:
Nearly 15 million children in the United States—21% of all children—live in families
with incomes below the federal poverty level ($26,200 a year for a family of four).
Research shows that, on average, families need an income of about twice that level
to cover basic expenses. Using this standard, 43% of children live in low-income
families.2
7)
The pie graph below can be used to illustrate the statement from the NCCP.
Identify what each section and the full circle represent in terms of the context and
the percent. Section 1 is the darker section.
The full circle represents ____________________ and is ______%.
Section 1 represents _____________________ and is _______%.
Section 2 represents ______________________ and is _______%.
2
National Center for Children in Poverty. (n.d.). Child poverty. Retrieved June 20, 2020, from
www.nccp.org/topics/childpoverty.html.
Copyright © 2020, The Charles A. Dana Center at The University of Texas at Austin
Foundations of Mathematical Reasoning Version 3.0 (2020)
Student Pages
8)
9)
Can the statement from the NCCP be restated to say that 21% of people below the
federal poverty level in the United States are children? Select the best answer.
a)
Yes, because the reference value in both statements is the children in the
United States.
b)
Yes, because both statements are about children living in poverty so the
percents are the same. The reference values do not matter.
c)
No, because the percent of children is really much higher because families
really need much more money than the federal poverty level.
d)
No, because the reference value in the first statement is the total number of
children. The reference value in the second statement is the total number of
people below the poverty level.
Based on the information in the paragraph, which of the following is the best
estimate for the number of children in the United States?
a)
30 million
b)
75 million
c)
100 million
d)
There is not enough information to make an estimate.
10) Consider a cause you are passionate about. What are some ways you can
communicate the importance of your cause to others by using numbers?
Copyright © 2020, The Charles A. Dana Center at The University of Texas at Austin