Download TRS 92 Basic Skills Remediation Packet

TRS 92 Foundational Skills Remediation Packet
Requirements
This packet contains four categories of problems. You must …
1. Show work for problems unless the instructions tell you otherwise. In order to save you
printing costs, we have not left room for your work so you will need to use your own
paper.
2. Take each completed category (your work and the original assignment) to the Algebra
Alcove for a signature from an instructor or tutor. The instructor/tutor will “spot check”
a few of the problems, and, if they are correct, sign the page to certify that it is
completed. You will need to correct any incorrect problems.
3. You may only have two pages signed off at a time. So you will need to make at least two
visits to the Algebra Alcove.
4. When you have signatures on all four pages, turn the completed packet in to your
instructor. Do not turn in this cover sheet.
Note on using calculators: It is important that you are able to understand the concept behind
this work. If you need a calculator to perform an operation such as division or multiplication,
use it. However, do not rely on the calculators for the concepts such as order of operations or
working with negatives. Once again, it’s up to you to make the most of this learning
opportunity.
Deadline: Thursday, May 17, 2007
Support
Your instructor and the Algebra Alcove are available to help you. Following are a list of
websites that have tutorials that you may also find helpful.
http://www.wtamu.edu/academic/anns/mps/math/mathlab/beg_algebra/index.htm
This website has many tutorials with detailed explanations and examples. Each tutorial starts
very Foundational and progresses to more complex operations, so you may need to scroll down
to find the sections you need. Most of the tutorial topics are obvious, but the following two
contain topics not mentioned in the title.
Tutorial 4: Introduction to Variable Expressions and Equations – contains Order of
Operations
Tutorial 8: Properties of Real Numbers – contains Distributive Property
http://www.visualfractions.com/
Contains visual representations of operations with fractions. This may help you understand the
reason behind the rules.
http://amby.com/educate/math/4-2_prop.html
Illustrates how to use proportions to solve percent problems.
http://www.purplemath.com/modules/index.htm
Has many tutorials on all the Foundational skill topics except percent. Includes step-by-step
examples, has a little less explanation than the “wtamu” site listed above.
TRS 92 Foundational Skills Packet
Page 2 of 5
Name:_________________________Time class meets: _______________________________
Skill Category: Fractions
1. Explain what the numerator and denominator of a fraction represent (not just their
position in the fraction). You may want to include drawings in your explanation.
3 7
2. Using  as an example, explain the steps in adding fractions.
5 2
4 7
3. Using  as an example, explain how to multiply fractions.
9 6
5 3
4. Using  as an example, explain how to divide fractions.
4 8
5. Explain why you need common denominators to add or subtract fractions. You may
want to include drawings in your explanation.
2 7
3y
6 7
5

6. 1 
7.
8.
5 8
8
5 3
2x
3
5
9. 3 
10.  2
3
4
8
11. Find the answers to the following problems.
6x3
1
6
3
1
1 1
2

7
7 2
Based on the relationship between multiplication and division demonstrated above, answer
the following questions:
a) Identify the multiplication problem would give the same result as the problem:
2 2

9 3
b) Identify the division problem would give the same result as the problem:
1
7
4
I have reviewed the work on this category and checked at least two problems. The work is
complete and the problems I checked are correct.
Signature of Algebra Alcove Instructor or Tutor:
_____________________________________
TRS 92 Foundational Skills Packet
Page 3 of 5
Name:_________________________Time class meets: _______________________________
Skill Category: Percent
1. Explain what percent means. You may want to include drawings.
2. Explain why you move the decimal two places to the left when converting a percent to a
decimal.
3. Estimate 23% of 81. Explain how you estimated.
4. Estimate what percent 13 is of 20. Explain how you estimated.
For each problem, first estimate your answer, then calculate it. Show work for the calculations.
5. 35 is what percent of 65?
6. What is 28% of 120?
7. 70% of what is 90?
8. A jacket is priced at $79. It is on sale for 33% off.
a) What percent of the original price will you have to pay?
b) Calculate the total you will have to pay if you buy the jacket on sale and also have to
pay 7% tax.
I have reviewed the work on this category and checked at least two problems. The work is
complete and the problems I checked are correct.
Signature of Algebra Alcove Instructor or Tutor:
_____________________________________
TRS 92 Foundational Skills Packet
Page 4 of 5
Name:_________________________Time class meets: _______________________________
Skill Category: Rational Numbers
Note: You do not have to show work for this category.
1. Explain a context in which the following calculations might occur. Include an
explanation of why the answer makes sense in the context. (Hint: Situations you might
consider are money, altitude, temperature.)
a) -10 – 15
b) 12 + (-9)
2. Calculate each of the following:
Column 1
Column 2
5–4
5 + (-4)
5 – (-4)
5+4
-5 – 4
-5 + (-4)
-5 – (-4)
-5 + 4
Notice the pattern between the subtraction problems in Column 1 and the addition problems
in Column 2. Based on the relationship between addition and subtraction demonstrated
above …
a) Identify the addition problem that would give the same result as the problem:
6 –(-5)
b) Identify the addition problem that would give the same result as the problem:
7-8
c) Identify the subtraction problem that would give the same result as the problem:
8 +(-5)
d) Identify the subtraction problem that would give the same result as the problem:
-9 + (-3)
3. Explain your steps or thinking in calculating 6 – (-8). (Hint: How do you make sense of
this problem to yourself?)
6. 12 ÷(-4)
4.  5  3  2  3
5.  4 3
7. -12 ÷(-4)
8.  6  2  3  2  4
I have reviewed the work on this category and checked at least two problems. The work is
complete and the problems I checked are correct.
Signature of Algebra Alcove Instructor or Tutor:
_____________________________________
TRS 92 Foundational Skills Packet
Page 5 of 5
Name:_________________________Time class meets: _______________________________
Skill Category: Expressions and Equations
1.
2.
3.
4.
5.
Explain, using examples, what “like terms” are.
Explain, using examples, how to add or subtract like terms.
Demonstrate and explain the Distributive Property.
Solve 3x – 7 = 12. Explain each step.
Make up a problem that demonstrates each step of the Order of Operations.
Simplify (be sure to show each step in your work):
6. 60  (3)  2
2 3  1) 2
7.
23
2
10.  5 2
9.  5
12. 5 + 3(x + 2)


8.
3  4  4  5 
2
11. -2x – 4x + 3xy – x
Solve (improper fractions are acceptable answers)
13. -4x + 6 = 20
14. 2 – 5x = -9
15. 25 = 3x - 8
I have reviewed the work on this category and checked at least two problems. The work is
complete and the problems I checked are correct.
Signature of Algebra Alcove Instructor or Tutor:
_____________________________________