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Algebra
Unit One: Assignment #1
Numbers and Operations
BASIC
Evaluate each of the following without the use of a calculator.
1. 234 + 782
7.
2 7

9 3
2. 982 – 649
8.
4 9

3 5
3. 23 × 236
9.
4.17 + 1.35
4. 5537 ÷ 7
10.
14.35 – 9.68
5.
3 2

5 3
11.
1.4 × 3.8
6.
7 3

6 4
12.
24.4 ÷ 2.1
13. 36
15.
4
38
14. 43
16.
7
142
Evaluate each of the following using a calculator.
17. Describe what 54 means.
18. Describe what 3 16 means.
19. Give an example of a rational number.
20. Give an example of an irrational number.
21. Give an example of a whole number.
22. Given an example of an integer.
Algebra
Unit One: Assignment #1
Numbers and Operations
Proficient
Evaluate each of the following without using a calculator.
23. 23,567 + 87, 952
24.
12,368 ÷ 124
25. 62,134 – 38, 976
26.
432 × 184
1
7
27. 2  3
4
10
28.
1
3
2 1
6
4
3 2
29. 2  1
5 3
30.
1
2
6 1
3 5
31. 12.376 + 14.198
32.
11.87 – 4.562
33. 3.87 × 1.64
34.
12.456 ÷ 4.12
35. Describe what the expression 65 means, and evaluate this expression using a calculator.
36. Describe what the expression
calculator.
7
40 represents, and evaluate this expression using a
37. Why is the number 6 considered a rational number?
38. What operation typically results in an irrational answer?
39. Why isn’t 16 an irrational number?
Advanced
40. [Connect concepts and procedures in a verbal explanation]
Provide a written explanation of how to add two fractions. Keep in mind the Six Traits as
they apply to mathematical writing.
41. [Apply knowledge and skills in an unfamiliar context]
In an alphametic puzzle, each letter of the puzzle stands for a different numerical digit. No
two letters stand for the same digit, and each letter represents the same digit throughout the
problem. To solve the alphametic, you must determine which digit is represented by each
letter. Solve the following alphametic. Provide a written explanation of the reasoning that
you used to come up with your answer.
SEND
+M O R E
MONEY
Algebra
Unit One: Assignment #1
42.
Numbers and Operations
[Learn a new concept above and beyond what you have been taught]
Read the handout on the “Closure Property” and complete the following tasks.
Task One
Determine if the following sets are closed under the given operations. Explain why you
think the set is or is not closed.
a.
b.
c.
d.
e.
The set of Whole Numbers under addition.
The set of Natural Numbers under subtraction.
The set of Integers under subtraction.
The set of Integers under multiplication.
The set of Integers under division.
Task Two
Provide a written explanation that describes what you learned about closure. Your
audience is another student in this class who has yet to learn about closure. Keep in mind
the Six Traits as they apply to mathematical writing.
43. [Analyze and critique the work of others]
The following work was shown by a student trying to add the following fractions:
3 2

4 5
Provide a written explanation that can be used to correct the student’s error and help the
student understand how to do the problem correctly. Your explanation should describe
what the student did wrong, why it is wrong, and what the student needs to do to get the
problem right.
44. [Apply what you have learned in a real life situation]
Determine the dimensions A, B, C, D, E, and F of the profile
gage shown in the picture to the right. [Mathematics For
Machine Technology, pg.43]