HIGHER COLLEGES OF TECHNOLOGY
MATH M020 Course Outline
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Course Title: Foundation Math 2
Course Number: FND M020
Course Credit Units: 5.00
Total Contact Periods Per Week: 5 – 6
Degree Level: New Foundations
Course Description:
This course is the second of two math courses in the Foundations Program. Foundation Math 2 (FND M020) focuses on
developing basic mathematical knowledge and skills and proficiency in applying those concepts to practical life. The
main resource for this course is an internet based course called ALEKS characterized by its ability to:
 provide individually targeted instruction
 provide Adaptive learning at students’ own pace
 check retention of knowledge and skills with regular individualized assessment

Additional Information:
Students who complete the Foundation Math 2 course will have the conceptual understanding and procedural
knowledge in the areas of numbers, measurement, geometry, algebra, data analysis, statistics and probability. Some of
the important skills that students will develop are:
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Grading Mode: N - Normal Grading Mode
Prerequisite Course(s):
Corequisite Course(s):
Equivalent Course(s): , College Algebra Math N105, MATH N02M, MATH N070, EARC N111, EARC N112, MATH
2135
Transfer Credit (TR), with reference to LP228
Course Learning Outcomes:
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the ability to reason mathematically
the ability to think critically, apply knowledge and analyze real life problems
the necessary foundation in mathematics to be successful in career programs
LO1: Understand and Apply concepts of Whole Numbers
LO2: Understand and Apply concepts of Fractions
LO3: Understand and Apply concepts of Decimal Numbers and use Percentage to solve real life applications
LO4 & 5: Understand and Apply concepts of Ratio/Proportion to Measurement
LO6: Understand and Apply concepts of Real Numbers with applications on Exponents, Scientific Notations and
Surds
LO7: Identify, Understand and Apply basic concepts of 2D and 3D Geometry to solve real life problems
LO8: Understand and Apply concepts of Data Analysis and Statistics to real life problems
LO9 & 10: Understand and Apply concepts in Algebraic Expressions, Equations and Inequalities
LO11: Develop skills to Graph and Analyze Linear Equations
LO12: Apply Real Numbers and Algebra concepts to Exponents and Polynomials
Teaching and Learning Strategies:
This course requires independent practice and exercise, computer based learning and structures blended with regular
standard classroom delivery on a need basis. Students must have an internet connection at home as ALEKS is the key
resource.
8-Feb-16 & 12:51 AM
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HIGHER COLLEGES OF TECHNOLOGY
Assessment and LEarning in Knowledge Spaces (ALEKS) is a web-based, artificially intelligent assessment and learning
system. ALEKS uses adaptive questioning to quickly and accurately determine exactly what a student knows and doesn't
know in a course. ALEKS then instructs the student on the topics he/she is most ready to learn. As a student works
through a course, ALEKS periodically reassesses the student to ensure that topics learned are also retained.
(http://www.aleks.com/about_aleks).
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Key Strategies
Active learning in class (during the 5-6 contact hours) by engaging the students in Learn By Doing activities,
both hands on and using technology.
A minimum of 5 hours of independent learning by students per week outside the regular contact hours.
Collaboration and sharing best practices among teachers.
Regular and prompt individualized feedback on student progress using the reports available for generation on
ALEKS.
Technology will be used to enhance the teaching and learning process. It is mandatory for all students to have
an iPad. In addition to the classroom interaction, all comprehensive assessments are to be conducted on these
iPads using a secure platform.
Unless an early exit, all students are expected to complete at least 6 comprehensive assessments to be eligible
to take the final comprehensive exam.
 Assessment Strategies:
Coursework - Pie: COVERING OUTCOMES 1 – 12 BASED ON STUDENT LEARNING PACE: 40%
This part of coursework is based on a comprehensive test taken under exam conditions. If a student meets a
certain benchmark (refer to EARLY EXIT BELOW), the student becomes eligible to take an exit exam under
exam conditions in the college. The comprehensive assessment assesses the successful mastery of a range of
skills and mathematical concepts.
Unless a student is an early exit, all students are expected to complete the initial assessment and at least 5
comprehensive assessments and early exits to be eligible to take the final Exit Exam.
(Outcomes: 1-12)
Coursework – MIDTERM EXAM: COVERING OUTCOMES 1 TO 6 - 20%
All students who are still registered in the course at the time of the midterm assessment must take it under
exam conditions. The midterm will cover LO 1 –6 to ensure the basic and pre-requisite skills for the more
complex learning outcomes are learnt and assessed.
Coursework – Quick Tables: 10%
The ALEKS course will generate the quick table assessments to ensure students acquire the necessary mental
mathematical abilities over addition, subtraction, multiplication and division.
The quick table assessments must be administered at the college under exam conditions.
QT must be officially started with the start of the ALEKS course. Initial QT average for the first 4 weeks will be
adopted for the final grade but students are strongly encouraged to continue improving their QT scores up to
the point of exit.
Final exam (MUST PASS AS SPECIFIED BELOW)– Early Exit Exams: COVERING OUTCOMES 1 – 12: 30%
Once a student has met the eligibility criteria in the comprehensive test, the student can take an early exit
exam under exam conditions at the college and can exit the course if he/she can meet the exit criteria (refer to
EARLY EXIT BELOW).
Total Weight: 100%
 Required Educational Resources:
o Student: (2010). ALEKS Basic math - 11 weeks McGraw-Hill. ISBN: 9780073219325
o Student: (2000). ALEKS Basic math - 18 weeks McGraw-Hill. ISBN: 9780072435511
o Student: (2000). ALEKS Basic math - 40 weeks McGraw-Hill. ISBN: 9780072435535
o Student: (2000). ALEKS Basic math - 6 weeks McGraw-Hill. ISBN: 9780073219318
 Additional Educational Resources:
8-Feb-16 & 12:51 AM
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HIGHER COLLEGES OF TECHNOLOGY
o Gen Ed Share Point Math 2 (FN-M020) HCT Foundations Math 2 e-book Black Board Vista e-learning materials
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and exercises One Note exercises and interactive e-materials Gen Ed Share Point Math 2 M020 AY 2011-2012
Formula Sheet Gen Ed Share Point Learning Outcomes Gen Ed Share Point Assessment Guidelines
o Student: (2011). Applications of critical thinking and numeracy (Mathematics foundation 2) HCT In-house
publication.
Attachments: Appendix A- formula sheet & appendix B ALEKS & HCT conversion table.
Special Comment:
o Students enrolled in Foundation Math FND-M020 should be at the CEFR B1+ level of English language proficiency.
Early exit:
FND M020
EVENT
No. of Topics
EXIT
Week 2
SUN 7 SEPT - SAT 13 SEPT
Week 3 – 7
INITIAL ASSESSMENT
EARLY EXIT 1 WITHOUT QT & MIDTERM
Sun 14 SEPT – SAT 18 OCT
Week 8-12
EARLY EXIT 2 WITH MIDTERM & QT
SUN 19 OCT-SAT 22 NOV
Week 13-16
EARLY EXIT 3 WITH MIDTERM & QT
SUN 23 NOV - SAT 20 DEC
Week 17-20
FINAL EXAM ATTEMPTS
WITH MID TERM & QT
Sun 4Jan –
HCT %
(PIE %)
40%
>=338(85%)
MID TERM EXAM EXIT EXAM SCORE
HCT Final Grade
10%
20%
30%
>=90%
NA
NA
NA
>=360
(>=90%)
>=95%
NA
NA
CONDITION
>=85%
>=360
(>=90%)
>=95%
Average of QT scores at MIDTERM SCORE
the point of exit
IN %
>=320
(>=80%)
>=80%
Average of QT scores at MIDTERM SCORE
the point of exit
IN %
>=262
(>=66%)
>=60%
Thu 29 Jan
Quick Table
Average of QT scores at MIDTERM SCORE
the point of exit
IN %
CONDITION
>=85%
CONDITION
>=75%
CONDITION
>=60%
MUST PASS
100% INITIAL ASSESSMENT SCORE
40% ALEKS SCORE +30% EXIT EXAM (>=85%)
converted to 100%
40% ALEKS SCORE + 10% QT+ 20% MID TERM+30%
EXIT EXAM (>=85%)
40% ALEKS SCORE + 10% QT+ 20% MID TERM+30%
EXIT EXAM (>=75%)
40% ALEKS SCORE + 10% QT+ 20% MID TERM+30%
EXIT EXAM (>=60%)
Final Average >= 60%
No submission should be allowed if final average is
below 60%
End of Semester
Week 20
SUBMISSION & APPROVAL
OF GRADES
All grades must be submitted regardless of final average
SUN 25 JAN - THU 29 JAN
8-Feb-16 & 12:51 AM
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HIGHER COLLEGES OF TECHNOLOGY
Geometry - (Use  = 3.14)
Perimeter
Perimeter of a square
P = 4𝑠
Perimeter of a triangle
P = 𝑠1 + 𝑠2 + 𝑠3
Appendix A –
FORMULA SHEET
Perimeter of a rectangle
P =2𝑙 + 2𝑤
Circumference of a circle
C = 2𝜋𝑟
C = 𝜋𝑑
Area
Area of a square
A = 𝑠2
Area of a rectangle
Area of a circle
A = 𝜋𝑟 2
Area of a triangle
A = 𝑙𝑤
Area of a parallelogram
A= 𝑏ℎ
2
Area of a trapezoid
A = 𝑏ℎ
A=
Volume
Volume of a cube
V = 𝑠3
Volume of a cylinder
Volume of a rectangular prism/cuboid
V = 𝑙𝑤ℎ
Volume of a sphere
V = 𝜋𝑟 2 ℎ
Volume of a Cone
V = 𝜋𝑟 3
3
Volume of a triangular prism
1
1
2
(𝑎 + 𝑏)ℎ
4
V = 𝜋𝑟 2 ℎ
3
The general formula for the Volume of a pyramid
1
V = Area of the base × Height
3
The volume of a pyramid with a rectangular base
1
V = Length of base × Width of base × Height
3
Surface Area
Surface Area of a cube
SA = 6 𝑠 2
Surface area of the cone
SA = 𝜋𝑟 2 + 𝜋𝑟𝑠
Surface area of a rectangular prism
SA = 2(𝑤ℎ + 𝑙𝑤 + 𝑙ℎ)
1
1
2
V = 𝑙𝑤ℎ
Surface Area of a sphere
SA = 4𝜋𝑟 2
Surface area of a cylinder
SA = 2𝜋𝑟 2 + 2𝜋𝑟ℎ
Pythagorean Theorem:
𝑎2 + 𝑏 2 = 𝑐 2
Linear Equations
Equation of a straight line
𝒚 = 𝒎𝒙 + 𝒄
Slope of a line passing through two points (𝒙𝟏 , 𝒚𝟏 ), (𝒙𝟐 , 𝒚𝟐 )
(𝒚 −𝒚 )
𝒎 = (𝒙𝟐 −𝒙𝟏)
𝟐
𝟏
𝒎 : slope , 𝒄 : y-intercept
8-Feb-16 & 12:51 AM
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HIGHER COLLEGES OF TECHNOLOGY
Rules of Exponents
a
an
Rule 5 of Exponents:    n , b ≠ 0
 b b
n
Rule 1 of Exponents: a  a  a
m
Rule 2 of Exponents:
n
m n
….
am
 a m -n , a  0
an
Rule 6 of Exponents: a0 = 1. a  0
  a
Rule 7 of Exponents: a  n 
Rule 3 of Exponents: a m
n
mn
1
an
r
1
 an ; a ≠ 0
n
a
  a b
Rule 4 of Exponents: ab
n
n n
The square of a binomial (𝑎 ± 𝑏)2 = 𝑎2 ± 2𝑎𝑏 + 𝑏 2
Sequences
Arithmetic Sequence
𝑎𝑛 = 𝑎1 + (𝑛 − 1)𝑑
Geometric Sequence
𝑎𝑛 = 𝑎1 𝑟 𝑛−1
Percentages
Amount of Change
A = RB
New Amount
N=BA
Original Amount
B=NA
N = B(1  R)
B = ( 1 ±𝑅)
𝑁
Temperature
Fahrenheit to Celsius:
5
𝐶 = (𝐹 − 32)
Celsius to Fahrenheit:
𝐹=
9
9
5
𝐶 + 32
Speed
Speed
𝑠=
𝑑
𝑡
Simple and Compound Interest
P: principal (your first deposit)
r: annual interest rate
n: number of times interest is compounded each year
t: total time in years
A: accumulated amount after n years, including interest.
1.Simple interest
𝐼 = 𝑃𝑟𝑡
2. If interest is compounded once a year
A = P(1 + r)t
8-Feb-16 & 12:51 AM
3.If interest is compounded n times a year
A = P(1 + r/n)nt
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HIGHER COLLEGES OF TECHNOLOGY
Appendix B. Conversion Table (ALEKS Topics to HCT % Grade) for Math 2
8-Feb-16 & 12:51 AM
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HIGHER COLLEGES OF TECHNOLOGY
FND M020
PIE
PIE HCT
Score %
%
400
399
398
397
396
395
394
393
392
391
390
389
388
387
386
385
384
383
382
381
380
379
378
377
376
375
374
373
372
371
370
369
368
367
366
365
364
363
362
361
100
100
100
99
99
99
99
98
98
98
98
97
97
97
97
96
96
96
100
100
100
100
100
100
100
100
100
100
100
100
100
100
100
100
100
100
96
95
95
95
95
94
94
94
94
93
93
93
93
92
92
92
92
91
91
91
91
90
100
100
100
100
100
99
99
99
99
98
98
98
98
97
97
97
97
96
96
96
96
95
PIE
PIE HCT
Score %
%
338
337
336
335
334
333
332
331
330
329
328
327
326
325
324
323
322
321
85
84
84
84
84
83
83
83
83
82
82
82
82
81
81
81
81
80
320 80 80
319
318
317
316
315
314
313
312
311
310
309
308
307
306
305
304
303
80
80
79
79
79
79
78
78
78
78
77
77
77
77
76
76
76
360 90 95
359
358
357
356
355
354
353
352
351
350
349
348
347
346
345
344
343
342
341
340
339
90
90
89
89
89
89
88
88
88
88
87
87
87
87
86
86
86
86
85
85
85
90
88
88
88
88
86
86
86
86
84
84
84
84
82
82
82
82
80
95
95
94
94
94
94
93
93
93
93
92
92
92
92
91
91
91
91
90
90
90
8-Feb-16 & 12:51 AM
80
80
79
79
79
79
78
78
78
78
77
77
77
77
76
76
76
PIE
PIE HCT
Score %
%
302
301
300
299
298
297
296
295
294
293
292
291
290
289
288
287
286
285
284
283
282
281
280
279
278
277
276
275
274
273
272
271
270
269
268
267
266
265
264
263
76
75
75
75
75
74
74
74
74
73
73
73
73
72
72
72
72
71
76
75
75
75
75
74
74
74
74
73
73
73
73
72
72
72
72
71
71
71
71
70
70
70
70
69
69
69
69
68
68
68
68
67
67
67
67
66
66
66
71
71
71
70
70
70
70
68
68
68
68
65
65
65
65
63
63
63
63
60
60
60
PIE
PIE HCT
Score %
%
262 66 60
261
260
259
258
257
256
255
254
253
252
251
250
249
248
247
246
245
244
65
65
65
65
64
64
64
64
63
63
63
63
62
62
62
62
61
58
58
58
58
57
57
57
57
57
57
57
57
56
56
56
56
56
243
242
241
240
239
238
237
236
235
234
233
232
231
230
229
228
227
226
225
224
223
61
61
61
60
60
60
60
59
59
59
59
58
58
58
58
57
57
57
57
56
56
56
56
56
56
55
55
55
55
55
55
55
55
54
54
54
54
54
54
54
54
53
53
53
222
221
220
219
218
217
216
215
214
213
212
211
210
209
208
207
206
205
204
203
202
56
55
55
55
55
54
54
54
54
53
53
53
53
52
52
52
52
51
51
51
51
53
53
53
53
53
52
52
52
52
52
52
52
52
51
51
51
51
51
51
51
51
PIE
PIE HCT
Score %
%
201
200
199
198
197
196
195
194
193
192
191
190
189
188
187
186
185
184
183
PIE
PIE HCT
Score %
%
PIE
PIE HCT
Score %
%
50
50
50
50
49
49
49
49
48
48
48
48
47
47
47
47
46
46
50
50
50
50
49
49
49
49
48
48
48
48
47
47
47
47
46
46
137
136
135
134
133
132
131
130
129
128
127
126
125
124
123
122
121
120
34
34
34
34
33
33
33
33
32
32
32
32
31
31
31
31
30
30
34
34
34
34
33
33
33
33
32
32
32
32
31
31
31
31
30
30
73
72
71
70
69
68
67
66
65
64
63
62
61
60
59
58
57
56
18
18
18
18
17
17
17
17
16
16
16
16
15
15
15
15
14
14
18
18
18
18
17
17
17
17
16
16
16
16
15
15
15
15
14
14
182
181
180
179
178
177
176
175
174
173
172
171
170
169
168
167
166
165
164
163
162
46
46
45
45
45
45
44
44
44
44
43
43
43
43
42
42
42
42
41
41
41
41
46
46
45
45
45
45
44
44
44
44
43
43
43
43
42
42
42
42
41
41
41
41
30
30
29
29
29
29
28
28
28
28
27
27
27
27
26
26
26
26
25
25
25
25
30
30
29
29
29
29
28
28
28
28
27
27
27
27
26
26
26
26
25
25
25
25
55
54
53
52
51
50
49
48
47
46
45
44
43
42
41
40
39
38
37
36
35
34
14
14
13
13
13
13
12
12
12
12
11
11
11
11
10
10
10
10
9
9
9
9
14
14
13
13
13
13
12
12
12
12
11
11
11
11
10
10
10
10
9
9
9
9
161
160
159
158
157
156
155
154
153
152
151
150
149
148
147
146
145
144
143
142
141
140
139
138
40
40
40
40
39
39
39
39
38
38
38
38
37
37
37
37
36
36
36
36
35
35
35
35
40
40
40
40
39
39
39
39
38
38
38
38
37
37
37
37
36
36
36
36
35
35
35
35
119
118
117
116
115
114
113
112
111
110
109
108
107
106
105
104
103
102
101
100
99
98
97
24
24
24
24
23
23
23
23
22
22
22
22
21
21
21
21
20
20
20
20
19
19
19
19
24
24
24
24
23
23
23
23
22
22
22
22
21
21
21
21
20
20
20
20
19
19
19
19
33
32
31
30
29
28
27
26
25
24
23
22
21
20
19
18
17
16
15
14
13
12
11
10
9
8
7
6
5
4
3
2
1
0
8
8
8
8
7
7
7
7
6
6
6
6
5
5
5
5
4
4
4
4
3
3
3
3
2
2
2
2
1
1
1
1
0
0
8
8
8
8
7
7
7
7
6
6
6
6
5
5
5
5
4
4
4
4
3
3
3
3
2
2
2
2
1
1
1
1
0
0
96
95
94
93
92
91
90
89
88
87
86
85
84
83
82
81
80
79
78
77
76
75
74
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