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Motivating Students studying
high level Math
Shah Alam & Rawang
18 September 2013
Section 9, Shah Alam
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Agenda
1. Summary up to level F
2. Level G
3. Motivating Students
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D
C
B
8
72
14
136
4
1
3
1
6
12
2
1
8
72
14
136
8
72
14
136
8
72
14
136
What skills are requiredfor smooth progress in Levels E and F?
1stskill: Mental calcu lat ion ski l l
2ndskill: Correct ion sk i l l
3rdskill: Comprehension ski l l
22
1
44
2
44
10
44
12
4
1
11
6
2
1
E
F
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1stskill Mental calculation skill
28
1
24
1
24x2=, x3=, x4=28x2=, x3=, x4=or
28+28+28+
Mental calculation
4) 28+28=
5) 56+28=
6) 84+28=
Written
calculation
1) 242=2) 243=
3) 24
4=
E Can you find L.C.Mimmediately?
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5
41
116
21
41
31
612
21 22
1
44
2
44
10
44
12
2nd skill Correction skill Can you find whichpart is wrong?
F
Improve correct ion Ski ll gradual ly
Erase everything without checking his answer.
And make mistakes many times.
Can locate and correct
mistakes immediately
Takes long time to
locate the mistakes
Develop the habit to check the
answer before erasing
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8
7
214
13
6 8
7
214
13
6 8
72
14
136
8
72
14
136
3rd skill Comprehension skill
E
Students have tocomprehend newrules by themselves
Develop self-learning attitude
Ask the staff without thinking by herself
Cannot comprehend by
herself or takes long time
Can comprehend by
herself
Improve comprehension Ski ll gradually
Teach them how to learn
from worksheets.
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Summary
Develop self-learning attitude , and teach studentshow to learn from worksheets.
Enable students to calculate without writingcarrying/borrowing by the end of eachsection, and then proceed to next section.
Develop the habit to check the answerbefore erasing
1stskill: Mental calculation skill
2nd
skill: Correction skill
3rdskill: Comprehension skill
*You need to explain the rules, if students still have
difficulty
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The state that the studentstry to think by themselvesfirst when encounteringthe NLF.
Attitude/skills to learn from
the examples
D151-F G H I
8
When giving instruction, aim
for students to develop the
attitude/skills to learn from
the examples at theintroductory parts.
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From Level J onwards, thenumber of the examplesincreases so that students
can proceed by selflearning.
Level Number of
examples
38 28 99 54 80 174 138 119
9
Attitude/skills to learnfrom the examples
EF GHI JKL
J57
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Have students try to grasp how to solve from the
examples
Mark in timely manner (adjust the timing of the
marking individually)
Have students carefully look at the examples again,and give instruction concisely in case they cannotcorrect by themselves.
11
Studying
Marking
Makingcorrections
Please keep thesepoints in mind!
Basic instruction at the introductory parts
Skills
Attitude
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Level H1
Basics for Level H11
21Literal equations
31
41 Simultaneous
equations
in 2 variables
51
6171
81
91 In 3 and 4
variables101
111 Applications
121 Inequalities131
141
Functions and
graphs
151
161
171
181Simplifyingmonomials/polynomials191
Level I1 Basics for Level I11
multiplication21
31
Factorization41
51
6171
81
Square roots91101
111Quadratic
equations121131
141 Graphs of
quadratic
functions
151
161
171The Pythagorean
theorem181191
Level G
1Basics for Level G
11
21 Positive /negativenumbers&
31
41
51
&
6171
Four operations8191
101 Value of algebraicexpressions111
121 Simplifyingalgebraic
expressions
131
141
151
Equations161
171
181191 Applications
Especially in Level G, since a lot of NFLs are introduced, such aspositive/negative numbers, Algebraic expressions, and Exponents,consider to mark in timely manner based on each students level.
12
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Basic instruction for Level G
As mentioned previously, a lot ofNLFs which are not familiar withare introduced in Level G.
So , the points above is important.13
Attitude/skills to learn from the
examples
(1) Have students write the intermediate
steps as shown in the examples
(2) Have students read the explanations andnotes carefully.
(3) Consider assigning the marking in timely
manner for some students
Level G
1Basics for Level G
11
21 Positive /negativenumbers&
31
41
51
&
6171
Four operations8191
101 Value of algebraicexpressions111
121 Simplifyingalgebraic
expressions
131
141
151
Equations161
171
181191 Applications
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16.010016
254
G1-G20: Basic of Level G
G7b: Q8 and Q9
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11
6
72
21
5
1
9
5
2
21)
20
13
20
17(
9
52
21)
100
65
20
17(
9
5
21
2)65.0
20
17(
9
5
Convert immediately
Ability to judge 100 or 20
Examples of step in fraction
G1-G20: Basic of Level G
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18
7
31
7
107
6
3
5
7
6)
15
101(
7
6)
15
71
15
3(
7
6)
15
71
5
1(
6
7)
15
712.0(
6
11)
15
712.14.1(
Steps can be skipped
Must use decimals when
both are decimals
Need to convert improper
fraction immediately
If follow is + or -, and
denominator is multiples
of 15, no need to reduce
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G21-G70: Positive/Negative Numbers
Level G
1 Basics for Level G11
21Positive /negative numbers
& 31
41
51&
6171
Four operations8191
101 Value of algebraicexpressions111
121
Simplifying algebraicexpressions
131
141
151
Equations161
171
181
191 Applications
NLF for Advance
students
Basic rules of adding
and subtracting positiveand negative numbers
More Additional Notes
e.g. G21a&b, G25b.
More examples, from
G21 -30 got 10
examples.
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Level G1 Basics for Level
G11
21 Positive /negative
numbers
&
31
41
51&
61
71Four operations81
91
G21-
30
G31-
40
G41-
50
Rules for the signs +&-
Removing brackets
Including different
denominator
20
Please fill in the blanksand think about the
reason why we shouldbe careful in G41-50.
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2121
(2) Have students read the explanations
and notes carefully.(3) Consider assigning the marking in
timely manner for some students
G41a
G41 is better to assignas CW in case of firsttrial and have students
read the note carefully.
G21-G70: Positive/Negative Numbers
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Level G1 Basics for Level
G11
21 positive /negative
numbers
&
31
41
51&
61
71Four operations81
91
G51-
54
G55-
60
G61-
70
Rules for the multiplication
Including exponents
Rules for the division
22
Next point is G55-60.Please fill in theblanks and thinkabout the reason.
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G21-G70: Positive/Negative Numbers
It is not necessary to teach law of exponentialbecause the major difficulty is in getting the result.
If we teach law of exponential students may getconfused.
Write Intermediate step as shown in the example
Keep it simple!
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Four operations of
negative number.
G74To remind the
example used in G50bTo check whether
student are writing the
intermediate steps and
can correct theirmistakes.
G71-G100: Four Operation
Level G
1 Basics for Level G11
21Positive /negative numbers
& 31
41
51&
6171
Four operations8191
101 Value of algebraicexpressions111
121
Simplifying algebraicexpressions
131
141
151
Equations161
171
181
191 Applications
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G71-100
G176-200
Level G1
Basics for Level
G1121 Positive /
Negative
numbers
31
41
51
&
6171
Four operations8191
101 Value of algebraic
expressions111
121 Simplifyingalgebraic
expressions
131
141
151
Equations161
171
181191 Applications
Attitude/skills to calculate accurately
(1) Have students develop the attitude to
verify their answers
(2) Have students write the appropriate
intermediate steps
It is better to be careful here todevelop these 2 attitude.
25
G71-G100: Four Operation
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NLF for Advancestudents
Students to first write
out the expressions bysubstituting the variable(s)
with its assigned
numerical value.
The expressions are
grouped by equivalent
expressions.
G101-G120: Values of Algebraic Expressions
Level G
1 Basics for Level G11
21Positive /negative numbers
& 31
41
51&
6171
Four operations8191
101 Value of algebraicexpressions111
121
Simplifying algebraicexpressions
131
141
151
Equations161
171
181
191 Applications
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When substituting positivenumbers, no parenthesis isneeded except G104b, Q1
When substitute a fractioninto index, some students
may not need to addparenthesis as the step will belonger
22
)2
1(b
G101 is better to assignas CW in case of firsttrial and have studentsread the examplecarefully.
G101-G120: Values of Algebraic Expressions
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G101-G120: Values of Algebraic Expressions
Some students may forget usingparenthesis when substitutingfraction into square (review G104b)
3
1,
2
1 yxWhen
substitutes into 232 yx
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G121-
130
G131-
140
G141-
150
Combining like terms
using the distributive law to
remove the bracket.
removing the brackets
Level G
101 Value of algebraic
expressions111
121 Simplifying
algebraicexpressions
131
141
151
Equations161
171
181
191 Applications
29
G121-G150: Simplifying Algebraic Expressions
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yxyx
baba
34)4
1
3
1(12
126)42(3
Why 6a and (-4x)?
Why 12b and (-3y)?
For some students, G 141(expansion) might need to
assign as class work. Praising
is needed to increase
motivation.
G121-G150: Simplifying Algebraic Expressions
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G121-G150: Simplifying Algebraic Expressions
G122, Starting using
improper fraction
For some students, be strict to the format of answer;
ax + y (not y + ax)
x + a (not a + x)
For some students, G 141 (expansion) might need to
assign as class work.
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G151-
160
Level G
101 Value of algebraic
expressions111121Simplifying algebraic
expressions131
141
151
Equations161
171181
191 Applications
32
G161-
170
Introduction of equations
equations by using transpose
G151-G190: Equations
G171
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G171-
175removing the brackets
G176-
190
Equation with fractional
terms
33
Level G
101 Value of algebraic
expressions111
121Simplifying algebraic
expressions131
141
151
Equations161
171
181
191 Applications
G153 is better to assign
as CW in case of first
trial and have students
read the example carefully.
May need to explain thenotes.
S mmar of Le el G
Summary of level G
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G71-100
G176-200
Summary of Level G
Level G1
Basics for Level
G1121 Positive / Negative
numbers
31
41
51&
61
71Four operations81
91
101 Value of algebraic
expressions111
121Simplifying algebraic
expressions131141
151
Equations161
171
181
191 Applications
Attitude/skills to calculate accurately
(1) Have students develop the attitude to verifytheir answers
(2) Have students write the appropriateintermediate steps
Have them write
the intermediatesteps neatly here.
34
Summary of level G
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Todays Sharing
Motivating Student Studying High Levels
Mathematics
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Math Literacy = Numeracy
Mathematics is the only language shared by all human beings
regardless of culture, religion, or gender.
Pi 3.14159
Adding up the cost of a basket full of groceries involves the
same math process regardless of whether the total is
expressed in dollars, Ringgit, or yen.
With this universal language, all of us, no matter what our unit
of exchange, are likely to arrive at math results the same way.
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Simple Number Trick
1. Pick a two digit number
2. Add the digits
3. Subtract the sum from the original number
4. Then, add the digits of the result
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Answer
A two digit integer can be written as nm
(eg in 23, n=2 and m=3)
Then nm=10n+m
And the sum of the 2-digits is n+m
Original integersum of the 2-digits:
nm-(n+m)=10n+m-n-m=9n
Thus, the result of subtracting the sum of the digitsfrom the original integer is a multiple of nine
Wh d d t t d hi h l l
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Why do we need to study high level
Mathematics?
Level J Level K Level L
Level M Level N Level O
Level XT Level XV Level XM
Level XP Level XS
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Algebra(Level 7AJ, XV, XM)
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Essenceoflgebra
Arithmetic Variable Expression Equation
NumberFour
Operations
Inequality
SolvingEquation
Simplifying
EquationCombiningLike Term
Rational&
IrrationalNumber
ComplexNumber
Vector&
Matrix
Monomial&
Polynomial
Factorization
Algebra
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CalculusA small stone used for counting
(Level KO, XT)
C l l
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EssenceofCalculus
Sequences&
Series
Limit&
ContinuityDifferentiation Integration
Finite Infinite
GeometricArithmetic
DivergenceConvergence
DefiniteIntegral
IndefiniteIntegral
Derivative
Maxima,Minima
&Point of Inflection
Concavity
Trigonometry
Calculus
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Statistics
(Level XP & XS)
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Why is Mathematics useful?
What Is The Application Of
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What Is The Application Of
Mathematics In Daily Life?
Cooking
Grocery shopping
Budgeting household
expenses
Paying bills
Measuring space
Games
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Games
Sudoku
Tic-Tac-Toe
Reversi
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Functions & Graphs
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Sleep & Death Rate
Studies on the relationship
between the death rate of
men and an average number
of sleep hours per day
showed to fit quadratic function
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Brain, Muscle & Body Weight
The weight of the humans brain and muscle
are directly proportional to a persons body
weight
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Estimating Heights
An anthropologist can
use certain linear
functions to estimate
the height of a male or
female, given the length
of certain bones
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DifferentiationRate of Change = Derivative
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Production
Number of items produced over time
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Territorial Area, W T
It has been hypothesized
in statistical studies that
the area of the region canbe approximated by a
function that involves the
animals weight, 0dW
dT
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Application of DifferentiationMaxima & Minima
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Light Maximizing
V l M i i i
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Volume Maximizing
Pg253, 264
Eff ti f Ad ti i
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Effectiveness of Advertising
Rate of change of the number of units soldwith respect to the amount spent on advertising
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Medication in The Bloodstream
After injection, the amount of a medication in
the bloodstream will decrease after time
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Smart Phones
Usage of hand
phones over time:
Prediction of market in
terms of the demand
and potential revenue
Elasticity of Demand
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Elasticity of Demand
Responsiveness in the quantity demanded as aresult of change in price
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Movie Box-Office Revenue
Using the results of the before/ current movies
to predict the revenue of the upcoming movie
Population Growth
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Population Growth
What will the world human population be in 2014?
How about population growth in this island?
Solving Crime
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Solving Crime
Cooling of body for coroner to check when
was a murder committed taking the room
temperature into consideration
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Integration
Efficiency of A Machine Operator
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Efficiency of A Machine Operator
The rate at which a machine operators
efficiency changes with respect to time
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Bowling Scores
Find the probability of a range of scores
using normal distributed function
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Transportation Planning
Transportation planningis the field involved with the
sitting of transportation facilities (generally streets, highways,
sidewalks, bike lanes and public transport lines).
Transportation planner can determine the probabilities that
cars are certain distances apart.
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Trigonometry
Astronomy
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Astronomy
Measure the distance to nearby star
Mercury, Venus, Mars, Jupiter,
Saturn, the moon, and the sun
Geography
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Geography
Measure distances between landmarks, and
in satellite navigation systems on the oceans,
in aircraft, and in space
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Matrix
Business Analysis
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Business Analysis
Identify business needs and determine
solutions to business problems by solving
systems of linear equations
Computer Programming
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Computer Programming
Manipulate arrays of numbers for either
spreadsheets programs or graphics programs
How to study high level Math?
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How to study high level Math?
Make small notes using own words Copy formulas and examples into a book for easy
reference
Put marks on tough questions indicatingquestions that require more attention
Learn from example and simpler problems/
methods
Form smart table or chart for easy understanding
Copy formulas and examples into a book
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for easy reference
Put marks on tough questions indicatingti th t i tt ti
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questions that require more attention
Form smart table or chart for easy understanding
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Minimum
Value
b> 0
Method A1
b< 0
Method B2
Maximum
Value
b> 0
Method B1
b< 0
Method A2
b> 0 b< 0
Maximum Method B Method A
Minimum Method A Method B
Write them at an easy visible place in order to
k l f h d
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take a glance of them everyday
How to memorise and understand
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How to memorise and understand
formulas?
Write them at an easy visible place in order to take a
glance of them everyday
Say them out using the parrot fashion
Link it with the easier formula that is learnt before
Know how the formula came about ~ the derivation
of formula
Practice, practice, practice
Li k it ith th i f l
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Lets try this!
FBIMCAISAUOBAB
CCan you memorise this?
Link it with the easier formula
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FBIMCAISAUOBAB
C
If we can find a strategy to link allthe alphabets to a familiar pattern,we will be able to memorise it.
FBI MCA ISA UOB - ABC. When a strategy is able to ease ones
work, we shall learn!
Able to self-learn
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The role of the Instructorsis not to simply teach howto solve the problems.
Our mission as Instructor isto achieve the ideal statewhich enable students toself-learn from Level J
onwards with the attitude/skills shown on the left, andthis should be theinstruction we give to thestudents.
from Levels JKL
(1) Have students write the intermediatesteps as shown in the examples
(2) Have students read the explanationsand notes carefully.
(3) Consider assigning the marking intimely manner for some students
(1) Have students develop the attitudeto verify their answers
Attitude/skills to learn from the
examples
Attitude/skills to calculate accurately