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Learn Number and Algebra (Part 1) the Singapore Way

Name: Learn Number and Algebra (Part 1) the Singapore Way
Rating: 4.7 (6 reviews)

Learn with Mr Timothy Gan, one of the top Math tutors in Singapore | Singapore O Level Mathematics Syllabus

Created byTimothy Gan

Last updated 7/2021

English

What you'll learn

Number and Algebra 1 (sub-topics N1 to N4 based on Singapore GCE O Level Mathematics Syllabus [4048] 2021)
Numbers and their Operations: Prime and prime factorisation, HCF and LCM, integers and rational numbers, calculations with calculator
Numbers and their Operations: number line, approximation and estimation, standard form
Numbers and their Operations: Positive, negative, zero, fractional indices, laws of indices
Ratio and Proportion: Ratios involving rational numbers, writing ratio in simplest form, direct and inverse proportion
Percentage: Expression one quantity as a percentage of another, comparing 2 quantities by percentage, percentages greater than 100%
Percentage: Increasing/decreasing quantity by a given percentage, reverse percentages
Rate and Speed: Average rate, average speed

Course content

23 sections • 155 lectures • 8h 53m total length

Conceptual Bridging8:56
Worked Example 1: Test for Prime Numbers9:01
Worked Example 2: Why and How do we Prime Factorise?4:26
Worked Example 3: Explanation of Perfect Squares and Cubes8:26

Practice Question 1(a)2:18
This section consists of practice questions for the topics in Section 1: Prime and Prime Factorisation and Section 2: Highest Common Factor and Lowest Common Multiple. Download the worksheet (under 'Resource') for the questions. I encourage you to complete the questions on your own first before watching the video solutions for maximum benefit.
Practice Question 1(b)2:40
Practice Question 1(c)4:10
Walk through prime factorization by dividing 1400 by successive primes, revealing 2^3 × 5^2 × 7, and apply the same method to subsequent questions.
Practice Question 2(a)1:10
Practice Question 2(b)1:46
Practice Question 2(c)1:30
Express six over five as a prime factorization in index notation, showing the final form without intermediate steps, and check your answer for correctness.
Practice Question 3(a)1:21
Practice question demonstrates factoring 630 using prime factors, dividing by 2 and by 3 to reveal 2 × 3^2 × 5 × 7.
Practice Question 3(b)7:25
Practice Question 43:05
Practice Question 56:06
Practice Question 63:41
Practice Question 73:17
Practice Question 85:25
Practice question 8 leads you through prime factorization and the logic of making 4500K a perfect cube, finding the smallest positive integer K to achieve cube exponents.
Practice Question 98:06
Practice Question 104:03
Practice Question 115:15
Practice Question 127:54
Practice Question 13(a-c)5:38
Practice Question 13(d)5:51
Practice Question 14(a)6:23
Practice Question 14(b)5:00
Practice Question 14(c)4:07
Practice Question 153:09
Practice Question 162:39

Worked Example 1: Addition involving Negative Number4:48
Worked Example 2: Subtraction involving Negative Numbers3:55
Demonstrate subtraction involving negative numbers using a number line, combining negatives and positives, and simplifying expressions like minus minus to find results.
Worked Example 3: Multiplication of Negative Numbers2:49
Worked Example 4: Division of Negative Numbers2:51
Explore division of negative numbers by treating division as multiplication by reciprocals and applying sign rules, with examples showing negative divided by positive and negative by negative yielding positive.
Worked Example 5: Combined Operations of Numbers3:57
Explore how to simplify combined operations of negative numbers using brackets, order of operations, and signs, with worked examples on squaring, roots, division, and careful bracketed steps.
Exercise Question3:18

Practice Question 13:45
This section consists of practice questions for the topics in Section 4: Integers, Rational Numbers, Section 5: Number Line and Section 6: Calculations. Download the worksheet (under 'Resource') for the questions. I encourage you to complete the questions on your own first before watching the video solutions for maximum benefit.
Practice Question 21:47
Practice Question 30:52
Practice Question 41:25
Practice Question 51:29
Practice Question 60:53
Practice Question 73:24
Practice Question 87:04

Conceptual Bridging: Rounding Off1:21
Worked Example 1: Rounding Off3:16
Conceptual Bridging: Significant Figures (Rule 1)2:45
Conceptual Bridging: Significant Figures (Rule 2)2:41
Conceptual Bridging: Significant Figures (Rule 3)4:24
Conceptual Bridging: Significant Figures (Rule 4)2:28
Conceptual Bridging: Significant Figures (Rule 5)4:50
Explore how trailing zeros in whole numbers may be significant based on rounding to the nearest ten or hundred in rule 5 for significant figures.
Worked Example 2: Rounding Off to a Required Number of Significant Figures1:57
Worked Example 3: Estimation of Computations Using Significant Figures2:15
Estimate computations using significant figures and rounding to the nearest whole number, then assess reasonableness with real-life scales illustrated by height and distance examples.
Exercise Question2:05

Conceptual Bridging: Index Notation1:48
Worked Example 1: Expressing Number in Index Form3:12
Conceptual Bridging: Zero Indices1:51
Explore zero indices and exponent cancellation, showing that zero indices lead to one for nonzero bases. Note that certain exponent laws do not apply when indices are zero or negative.
Worked Example 2: Zero Indices1:04
Conceptual Bridging: Negative Indices2:14
Worked Example 3: Negative Indices3:24
Conceptual Bridging: Positive nth Root1:42
Worked Example 4: Rational Indices1:20
Conceptual Bridging: Rational Indices5:02
Worked Example 5: Rational Indices2:38
Conceptual Bridging: Equations involving Indices0:56
Worked Example 5: Equation involving Indices2:37

Conceptual Bridging: Laws of Indices6:24
Worked Example 1: Applying Law 1 of Indices2:15
Worked Example 2: Applying Law 2 of Indices3:06
Apply law 2 of indices to simplify expressions, use fraction form and cancellation to handle division, and practice evaluating index-based expressions.
Worked Example 3: Applying Law 3 and 4 of Indices2:49
Worked Example 4: Applying Law 1, 2, 3 and 4 of Indices3:04
Worked Example 5: Applying Law of Indices3:36
Apply the law of indices to simplify expressions, manipulating exponents on top and bottom, and practice with multiple examples to build proficiency.
Conceptual Bridging: Extensions of Laws of Indices to Zero and Negative Indices0:52
Worked Example 6: Applications of Laws of Indices, Zero and Negative Indices4:56
Worked Example 7: Applying Laws of Indices to Rational Indices1:57

Requirements

Description

Learn Number and Algebra (Part 1) the Singapore Way!

Let us structure the learning for you! Our Math learning content is designed by curriculum specialists and former Singapore Ministry of Education (MOE) Mathematics teachers with years of experience teaching Maths in our local secondary schools. The structure of the lessons is based on the Singapore GCE O Level 4048 Mathematics Syllabus (2021).

Our Course Learning Design

To help you/your child fully grasp mathematical concepts, we designed our course in the following way:

Conceptual Bridging section is where we would explain how some important concepts are being deduced or derived. We will strongly encourage you not to skip it in order to understand certain core concepts.
Worked Examples are questions during which we will slowly unpack and apply what you have learnt. Usually, we will guide students through by assuming that students have zero understanding of the topic before approaching the questions.
Exercises are extra practice questions to further sharpen and test your understanding. Some questions here are HOT (Higher-Order-Thinking) questions.
Essential Steps consist of tips and tricks or guides to help you to tackle a question.
Practice Questions are extra Mathematics problems for you to practice on the topics that you have learnt. We encourage you to download the Practice worksheets first and attempt and complete them before watching the video solutions so as to maximise the benefit of the practice questions.

Each section comes with lesson notes that you have to download to refer to before starting your lessons. For this course, the following 4 units are included (with 23 sections):

Unit 1 Numbers and their Operations

1. Prime and Prime Factorisation

2. HCF and LCM

3. Practice (Primes, HCF and LCM)

4. Integers, Rational Numbers

5. Calculations

6. Number Line

7. Practice (Real Numbers)

8. Approximation and Estimation

9. Positive, Negative, Zero, Fractional Indifference

10. Law of Indices

11. Standard Form

Unit 2 Ratio and Proportion

12. Ratios involving Rational Numbers

13. Writing Ratio in its Simplest Form

14. Direct and Inverse Proportion

15. Practice (Direct and Inverse Proportion)

Unit 3 Percentage

16. Expressing one quantity as a percentage of another

17. Comparing 2 quantities by percentage

18. Percentages greater than 100%

19. Increasing or decreasing quantity by a given percentage

20. Reverse percentages

21. Practice (Percentage)

Unit 4 Rate and Speed

22. Average Rate

23. Average Speed

Who this course is for:

Students taking Singapore GCE O Level Mathematics Syllabus [4048], IGCSE or any other equivalent
Students looking to deepen their learning on Number and Algebra
Parents looking for supplementary resources of Number and Algebra to help guide their children on their school work
Homeschool parents looking for structured Mathematics courses
Young adults/adults who wish to refresh their understanding of Number and Algebra

Learn Number and Algebra (Part 1) the Singapore Way

What you'll learn

Explore related topics

Course content

Prime and Prime Factorisation4 lectures • 31min

Highest Common Factor and Lowest Common Multiple3 lectures • 22min

Practice (Primes, HCF, LCM)24 lectures • 1hr 42min

Integers, Rational Numbers4 lectures • 12min

Number Line2 lectures • 6min

Calculations6 lectures • 22min

Practice (Real Numbers)8 lectures • 21min

Approximation and Estimation10 lectures • 28min

Positive, Negative, Zero, Fractional Indices12 lectures • 28min

Law of Indices9 lectures • 29min

Requirements

Description

Who this course is for: