# Middle and secondary

### Number system

##### Chapter 1: Knowing Our Numbers
 LO 1: Putting Large Numbers in Practice LO 2: Being Able to Compare Numbers LO 3: Correctly Identifying Place Values and Face Values of Numerals LO 4: Estimating Quantities — The Heart of Maths LO 5: Working with Roman Numerals

##### Chapter 2: Whole Numbers
 LO 1: Discovering Whole Numbers LO 2: Drawing Number Lines for Whole Numbers LO 3: Applying Commutative Law on Whole Numbers LO 4: Applying Associative Law on Whole Numbers LO 5: Applying Distributive Law on Whole Numbers LO 6: Affirming Other Properties of Whole Numbers LO 7: Addition and Subtraction of Whole Numbers LO 8: Multiplication and Division of Whole Numbers LO 9: Unfolding Patterns in Numbers

##### Chapter 3: Integers
 LO 1: Drawing Number Line for Integers LO 2: Exploring Addition of Integers and its Properties LO 3: Exploring Subtraction of Integers and its Properties LO 4: Understanding Multiplication of Integers and Its Properties LO 5: Exploring Division of Integers and its Properties LO 6: Knowing How to Use BODMAS Rule

##### Chapter 4: Real Numbers
 LO 1: Defining and applying Euclid’s division lemma and algorithm LO 2: Defining fundamental theorem of arithmetic LO 3: Applying fundamental theorem of arithmetic LO 4: Characterising irrational numbers LO 5: Calculating decimal expansions of rational numbers expansions

##### Chapter 5: Rational Numbers
 LO 1: Experience Rational Numbers Around Us LO 2: Drawing Number Line for Rational Numbers LO 3: Harnessing Properties of Rational Numbers LO 4: Writing Rational Numbers in Standard Form LO 5: Being Able to Compare Rational Numbers LO 6: Exploring Addition and Subtraction of Rational Numbers LO 7: Exploring Multiplication and Division of Rational Numbers LO 8: Finding Rational Numbers Between Two Given Rational Numbers LO 9: Living in An Ocean of Rational Numbers LO 10: Drawing Number Lines for Rational Numbers LO 11: Understanding Addition of Rational Numbers and its Properties LO 12: Understanding Subtraction of Rational Numbers and its Properties LO 13: Knowing Applications of Addition and Subtraction on Rational Numbers LO 14: Exploring Multiplication of Rational Numbers and its Properties LO 15: Exploring Division of Rational Numbers and its Properties LO 16: Understanding Applications of Multiplication and Division on Rational Numbers

##### Chapter 6: Exponents and Powers
 LO 1: Writing and Evaluating Exponential Form of Numbers LO 2: Multiplying Powers with the Same Base LO 3: Dividing Powers with the Same Base LO 4: Interpreting Power of a Power LO 5: Multiplying Powers with the Same Exponents LO 6: Dividing Powers with the Same Exponents LO 7: Writing Daily-Life Numbers as Exponents LO 8: Working with Negative Exponents LO 9: Knowing and Applying First Law of Exponents LO 10: Knowing and Applying Second Law of Exponents LO 11: Knowing and Applying Third Law of Exponents LO 12: Knowing and Applying Fourth Law of Exponents LO 13: Knowing and Applying Fifth Law of Exponents LO 14: Various Applications of Exponents

##### Chapter 7: Number Systems
 LO 1: Defining characteristics of rational numbers LO 2: Getting rational number equivalent of a decimal number LO 3: Getting decimal equivalent of a rational number LO 4: Defining and proving irrational numbers LO 5: Drawing number line for real numbers LO 6: Stating and using laws of integral exponents LO 7: Stating and using laws of rational exponents LO 8: Rationalising denominator

##### Chapter 8: Fraction and Decimals
 LO 1: Discovering the Ocean of Fractions We Live In LO 2: Drawing Number Lines for Fractional Numbers LO 3: Identifying Equivalent Fractions LO 4: Identifying Like and Unlike Fractions LO 5: Identifying Proper, Improper and Mixed Fractions LO 6: Being Able to Compare Fractions LO 7: Exploring Addition of Fractions LO 8: Exploring Subtraction of Fractions LO 9: Exploring Decimal Numbers Around Us LO 10: Finding Fraction Equivalent of Decimal Numbers LO 11: Finding Decimal Number Equivalent of Fractional Numbers LO 12: Identifying Like, Unlike and Equivalent Decimal Numbers LO 13: Being Able to Compare Decimal Numbers LO 14: Measurement of Money, Length and Capacity Using Decimal Numbers LO 15: Addition and Subtraction of Decimal Numbers LO 16: Knowing Fractions Around Us LO 17: Exploring Addition and Subtraction of Fractions LO 18: Understanding Multiplication and Division of Fractions LO 19: Knowing How to Simplify Numerical Expressions LO 20: Expressing Numbers to Different Decimal Places LO 21: Exploring Addition and Subtraction of Decimal Numbers LO 22: Understanding Multiplication and Division of Decimal Numbers LO 23: Gaining Confidence in Conversion of Units

##### Chapter 9: Playing with Numbers
 LO 1: Finding Factors and Multiples of Numbers LO 2: Defining and Using Even and Odd Numbers LO 3: Applying Tests of Divisibility LO 4: Undertaking Prime Factorisation LO 5: Finding and Using Highest Common Factor LO 6: Finding and Using Least Common Multiple LO 7: Understanding Properties of HCF and LCM LO 8: Utilising Divisibility By 10, 5, 2 LO 9: Utilising Divisibility By 9, 6, 3 LO 10: Utilising Divisibility By 11, 4

##### Chapter 10: Ratio and Proportions
 LO 1: Getting Simplest Form of Ratios LO 2: Being Able to Compare Ratios LO 3: Seeing and Using Proportion LO 4: Effectively Using Unitary Method

##### Chapter 11: Direct and Inverse Proportions
 LO 1: Using and Finding Direct Proportion LO 2: Using and Finding Indirect Proportion

##### Chapter 12: Comparing Quantities
 LO 1: Checking and Writing Equivalent Ratios LO 2: Expressing Quantities as Percentage LO 3: Seeking Equivalence of Percentages, Fractions, Decimals Numbers LO 4: Converting Ratios to Percents LO 5: Expressing Increase or Decrease as Percent LO 6: Expressing Profit or Loss As a Percentage LO 7: Calculating Simple Interest LO 8: Comparisons Using Percentages LO 9: Percentage Calculations for Expressing Profit and Loss LO 10: Expressing Discount LO 11: Calculating Sales Tax/Value Added Tax LO 12: Calculating Compound Interest

##### Chapter 13: Squares & Square Roots
 LO 1: Appreciating Perfect Squares LO 2: Appreciating Properties of Square Numbers LO 3: Defining and Finding Square Root and its Properties LO 4: Appreciating Logic of Square Root by Prime Factorisation and Applying it LO 5: Finding Square Root by Long Division LO 6: Finding Square Root of Fractions LO 7: Finding Square Root of Decimal Numbers

##### Chapter 14: Cubes & Cube Roots
 LO 1: Visualising Cubes LO 2: Expressing Cubes of Negative Integers and Rational Numbers LO 3: Defining and Finding Cube Roots LO 4: Finding Cube Roots of Negative and Rational Numbers

##### Chapter 15: Probability
 LO 1: Exploring probability of tossing coins LO 2: Exploring probability of throwing of dice LO 3: Expressing and solving miscellaneous problems on probability LO 4: Defining occurrence of an event LO 5: Defining theoretical probability of an event LO 6: Defining geometric probability

##### Chapter 16: Arithmetic Progressions
 LO 1: Defining sequences LO 2: Characterising arithmetic progressions LO 3: Finding general term of arithmetic progressions LO 4: Selecting of terms in arithmetic progressions LO 5: Finding sum of n terms of arithmetic progressions LO 6: Applying the concept of arithmetic progressions