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