# 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 |