INTRODUCTION TO INDICES (EXPONENTS) NOTES, WORKSHEETS & ANSWERS. Students learn to Understand numbers written in index form and write numbers in index form. Use BODMAS (PEMDAS) to calculate mathematics operations involving indices. Use scientific notation to write large and small numbers. Grade: 6th to 8th Learning Outcomes: Describe numbers written in index form. Write numbers in index form. Calculate mathematics operations involving indices. Use scientific notation to write large and small numbers. Also Comply with Australian Curriculum: Investigate index notation and represent whole numbers as products of powers of prime numbers (ACMNA149). Express numbers in scientific notation (ACMNA210). Indices (Exponents) Resources: INTRODUCTION TO INDICES Numbers in Index Form Worksheets

FRACTIONS EXIT TICKETS Two exit tickets for students to review fractions skills and understanding: Write shaded parts of the given diagram as a fraction. Locate fractions on number lines. Understand types of fractions: proper, improper and mixed numerals Identify and write equivalent fractions Simplifying fractions Compare and ordering fractions Write sequence fractions Add and subtract fractions with like denominators. Also included: Answer keys Note: the exit tickets are in PowerPoint format. Teacher types (inputs) the standards (outcomes) required for their class before printing the exit tickets. Please read the standards (outcomes) covered in the exit tickets on the description page. Grades: 3rd to 7th Comply with KS2 and KS3 Maths: Fractions. Also comply with Australian Curriculum: Count by quarters, halves and thirds, including with mixed numerals; locate and represent these fractions on a number line (ACMNA078) Investigate equivalent fractions used in contexts (ACMNA077) Compare and order common unit fractions and locate and represent them on a number line (ACMNA102) Investigate strategies to solve problems involving addition and subtraction of fractions with the same denominator (ACMNA103) Compare fractions with related denominators and locate and represent them on a number line (ACMNA125) Solve problems involving addition and subtraction of fractions with the same or related denominators (ACMNA126) More Resources: Colouring Pages Fun Activity Topics: Numbers Times Table Fractions Decimals Percentages Significant Figures Consumer Maths Financial Maths Algebra Pythagoras Theorem Measurement and Geometry Area Functions Visit my shop :)

FRACTIONS EXIT TICKETS Two exit tickets for students to review fractions skills and understanding: Write shaded parts of the given diagram as a fraction. Locate fractions on number lines. Understand types of fractions: proper, improper and mixed numerals Identify and write equivalent fractions Simplifying fractions Compare and ordering fractions Write sequence fractions Add and subtract fractions with like denominators. Also included: Answer keys Note: the exit tickets are in PowerPoint format. Teacher types (inputs) the standards (outcomes) required for their class before printing the exit tickets. Please read the standards (outcomes) covered in the exit tickets on the next page. Grades: 3rd to 7th Comply with KS2 and KS3 Maths: Fractions. Also comply with Australian Curriculum: Count by quarters, halves and thirds, including with mixed numerals; locate and represent these fractions on a number line (ACMNA078) Investigate equivalent fractions used in contexts (ACMNA077) Compare and order common unit fractions and locate and represent them on a number line (ACMNA102) Investigate strategies to solve problems involving addition and subtraction of fractions with the same denominator (ACMNA103) Compare fractions with related denominators and locate and represent them on a number line (ACMNA125) Solve problems involving addition and subtraction of fractions with the same or related denominators (ACMNA126) More Resources: Colouring Pages Fun Activity Topics: Numbers Times Table Fractions Decimals Percentages Significant Figures Consumer Maths Financial Maths Algebra Pythagoras Theorem Measurement and Geometry Area Functions Visit my shop :)

Algebra worksheets and answers to practise simplifying algebraic expressions that involve multiplication and division. introduce the index law of multiplication. Level of Difficulty: Beginner (Easy) Grades: 7th to 9th Also suitable for Australian Curriculum Simplify algebraic expressions involving the four operations (ACMNA192) More Resources: Colouring Pages Fun Activity Topics: Numbers Times Table Fractions Decimals Percentages Significant Figures Consumer Maths Financial Maths Algebra Measurement and Geometry Visit my shop :)

This resource contains rounding decimal worksheets and answers. Level of Difficulty: Beginner Grades: 5th to 8th Learning Outcomes: Use place value understanding to round decimals to any place. Also suitable for Australian Curriculum Round decimals to a specified number of decimal places (ACMNA156) More Resources: Colouring Pages Fun Activity Topics: Numbers Times Table Fractions Decimals Percentages Significant Figures Consumer Maths Financial Maths Algebra Measurement and Geometry Visit my shop :)

Maths for Smarty Set 3 contains 2 templates for students to practise adding and subtracting numbers up to 999. This is a fun activity with a hard skill level. Students fill each shape by choosing a number within the given ranges then add or subtract the numbers to make true equations. Maths for Smarty templates are worth keeping. Students can use the same template repeatedly to create as many equations as they can. This resource is designed in 2 formats: colours and black & white. Students can colour the shapes to make the activity more fun. Maths for Smarty is available in three skill levels: Set 1 (Easy) Set 2 (Medium) Set 3 (Hard) Skill Level: Hard Grades: 3rd to 7th Learning Outcomes: Select and apply efficient mental and written strategies and appropriate digital technologies to solve problems involving the addition and subtraction of whole numbers. More Resources: Colouring Pages Fun Activity Topics: Numbers Times Table Fractions Decimals Percentages Significant Figures Consumer Maths Financial Maths Algebra Measurement and Geometry Visit my shop :)

Maths for Smarty Set 2 contains 2 templates for students to practise adding and subtracting numbers up to 999. This is a fun activity with a medium skill level. Students fill each shape by choosing a number within the given ranges then add or subtract the numbers to make true equations. Maths for Smarty templates are worth keeping. Students can use the same template repeatedly to create as many equations as they can. This resource is designed in 2 formats: colours and black & white. Students can colour the shapes to make the activity more fun. Maths for Smarty is available in three skill levels: Set 1 (Easy) Set 2 (Medium) Set 3 (Hard) Skill Level: Medium Grades: 3rd to 7th Learning Outcomes: Select and apply efficient mental and written strategies and appropriate digital technologies to solve problems involving the addition and subtraction of whole numbers. More Resources: Colouring Pages Fun Activity Topics: Numbers Times Table Fractions Decimals Percentages Significant Figures Consumer Maths Financial Maths Algebra Measurement and Geometry Visit my shop :)

Maths for Smarty Set 1 contains 2 templates for students to practise adding and subtracting numbers up to 999. This is a fun activity with an easy skill level. Students fill each shape by choosing a number within the given ranges then add or subtract the numbers to make true equations. Maths for Smarty templates are worth keeping. Students can use the same template repeatedly to create as many equations as they can. This resource is designed in 2 formats: colour and black & white. Students can colour the shapes to make the activity more fun. Maths for Smarty is available in three skill levels: Set 1 (Easy) Set 2 (Medium) Set 3 (Hard) Skill Level: Easy Grades: 3rd to 7th **Learning Outcomes: ** Select and apply efficient mental and written strategies and appropriate digital technologies to solve problems involving the addition and subtraction of whole numbers. More Resources: Colouring Pages Fun Activity Topics: Numbers Times Table Fractions Decimals Percentages Significant Figures Consumer Maths Financial Maths Algebra Measurement and Geometry Visit my shop :)

Factors of Numbers Puzzle 1 Activity A fun activity to keep your learners engaged in math learning and apply mathematical strategies to complete the puzzle. In this activity learners practise finding factors of a number and arranging the given factors to fill all boxes. The aims of this activity are: To increase their fluency and confidence in multiplication and division skills. To develop understanding of a variety of problems involving factors of a number. Answer keys are also included. Teaching Ideas: Students cut each factor and glue it to the correct box. Or students write each factor in the correct box. Grades: 4th to 6th Learning Outcomes: • Identify factors of whole numbers in the range 1-100 and use them to solve problems. • Recognize that a whole number is a multiple of each of its factors. Also comply with Australian Curriculum: Identify and describe factors and multiples of whole numbers and use them to solve problems (ACMNA098). Develop efficient mental and written strategies and use appropriate digital technologies for multiplication and for division where there is no remainder (ACMNA076) Factors of Numbers: Factors of Number Puzzle 1 Factors of Number Puzzle 2 Factors of Number Puzzle 3

Factors of Numbers Puzzle 2 Activity A fun activity to keep your learners engaged in math learning and apply mathematical strategies to complete the puzzle. In this activity learners practise finding factors of a number and arranging the given factors to fill all boxes. The aims of this activity are: To increase their fluency and confidence in multiplication and division skills. To develop understanding of a variety of problems involving factors of a number. Answer keys are also included. Teaching Ideas: Students cut each factor and glue it to the correct box. Or students write each factor in the correct box. Grades: 4th to 6th Learning Outcomes: • Identify factors of whole numbers in the range 1-100 and use them to solve problems. • Recognize that a whole number is a multiple of each of its factors. Also comply with Australian Curriculum: Identify and describe factors and multiples of whole numbers and use them to solve problems (ACMNA098). Develop efficient mental and written strategies and use appropriate digital technologies for multiplication and for division where there is no remainder (ACMNA076) Factors of Numbers: Factors of Number Puzzle 1 Factors of Number Puzzle 2 Factors of Number Puzzle 3

Factors of Numbers Puzzle 3 Activity A fun activity to keep your learners engaged in math learning and apply mathematical strategies to complete the puzzle. In this activity learners practise finding factors of a number and arranging the given factors to fill all boxes. The aims of this activity are: To increase their fluency and confidence in multiplication and division skills. To develop understanding of a variety of problems involving factors of a number. Answer keys are also included. Teaching Ideas: Students cut each factor and glue it to the correct box. Or students write each factor in the correct box. Grades: 4th to 6th Learning Outcomes: • Identify factors of whole numbers in the range 1-100 and use them to solve problems. • Recognize that a whole number is a multiple of each of its factors. Also comply with Australian Curriculum: Identify and describe factors and multiples of whole numbers and use them to solve problems (ACMNA098). Develop efficient mental and written strategies and use appropriate digital technologies for multiplication and for division where there is no remainder (ACMNA076) Factors of Numbers: Factors of Number Puzzle 1 Factors of Number Puzzle 2 Factors of Number Puzzle 3

Algebraic Puzzles in Geometric Shapes and Step-by-Step Solutions Algebraic puzzles to keep your learners engaged in algebra and measurement learning. The learners use perimeter and area formulas for 2D shapes and apply algebraic techniques such as the balancing method to complete each puzzle. Puzzle A: find the expression for unknown lengths. The perimeter (P ) of each shape is given and each variable (letter) has a distinct value. Puzzle B: find the expression for unknown lengths. The area (A ) of each shape is given and each variable (letter) has a distinct value. Grades: 7th to 10th Learning Outcomes: Use the formulas for the perimeter and area of two-dimensional shapes in problem-solving Create algebraic expressions and evaluate them by substituting a given value. Solve linear equations using algebraic techniques. Also comply with Australian Curriculum Introduce the concept of variables as a way of representing numbers using letters (ACMNA175). Communicate and connect mathematical ideas using appropriate terminology, diagrams and symbols (MA4-1WM). Solve simple linear equations (ACMNA179). Solve linear equations using algebraic techniques and verify solutions by substitution (ACMNA194). Establish the formulas for areas of rectangles, triangles and parallelograms, and use these in problem-solving (ACMMG159) More Algebra Resources: Algebra

Inequalities on a Number Line Worksheets and Answers Worksheets to keep your learners engaged in math learning and apply mathematical strategies to complete a variety of question styles about inequalities on number lines. Worksheet A: Describing the inequality represented by each number line. Worksheet B: MATCHING ACTIVITY Worksheet C: Graphing inequalities on a number line. Worksheet D: Graphing inequalities on a number line. Grades: 6th to 9th Learning Outcomes: Describe and write inequalities on a number line Graph inequalities on a number line Also comply with for Australian Curriculum Introduce the concept of variables as a way of representing numbers using letters (ACMNA175). Communicate and connect mathematical ideas using appropriate terminology, diagrams and symbols (MA4-1WM).

Differential Calculus: The Equation of Tangents to a Curve problems and step-by-step solutions. Students think critically, demonstrate knowledge of functions and differential calculus. Apply the appropriate formulas, sketch the graph of y = f(x) and their tangents. Use mathematical strategies to solve all questions. Learning Outcomes: Use first principles to find the derivative of simple polynomials. Understand the derivative as the gradient of the tangent to the curve of y = f(x) at a point. Find the gradient of the tangents at a point on the curve. Find the equation of the tangent to the curve at a point. Practise sketching a curve and the tangents. Grades: 10th to 12th Also suitable for Australian Curriculum Examine the behaviour of the difference quotient (f(x+h)−f(x))/h as h→0 as an informal introduction to the concept of a limit (ACMMM081) Interpret the derivative as the gradient of the tangent to the graph of y = f(x) at a point (ACMMM085) Estimate numerically the value of the derivative at a point, for simple power functions (ACMMM086) understand the concept of the derivative as a function (ACMMM089)

Differential Calculus: The Equation of Tangent and Normal to a Curve problems and step-by step solutions. Students think critically, demonstrate knowledge of functions and differential calculus. Apply the appropriate formulas, sketch the graph of y = f(x) with the tangent and normal. Use mathematical strategies to solve all questions. Learning Outcomes: Understand the derivative as the gradient of the tangent to the curve of y = f(x) at a point. Understand that the normal on the curve is perpendicular to the tangent. Find the gradient of the tangent and normal at a point on the curve. Find the equation of the tangent and normal of the curve at a point. Practise sketching a curve with the tangent and normal. Find the angle of inclination. Grades: 11th to 12th Also comply with Australian Curriculum Interpret the derivative as the gradient of the tangent to the graph of y = f(x) at a point (ACMMM085) Estimate numerically the value of the derivative at a point, for simple power functions (ACMMM086) understand the concept of the derivative as a function (ACMMM089) Differential Calculus Resources: Differential Calculus -The Equation of Tangents to a Curve- Critical Thinking

PARABOLA & CIRCLE PROBLEMS - FUNCTIONS & GRAPHS REVIEW for Math Test Preparation. Working mathematically & critical thinking to solve problems involving function and relation graphs. The resource contents: Worksheets + Step by step solutions + Teacher notes. Problem 1 in 2 skills: Easy: Steps to solve the problem are given. Hard: Steps to solve the problem are not given. Problem 2: Steps to solve the problem are not given. Grades: 10th & 12th Learning Outcomes: Recognise features of the graphs of x^2 + y^2 = r^2 and (x − h)^2 + (y − k)^2 = r^2, including their circular shapes, their centres and their radii. Recognise features of the graph of y = x^2 including its parabolic shape and its axis of symmetry. Find the intersection points of a parabola and a circle. Also comply with Australian Curriculum: Understand the concept of the graph of a function (ACMMM024) Recognise features of the graphs of x^2 + y^2 = r^2 and (x − h)^2 + (y − k)^2 = r^2, including their circular shapes, their centres and their radii. (ACMMM020) Recognise features of the graph of y = x^2 including its parabolic shape and its axis of symmetry. (ACMMM021) MA-F1: Working with functions. More Function Resources: Mapping Diagrams and Functions Workbook Classifying and Mapping Relations Workbook Parabolas & Circles-Functions & Graphs Review- Math Test Prep Visit my shop :)

Algebra Mazes for students to practise simplifying algebraic expressions (Adding, subtracting, multiplying and dividing algebraic expressions) The resource is in Printable (pdf) and PowerPoint Slides. Level of Difficulty: Beginner (Easy) Grades: 7th to 9th Teaching Ideas: Students work individually or in pairs to complete the algebra mazes then they swap their page with their friend or another pair to check the answers. Learning Outcomes: Recognise and use equivalent algebraic expressions (e.g. a + a = 2 x a = 2a, b + b +b +b = 4 x b = 4b) Recognise like terms and add and subtract them to simplify algebraic expressions, eg a + 2b +3a =4a + 2b Practise simplifying algebraic expressions that involve multiplication and division. Simplify algebraic expressions involving the four operations Also suitable for Australian Curriculum Simplify algebraic expressions involving the four operations (ACMNA192) More Resources: Colouring Pages Fun Activity Topics: Numbers Times Table Fractions Decimals Percentages Significant Figures Consumer Maths Financial Maths Algebra Measurement and Geometry Visit my shop :)

Multiplying Fractions Using Cancelling Common Factors Skills Level: Beginner (Easy) Grades: 5th to 8th Learning Outcomes: • Practise multiplying fractions using cancelling common factors. • Writing fractions in their simplest form. • Worksheets to practise multiplying fractions using cancelling common factors. • Worksheets A to D with examples help students multiply fractions using the cancelling common factors method. • Worksheets E and F (colouring pages) without examples. • The worksheets are in portrait and landscape formats. • Answer keys are also included. More Resources: Colouring Pages Fun Activity Topics: Numbers Times Table Fractions Decimals Percentages Significant Figures Consumer Maths Financial Maths Algebra Measurement and Geometry Visit my shop :)

This resource contains note and worksheets about rounding multi-digit numbers to the nearest any place value or correct to 1, 2 or 3 decimal places. Answer keys are also included. Level of Difficulty: Beginner Grades: 5th to 8th Learning Outcomes: • Use place value understanding to round whole numbers to the nearest whole number, 10, 100, 1000 or up to million. • Use place value understanding to round decimals to any place. Also suitable for Australian Curriculum Round decimals to a specified number of decimal places (ACMNA156) More Resources: Colouring Pages Fun Activity Topics: Numbers Times Table Fractions Decimals Percentages Significant Figures Consumer Maths Financial Maths Algebra Measurement and Geometry Visit my shop :)