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).

SQUARE NUMBERS 1 to 16 & SQUARE ROOT Three activities to keep your learners engaged in math learning and apply mathematical strategies to complete all the activities. This activity is to increase their fluency and confidence in number skills involving square numbers and square roots. Answer keys are also included. ACTIVITY 1: FINDING SQUARE ROOTS ACTIVITY 2: COMPLETING PAIRS OF NUMBER & SQUARE ROOT ACTIVITY 3: SQUARE NUMBERS MAZE (SQUARE NUMBERS WITH FOUR OPERATIONS) Grade: 5th to 8th Learning Outcomes: Investigate and use square roots of perfect square numbers 1 to 16. Select and apply efficient mental and written strategies and appropriate digital technologies to solve problems involving all four operations with square roots. Also Comply with Australian Curriculum: Investigate and use square roots of perfect square numbers (ACMNA150). Select and apply efficient mental and written strategies and appropriate digital technologies to solve problems involving all four operations with whole numbers (ACMNA123).

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

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)

Right Triangle Trigonometry Workbook - TRUE BEARINGS Scaffolded notes + worksheets + step-by-step solutions + teacher notes + mini folded notes to learn and practise: Identify and write the true bearings of a location. Draw the true bearings of a location. Solve a variety of trigonometry problems involving bearings (critical and creative thinking). There are two styles of workbook. Style 1: Cover, fill in the blank notes and worksheets Style 2: Cover, completed (filled) notes and worksheets Total pages in each workbook: 12 Easy classroom preparation: For the workbook: print and staple all pages together to make a book. For the mini folded notes: print, fold and glue the pages to make a mini notebook. Teacher notes displayed on whiteboards. Grades: 9th to 12th Also comply with Australian Curriculum: Apply trigonometry to solve right-angled triangle problems (ACMMG224). Solve right-angled triangle problems including those involving direction and angles of elevation and depression (ACMMG245). Solve problems involving bearings. (ACMEM120). Solve practical problems involving the trigonometry of right-angled and non-right-angled triangles, including problems involving angles of elevation and depression and the use of bearings in navigation. (ACMGM037). Right Triangle Trigonometry Workbook - Angles of Elevation & Depression

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

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 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

NUMBERS IN INDEX FORM WORKSHEETS & ANSWERS Students practise: Identify the base number and index (power or exponent) of numbers written in index form. 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). Use index notation with numbers to establish the index laws with positive integral indices and the zero index (ACMNA182). Express numbers in scientific notation (ACMNA210) Indices (Exponents) Resources: INTRODUCTION TO INDICES Numbers in Index Form Worksheets

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

AREA OF 2D SHAPES ACTIVITY Math Challenge Activity- to keep your learners engaged, thinking critically and making connections to 2D shapes. This activity requires learners to Determine which shape has complete dimensions to calculate its area Calculate the area of the other shapes including their type. Find the exact value of each pronumeral. The activity encourages them to think creatively and come up with mathematical strategies to solve unknown lengths. The aims of this activity are to: Increase their fluency and confidence in geometry and measurements Develop understanding of a variety of problems with 2D shapes. Step-by-step solutions are also included. Grades: 6th to 9th Learning Outcomes: Solve problems involving the area of 2D Shapes. Find the unknown lengths (Critical Thinking) Also comply with Australian Curriculum: Establish the formulas for areas of rectangles, triangles and parallelograms, and use these in problem-solving (ACMMG159) Critical Thinking Problems: Area of Composite Shape-Critical thinking Activity-Math Challenge 1 Area of Composite Shape-Critical thinking Activity-Math Challenge 2 Area of 2D Shapes-Critical thinking Activity-Math Challenge 3

AREA OF COMPOSITE SHAPES ACTIVITY Math Challenge Activity- to keep your learners engaged, thinking critically and making connections to 2D shapes. This activity requires learners to determine the area of circles and squares based on the given dimensions. It also encourages them to think creatively and come up with mathematical strategies to solve unknown lengths and compare the areas of circles and squares and shaded parts. The aim of this activity is to: Increase their fluency and confidence in geometry and measurements Develop understanding of a variety of problems with 2D shapes. Step-by-step solutions are also included. Grades: 6th to 9th Learning Outcomes: Solve problems involving the area of circles and squares. Calculate the area of composite shapes. Determine the ratio of square area to circle area. Determine the ratio of shaded areas. Also comply with Australian Curriculum: Calculate areas of composite shapes (ACMMG216) Critical Thinking Problems: Area of Composite Shape-Critical thinking Activity-Math Challenge 1 Area of Composite Shape-Critical thinking Activity-Math Challenge 2 Area of 2D Shapes-Critical thinking Activity-Math Challenge 3

AREA OF COMPOSITE SHAPE ACTIVITY Math Challenge Activity- to keep your learners engaged, thinking critically and making connections to 2D shapes. This activity requires learners to determine the area of a shape based on the given dimensions. It also encourages them to think creatively and come up with mathematical strategies to solve unknown lengths. The aim of this activity is to: Increase their fluency and confidence in geometry and measurements Develop understanding of a variety of 2D shapes in real life problems. In this activity, students will practice finding the area of a composite (irregular) figure involving a rectangle, a triangle and semi-circles. Step-by-step solutions are also included. Grades: 6th to 9th Learning Outcomes: Establish the formulas for the areas of rectangles, triangles and parallelograms, and use them in problem-solving. Solve problems involving the area of circles. Calculate the area of the composite shape. Also comply with Australian Curriculum: Calculate areas of composite shapes (ACMMG216) Critical Thinking Problems: Area of Composite Shape-Critical thinking Activity-Math Challenge 1 Area of Composite Shape-Critical thinking Activity-Math Challenge 2 Area of 2D Shapes-Critical thinking Activity-Math Challenge 3

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 :)

SOLVE TWO & THREE-STEP LINEAR EQUATIONS USING THE BALANCE METHOD WORKBOOK To learn and practise: Connect mathematical ideas using appropriate terminology, diagrams and symbols. Solve two & three-step linear equations using the Balance Method Solve linear equations and verify solutions by substitution. The resource contents: workbooks (Scaffolded notes + worksheets) + step by step solutions + folded notes + teacher notes. Grades: 7th to 9th Learning Outcomes: Solve two & three-step linear equations using the Balance Method Also suitable 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). Solve simple linear equations (ACMNA179). Solve linear equations using algebraic techniques and verify solutions by substitution (ACMNA194). More Algebra Resources: Algebra Mazes Simplifying Algebraic Expressions Simplifying Algebraic Expressions Represent Algebraic Expressions on Flowcharts Solve One & Two Step Linear Equations by Backtracking Flowcharts Solve One Step Linear Equations-Balance Method Visit my shop :)

SOLVE LINEAR EQUATIONS USING THE BALANCE METHOD WORKBOOK To learn and practise: • Connect mathematical ideas using appropriate terminology, diagrams and symbols • Solve one-step linear equations using the Balance Method • Solve linear equations and verify solutions by substitution. The resource contents: workbooks (Scaffolded notes + worksheets) + answer keys + folded notes + teacher notes. Grades: 7th to 9th Learning Outcomes: Solve one step linear equations using the Balance Method Also suitable 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). Solve simple linear equations (ACMNA179). Solve linear equations using algebraic techniques and verify solutions by substitution (ACMNA194). More Algebra Resources: Algebra Mazes Simplifying Algebraic Expressions Simplifying Algebraic Expressions Represent Algebraic Expressions on Flowcharts Solve One & Two Step Linear Equations by Backtracking Flowcharts Visit my shop :)

SOLVE LINEAR EQUATIONS USING BACKTRACKING WORKBOOK to learn and practise: Solve linear equations using the backtracking method. The resource contents: workbooks (Scaffolded notes + worksheets) + answer keys + mini folded notes + teacher notes. Grades: 7th to 9th Learning Outcomes: Understand the difference between algebraic expressions where pronumerals are used as variables, and equations where pronumerals are used as unknowns. Solve linear equations using the backtracking method. Also comply iwith 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). Solve simple linear equations (ACMNA179). Solve linear equations using algebraic techniques and verify solutions by substitution (ACMNA194). More Algebra Resources: Algebra Mazes Simplifying Algebraic Expressions Simplifying Algebraic Expressions Represent Algebraic Expressions on Flowcharts

REPRESENT ALGEBRAIC EXPRESSIONS ON FLOWCHARTS WORKBOOK Scaffolded notes + worksheets + answer keys + mini folded notes + teacher notes to learn and practise: • The concept of algebra uses variables and numbers • Represent algebraic expressions using flowcharts • The concept of variables as a way of representing numbers using letters. Grades: 7th to 9th Learning Outcomes: Understand the concept of algebra uses variables and numbers. Represent algebraic expressions using flowcharts. Understand the concept of variables as a way of representing numbers using letters. 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) Recognise and explains mathematical relationships using reasoning (MA4-3WM) Generalise number properties to operate with algebraic expressions (MA4-8NA) More Algebra Resources: Algebra Mazes | Simplifying Algebraic Expressions Simplifying Algebraic Expressions