The following problem incorporates linear simultaneous equations within an index problem (prime factorization). This question is for those students looking to get 8+ and have the ability to transfer various skills to different contexts. Though this is only one question it will take a lot of time for students to attempt and then walk through the solution. The solution is attached to the slides.
Lesson introduces students to drawing and writing equations of circles with centers around the origin and (p,q). The lesson walks through how the equation of a circle is from by linking it with Pythagoras theorem. After the understanding of a circle with center (0,0), the lesson then moves to connect circles with the concept of translations, thus creating equations with centers at (p.q). The package includes lesson presentation, introductory activity to understand circle and its transformations, along with class work and homework exercises.
The following PowerPoint contains about 3-4 days worth of lessons and is a complete package for teaching exact values to students (targeting students grades 7+). Lessons Include:
Introduction to Exact Values
Evaluating using Exact Values
Application Problems (including surds)
Problems involving Algebra (including quadratics)
The Lesson walks through the basic trigonometric ratios and special triangles introducing trigonometric graphs and alternative ways of remembering 0 and 90 degree angles. Various questions from multiple exam boards and textbooks have been use to give students a range of contexts to apply special triangles. QUestions used tend to incorporate multiple transferable skills such as: surds, algebraic fractions, quadratics, sine law, area of non-right angle triangles etc. Lesson is to be used after students have mastered basic right angle trigonometry and some questions are only useful if students have learn non-right angle trigonometry.
Full completing the square lesson. Includes completing the square for both simple and complex trinomials and solving using completing the square. Lesson includes full process of how completing the square works with all steps in between.
The following starter questions are for students targeting grades 7-9. Questions are taken from various exam boards and include solutions. Encourages students to think and apply their skills in different contexts. Entire PowerPoint includes over 50 questions in the following categories:
Coordinate Geometry - Circles
Geometric Problems and Proof
Coordinate Geometry – Lines & Curves
Algebraic Problems – including ratio
Indices and Surds
Lesson 1: Quadratic Sequences
Lesson 2: Completing the Square
Lesson 3: Iteration
Lesson 4: Composite Functions
Each lesson includes worked examples and practice questions. Alternative methods are shown for completing the square. Iteration lesson includes a video and graphical representation of how iteration works to deepen student understanding.
20 Maths starters for targeting grades 4 - 6 on a Higher Paper. Also works well if teaching a boarder line class with a few students writing the Foundation Exam. Most starters have complete solutions. Questions are taken from various Edexcel Exam papers and contains questions from levels 4 - 9. Certain higher level questions are given for students to transfer their skills and obtain some of the marks.
The following PowerPoint will take at least 2 days to complete. The lesson starts with Geometric Sequences and links it to Exponential Functions. The lesson also looks at the connection between geometric sequences, exponential functions and compound interest. By the end of the lesson students should be able to find the nth term of a geometric sequence and the equation of an exponential function.