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Model model Lesson for teachers of igcse

The document outlines a lesson plan focused on solving quadratic inequalities graphically, including learning objectives, vocabulary, and instructional steps. It emphasizes understanding inequalities, the graphical representation of solutions, and the specific process required to solve quadratic inequalities. Activities include modeling, scaffolded practices, and a summative exit ticket to assess understanding.

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Title: Solving quadratic inequalities (Algebra ) Lesson objectives/ Lesson aim By the end of the lesson, you will: Solve quadratic inequalities graphically. Lesson goals/Learning outcomes Inequalities show the relationship between two expressions that are not equal to one another. The symbols used for inequalities are <, >, ≤, ≥. (continue on slide no-7) Starter/ Do Now activity/ Warmer Slide no -5 Scaffolder practice ( You do) Slide 11 Instruction and Modelling (I do/We do) Slide 6 to 10 Lesson at a glance Vocabulary Algebra, Inequalities, Equations, Expression, Equation Quadratic functions, Root, Coefficient, Factors etc Checking for understanding Slide 12 Plenary/Exit Ticket Slide 15 and 16 Extension Task/Challange Slide 13&14
Title: Solving quadratic inequalities (Algebra ) Lesson objectives: By the end of the lesson, you will: Solve quadratic inequalities graphically.
Lesson Goals/ Learning outcome To achieve this, you will need to know: • Inequalities show the relationship between two expressions that are not equal to one another. • The symbols used for inequalities are <, >, ≤, ≥. • The process to solve inequalities is the same as the process to solve equations • That extra care should be taken when the unknown in an inequality has a negative coefficient. • An inequality can be represented graphically as a region on one side of a line. • Inequalities that use < or > symbols are plotted with a dashed line to show that the line is not included in the region. • How to find the roots of a quadratic function • How to sketch a graph of a quadratic functions • How to rearrange quadratic equations if they are not equal to zero. • How to solve quadratic inequalities in one variable, by factorising and sketching the graphs • How to solve a quadratic inequality (a = 1 and a>1)
Vocabulary • Algebra • Inequalities • Equations • Expression • Equation • Quadratic functions • Root • Coefficient • Factors etc
STARTER/Retrieval/Warmer Solve the following quadratic equations
Instruction and Modelling(I do/We do) Solve x² + 6x + 8 ≤ 0 Step 1: Start by solving the inequality as an equation Solve x² + 6x + 8 = 0 (x + 4)(x + 2) = 0 x = -4, x = -2 Teacher Example 1- I do These are the point where the quadratic graph intersects the -axis Step 2: Now we need to sketch the graph
Solve x² + 6x + 8 ≤ 0 This means: for what values of x is the graph below the - axis? Teacher Example 1 continued Original question: Step 3: Highlight the part of the graph below the -axis The graph is below the -axis between -4 and -2. Let’s write that as an inequality… ANSWER:
Solve x²+ 6x + 8 ≥ 0 What’s different this time? Solution on the next slides Teacher Example 2 - We do
Solve x² + 6x + 8 ≥ 0 Step 1: Start by solving the inequality as an equation Solve x² + 6x + 8 = 0 (x + 4)(x + 2) = 0 x = -4, x = -2 Teacher Example 2 These are the point where the quadratic graph intersects the -axis Step 2: Now we need to sketch the graph
Solve x² + 6x + 8 ≥ 0 This means: for what values of x is the graph above the - axis? Teacher Example 2 continued Original question: Step 3: Highlight the part of the graph above the -axis We have highlighted TWO separate parts of the graph, so need to write our answer as TWO separate inequalities ANSWER: and What can you say about the values of points in this region? What can you say about the values of points in this region?
Scaffolded practice (You do) Complete the grid to solve the inequalities.
Check for understanding/ Assessment opportunities In pairs, summarise the steps needed to solve a quadratic inequality Step 1 Start by solving the inequality as a quadratic equation equal to 0 Step 2 Sketch the graph. Your solutions are the points where the quadratic graph intersects the-axis Step 3 Consider the original inequality- highlight the correct part of the graph Step 4 Write your solutions as an inequality using your graph Did you discuss these points? TURN AND TALK
Extension Work (You do/independent practice) 𝑥 𝑦 − 4 −1 𝑦 =(𝑥+4)(𝑥 +1) or 𝑥 𝑦 −3 3 𝑦=(𝑥+3)(𝑥 −3) − 3 < 𝑥< 3 ? ? Solve Solve
EXTENSION: Solve Solve ? ? 1 2
Exit Ticket – Spot the mistakes SILENT SOLO Only one answer is correct! You need to identify the mistakes and decide which is the correct answer – happy sleuthing!
Model model Lesson for teachers of igcse