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1. linear equations in two variables introduction, solution and graphing
- 1. What are linear equations in two variables? Learning Objective
- 2. To interpret basic concepts To find solution of equation with 2 variables To graph linear equation with 2 variables Learning Outcomes
- 3. Linear Equations in Two Variables Let’s look at a few equations. 7x + 5 = 33 x + 5y = 8 What do you notice?
- 4. Linear Equations in Two Variables Let’s look at a few equations. 7x + 5 = 33 x + 5y = 8 Both are linear equations!
- 5. Linear Equations in Two Variables Let’s look at a few equations. 7x + 5 = 33 only one variable x x + 5y = 8 two variables x and y Both are linear equations!
- 6. Linear Equations in Two Variables Let’s look at a few equations. x + 5y = 8 two variables x and y This is a linear equation in two variables!
- 7. Linear Equations in Two Variables Let’s look at a few equations. x + 5y = 8 two variables x and y Every linear equation in two variables has a standard form. This is a linear equation in two variables!
- 8. Linear Equations in Two Variables Let’s look at a few equations. x + 5y = 8 two variables x and y Every linear equation in two variables has a standard form. ax + by + c = 0 This is a linear equation in two variables!
- 9. Linear Equations in Two Variables Let’s look at a few equations. x + 5y = 8 two variables x and y Every linear equation in two variables has a standard form. ax + by + c = 0; Where x and y are variables. This is a linear equation in two variables!
- 10. Linear Equations in Two Variables Let’s look at a few equations. x + 5y = 8 two variables x and y Every linear equation in two variables has a standard form. ax + by + c = 0; Where x and y are variables, And a, b and c are constants. Can you arrange the given equation in standard form?
- 11. Linear Equations in Two Variables Let’s look at a few equations. x + 5y = 8 two variables x and y x + 5y – 8 = 0 Every linear equation in two variables has a standard form. ax + by + c = 0; Where x and y are variables, And a, b and c are constants. That’s the standard form.
- 12. Linear Equations in Two Variables Can you write this equation in standard form? 2x = 3 Hint: The RHS should be 0.
- 13. Linear Equations in Two Variables How will we write this equation in two variables? 2x = 3 2x - 3 = 0 Hint: Add a variable such that it’s value is 0.
- 14. Linear Equations in Two Variables How will we write this equation in two variables? 2x = 3 2x + 0y - 3 = 0 Why cannot the variable be x?
- 15. Linear Equations in Two Variables How will we write this equation in two variables? 2x = 3 2x + 0y - 3 = 0 That’s our standard form!
- 16. To interpret basic concepts To find solution of equation with 2 variables To graph linear equation with 2 variables Learning Outcomes How confident do you feel?
- 17. To interpret basic concepts To find solution of equation with 2 variables To graph linear equation with 2 variables Learning Outcomes How confident do you feel?
- 18. Linear Equations in Two Variables Let’s consider this equation! 2x + 3y = 12
- 19. Linear Equations in Two Variables Let’s consider this equation! 2x + 3y = 12 Let’s say value of x is 2. What will the value of y be?
- 20. Linear Equations in Two Variables Let’s consider this equation! 2x + 3y = 12 Let’s say value of x is 2. ∴ 2(2) + 3y = 12 Let’s substitute the value of x.
- 21. Linear Equations in Two Variables Let’s consider this equation! 2x + 3y = 12 Let’s say value of x is 2. ∴ 2(2) + 3y = 12 ∴ 4 + 3y = 12 Let’s move 4 to the RHS!
- 22. Linear Equations in Two Variables Let’s consider this equation! 2x + 3y = 12 Let’s say value of x is 2. ∴ 2(2) + 3y = 12 ∴ 4 + 3y = 12 ∴ 3y = 12 - 4 Let’s move 4 to the RHS!
- 23. Linear Equations in Two Variables Let’s consider this equation! 2x + 3y = 12 Let’s say value of x is 2. ∴ 2(2) + 3y = 12 ∴ 4 + 3y = 12 ∴ 3y = 8 What is the value of y?
- 24. Linear Equations in Two Variables Let’s consider this equation! 2x + 3y = 12 Let’s say value of x is 2. ∴ 2(2) + 3y = 12 ∴ 4 + 3y = 12 ∴ 3y = 8 ∴ y = 8 3 What is the value of y?
- 25. Linear Equations in Two Variables Let’s consider this equation! 2x + 3y = 12 Let’s say value of x is 2. ∴ 2(2) + 3y = 12 ∴ 4 + 3y = 12 ∴ 3y = 8 ∴ y = 8 3 ∴ x = 2 & y = 8 3 This is the solution of this equation!
- 26. Linear Equations in Two Variables Let’s consider this equation! 2x + 3y = 12 Let’s say value of x is 2. ∴ 2(2) + 3y = 12 ∴ 4 + 3y = 12 ∴ 3y = 8 ∴ y = 8 3 ∴ x = 2 & y = 8 3 The solution is also written as (2, 𝟖 𝟑 ).
- 27. Linear Equations in Two Variables Let’s consider this equation! 2x + 3y = 12 Solutions: 1. (2, 8 3 ) Can you write a few more solutions?
- 28. Linear Equations in Two Variables Let’s consider this equation! 2x + 3y = 12 Solutions: 1. (2, 8 3 ) 2. (0,4) 3. (6,0) 4. (1, 10 3 )…. What do you notice?
- 29. Linear Equations in Two Variables Let’s consider this equation! 2x + 3y = 12 Solutions: 1. (2, 8 3 ) 2. (0,4) 3. (6,0) 4. (1, 10 3 )…. There are too many solutions.
- 30. Linear Equations in Two Variables Let’s consider this equation! A linear equation in two variables has _____________ solutions.
- 31. Linear Equations in Two Variables Let’s consider this equation! A linear equation in two variables has infinitely many solutions.
- 32. Linear Equations in Two Variables Find four different solutions for this equation. x + 2y = 6 Hint: Always use 0 as the value of the variables.
- 33. Linear Equations in Two Variables Find four different solutions for this equation. x + 2y = 6 Solutions: 1. (2,2) 2. (0,3) 3. (6,0) 4. (4,1)…. Hint: Always use 0 as the value of the variables.
- 34. To interpret basic concepts To find solution of equation with 2 variables To graph linear equation with 2 variables Learning Outcomes How confident do you feel?
- 35. To interpret basic concepts To find solution of equation with 2 variables To graph linear equation with 2 variables Learning Outcomes How confident do you feel?
- 36. Linear Equations in Two Variables Let’s draw a graph for this equation! x + 2y = 6 Solutions: 1. (0,3) 2. (2,2) 3. (4,1) 4. (6,0)…. We will use each solution as a single point!
- 37. Linear Equations in Two Variables Let’s draw a graph for this equation! x + 2y = 6 Now, let’s draw a graph! x y Point 0 3 (0,3) 2 2 (2,2) 4 1 (4,1) 6 0 (6,0)
- 38. Linear Equations in Two Variables Let’s draw a graph for this equation! x + 2y = 6 x y Point 0 3 (0,3) 2 2 (2,2) 4 1 (4,1) 6 0 (6,0) Y X O Let’s mark the co-ordinates!
- 39. Linear Equations in Two Variables Let’s draw a graph for this equation! x + 2y = 6 x y Point 0 3 (0,3) 2 2 (2,2) 4 1 (4,1) 6 0 (6,0) Y X O Let’s write the co-ordinates!
- 40. Linear Equations in Two Variables Let’s draw a graph for this equation! x + 2y = 6 x y Point 0 3 (0,3) 2 2 (2,2) 4 1 (4,1) 6 0 (6,0) Y X O Let’s mark the points! 1 2 3 4 5 6 7 1 2 3 4 5 6 7 8 9
- 41. Linear Equations in Two Variables Let’s draw a graph for this equation! x + 2y = 6 x y Point 0 3 A(0,3) 2 2 (2,2) 4 1 (4,1) 6 0 (6,0) Y X O Let’s mark the points! 1 2 3 4 5 6 7 1 2 3 4 5 6 7 8 9 A
- 42. Linear Equations in Two Variables Let’s draw a graph for this equation! x + 2y = 6 x y Point 0 3 A(0,3) 2 2 B(2,2) 4 1 (4,1) 6 0 (6,0) Y X O Let’s mark the points! 1 2 3 4 5 6 7 1 2 3 4 5 6 7 8 9 B A
- 43. Linear Equations in Two Variables Let’s draw a graph for this equation! x + 2y = 6 x y Point 0 3 A(0,3) 2 2 B(2,2) 4 1 C(4,1) 6 0 (6,0) Y X O Let’s mark the points! 1 2 3 4 5 6 7 1 2 3 4 5 6 7 8 9 C B A
- 44. Linear Equations in Two Variables Let’s draw a graph for this equation! x + 2y = 6 x y Point 0 3 A(0,3) 2 2 B(2,2) 4 1 C(4,1) 6 0 D(6,0) Y X O Let’s mark the points! 1 2 3 4 5 6 7 1 2 3 4 5 6 7 8 9 D C B A
- 45. Linear Equations in Two Variables Let’s draw a graph for this equation! x + 2y = 6 x y Point 0 3 A(0,3) 2 2 B(2,2) 4 1 C(4,1) 6 0 D(6,0) Y X O This is the graph for x + 2y = 6. 1 2 3 4 5 6 7 1 2 3 4 5 6 7 8 9 A B C D
- 46. To interpret basic concepts To find solution of equation with 2 variables To graph linear equation with 2 variables Learning Outcomes How confident do you feel?
- 47. To interpret basic concepts To find solution of equation with 2 variables To graph linear equation with 2 variables Learning Outcomes How confident do you feel?
- 48. What are linear equations in two variables? Learning Objective
- 49. Linear Equations in Two Variables Learning Activity Draw the graph of x + y = 7.
Editor's Notes
- An overview of the content of the lesson Must be in the form of a question where appropriate Students should be able to answer the question at the end - either fully, partly or in a way that demonstrates they understand what gaps in their knowledge they need to address Verbs such as to understand / to know / to gain confidence / to learn Ask students to give the question a go and point out that, at the end of the lesson, they should be able to answer fully
- Measurable outcomes that students can demonstrate and self-assess against Must be written using Bloom’s taxonomy verbs Verbs based on students ability and pitch of lesson It must be clear that students understand the outcomes before moving on Make an activity of this slide: Ask students to read this aloud Ask them to paraphrase Ask that they explain what they mean Ask what they already know related to these outcomes There may be as few as 2 outcomes, or max 4
- The next slides should be focused on achieving first outcome Make reference to the outcome in the teaching Fill this with thinking skills activities, peer assessment, higher-order questioning, engaging activities and challenge
- The next slides should be focused on achieving first outcome Make reference to the outcome in the teaching Fill this with thinking skills activities, peer assessment, higher-order questioning, engaging activities and challenge
- The next slides should be focused on achieving first outcome Make reference to the outcome in the teaching Fill this with thinking skills activities, peer assessment, higher-order questioning, engaging activities and challenge
- The next slides should be focused on achieving first outcome Make reference to the outcome in the teaching Fill this with thinking skills activities, peer assessment, higher-order questioning, engaging activities and challenge
- The next slides should be focused on achieving first outcome Make reference to the outcome in the teaching Fill this with thinking skills activities, peer assessment, higher-order questioning, engaging activities and challenge
- The next slides should be focused on achieving first outcome Make reference to the outcome in the teaching Fill this with thinking skills activities, peer assessment, higher-order questioning, engaging activities and challenge
- The next slides should be focused on achieving first outcome Make reference to the outcome in the teaching Fill this with thinking skills activities, peer assessment, higher-order questioning, engaging activities and challenge
- The next slides should be focused on achieving first outcome Make reference to the outcome in the teaching Fill this with thinking skills activities, peer assessment, higher-order questioning, engaging activities and challenge
- The next slides should be focused on achieving first outcome Make reference to the outcome in the teaching Fill this with thinking skills activities, peer assessment, higher-order questioning, engaging activities and challenge
- The next slides should be focused on achieving first outcome Make reference to the outcome in the teaching Fill this with thinking skills activities, peer assessment, higher-order questioning, engaging activities and challenge
- The next slides should be focused on achieving first outcome Make reference to the outcome in the teaching Fill this with thinking skills activities, peer assessment, higher-order questioning, engaging activities and challenge
- The next slides should be focused on achieving first outcome Make reference to the outcome in the teaching Fill this with thinking skills activities, peer assessment, higher-order questioning, engaging activities and challenge
- The next slides should be focused on achieving first outcome Make reference to the outcome in the teaching Fill this with thinking skills activities, peer assessment, higher-order questioning, engaging activities and challenge
- Revisit the first outcome and use the polling function to allow students to privately self-assess You may feel that the students do not need privacy to self-assess and in this instance, the chat box may be used Polling must be used until you can fully assess their confidence to use the chat box and express honesty If students self-assess as a 4/5, ensure that you are fully confident in their assessment Ask questions Ask for examples Students to ask each other questions If a few students self-assesses as a 3, but others as a 4/5, discretely ask the higher ones to give examples and to explain their achievement/understanding If all students are a 3 or below, do not move on. Move to a blank page at the end of the presentation and use as a whiteboard to further explain If students are ½, go back to the beginning Always ask students what the gaps are and help them to identify these in order to promote metacognition
- 1. The outcome changes colour when achieved to the same colour as the objective to demonstrate the connection, progress and what happens next
- The next slides should be focused on achieving first outcome Make reference to the outcome in the teaching Fill this with thinking skills activities, peer assessment, higher-order questioning, engaging activities and challenge
- The next slides should be focused on achieving first outcome Make reference to the outcome in the teaching Fill this with thinking skills activities, peer assessment, higher-order questioning, engaging activities and challenge
- The next slides should be focused on achieving first outcome Make reference to the outcome in the teaching Fill this with thinking skills activities, peer assessment, higher-order questioning, engaging activities and challenge
- The next slides should be focused on achieving first outcome Make reference to the outcome in the teaching Fill this with thinking skills activities, peer assessment, higher-order questioning, engaging activities and challenge
- The next slides should be focused on achieving first outcome Make reference to the outcome in the teaching Fill this with thinking skills activities, peer assessment, higher-order questioning, engaging activities and challenge
- The next slides should be focused on achieving first outcome Make reference to the outcome in the teaching Fill this with thinking skills activities, peer assessment, higher-order questioning, engaging activities and challenge
- The next slides should be focused on achieving first outcome Make reference to the outcome in the teaching Fill this with thinking skills activities, peer assessment, higher-order questioning, engaging activities and challenge
- The next slides should be focused on achieving first outcome Make reference to the outcome in the teaching Fill this with thinking skills activities, peer assessment, higher-order questioning, engaging activities and challenge
- The next slides should be focused on achieving first outcome Make reference to the outcome in the teaching Fill this with thinking skills activities, peer assessment, higher-order questioning, engaging activities and challenge
- The next slides should be focused on achieving first outcome Make reference to the outcome in the teaching Fill this with thinking skills activities, peer assessment, higher-order questioning, engaging activities and challenge
- The next slides should be focused on achieving first outcome Make reference to the outcome in the teaching Fill this with thinking skills activities, peer assessment, higher-order questioning, engaging activities and challenge
- The next slides should be focused on achieving first outcome Make reference to the outcome in the teaching Fill this with thinking skills activities, peer assessment, higher-order questioning, engaging activities and challenge
- The next slides should be focused on achieving first outcome Make reference to the outcome in the teaching Fill this with thinking skills activities, peer assessment, higher-order questioning, engaging activities and challenge
- The next slides should be focused on achieving first outcome Make reference to the outcome in the teaching Fill this with thinking skills activities, peer assessment, higher-order questioning, engaging activities and challenge
- The next slides should be focused on achieving first outcome Make reference to the outcome in the teaching Fill this with thinking skills activities, peer assessment, higher-order questioning, engaging activities and challenge
- The next slides should be focused on achieving first outcome Make reference to the outcome in the teaching Fill this with thinking skills activities, peer assessment, higher-order questioning, engaging activities and challenge
- As previously.
- As previously.
- The next slides should be focused on achieving first outcome Make reference to the outcome in the teaching Fill this with thinking skills activities, peer assessment, higher-order questioning, engaging activities and challenge
- The next slides should be focused on achieving first outcome Make reference to the outcome in the teaching Fill this with thinking skills activities, peer assessment, higher-order questioning, engaging activities and challenge
- The next slides should be focused on achieving first outcome Make reference to the outcome in the teaching Fill this with thinking skills activities, peer assessment, higher-order questioning, engaging activities and challenge
- The next slides should be focused on achieving first outcome Make reference to the outcome in the teaching Fill this with thinking skills activities, peer assessment, higher-order questioning, engaging activities and challenge
- The next slides should be focused on achieving first outcome Make reference to the outcome in the teaching Fill this with thinking skills activities, peer assessment, higher-order questioning, engaging activities and challenge
- The next slides should be focused on achieving first outcome Make reference to the outcome in the teaching Fill this with thinking skills activities, peer assessment, higher-order questioning, engaging activities and challenge
- The next slides should be focused on achieving first outcome Make reference to the outcome in the teaching Fill this with thinking skills activities, peer assessment, higher-order questioning, engaging activities and challenge
- The next slides should be focused on achieving first outcome Make reference to the outcome in the teaching Fill this with thinking skills activities, peer assessment, higher-order questioning, engaging activities and challenge
- The next slides should be focused on achieving first outcome Make reference to the outcome in the teaching Fill this with thinking skills activities, peer assessment, higher-order questioning, engaging activities and challenge
- The next slides should be focused on achieving first outcome Make reference to the outcome in the teaching Fill this with thinking skills activities, peer assessment, higher-order questioning, engaging activities and challenge
- As previously.
- As previously.
- An overview of the content of the lesson Must be in the form of a question where appropriate Students should be able to answer the question at the end - either fully, partly or in a way that demonstrates they understand what gaps in their knowledge they need to address Verbs such as to understand / to know / to gain confidence / to learn Ask students to give the question a go and point out that, at the end of the lesson, they should be able to answer fully
- The next slides should be focused on achieving first outcome Make reference to the outcome in the teaching Fill this with thinking skills activities, peer assessment, higher-order questioning, engaging activities and challenge