Mon Mar 26th – More work on Vectors

LEARNING OBJECTIVE: Further practice and extensions of the vector notation and concepts

SUCCESS CRITERIA: You will be able to solve vector problems using drawings and sketches to help to work out answers

ENGAGEMENT ACTIVITY: Watch this Video

LESSON: Use Question 5 in Higher text book to consolidate Fridays lesson – introducing vectors.

Continue to work through Ex 18 A Q 6 Onwards.

EXTENSION WORK: Have a go at the A* questions on page 396

 

Fri Mar 23rd – Vectors – What they are and how to add and subtract them

LEARNING OBJECTIVE: Discover what a vector is and understanding what adding and subtracting a vector means

SUCCESS CRITERIA: You will understand a vector is a numerical way of representing a movement on a grid and appreciate how movements on a grid can be written as additions and sbtyractions of vectors.

KEYWORDS: VECTOR, MAGNITUDE, DIRECTION

ENGAGEMENT ACTIVITY: Have a go at these three questions

LESSON: Work through this MyMthas Lesson.

The use this Vector Grid to develop the ideas and notation of vectors.

If any time left have a go at ex 18A page 394

PLENARY: Answers, Checking understanding with students

 

Thurs Mar 22nd – Exam question Practice – Quadratic Equations / Expanding Brackets

LEARNING OBJECTIVE: Applying skills leaned in Solving quadratic equations to solve higher level exam questions

SUCCESS CRITERIA: You will be able to solve higher level algebra questions

ENGAGEMENT ACTIVITY: Hand out difference of two squares questions for students to have a go at

LESSON: Quick check on Starter questions, then hand out exam questions for them to have a go at.

Support students working on exam questions around the room.

PLENARIES: Checking on solutions, supporting small groups / individuals. Stopping whole class to go over problems
if necessary.

Fri – 16th Mar – Solving Quadratics that do not factorise using the ‘Quadratic Formula’

LEARNING OBJECTIVE: TO solve quadratic equations using the quadratic formula

SUCCESS CRITERIA: You will be able to solve equations that DO NO factorise using the quadratic Formula

ENGAGEMENT ACTIVITY:

Use these values to work out what these expressions are equal to:

a = 3, b = -2, c = -4, d =-½

1. ab + c
   
2. a(b - c)
   
3. a + b + c
   
4. bc + ac
   
5. abc/d
   
6. ad(c – b)
   
7. cd – ab
   
8. abc – b + c +d
   

LESSON: Work through Quadratic Formula Lesson, use question screens over and over again to give lots of practice in using the formula. Give students a chance to solve all questions on final screen

Have a go at Ex 20J page 226 of Higher Text Book

PLENARY: Checking answers, exam question if time

Thurs – 15th Mar – Solving a quadratic that will not factorise

LEARNING OBJECTIVE: Discover other methods of solving quadratics when they will not factorise

SUCCESS CRITERIA: You will be able to solve quadratics that do not factorise.

ENGAGEMENT ACTIVITIES:

Can You expand these equations

1. (x+2)²
   
2. (x-4)²
   
3. (x+5)²
   
4. (x- 3)²
   
5. (x+1.5)²
   
6. (x – 3.5)²
   

LESSON

Look at the following quadratics,

1. Can you factorise them?
   
2. If no, can you guess a solution using trial and improvement methods?
   

x² + 4x – 8 = 0

x² - 8x – 4 = 0

1. 
    Look at (x+2)² and the expression x² + 4x + 2 – How are they different?
   

   What can we do to make this equation balance correctly
   

   (x+2)² ????? = x² + 4x + 2
   

   Examples
   

   1. x² + 8x - 7
      
   2. x² - 14x - 11
      
   3. x² + 7x - 4
      

   Can you write the following equations in this form
   

   (x + a)² –b or (x - a)² –b
   

2. x² + 14x - 1
   
3. x² - 6x + 3
   
4. x² + 6x + 7
   
5. x² - 4x - 1
   
6. x² + 3x + 3
   
7. x² - 5x - 5
   
8. x² + x - 1
   
9. x² + 8x - 6
   
10. x² + 2x -1
    
11. x² - 2x - 7
    

    Look at these pairs of equations, can you complete the square and then solve the equations (leave your answer in surd form)
    

12. x² + 14x – 5 = 0 , (x + 7)²
    
13. x² -6x + 3 = 0 ,(x - 3)²
    
14. x² +6x + 7 = 0 ,(x + 3)²
    
15. x² - 4x - 1 = 0 ,(x - 2)²
    
16. x² + 3x + 3 = 0 ,(x + 1½ )²
    
17. x² - 5x – 5 = 0 ,(x - 3)²
    
18. x² + x - 1 = 0 ,(x + ½)²
    
19. x² + 8x - 6 = 0 ,(x + 4)²
    
20. x² + 2x -1 = 0 ,(x + 1)²
    
21. x² -2x - 7 = 0 ,(x - 1)²
     
    

PLENARY: Checking answers, stopping class and going over problems when stuck.

Mon 12th Mar – Solving quadratic Equations by Factorising

LEARNING OBJECTIVE: How to spot the factors in a quadratic equation and then use these to solve it.

SUCCESS CRITERIA: You will be able to factorise a quadratic equation and then work out the solutions.

ENGAGEMENT ACTIVITY:

Expand the following:

1. (x + 2) (x + 4)
   
2. (x - 2) (x + 5)
   
3. (2x +3) (x – 2)
   
4. (3x – 4)( 5 – 2x)
   
5. (3x + 5)²
   

LESSON: Using the answers to the above explain the process of factorising: Then have ago at factorising and then solving these equations:

1. x² + 8x + 16 = 0
   
2. x² + 6x + 9 = 0
   
3. x² - 16x + 64 = 0
   
4. x² + 11x + 30 = 0
   
5. x² + x – 12 = 0
   
6. x² -5x - 24 = 0
   
7. 2x² + 8x + 6 = 0
   
8. 6x² + 19x + 10 = 0
   
9. x² + 6x + 9 = 0
   
10. 8x² -3x -10 = 0
    

Check Answers

Then have a go at question 14 onwards in second exercise on worksheet

PLENARY: Checking Answers and understanding, Exam question if time

Fri 9th March – Dealing with algebraic Fractions

LEARNING OBJECTIVE: You will discover how to adapt the addition of fractions skills to algebraic fractions

SUCCESS CRITERIA: You will be able to solve algebraic fractions problems

ENGAGEMENT ACTIVITY: Try These Questions

LESSON: Using adding Fractions examples to show how to add algebraic fractions on IWB.

Examples

Work through Page 18 of questions from Online Text Book

PLENARY Checking Answers, Exam questions.

Thurs 9th March – Algebra – Solving equations – From simple to Quadratic Equations

LEARNING
OBJECTIVE: Revise and extend skills in algebra to solve equations

SUCCESS
CRITERIA: You will be able to solve equations using algebra of these difficulties

1. Simple equations (unknown on one side only)
   
2. Expanding brackets and simplifying
   
3. Unknown on both sides
   
4. Expand brackets on either side of equality and then simplify and solve
   
5. Equations with x² in them – Quadratics that will factorise
   
6. Equations that are written as fractions
   
7. The difference of two squares type problems
   

ENGAGEMENT
ACTIVITY:

Can you solve these equations:

1. 5x + 4 = 19
   
2. 6x + 3 = 4x + 23
   
3. 3(2x-3) = 5(1-3x)
   
4. x² - 4x + 12
   

LESSON: Discuss answers to above questions, and revise skills needed to solve them.

Work through Page 18 from this text book

PLENARY: Checking Answers, If time look at a past paper question

Mon 5th March – Higher Level Calculator Paper revision

LEARNING OBJECTIVE: Revise Topics on Higher Level Calculator Paper.

SUCCESS CRITERIA: You will be able to achieve / improve your target grade.

STARTER: Have a go at these questions

LESSON: Look at this exam paper (Nov 2011)

These topics /Questions

BODMAS – question 1

Compound Interest – Q2

HCF/LCM – Q3

Area Problem – q 8b

Exchange Rate questions – Q9

Straight Line Graphs - Q13

Moving Average Q15

Similar Triangles Q17

Using Quadratic Rule Formula = Q19 (Very Hard)

Cosine Rule – q20 Part 2

Histograms / Frequency density – Q21

Geometric Proof – Q22

Difficult Algebra Factorising – Q 23

Surface Area of Hemisphere – Q 24 (Area / Volume /TSA)

Accuracy – Upper and Lower Bounds) – q25

 

 

Thurs/Fri 1st/2nd march – Using Past exam papers November 2010)to revise exam questions and exam techniques

LEARNING OBJECTIVE: To revise Higher level topics

SUCCESS CRITERIA: You will be able to solve higher level exam questions and gain a grade B or higher in the exam paper

STARTER: Hand back all marked exam papers, give students a chance to look at their results and talk to each other (and me about them). Show grade boundaries on IWB so students can assess their levels.

LESSON: Work through questions that were badly done / not done with all students – encourage them to do the explaining.

Jun 2010 3H, Mark Scheme

Nov 2010 4H, Mark Scheme

PLENARY: Looking at individual questions