Which ones are you using?

1. Team Worker Creative Thinker Effective Participator Independent Enquirer Reflective Learner Self Manager Real life cross/curricular links? Where are we in our journey? Which ones are you using? PLT Skills LESSON OBJECTIVES Always aim high! We are learning to: • Enhance Mathematical basic skills knowledge. (Which PLT skills?) • Accurately draw probability trees for dependent events and work out probabilities from this. (Grade A*) AUTHOR www.mistrymaths.co.uk

2. Which ones are you using? LEARNING JOURNEY Team Worker Creative Thinker Effective Participator Independent Enquirer Reflective Learner Self Manager PLT Skills

3. Which ones are you using? Team Worker Creative Thinker Effective Participator Independent Enquirer Reflective Learner Self Manager STARTER PLT Skills TASK Find the median of: 2, 4, 7, 11 2) x - 7 When x = -6 2 1) Expand 5(-3x + 2) 3) -15x + 10 = 5.5 = 2 = 29 = (-6) - 7 Write the value 5 cubed. 4) Calculate Find the HCF of 18 and 30. 5) 6) = 7 and -7 = 125 = 6 Simplify: 5e + 8y – 9e – 7y Solve: 8(x + 4) = 56 25% of 36 miles 7) 8) 9) = 9 = -4e = 56 8x + 32 + y = EXTENSION = 24 8x x = 3 7m Calculate the area of the trapezium 4m 2 Area = Area = 36m Area = (a + b)h (7 + 11)4 11m

4. Which ones are you using? Team Worker Creative Thinker Effective Participator Independent Enquirer Reflective Learner Self Manager PROBABILITY TREES PLT Skills EXAMPLE P(The same colour) = P(B,B) + P(G,G) = Hubert has 10 coloured counters in a bag. Three of the counters are blue and seven of the counters are green. He removes a counter at random from the bag and notes the colour and does not replace it. He then chooses a second counter. Record the information on a tree diagram and work out the probabilities of the different outcomes. + = = P(BG in any order) = P(B,G) + P(G,B) = + = = ALWAYS MULTIPLY THE BRANCHES FIRST PICK SECOND PICK 21 21 42 21 21 42 42 48 8 7 6 3 7 3 3 6 3 2 2 6 3 6 7 7 7 7 P(B,B) = X = Blue 90 90 90 9 90 90 90 9 90 90 90 9 15 15 10 9 10 10 10 10 10 9 9 9 90 9 Blue COUNTERS HAVE NOT BEEN REPLACED SO THE PROBABILITY DOES CHANGE ON THE SECOND PICK P(B,G) = Green X = Blue P(G,B) = X = Green P(G,G) = X = Green

5. Which ones are you using? Team Worker Creative Thinker Effective Participator Independent Enquirer Reflective Learner Self Manager First Pick Second Pick Milk Dark PROBABILITY TREES PLT Skills TASK (GRADE A*) 1) Lucy has a box of 30 chocolates. 18 are milk chocolate and the rest are dark chocolate. She takes a chocolate at random from the box and eats it. She then chooses a second. Draw a tree diagram to show all the possible outcomes. P(Milk and Milk) = Milk P(Milk and Dark) = Dark P(Dark and Milk) = Milk Dark P(Dark and Dark) = Q1 beads

6. Which ones are you using? Team Worker Creative Thinker Effective Participator Independent Enquirer Reflective Learner Self Manager PROBABILITY TREES PLT Skills TASK (GRADE A*) 2) Jimmy has five coloured counters in a bag. Two of the counters are blueand the rest are red. He removes a counter at random from the bag and notes the colour but does not replace it. He then chooses a second counter. Draw a tree diagram showing all possible outcomes. FIRST PICK SECOND PICK ALWAYS MULTIPLY THE BRANCHES 3 6 6 6 3 2 2 3 1 6 3 2 2 2 3 1 2 2 3 2 2 1 3 12 6 6 P(B,B) = X = Blue 20 20 20 5 10 10 20 4 20 20 20 20 20 4 5 4 5 4 4 5 5 4 5 4 4 5 Blue COUNTERS HAVE NOT BEEN REPLACED SO THE PROBABILITY DOES CHANGE ON THE SECOND PICK P(B,R) = Red X = Blue P(R,B) = X = Red (a) P(Blue,Blue) = (b) P(Red,Red) = (c) P(One blue and one red in any order) = = = P(R,R) = X = Red = = + Q1 beads

7. Which ones are you using? Team Worker Creative Thinker Effective Participator Independent Enquirer Reflective Learner Self Manager PROBABILITY TREES PLT Skills TASK (GRADE A*) 3) The probability Manchester City will win the Premiership is 0.7. If they do, the probability they will go on to win the F.A. Cup is 0.6. But if they don’t, it’s only 0.5. Draw a tree diagram to represent this information. ALWAYS MULTIPLY THE BRANCHES FA CUP PREMIERSHIP P(W,W) = 0.42 x 0.6 = 0.7 Win 0.6 Win 0.7 0.4 P(W,L) = Lose 0.28 x 0.4 = 0.7 0.15 x 0.5 = 0.3 Win P(L,W) = 0.5 0.3 Lose 0.5 P(L,L) = 0.15 x 0.5 = 0.3 Lose P(Only one W) = 0.28 + 0.15 Use a tree diagram to find the probability that they win (a) the ‘double’ (b) only one of them 0.43 0.42 P(Double) = = Q1 beads

8. Which ones are you using? Team Worker Creative Thinker Effective Participator Independent Enquirer Reflective Learner Self Manager PROBABILITY TREES PLT Skills EXTENSION (GRADE A*) 1) A shop offers a package where customers can choose either a video player or a DVD player or a Hi-fi system and either a flat screen or a normal screen television. Over a period of time, 35% of the customers choose a video player and 60% choose a DVD player. The rest choose a Hi-fi system. Independently 75% of the customers choose flat screen televisions. (b) All customers were entered into a prize draw. What is the probability that the winner bought a Hi-Fi system with a normal screen television? (a) Complete the tree diagram below: Probability adds up to one whole 0.0125 0.25 0.25 0.05 0.0125 0.25 P(H,N) = = 0.05 x 0.25 Q1 beads

9. Which ones are you using? Team Worker Creative Thinker Effective Participator Independent Enquirer Reflective Learner Self Manager PROBABILITY TREES PLT Skills EXTENSION (GRADE A*) 2) Sports activities are held after school. Zoe attends these classes on Monday and Wednesday. She can choose one of badminton, dance or netball on each day. The probability she chooses badminton is 0.5. The probability she chooses dance is 0.4. Assume Zoe’s choices are independent. (b) What is the probability Zoe will choose the same sports activity on both days? (a) Complete the tree diagram below: 0.01 P(Same sport) = 0.25 + + 0.16 0.42 Probability adds up to one whole = 0.25 P(B,B) = = 0.5 x 0.5 0.1 0.16 P(D,D) = = 0.4 x 0.4 0.1 0.1 0.1 0.01 P(N,N) = = 0.1 x 0.1 Q1 beads

10. Which ones are you using? Team Worker Creative Thinker Effective Participator Independent Enquirer Reflective Learner Self Manager • LINK BACK TO OBJECTIVES • Accurately draw probability trees for dependent events and work out probabilities from this. What grade are we working at? DISCOVERY PLT Skills

11. Which ones are you using? Team Worker Creative Thinker Effective Participator Independent Enquirer Reflective Learner Self Manager PROBABILITY TREES PLT Skills PLENARY ACTIVITY – ROCK, PAPER AND SCISSORS TASK Complete a fully labelled tree diagram to shows the outcomes of a rock, paper and scissors game between two players.

12. Which ones are you using? Team Worker Creative Thinker Effective Participator Independent Enquirer Reflective Learner Self Manager PROBABILITY TREES PLT Skills Player B PLENARY ACTIVITY Draw 1/3 x 1/3 = 1/9 Scissors Player A 1/9 A Wins 1/3 x 1/3 = Scissors Paper 1/3 x 1/3 = B Wins 1/9 Stone B Wins 1/3 x 1/3 = 1/9 Scissors 1/9 Draw 1/3 x 1/3 = Paper Paper 1/3 x 1/3 = A Wins 1/9 Stone 1/9 A Wins 1/3 x 1/3 = Scissors Stone 1/9 B Wins 1/3 x 1/3 = Paper Draw 1/9 1/3 x 1/3 = Stone 1/3 1/9 + 1/9 + 1/9 1/9 + 1/9 + 1/9 P(Draw) = P(B Wins) = P(A Wins) = = 1/3 = 1/3 = 3/9 = 3/9

13. What grade are we working at? Where are we in our journey? What have you learnt? Draw your brain In your brain, write or draw everything you can remember about drawing probability trees for dependent events. It can be a skill or a reflection, or something else that might be prominent in your brain.

14. Team Worker Positive Thinker Creative Entrepreneur Independent Learner Reflective Learner Responsible Citizen SELF ASSESSMENT Enterprise Skills Which ones are you using? Plenary Activity How well do you understand the task? . I fully understand I don’t understand I nearly understand www.mistrymaths.co.uk

15. Team Worker Positive Thinker Creative Entrepreneur Independent Learner Reflective Learner Responsible Citizen SELF ASSESSMENT Enterprise Skills Which ones are you using? Plenary Activity WWW (What Went Well) EBI (Even Better If) On your post it notes… Think about how you can improve your work. www.mistrymaths.co.uk