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 independent events and work out probabilities from this. (Grade B) 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 mean of: 2, 3, 5, 10 2) x + 4 When x = -5 2 1) Expand 4(-4x + 5) 3) -16x + 20 = 2 = 5 = = 29 = (-5) + 4 Write the value of pi to 2d.p. 4) Calculate Find the LCM of 6 and 4. 5) 6) = 4 and -4 = 3.14 = 12 Simplify: 5e + 6y – 7e – 5y Solve: 7(x + 3) = 56 75% of 24 miles 7) 8) 9) = 18 = -2e = 56 7x + 21 + y = EXTENSION = 35 7x x = 5 6m Calculate the area of the trapezium 3m 2 Area = Area = 22.5cm Area = (a + b)h (6 + 9)3 9m

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) = 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 before replacing it. He then chooses a second counter. Record the information on a tree diagram and work out the probabilities of the different outcomes. P(B,B) + P(G,G) = + = = P(BG in any order) = P(B,G) + P(G,B) = + = = ALWAYS MULTIPLY THE BRANCHES FIRST PICK SECOND PICK 21 21 49 21 21 42 49 58 29 21 3 9 3 3 3 7 7 3 3 7 7 7 9 3 7 7 P(B,B) = X = Blue 100 100 100 100 100 100 100 100 100 100 50 50 10 10 10 10 10 10 10 10 10 10 10 10 10 10 Blue COUNTERS HAVE BEEN REPLACED SO THE PROBABILITY DOES NOT 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 PROBABILITY TREES PLT Skills TASK (GRADE B) 1) Fill in the probability tree below to display the outcomes of flipping a fair coin twice: 2nd Flip 1st Flip X = 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 H P(H,H)=………………… …... ….... 4 4 4 4 2 2 2 2 2 2 2 2 2 2 2 2 2 2 H ….... X = T …... P(H,T)=……………….... X = H …... ….... P(T,H)=……………….... ….... T …… X = ….... P(T,T)=…………………. T

6. Which ones are you using? Team Worker Creative Thinker Effective Participator Independent Enquirer Reflective Learner Self Manager Second Choice First Choice PROBABILITY TREES PLT Skills TASK (GRADE B) 2) Rebecca has nine coloured beads in a bag. Four of the beads are blackand the rest are green. She removes a bead at random from the bag and notes the colour before replacing it. She then chooses a second bead. (a) Draw a tree diagram showing all possible outcomes. (b) Calculate the probability that Rebecca chooses: (i) 2 green beads (ii) A black followed by a green bead (iii) The same colour. 41 16 25 81 81 81 black black green black green green = + P(same colour) = 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 B) 3) (a) Complete a tree diagram to show all the probabilities of obtaining even and odd numbers. Even P(E,E) = X = 6 6 2 3 2 3 3 2 3 2 3 2 3 2 2 3 4 9 Even 25 5 25 25 5 5 5 25 5 5 5 5 5 5 5 5 5 5 P(E,O) = X Odd = P(O,E) = X Even = Odd P(O,O) = Odd X = (b) Calculate the probability of spinning two numbers which multiply to given an even number. P(Spinning two numbers which multiply to make an even) = P(EE) + P(EO) + P(OE) = + + = Q1 beads

8. Which ones are you using? Team Worker Creative Thinker Effective Participator Independent Enquirer Reflective Learner Self Manager 0.3 0.4 x 0.3 = 0.12 Race Tennis 0.4 x 0.7 = 0.28 0.3 0.6 x 0.3 = 0.18 0.6 0.7 0.6 x 0.7 = 0.42 P(Lose and Win) for Becky = 0.28 P(Win and Win) for Peter = 0.12 PROBABILITY TREES PLT Skills EXTENSION (GRADE A) 1) Peter and Becky run a race and play a tennis match. The probability that Peter wins the race is 0.4. The probability that Becky wins the tennis is 0.7. (a)Complete the tree diagram below. (b) Use your tree diagram to calculate (i)the probability that Peter wins both events. (ii) The probability that Becky loses the race but wins at tennis. Peter Win Peter Win 0.4 Becky Win 0.7 Peter Win Becky Win Becky Win Q1 beads

9. Which ones are you using? Team Worker Creative Thinker Effective Participator Independent Enquirer Reflective Learner Self Manager Second Choice First Choice PROBABILITY TREES PLT Skills EXTENSION (GRADE A) 2) Peter has ten coloured cubes in a bag. Three of the cubes are red and seven are blue. He removes a cube at random from the bag and notes the colour but does not replace it. He then chooses a second cube at random. Record the information in a tree diagram. red red blue red blue blue 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 independent 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 – GRADE B EXAMINATION QUESTION Weather records are kept in a town called Snowville. They show that in a typical April it snows on 20 days out of the 30 days in the month. (a) Complete a fully labelled tree diagram showing the probabilities of it snowing or not snowing on the first two Sundays in April in Snowville. (4 marks) SECOND SUNDAY FIRST SUNDAY 2 4 2 2 2 1 2 2 2 2 1 1 1 4 1 9 9 9 9 9 9 9 3 3 3 3 3 3 3 3 P(S,S) = X SNOW = SNOW = NOT SNOW P(S,NS) = X = SNOW P(NS,S) = X = = NOT SNOW NOT SNOW X P(NS,NS) = = (b) Calculate the probability that it snows on only one of these two Sundays. You must show your working. + = P(S,NS or NS, S) = (3 marks)

12. 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 independent events. It can be a skill or a reflection, or something else that might be prominent in your brain.

13. 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

14. 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