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Which ones are you using?

Creative Entrepreneur. Independent Learner. Reflective Learner. Responsible Citizen. Team Worker. Positive Thinker. Real life cross/curricular links?. Where are we in our journey?. Which ones are you using?. Enterprise Skills. LESSON OBJECTIVES. Always aim high!. We are learning to:

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Which ones are you using?

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  1. Creative Entrepreneur Independent Learner Reflective Learner Responsible Citizen Team Worker Positive Thinker Real life cross/curricular links? Where are we in our journey? Which ones are you using? Enterprise Skills LESSON OBJECTIVES Always aim high! We are learning to: • Enhance our Mathematical learning skills. (Which Enterprise skills?) • Accurately construct stem and leaf diagrams and work out the mode, median and range. (Level 6) AUTHOR www.mistrymaths.co.uk

  2. Creative Entrepreneur Independent Learner Reflective Learner Responsible Citizen Team Worker Positive Thinker LEARNING JOURNEY Enterprise Skills Which ones are you using?

  3. Creative Entrepreneur Independent Learner Reflective Learner Responsible Citizen Team Worker Positive Thinker BRAIN IN GEAR Enterprise Skills Which ones are you using? EXAMPLE DITDIONA can be rearranged to make ADDITION TASK Work out the following Mathematical anagrams: Mode Median Range EXTENSION Develop your own Mathematical anagrams as above as a creative entrepreneur.

  4. Creative Entrepreneur Independent Learner Reflective Learner Responsible Citizen Team Worker Positive Thinker STARTER Enterprise Skills Which ones are you using? TASK EXTENSION 1) Work out the averages and range for: 2, 3, 6, 6, 8 1) Solve the equation: 7𝑥 + 9 = 3𝑥 + 17 6 Mode = - 3𝑥 - 3𝑥 6 Median = 9 4𝑥 17 = + Mean = = 5 - 9 - 9 4𝑥 = 8 Range = 8 - 2 = 6 ÷ 4 ÷ 4 2) 2 Work out the value of b – 4ac when a=2, b=5, c=-2 𝑥 2 = – 4 = 41 2 x x 2 5 -2 + 16 = 25 3) x x x Reflect the object in the line x = 1 2 + 3 + 6 + 6 + 8 5

  5. Creative Entrepreneur Independent Learner Reflective Learner Responsible Citizen Team Worker Positive Thinker Enterprise Skills Which ones are you using? STEM AND LEAF DIAGRAMS EXAMPLES 2) 16 children in a class have a competition to find out who sells the most items in one day. Below are the results: 1) The speeds of vehicles in 30mph zone are recorded. Below are the results: 33 29, 31, 28, 42, 39, 42, 35, 32 21, 12, 24, 24, 26, 12, 25, 27, 45 37, 29, 35, 23, 27, 35, 32, 25 30, 35, 12, 13, 17, 24, 17, (a) Draw a stem and leaf diagram to represent this data. (a) Draw a stem and leaf diagram to represent this data. Smallest = 23 Smallest = 12 45 Biggest = 8 9 7 3 2 7 9 Biggest = 35 1 2 2 7 2 3 7 2 3 5 5 1 7 3 5 9 4 5 5 2 1 4 4 6 Key: 3I5 means 35 Key: 2I5 means 25 5 4 2 2 3 0 2 5 (b) Work out the mode Most common (b) Work out the mode Most common 35mph No mode (c) Work out the median (c) Work out the median 33mph 24 (d) Work out the range (d) Work out the range Biggest - Smallest Biggest - Smallest 11 3 45 - 23 35 - 12 22 23 16 17 (e) What fraction were over the 30mph limit? (e) What fraction sold 30 or more? Eleven were more than 30mph Three sold 30 or more

  6. Creative Entrepreneur Independent Learner Reflective Learner Responsible Citizen Team Worker Positive Thinker Enterprise Skills Which ones are you using? STEM AND LEAF DIAGRAMS TASK 1 (LEVEL 4) 1) Write out all the numbers shown in each of the stem and leaf diagrams below: Key: 6I4 means 64 Key: 11I5 means 115 (a) (d) 2 5 68 9 5 2 7 (b) (c) 5 2 5 1 6 9 8 1 9 0 3 4 69 1 3 8 7 8 3 7 6 0 3 1 5 2 8 5 4 4 5 3 1 0 5 6 70 2 1 4 4 2 2 7 7 2 6 3 7 1 2 71 2 9 3 4 6 58, 59, 52, 56, 59, 51, 27, 29, 25, 25, 65, 63, 65, 60, 64, 685, 682, 33, 37, 38, 3, 4, 1, 698, 76, 691, 72, 77 697, 72, 72, 74, 42 41, 14, 15, 18, 12, 706, 705, 703, 701, 700, 27, 23, 21, 712, 719 34, 36 EXTENSION 1 (LEVEL 5) 2) Write out all the numbers shown below in the back-to-back stem and leaf diagram for results in a Mathematics test out of 30 for both boys and girls. Key: 0I8 means 8 Girl’s scores Boy’s scores 8, 8, 9 ,2 5 5 2 8 9 0 8 19 ,18 ,17 ,16 1 9 8 7 6 0 5 16, 19, 9 19 15, 18, 9 10, 8 6 26, 24, 26, 27, 21, 28 6 1 6 2 4 7 8 29 ,28 ,27 ,25 9 3 ,23 9 8 5 7 ,29

  7. Creative Entrepreneur Independent Learner Reflective Learner Responsible Citizen Team Worker Positive Thinker Enterprise Skills Which ones are you using? STEM AND LEAF DIAGRAMS TASK 2 (LEVEL 6) 1) Draw a stem and leaf diagram for the data below: (a) 5, 23, 31, 2,18, 7, 25, 21, 10, 1, 33, 22, 39 (b) (c) (d) 32, 21, 12, 5,12, 6, 36, 22, 14, 2, 26, 17, 29 47, 31, 22, 31,25, 40, 44, 36, 27, 29, 36, 39 77, 85, 92, 72, 84, 76, 89, 76, 85, 67, 61, 75 7 6 1 2 5 7 9 2 2 6 0 5 1 5 0 2 7 6 7 5 2 6 7 9 3 6 1 1 6 7 1 2 2 4 1 0 8 5 4 5 9 8 0 7 4 4 2 1 2 9 6 2 2 3 1 5 9 2 6 3 2 1 9 3 3 Key: 3I6 means 36 Key: 8I4 means 84 Key: Key: 1I4 means 14 2I3 means 23 EXTENSION 2 (LEVEL 6) 1) Draw a stem and leaf diagram for the data below: (b) 1261, 1275, 1253, 1255, 1260, 1278, 1257, 1258, 1266, 1279 134, 154, 144, 131, 137, 142, 145, 150, 146, 149 (a) 13 4 7 1 8 5 3 125 7 9 6 4 14 2 5 0 6 126 1 4 0 15 127 5 8 Key: 13I7 means 137 Key: 127I5 means 1275

  8. Creative Entrepreneur Independent Learner Reflective Learner Responsible Citizen Team Worker Positive Thinker Enterprise Skills Which ones are you using? STEM AND LEAF DIAGRAMS TASK 3 (LEVEL 6) 2) The journey times, in minutes, for students on the school bus are shown below: 1) The pulse rates of 11 teachers are recorded. Below are the results: 22 31, 21, 30, 19, 21, 18, 24, 78 60, 59, 64, 65, 57, 65, 74, 63, 71, 52, 22, 18 33, 29, 28, 32, 24, (a) Draw a stem and leaf diagram to represent this data. (a) Draw a stem and leaf diagram to represent this data. Smallest = 52 Smallest = 18 78 Biggest = 33 Biggest = 5 2 7 9 9 8 1 8 6 0 3 4 5 5 8 9 2 1 4 2 2 4 1 Key: 6I3 means 63 Key: 2I4 means 24 8 7 1 4 3 3 0 1 2 (b) Work out the mode Most common (b) Work out the mode Most common 65 No mode (c) Work out the median (c) Work out the median 64 24 minutes (d) Work out the range (d) Work out the range Biggest - Smallest Biggest - Smallest 4 3 78 - 52 33 - 18 26 15 minutes 15 11 (e) What fraction were over the pulse rate of 70? (e) What fraction took half an hour or more? Three were more than 70 Four were 30 or more

  9. Creative Entrepreneur Independent Learner Reflective Learner Responsible Citizen Team Worker Positive Thinker Enterprise Skills Which ones are you using? STEM AND LEAF DIAGRAMS TASK 3 (LEVEL 6) 4) The number of e-mails received over 10 days are shown below: 3) The number of lates to school in a week are shown below: 7 32, 15, 26, 25, 8, 16, 24, 7, 5, 12 ,18 15, 23, 16, 27, 12, 19, 38 11, 15, 25, 13, 30, 25, 14, (a) Draw a stem and leaf diagram to represent this data. (a) Draw a stem and leaf diagram to represent this data. Smallest = Smallest = 7 5 38 Biggest = 27 Biggest = 0 7 8 7 0 5 5 1 1 5 6 9 3 4 1 2 2 5 6 8 Key: 1I2 means 12 4 5 6 2 5 5 Key: 2I5 means 25 2 3 7 3 2 8 0 (b) Work out the mode Most common (b) Work out the mode Most common 12 25 (c) Work out the median (c) Work out the median 15 19 (d) Work out the range (d) Work out the range Biggest - Smallest Biggest - Smallest 8 4 2 27 - 5 38 - 7 22 17 10 5 31 (e) What fraction were less than 15? (e) What fraction were over 20 lates? Eight were over 20 lates Four were under 15 e-mails =

  10. Creative Entrepreneur Independent Learner Reflective Learner Responsible Citizen Team Worker Positive Thinker Enterprise Skills Which ones are you using? STEM AND LEAF DIAGRAMS TASK 3 (LEVEL 6) 6) The ages of patients seen by a doctor on a particular day are shown below: 5) The number of text messages sent a week by 16 students is shown below: ,35 ,39 46 48, 27, 39, 55, 16, 24, 37, 23 32, 6, 14, 16, 22, 24, 35, ,28 ,56 35 40, 38, 58, 12, 51, 49, 47, 27 16, 23, 19, 16, 5, 19, 17, (a) Draw a stem and leaf diagram to represent this data. (a) Draw a stem and leaf diagram to represent this data. Smallest = Smallest = 5 12 2 6 1 35 58 0 Biggest = Biggest = 6 5 8 7 2 4 6 6 7 9 9 1 4 6 3 5 5 7 8 9 9 2 2 3 7 3 4 Key: Key: 3I2 means 32 5I5 means 55 6 7 0 4 8 9 3 2 5 1 5 8 6 5 (b) Work out the mode Most common (b) Work out the mode Most common 16 texts No mode (c) Work out the median (c) Work out the median 19 texts 39 texts (d) Work out the range Biggest - Smallest (d) Work out the range 14 2 1 7 35 - 5 Biggest - Smallest 30 10 16 20 8 58 - 12 (e) What fraction were less the 30 texts? 46 (e) What fraction were not adults? = Fourteen were less than 30 texts = Two were children

  11. Creative Entrepreneur Independent Learner Reflective Learner Responsible Citizen Team Worker Positive Thinker Enterprise Skills Which ones are you using? STEM AND LEAF DIAGRAMS EXTENSION 3 (LEVEL 6) 2) The heights of plants (mm) in a greenhouse are shown below: 1) The heights (cm) of 11 students is shown below: 134, 135, 126, 152, 134, 144, 121, 168, 151, 164, 140, 146, 177, 188, 142 145, 147, 136, 158, 141, 154 163, 159, 166, 172, 172, 165, (a) Draw a stem and leaf diagram to represent this data. (a) Draw a stem and leaf diagram to represent this data. Smallest = 121 Smallest = 140 158 Biggest = 12 1 6 188 Biggest = 0 14 6 6 4 4 13 5 1 4 9 15 5 7 1 2 4 14 Key: 14I1 means 141 8 16 6 3 5 4 Key: 18I1 means 181 8 2 15 17 2 2 7 (b) Work out the mode Most common 18 8 134cm (b) Work out the mode Most common (c) Work out the median 172mm (c) Work out the median 141cm 164.5mm (d) Work out the range Biggest - Smallest 158 - 121 (d) Work out the range 12 6 6 37cm Biggest - Smallest (e) What fraction were less the 140cm? 7 14 11 188 - 140 = 48mm Six were less than 140cm (e) What fraction were more than 1.5m? Twelve were more than 1.5m

  12. Creative Entrepreneur Independent Learner Reflective Learner Responsible Citizen Team Worker Positive Thinker Enterprise Skills Which ones are you using? STEM AND LEAF DIAGRAMS EXTENSION 4 (LEVEL 6) 1) The back-to-back stem and leaf diagram below shows the Mathematics score for the same test for two different classes: Class B Class A 6 0 7 9 9 6 4 1 1 3 3 3 6 6 9 2 Key: 3I2 means 32 7 3 1 8 4 0 1 2 5 3 2 0 1 9 8 2 2 2 1 6 6 3 4 3 0 0 5 4 Compare the averages and range for both classes. Class A Class B 13marks Mode = Mode = 32marks 19.5marks Median = 27marks Median = Mean = Mean = 20 19 20.8marks (1d.p.) Mean = Mean = 26.9marks (1d.p.) Range = Range = 43 - 6 45 - 7 Range = 37marks Range = 38marks

  13. Creative Entrepreneur Independent Learner Reflective Learner Responsible Citizen Team Worker Positive Thinker Enterprise Skills Which ones are you using? STEM AND LEAF DIAGRAMS MINI-PLENARY (SPOT THE MISTAKES) Find the mistakes below: 2) 1) Median = 3.1 Range = 5.3 – 1.4 Range = 3.9cm Not ordered Mode = 3.6cm

  14. Creative Entrepreneur Independent Learner Reflective Learner Responsible Citizen Team Worker Positive Thinker • LINK BACK TO OBJECTIVES • Accurately construct stem and leaf diagrams and work out the mode, median and range. What level are we working at? DISCOVERY Enterprise Skills Which ones are you using?

  15. Creative Entrepreneur Independent Learner Reflective Learner Responsible Citizen Positive Thinker Team Worker Enterprise Skills Which ones are you using? STEM AND LEAF DIAGRAMS PLENARY ACTIVITY The following are the results of the final 12 throws in the men’s and women’s javelin in the 2012 London Olympics. The distances are in metres. Men Women Draw a stem and leaf diagram(s) and discuss your findings. Men Women Men Women 5 3 2 3 7 6 9 2 3 3 5 7 6 5 5 6 5 0 6 8 2 3 5 6 8 8 2 2 7 6 0 5 5 6 6 7 5 3 7 2 6 9 9 3 7 2 3 2 3 5 6 8 8 2 2 7 8 Mode = 82m Mode = 65m 3 9 Median = 84m Median = 65m 17m 21m Range = Range =

  16. What level 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 constructing stem and leaf diagrams and working out the mode, median and range. It can be a skill or a reflection, or something else that might be prominent in your brain.

  17. 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

  18. 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

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