# Which ones are you using?

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

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

Creative Entrepreneur
Positive Thinker Creative Entrepreneur Independent Learner Reflective Learner Responsible Citizen Team Worker 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: DEOM EAMIND GRANE Mode Median Range EXTENSION Develop your own Mathematical anagrams as above as a creative entrepreneur. 3

Creative Entrepreneur
Positive Thinker Creative Entrepreneur Independent Learner Reflective Learner Responsible Citizen Team Worker 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 Mode = 6 - 3𝑥 - 3𝑥 Median = 6 4𝑥 + 9 = 17 5 Mean = = 5 - 9 - 9 Range = 4𝑥 = 8 8 - 2 = 6 2) Work out the value of b – 4ac when a=2, b=5, c=-2 2 ÷ 4 ÷ 4 𝑥 = 2 5 2 4 x 2 x -2 = 25 + 16 = 41 3) x x x Reflect the object in the line x = 1 4

Creative Entrepreneur Eleven were more than 30mph
Positive Thinker Creative Entrepreneur Independent Learner Reflective Learner Responsible Citizen Team Worker Enterprise Skills Which ones are you using? STEM AND LEAF DIAGRAMS EXAMPLES 1) 2) The speeds of vehicles in 30mph zone are recorded. Below are the results: 16 children in a class have a competition to find out who sells the most items in one day. Below are the results: 39, 42, 35, 29, 28, 42, 31, 33 26, 12, 25, 21, 12, 24, 24, 32 32, 35, 35, 27, 37, 23, 29, 27, 45 17, 24, 12, 17, 30, 13, 35, 25 (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 2 3 7 7 8 9 9 Biggest = 45 1 2 2 2 3 7 7 Biggest = 35 3 1 2 3 5 5 5 7 9 2 1 4 4 4 Key: 5 5 6 3I5 means 35 Key: 4 2I5 means 25 2 2 5 3 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 22 23 (e) What fraction were over the 30mph limit? (e) What fraction sold 30 or more? 11 17 Eleven were more than 30mph 3 16 Three sold 30 or more 5

Creative Entrepreneur
Positive Thinker Creative Entrepreneur Independent Learner Reflective Learner Responsible Citizen Team Worker 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 (a) 2 5 5 7 9 (b) 5 1 2 6 8 9 9 (c) 1 3 4 (d) 68 2 5 Key: 11I5 means 115 3 3 7 8 6 3 4 5 5 1 2 4 5 8 69 1 7 8 4 1 2 7 2 2 2 4 6 7 2 1 3 7 70 1 3 5 6 3 4 71 2 9 25, 25, 27, 29, 51, 52, 56, 58, 59, 59, 6 33, 37, 38, 60, 63, 64, 65, 65, 682, 685, 1, 3, 4, 41, 42 72, 72, 72, 74, 76, 77 691, 697, 698, 12, 14, 15, 18, 700, 701, 703, 705, 706, 21, 23, 27, 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 5 ,2 8 9 1 2 5 6 4 7 3 8, 8, 9 19 ,18 ,17 ,16 10, 15, 16, 18, 19, 19 29 ,29 ,28 ,27 ,25 ,23 21, 24, 26, 26, 27, 28 6

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

Creative Entrepreneur
Positive Thinker Creative Entrepreneur Independent Learner Reflective Learner Responsible Citizen Team Worker Enterprise Skills Which ones are you using? STEM AND LEAF DIAGRAMS TASK 3 (LEVEL 6) 1) 2) The pulse rates of 11 teachers are recorded. Below are the results: The journey times, in minutes, for students on the school bus are shown below: 21, 18, 24, 31, 21, 30, 19, 22 63, 71, 52, 65, 65, 74, 57, 60, 59, 64, 78 24, 32, 33, 28, 22, 29, 18 (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 5 2 7 9 Biggest = Biggest = 33 1 8 8 9 6 3 4 5 5 2 1 1 2 2 4 4 8 9 Key: 6I3 means 63 7 1 4 8 Key: 2I4 means 24 3 1 2 3 (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 26 15 minutes (e) What fraction were over the pulse rate of 70? (e) What fraction took half an hour or more? 3 11 Three were more than 70 4 15 Four were 30 or more 8

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

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

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

Creative Entrepreneur
Positive Thinker Creative Entrepreneur Independent Learner Reflective Learner Responsible Citizen Team Worker 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 A Class B 6 7 9 9 6 4 1 1 2 3 3 3 6 6 9 7 4 3 3 1 2 1 1 2 5 8 Key: 3I2 means 32 9 8 2 2 2 1 3 4 6 6 3 4 5 Compare the averages and range for both classes. Class A Class B Mode = 32marks Mode = 13marks Median = 27marks Median = 19.5marks Mean = Mean = 19 20 Mean = 20.8marks (1d.p.) Mean = 26.9marks (1d.p.) Range = 43 - 6 Range = 45 - 7 Range = 37marks Range = 38marks 12

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

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

Creative Entrepreneur
Positive Thinker Creative Entrepreneur Independent Learner Reflective Learner Responsible Citizen 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 83 85 86 82 87 88 79 76 93 Women 73 65 67 52 66 53 60 72 Draw a stem and leaf diagram(s) and discuss your findings. Women Men Men Women 3 3 2 5 7 6 9 5 2 3 3 7 6 6 5 5 5 6 8 2 2 2 3 5 6 7 8 8 6 5 5 5 6 6 7 3 2 7 6 9 9 3 7 2 3 8 2 2 2 3 5 6 7 8 8 Mode = 82m Mode = 65m Median = 84m Median = 65m 9 3 Range = 17m Range = 21m 15

Where are we in our journey? What level are we working at?
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. Where are we in our journey? What level are we working at?

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

Creative Entrepreneur
Positive Thinker Creative Entrepreneur SELF ASSESSMENT Independent Learner Reflective Learner Responsible Citizen Team Worker 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.