Positive Thinker Creative Entrepreneur Independent Learner Reflective Learner

Positive Thinker Creative Entrepreneur Independent Learner Reflective Learner Enterprise Skills LESSON OBJECTIVES Responsible Citizen Team Worker Which ones are you using? 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) Where are we in our journey? AUTHOR www. mistrymaths. co. uk Real life cross/curricular links?

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

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

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

Positive Thinker Creative Entrepreneur Independent Learner Reflective Learner Enterprise Skills. STEM AND LEAF DIAGRAMS EXAMPLES 1)The speeds of vehicles in 30 mph zone are recorded. Below are the results: 39, 42, 35, 29, 28, 42, 31, 33 32, 35, 27, 37, 23, 29, 27, 45 (a) Draw a stem and leaf diagram to Smallest = 23 represent this data. Biggest = 45 2 3778 99 3 12 3 5 5 5 7 9 4 225 Key: 3 I 5 means 35 (b) Work out the mode Most common 35 mph (c) Work out the median to find out who sells the most items in one day. Below are the results: 26, 12, 25, 21, 12, 24, 32 17, 24, 12, 17, 30, 13, 35, 25 (a) Draw a stem and leaf diagram to Smallest = 12 represent this data. Biggest = 35 1 22 2 37 7 2 1 4 4 4 55 6 3 02 5 Key: 2 I 5 means 25 (b) Work out the mode Most common No mode (c) Work out the median 24 Biggest - Smallest 35 - 12 22 (e) What fraction were over the 30 mph limit? Eleven were more than 30 mph Which ones are you using? (d) Work out the range Biggest - Smallest 45 - 23 11 17 Team Worker 2)16 children in a class have a competition 33 mph (d) Work out the range Responsible Citizen 23 (e) What fraction sold 30 or more? Three sold 30 or more 3 16

Positive Thinker Creative Entrepreneur Independent Learner Reflective Learner Responsible Citizen Team Worker Which ones are you using? Enterprise Skills. 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: 6 I 4 means 64 (a) 2 5 5 7 9 Key: 11 I 5 means 115 3 378 4 12 25, 27, 29, 33, 37, 38, 41, 42 (b) 5 1 2 6 8 9 9 6 0345 5 7 2224 6 7 (c) 0 1 3 4 51, 52, 56, 58, 59, 60, 63, 64, 65, 72, 72, 74, 76, 77 (d) 68 2 5 69 1 7 8 70 01 3 5 6 71 2 9 1 2458 2 13 7 3 46 682, 685, 691, 697, 698, 700, 701, 703, 705, 706, 712, 719 1, 3, 4, 12, 14, 15, 18, 21, 23, 27, 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: 0 I 8 means 8 Girl’s scores 5 , 2 19 , 18 , 17 , 16 29 , 29, 28 , 27 , 25 , 23 Boy’s scores 52 0 88 9 98 76 1 05 6 8 9 9 8 753 2 1466 7 8 8, 8, 9 10, 15, 16, 18, 19 21, 24, 26, 27, 28

Positive Thinker Creative Entrepreneur Independent Learner Reflective Learner Enterprise Skills. STEM AND LEAF DIAGRAMS TASK 2 (LEVEL 6) Responsible Citizen Team Worker Which ones are you using? 1) Draw a stem and leaf diagram for the data below: (a) 5, 23, 31, 2, 18, 7, (b) 32, 21, 12, 5, 12, 6, 36, (c) 47, 31, 22, 31, 25, 40, (d) 77, 85, 92, 72, 84, 76, 25, 21, 10, 1, 33, 22, 14, 2, 26, 17, 29 44, 36, 27, 29, 36, 39 89, 76, 85, 67, 61, 75 22, 39 0 1257 1 08 2 1235 3 139 Key: 2 I 3 means 23 0 1 2 3 25 6 2247 1269 26 2 2579 3 11 6 6 9 4 04 7 Key: 3 I 6 means 36 Key: 1 I 4 means 14 6 7 8 9 17 25 667 4559 2 Key: 8 I 4 means 84 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 13 1 4 7 14 2 4 5 6 9 15 0 4 Key: 13 I 7 means 137 (b) 1261, 1275, 1253, 1255, 1260, 1278, 1257, 1258, 1266, 1279 125 3 5 7 8 126 0 1 6 127 5 8 Key: 127 I 5 means 1275

Positive Thinker Creative Entrepreneur Independent Learner Reflective Learner Enterprise Skills. STEM AND LEAF DIAGRAMS TASK 3 (LEVEL 6) 1)The pulse rates of 11 teachers are recorded. Below are the results: 63, 71, 52, 65, 74, 57, 60, 59, 64, 78 (a) Draw a stem and leaf diagram to Smallest = 52 represent this data. Biggest = 78 5 27 9 6 03 4 5 5 7 14 8 Key: 6 I 3 means 63 (b) Work out the mode Most common 65 (c) Work out the median Responsible Citizen Which ones are you using? 2)The journey times, in minutes, for students on the school bus are shown below: 21, 18, 24, 31, 21, 30, 19, 22 24, 32, 33, 28, 22, 29, 18 (a) Draw a stem and leaf diagram to Smallest = 18 represent this data. 1 889 2 112 2 4 4 8 9 3 0 12 3 Biggest = 33 Key: 2 I 4 means 24 (b) Work out the mode Most common No mode (c) Work out the median 64 24 minutes (d) Work out the range Biggest - Smallest 78 - 52 Biggest - Smallest 33 - 18 26 (e) What fraction were over the pulse rate of 70? Three were more than 70 Team Worker 3 11 15 minutes (e) What fraction took half an hour or more? Four were 30 or more 4 15

Positive Thinker Independent Learner Creative Entrepreneur Reflective Learner Enterprise Skills. STEM AND LEAF DIAGRAMS TASK 3 (LEVEL 6) 3)The number of lates to school in a week are shown below: 8, 16, 24, 32, 26, 25, 15, 7 14, 25, 30, 11, 13, 15, 19, 38 (a) Draw a stem and leaf diagram to Smallest = 7 represent this data. 0 1 2 3 Biggest = 38 78 13 45 56 9 45556 028 Key: 2 I 5 means 25 Responsible Citizen Team Worker Which ones are you using? 4)The number of e-mails received over 10 days are shown below: 15, 23, 16, 7, 5, 27, 12 , 18 (a) Draw a stem and leaf diagram to Smallest = 5 represent this data. 0 57 1 22 56 8 2 37 Biggest = 27 Key: 1 I 2 means 12 (b) Work out the mode Most common (c) Work out the median 25 12 15 19 (d) Work out the range 31 22 Biggest - Smallest 27 - 5 Biggest - Smallest 38 - 7 (e) What fraction were over 20 lates? Eight were over 20 lates 8 17 (e) What fraction were less than 15? Four were under 15 e-mails 4 = 2 10 5

Positive Thinker Creative Entrepreneur Independent Learner Reflective Learner Enterprise Skills. STEM AND LEAF DIAGRAMS TASK 3 (LEVEL 6) Responsible Citizen Team Worker Which ones are you using? 5)The number of text messages sent a 6)The ages of patients seen by a doctor on 32, 6, 14, 16, 24, 35, 22, 23 17, 19, 5, 16, 23, 27 16, 24, 37, 48, 27, 39, 55, 46 , 35 , 39 47, 49, 58, 51, 40, 12, 38, 35 , 28 , 56 week by 16 students is shown below: (a) Draw a stem and leaf diagram to Smallest = 5 represent this data. 0 1 2 3 Biggest = 35 56 466 67 9 9 23 3 47 25 Key: 3 I 2 means 32 (b) Work out the mode Most common 16 texts (c) Work out the median a particular day are shown below: (a) Draw a stem and leaf diagram to represent this data. Smallest = 12 1 2 3 4 5 26 47 8 55 7 8 9 9 06 7 8 9 15 6 8 Biggest - Smallest 35 - 5 30 (e) What fraction were less the 30 texts? Fourteen were less than 30 texts 14 = 7 8 16 Key: 5 I 5 means 55 (b) Work out the mode Most common No mode (c) Work out the median 19 texts (d) Work out the range Biggest = 58 39 texts (d) Work out the range Biggest - Smallest 58 - 12 46 (e) What fraction were not adults? 2 = 1 Two were children 20 10

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

Positive Thinker Creative Entrepreneur Independent Learner Reflective Learner Enterprise Skills. STEM AND LEAF DIAGRAMS EXTENSION 4 (LEVEL 6) Responsible Citizen Team Worker Which ones are you using? 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 0 799 6 4 1 1 2 3 33 669 Key: 3 I 2 means 32 7 4 3 3 1 0 2 0 112 5 8 9 8 2 2 2 1 3 4 66 300 4 5 Compare the averages and range for both classes. Class A Class B Mode = 13 marks Median = 19. 5 marks Mode = 32 marks Median = 27 marks Mean = 26. 9 marks (1 d. p. ) 20 Mean = 20. 8 marks (1 d. p. ) Range = 43 - 6 Range = 37 marks Range = 45 - 7 Range = 38 marks 19

Positive Thinker Creative Entrepreneur Independent Learner Reflective Learner Responsible Citizen Team Worker Which ones are you Enterprise Skills. STEM AND LEAF DIAGRAMS using? MINI-PLENARY (SPOT THE MISTAKES) Find the mistakes below: 2) 1) Median = 3. 1 Range = 5. 3 – 1. 4 Range = 3. 9 cm Not ordered Mode = 3. 6 cm

Positive Thinker Creative Entrepreneur Enterprise Skills Independent Learner Reflective Learner DISCOVERY Responsible Citizen Team Worker 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?

Positive Thinker Creative Entrepreneur Independent Learner Reflective Learner Enterprise Skills. STEM AND LEAF DIAGRAMS PLENARY ACTIVITY Team Worker Responsible Citizen Which ones are you using? 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 82 88 79 76 93 Women 73 65 65 67 52 66 66 53 53 60 72 65 Draw a stem and leaf diagram(s) and discuss your findings. Men 7 69 8 2 2 23 5 6 7 8 8 9 3 Mode = 82 m Median = 84 m Range = 17 m Women 5 23 3 6 0 5 5 566 7 7 23 Mode = 65 m Median = 65 m Range = 21 m Women Men 33 2 5 76 6 5 55 0 6 32 7 6 9 8 2 2 23 5 6 7 8 8 9 3

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?

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

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