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Which ones are you using?

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:

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Which ones are you using?

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  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 cumulative frequency curves and box and whisker plots. (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 2) th Find the n term of: 3, 8, 13, 18,.. 1) 3) 8 1 5 5 10 11 14 35 70 = 5n - 2 = = = = = = = = = 20 100 100 30 21 12 24 5 40 Find of 1 min 4) 5) 6) 5 = of 60 seconds 12 =25 seconds Work out: -6 – 9 + 6 Work out: 3 x 32 ÷ 4 Write as a %: 7) 8) 9) 2 =35% =-9 =3 x 32 ÷ 16 EXTENSION =3 x 2 2 7 5 5 12 6 = = = - x + 30 21 30 8 =6 21 3 Write as a percentage. =70%

  4. Which ones are you using? Team Worker Creative Thinker Effective Participator Independent Enquirer Reflective Learner Self Manager CUMULATIVE FREQUENCY PLT Skills EXAMPLE 1 A golf club has 200 members. Their ages are shown in the frequency table below. Draw a cumulative frequency curve to represent this information. a < 10 8 8 +26 a < 20 34 a < 30 +32 66 a < 40 +45 111 +37 a < 50 148 +29 a < 60 177 a < 70 +16 193 a < 80 +7 200

  5. Which ones are you using? Team Worker Creative Thinker Effective Participator Independent Enquirer Reflective Learner Self Manager CUMULATIVE FREQUENCY PLT Skills EXAMPLE 1 A golf club has 200 members. Their ages are shown in the frequency table below. Draw a cumulative frequency curve to represent this information. 8 8 10 34 34 20 30 66 66 40 111 111 50 148 148 60 177 177 70 193 193 80 200 200

  6. CUMULATIVE FREQUENCY EXAMPLE 2 Use your cumulative frequency curve to work out the Median, Lower Quartile, Upper Quartile and Inter-Quartile Range. The draw a whisker plot with this information. We can now use this to find the following information.. Median 37 Lower quartile 25 Upper quartile 51 Lowest Value 0 Highest Value 80 Interquartile range 51 - 25 26 This information can now be used to draw a box and whisker diagram..

  7. CUMULATIVE FREQUENCY TASK (GRADE B) 1) Every day James does a test to see how many units of sugar are present in his blood. The results of these tests over a period of 50 days are shown in the table below. (a) Draw a cumulative frequency curve (b) Use your graph to find the median value of x. Plot the upper bound (c) 5 45 0 2 (b) MEDIAN = 9 14 39 47 50 (c) If the sugar content of James’ blood is greater than 11.5 units, then it is harmful to his health. Use your graph to find an estimate of the number of times these readings were greater than 11.5 units. Show clearly on your graph how you got your answer.

  8. CUMULATIVE FREQUENCY TASK (GRADE B) 2) The lengths of a number of nails were measured to the nearest 0.01 cm, and the following frequency distribution was obtained. (a) Draw a cumulative frequency curve (b) Use your graph to find the median value of x. Plot the upper bound 2 UQ = 1.08 6 16 (b) MEDIAN = 1.066 40 72 LQ = 1.05 89 96 100 (c) Work out the inter-quartile range IQR = 1.08 – 1.05 = 0.03

  9. CUMULATIVE FREQUENCY TASK (GRADE B) 3) The table shows the times, in minutes, spent on homework one evening by a group of Year 10 students. 4 11 21 36 40 CF (a) Complete the table above to find how many students took part in this survey. (b) Draw a cumulative frequency curve to represent the data. (c) Use this curve to find the median time spent on homework by this group of students. (d) Use your curve to find values for the upper quartile and the lower quartile. Hence find the interquartile range. (e) Draw a box and whisker plot for the data. 40 UQ = 37mins 30 20 LQ = 20mins MEDIAN = 30mins 10 40 10 20 30 50 IQR = 37 – 20 = 17mins Time (mins)

  10. CUMULATIVE FREQUENCY TASK (GRADE B) 4) The number of passengers on a bus route was recorded over a period of time, to give the following data. 3 10 22 35 64 90 CF 90 (a) Complete the table and use this to draw a cumulative frequency curve to represent this data. (b) Use your curve to find the median number of passengers on this bus route. (c) Find values for the upper quartile and the lower quartile, and hence find the interquartile range. (d) Draw a box and whisker plot to represent your data. 80 UQ = 52 70 60 50 MEDIAN = 45passengers 40 30 LQ = 30 IQR = 52 – 30 = 22passengers 20 10 Passengers 40 10 20 30 50 60

  11. Which ones are you using? Team Worker Creative Thinker Effective Participator Independent Enquirer Reflective Learner Self Manager CUMULATIVE FREQUENCY PLT Skills EXTENSION (GRADE B) Draw cumulative frequency curves and box and whiskers plots for each question below: 1) (a) 55 95 73 8 35 20 85 100 (b) 38 92 63 2 20 5 80 100 (c) 28 1 10 22 4 30 25

  12. Which ones are you using? Team Worker Creative Thinker Effective Participator Independent Enquirer Reflective Learner Self Manager • LINK BACK TO OBJECTIVES • Accurately draw cumulative frequency curves and box and whisker plots. What grade are we working at? DISCOVERY PLT Skills

  13. Which ones are you using? Team Worker Creative Thinker Effective Participator Independent Enquirer Reflective Learner Self Manager CUMULATIVE FREQUENCY PLT Skills PLENARY ACTIVITY – GRADE B EXAMINATION QUESTION The cumulative frequency diagram of the heights of 80 red kangaroos is shown below. The table below summarises the heights of 80 grey kangaroos. Red Kangaroos Grey Kangaroos UQ = 160 Explain why the heights of the grey kangaroos are more consistent than the heights of the red kangaroos. You must show your working. (4 marks) The smaller the IQR the more consistent IQR Grey = 120 – 85 = 35kangaroos IQR Red = 160 – 112 = 48kangaroos LQ = 112 As the IQR for grey kangaroos is 13 less, their heights are more consistent.

  14. 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 cumulative frequency curves and box and whisker plots. It can be a skill or a reflection, or something else that might be prominent in your brain.

  15. 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

  16. 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

  17. CUMULATIVE FREQUENCY TASK (GRADE B) 1) Every day James does a test to see how many units of sugar are present in his blood. The results of these tests over a period of 50 days are shown in the table below. (a) Draw a cumulative frequency curve (b) Use your graph to find the median value of x. (c) If the sugar content of James’ blood is greater than 11.5 units, then it is harmful to his health. Use your graph to find an estimate of the number of times these readings were greater than 11.5 units. Show clearly on your graph how you got your answer.

  18. CUMULATIVE FREQUENCY TASK (GRADE B) 2) The lengths of a number of nails were measured to the nearest 0.01 cm, and the following frequency distribution was obtained. (a) Draw a cumulative frequency curve (b) Use your graph to find the median value of x. (c) Work out the inter-quartile range

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