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Enhancing Mathematical Skills: Constructing Histograms

In this lesson, we aim to enhance mathematical skills knowledge by accurately constructing histograms. We explore the misconceptions related to bar charts and understand the concept of frequency density. Examples and tasks are provided to practice constructing histograms.

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Enhancing Mathematical Skills: Constructing Histograms

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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 construct histograms. (Grade A) 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: 6, 10, 14, 18,.. 1) 3) 10 7 2 2 12 7 12 7 35 = 4n + 2 = = = = = = = = = 20 100 100 20 12 30 3 15 5 Find of 2 hours 4) 5) 6) 5 = of 120 mins 12 =50 mins Work out: -6 – 2 + 5 Work out: 3 x 45 ÷ 3 Write as a %: 7) 8) 9) 2 =12% =-3 =3 x 45 ÷ 9 EXTENSION =3 x 5 2 4 5 5 12 3 = = = x - + 20 12 5 =15 20 12 3 Write as a percentage. =35%

  4. Which ones are you using? Team Worker Creative Thinker Effective Participator Independent Enquirer Reflective Learner Self Manager HISTOGRAMS PLT Skills This is why we draw histograms when bars are of unequal width INTRODUCTION Why is the bar chart misleading? Frequency Density = Frequency ÷ Width The area of the bars give a false impression of the amount of fish caught

  5. HISTOGRAMS 3.0 2.0 1.0 0 20 40 60 80 100 120 EXAMPLE The frequency table below gives information on the speeds (km/h) of a sample of drivers. Construct a Histogram for this data. 40 30 20 10 10 2 3 1.5 1.5 2.5 A histogram to show the speeds of a sample of drivers Frequency Density Speed (km/h)

  6. Which ones are you using? Team Worker Creative Thinker Effective Participator Independent Enquirer Reflective Learner Self Manager HISTOGRAMS PLT Skills TASK (GRADE A) 1) The table shows the distribution of ages in a health club. Draw a histogram to illustrate this data. FD A histogram to show the ages in a health club 5 70 170 50 20

  7. Which ones are you using? Team Worker Creative Thinker Effective Participator Independent Enquirer Reflective Learner Self Manager HISTOGRAMS PLT Skills TASK (GRADE A) 2) Batteries are tested by putting them into toys and seeing how long they last. Here are the results of 60 tests. Draw a histogram to show this information. FD A histogram to show the life of batteries 0.08 Frequency Density 0.15 0.2 0.20 0.09 0.15 0.045 0.10 0.05

  8. Which ones are you using? Team Worker Creative Thinker Effective Participator Independent Enquirer Reflective Learner Self Manager HISTOGRAMS PLT Skills EXTENSION (GRADE A) Draw histograms for these grouped frequency distributions. 1) (a) Frequency Density → 2.5, 6.5, 6, 2, 1, 1.5 (b) Frequency Density → 4, 27, 15, 3 (c) Frequency Density → 17, 18, 12, 6.67 (d) Frequency Density → 0.4, 1.2, 2.8, 1 (e) Frequency Density → 9, 21, 13.5, 9

  9. Which ones are you using? Team Worker Creative Thinker Effective Participator Independent Enquirer Reflective Learner Self Manager • LINK BACK TO OBJECTIVES • Accurately construct histograms. What grade are we working at? DISCOVERY PLT Skills

  10. Which ones are you using? Team Worker Creative Thinker Effective Participator Independent Enquirer Reflective Learner Self Manager HISTOGRAMS PLT Skills PLENARY ACTIVITY – GRADE A EXAMINATION QUESTION The unfinished histogram and table gives the information about heights, in cm, of the Year 11 students at Mathstown High School. 4 FD 1.5 3.5 35 3.5 x 10 = 3 4 2.5 18 3.6 x 5 = 2 22 2.2 x 10 = 1.5 1.2 1 12 0.6 x 20 = 0.5 (a) Use the histogram to complete the table. (b) Use the table to complete the histogram. Frequency = Frequency Density x Width

  11. 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 accurately constructing histograms. It can be a skill or a reflection, or something else that might be prominent in your brain.

  12. 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

  13. 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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