We are learning to: - Enhance our Mathematical learning skills. (Which Enterprise skills?) -Accurately construct stem and leaf diagrams and work out the

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!LESSON OBJECTIVES

Creative Entrepreneur

Responsible Citizen

Independent Learner

Positive Thinker

Team Worker

Reflective Learner

Enterprise SkillsWhich ones are you

using?

AUTHORWhere are we in

our journey?

Real life cross/curricular

links?www.mistrymaths.co.uk

http://www.mistrymaths.co.uk/

LEARNING JOURNEY


Responsible Citizen

Independent Learner

Positive Thinker

Team Worker

Reflective Learner

Enterprise Skills Which ones are you using?

BRAIN IN GEAR


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Work out the following Mathematical anagrams:

TASK

EXTENSION

Develop your own Mathematical anagrams as above as a creative entrepreneur.

DEOM

EAMIND

GRANE

EXAMPLEDITDIONA can be rearranged to make ADDITION

Mode

Median

Range

STARTER

EXTENSIONTASK


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1)Solve the equation:Work out the averages and range for: 2, 3, 6, 6, 8

1)

Mode =6Median = 6Mean = 2 + 3 + 6 + 6 + 8

5 = 5Range = 8 - 2 = 6

2)Work out the value of b – 4ac when a=2, b=5, c=-2

2

25 – 4 x 2 x -2 = 25 +16 = 413)

Reflect the object in the line x = 1

xx

x

7 𝑥 + 9 = 3 + 17𝑥- 3𝑥 - 3𝑥4 𝑥 + 9 = 17

- 9 - 9

4 𝑥 = 8÷ 4 ÷ 4𝑥 = 2

STEM AND LEAF DIAGRAMS


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Enterprise Skills Which ones are you using?EXAMPLES

1)The speeds of vehicles in 30mph zone are recorded. Below are the results:

42, 28,35, 23,32, 27,

29, 42,35,

31,35,27,

39,37,

3329,

(a) Draw a stem and leaf diagram to represent this data.

(b) Work out the mode

(c) Work out the median

(d) Work out the range

(e) What fraction were over the 30mph limit?

Smallest = 23452

34

Biggest =

45

3 7 7 8 9 91 2 3 5 5 5 7 9225

Key: 3I5 means 35

Most common35mph

33mph

Biggest - Smallest45 - 2322

Eleven were more than 30mph

1117

2)16 children in a class have a competition to find out who sells the most items in one day. Below are the results:

12, 12,12, 13,17, 17,

21, 24,24,

24,25,25

26,30,

3235,





(e) What fraction sold 30 or more?

Smallest = 12351

23

22 2 3 7 71 4 4 455602 5

Key: 2I5 means 25

Biggest =

Most commonNo mode

24


Three sold 30 or more 316


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Enterprise Skills Which ones are you using?TASK 1 (LEVEL 4)


Write out all the numbers shown in each of the stem and leaf diagrams below:1)

234

3 7 89

1 25

55 7 95

567

0 3 42 2

21 6 8

2 4 6

9

7

012

2 4 51 3

31 4

3

87

4 6

686970

1 7 80 1

52

713

2 95 6

EXTENSION 1 (LEVEL 5)

Key: 6I4 means 64

Key:11I5 means 115

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.

2)

88 9

012

0 5 61 4

8 99

6 6 7 8

256789357899

Girl’s scores Boy’s scores

25,25,27,29,33,37,38,41,42

51,52,56,58,59,59,60,63,64,65, 65,72,72,72,74,76,77

1, 3, 4,12,14,15,18,21,23,27,34,36

682,685,691,697,698,700,701,703,705,706,712,719

8, 8, 9

10,15,16,18,19,19

21,24,26,26, 27,28

,25,16,17,18 19

,23,25,27,28,2929

(a) (b) (c) (d)

Key: 0I8 means 8


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Draw a stem and leaf diagram for the data below:1)

EXTENSION 2 (LEVEL 6)

(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

(a)5, 23, 31, 2,18, 7, 25, 21, 10, 1, 33,

22, 39

Draw a stem and leaf diagram for the data below:1)(a)134, 154, 144, 131, 137,

142, 145, 150, 146, 149(b) 1261, 1275, 1253, 1255, 1260,

1278, 1257, 1258, 1266, 1279

0123

1 2 5 70 81 2 3 5139

Key: 2I3 means 23

0123

2 5 62 2 4 71 2 6 92 6

Key: 1I4 means 14

234

2 5 7 9116 6 904 7

Key: 3I6 means 36

6789

1 72 5 6 6 74 5 5 92

Key: 8I4 means 84

131415

1 4 72 4 5 6 90 4

Key: 13I7 means 137

125126127

3 5 7 801 65 8

Key: 127I5 means 1275


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1)The pulse rates of 11 teachers are recorded. Below are the results:

71, 65, 7859,65, 74, 64,57,52,63, 60,





(e) What fraction were over the pulse rate of 70?

2)The journey times, in minutes, for students on the school bus are shown below:

18, 21,33, 29,24, 28,

31, 30,32,

19,24,21,22,

2218





(e) What fraction took half an hour or more?

Smallest = 5278Biggest = 5

67

2 7 903 4 5 514 8

Most common65

64


Three were more than 70

311

Smallest = 1833Biggest =

123

8 8 91 1 2 2 4 4 8 90 1 2 3

Most commonNo mode

24 minutes

Biggest - Smallest33 - 1815 minutes

Four were 30 or more 415

Key: 6I3 means 63 Key: 2I4 means 24


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3)The number of lates to school in a week are shown below:

16, 26,25, 13,14, 30,

32, 25,25,

15,24,19,

8,11,

715,





(e) What fraction were over 20 lates?

38

4)The number of e-mails received over 10 days are shown below:

23, 5, ,187, 27, 12,16,15, 12





(e) What fraction were less than 15?


123

7 813 4 5 5 6 94 5 5 5 60 2 8

Most common25

19


Eight were over 20 lates

817

Smallest = 527Biggest =

012

5 72 2 5 6 83 7

Most common12

15


Four were under 15 e-mails

410

= 2 5



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5)The number of text messages sent a week by 16 students is shown below:

6, 24,19, 16,17, 5,

16, 35,19,

22,14,27

32,16,

2323,





(e) What fraction were less the 30 texts?

6)The ages of patients seen by a doctor on a particular day are shown below:

24, 27,58, 12,47, 51,

48, 39,49,

55,37,35

16,40,

4638,





(e) What fraction were not adults?

,28,35

,56,39


123

5 64 6 6 6 7 9 92 3 3 472 5

Most common16 texts

19 texts


Fourteen were less than 30 texts

1416

= 7 8


2345

2 64 7 85 5 7 8 9 906 7 8 91 5 6 8

Most commonNo mode

39 texts


Two were children

220

= 1 10



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Enterprise Skills Which ones are you using?EXTENSION 3 (LEVEL 6)


1)The heights (cm) of 11 students is shown below:

144, 126,

147,136, 145,152, 135,

158,

134,134,121,142141,





(e) What fraction were less the 140cm?

2)The heights of plants (mm) in a greenhouse are shown below:

188, 164,165,172, 159,146, 168,

166,151,140,177,

163,





(e) What fraction were more than 1.5m?

172, 154


131415

164 4 5 612 4 5 72 8

Most common134cm

141cm

Biggest - Smallest158 - 12137cm

Six were less than 140cm

611


15161718

0 614 934 5 6 82 2 78

Most common172mm

164.5mm

Biggest - Smallest188 - 14048mm

Twelve were more than 1.5m

1214

= 6 7

Key:14I1 means 141 Key: 18I1 means 181


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Reflective Learner

Enterprise Skills Which ones are you using?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:

01234

7 92 3

93 3 6 6 9

0 1 1 2 5 84 6 65

6146013347122289003

Key: 3I2 means 32

Class A Class B

Compare the averages and range for both classes.

Class A Class B

Mode =

Median =32marks

27marks

Mean =19

Mean = 26.9marks (1d.p.)

Range = 43 - 6Range = 37marks

Mode = 13marksMedian = 19.5marks

Mean =20

Mean = 20.8marks (1d.p.)

Range = 45 - 7Range = 38marks


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Enterprise Skills Which ones are you using?MINI-PLENARY (SPOT THE MISTAKES)


Find the mistakes below:1) 2)

Not ordered

Median = 3.1

Range = 5.3 – 1.4Range = 3.9cm

Mode = 3.6cm

DISCOVERY

LINK BACK TO OBJECTIVES

- Accurately construct stem and leaf diagrams and work out the mode, median and range.


Responsible Citizen

Independent Learner

Positive Thinker

Team Worker

Reflective Learner


What level are we

working at?


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Enterprise Skills Which ones are you using?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.

83 85 86 82 87 82

88 82 88 79 76 93

73 65 65 67 52 66

66 53 53 60 72 65

Men

Women

Draw a stem and leaf diagram(s) and discuss your findings.

789

Men6 92 2 2 3 5 6 7 8 8

3

Women567

2 3 30 5 5 56 6 7

2 3

567

89

Women Men2330555667

23 6 92 2 2 3 5 6 7 8 8

3Mode = 82m Mode = 65m

Median = 84m Median =65mRange = 17m Range = 21m

Draw your brain

What have you learnt?

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.

What level are we

working at?

Where are we in our

journey?

.

How well do you understand the task?

I don’t understand

I nearly understand

I fully understand


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SELF ASSESSMENT

Plenary Activity

www.mistrymaths.co.uk


SELF ASSESSMENT

Plenary Activity

On your post it notes…

Think about how you can improve your

work.

WWW (What Went Well)

EBI (Even Better If)


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www.mistrymaths.co.uk


Documents

We are learning to: - Enhance our Mathematical learning skills. (Which Enterprise skills?) -Accurately construct stem and leaf diagrams and work out the