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Mathematics Teaching Self-evaluation Tools

You are viewing a limited version of the NCETMâ€™s self-evaluation tools. Any answers you save during this session will be removed after seven days. Log in or sign up to view, and use, the full version of the tools.

For the following questions, select the statement which most accurately matches your level of confidence (1 is not confident and 4 is very confident) or choose from the alternatives detailed in the question. You do not have to answer all questions. Your answers will be saved so you can exit and come back to your self-evaluation at any time. Click Save and Results to view the next steps for questions you have answered.

1.

How confident are you that you can find opportunities for:

1

2

3

4

a.

adults to use and apply their skills in handling data?

There are many opportunities for adults to handle data.

Example: Conduct a survey with the group. For example, they may investigate the number of smokers/non-smokers, the number of units of alcohol they drink per week, or how many hours they spend a week watching television. They can present the information in whatever ways they choose, such as numerically or pictorially, and discuss the different ways, interpreting the results. They might look at different types of buildings in a street and represent the number or purpose of the buildings in pictograms; they could show the ages of the building or the numbers of floors or rooms in block graphs.

2.

How confident are you that you can explain the meanings of:

1

2

3

4

a.

a tally chart and a frequency table?

A tally chart is used to record data as it is counted. The data is recorded in groups of five to make it easy to find the totals when the count is finished. The frequency is the total number of times that each category of data occurs.

This tally chart shows the number of people buying stamps from a local Post Office at different times during the day.

A frequency table gives the name of each category of data as well as its frequency.

This frequency table shows the colour of cars in a car park.

The pictogram shows the number of babies taken to a clinic in a particular week.

How many babies in total were taken to the clinic in this week?

On which days were the same number of babies taken to the clinic?

Why do you think there were no babies taken on Wednesday?

How many more babies were taken on Thursday than on Tuesday?

c.

The distinctions between a bar chart and a bar line graph?

A bar chart (or bar graph) is used to display discrete data. Bars of equal width represent the frequencies of the categories and there are gaps of equal width between the bars. The bars can be drawn horizontally or vertically. Both the axes have labels.

These bar charts show the eye colours of 40 adults.

A vertical bar-line graph can be drawn instead of a bar chart. The bars are replaced by vertical lines.

Dual bar charts compare data. In a dual bar chart two bars are drawn side by side. The bars can be horizontal or vertical.

This bar chart compares the marks of two girls in four different subjects.

d.

a pie chart?

A pie chart shows the proportions of different categories of discrete data. A pie chart is a circle divided into sectors. The whole circle represents all the data. Each sector represents the number of items in that category of data.

This pie chart shows that a dog is the favourite pet of half the people asked and that a cat is the favourite pet of a quarter of them.

Example: Don works in a large DIY shop. They have just started selling a new brand of paint and want Don to see how it is doing and how much of each colour they need to order. He has to do a presentation for his line manager and decides to show the information in a pie chart as well as a table. There are some things missing from the table and the pie chart. Fill in as many as you can.

Paint colour

Sales

45

Forest Green

Buttercup Yellow

135

Rainy Blue

Total

360

e.

a line graph?

A line graph is sometimes called a time series graph. The line graph shows the change in a quantity over a period of time. The scale on the horizontal axis represents time.

When a line graph is drawn, only the points that are plotted represent actual values. The points between may or may not have meaning. Points are joined with straight lines to show the trend of the data.

This line graph shows John’s pulse rate in beats per minute when it was taken every 6 hours over 3 days.

Double line graphs are also used to compare two sets of data. For examplea a hydraulics company sells two different types, A and B, of a particular component. The line graph shows a comparison of the profits (in thousands of pounds) from the sales of these two components for the time period 2000 to 2005.

f.

a scatter graph?

A scatter graph shows paired observations which may indicate a relationship between the variables; for example, the heights of a number of people could be plotted against their arm span measurements. If height is roughly related to arm span, the points that are plotted will tend to lie along a straight line.

This scatter graph shows the relationship between the hours of sunshine and the number of cartons of orange juice sold in a supermarket on 9 consecutive days during the summer.

3.

How confident are you that you can explain and illustrate the meanings of:

1

2

3

4

a.

discrete data and continuous data?

Discrete data results from, say, counting the number of coins in someone’s pockets, the number of peas in a pod, the number of lengths swum in a sponsored swim.

Continuous data results from measurements such as lengths of arms or weights of crisp packets. It can only be measured to a certain degree of accuracy.

One good example to illustrate the difference is that someone’s shoe size is discrete but the length of their foot is continuous.

4.

Given a set of data, how confident are you that you can find:

1

2

3

4

a.

the range?

The range is a measure of spread in statistics. It is the difference between the greatest value and the least value in a set of numerical data. For example, the number of vegetarian meals ordered in a restaurant every hour between 7pm and 11pm on a particular evening was:

12 8 20 15

The range is 20 – 8 = 12.

b.

the mode?

The mode is the most commonly occurring value in a set of data or the class with the largest frequency in a set of grouped data. for example, in this set of marks in a test out of 20:

10 15 19 12 15 17 15 15 17 18

the modal mark is 15.

In a bar chart, the mode is the group with the tallest bar. For example, this bar chart shows the number of goals scored by a football team in 20 matches. The mode was 2 goals because this was the number of goals that the team scored most frequently.

c.

the mean?

The mean of a set of data is the sum of the quantities divided by the number of quantities. For example, the mean of:

5 6 14 15 45

is (5 + 6 + 14 + 15 + 45) ÷ 5 = 17.

d.

the median?

The median is the middle number or value when all values in a set of data are arranged in ascending order. For example, the median of 5, 6, 14, 15 and 45 is 14.

When there is an even number of values, the mean of the two middle values is calculated. for example, the median of 5, 6, 7, 8, 14 and 45 is (7 + 8) ÷ 2 = 7.5.

5.

How confident are you that you can explain how:

1

2

3

4

a.

the different averages and the range can be used to compare two sets of data?

Example: As part of a ‘getting more healthy’ campaign, six men and six women decided to weigh themselves. Their weights are shown in the table.

Weights in kilograms

Men

74

86

93

80

120

95

Women

63

60

67

80

65

70

Which of the sets of weights, men or women, has the biggest range?

How much bigger is the mean weight of the men than the mean weight of the women?

6.

How confident are you that you can:

1

2

3

4

a.

explain which average of mean, median and mode is the â€˜bestâ€™ one to use in a particular situation?

The mean can be affected by very large or very small values compared with the rest of the values so may not be the most appropriate in those circumstances.

The median is not affected by extreme values so may be more appropriate than the mean in those circumstances. For example, in a group of people, if the salary of one person is 10 times the next lowest salary, the mean salary of the group will be higher because of the unusually large one. In this case the median salary may be better to represent the typical salary level of the group.

The mode can be the most appropriate average to use if the data is in categories. For example, if a sandwich shop sells 12 different types of sandwich, the mode represents the most popular sandwich.

Example: For the following situations, decide which average (mean, median or mode) is the most appropriate to use.

The manager of a shoe shop needs to decide how many of each size to buy for a particular style of shoe.

John wants to know whether he is smaller or taller than the average height of the other boys in his class.

Michelle goes running every day and she times herself so that she can work out her average running time each week. One Monday she hurts her foot and can only walk on that day and the next, but still wants to know her average time for the week.

A company keeps information about the ethnic origins of its employees and records the information in a table.

White

Black

Asian

Mixed

20

5

10

3

7.

How confident are you that you can estimate probability:

1

2

3

4

a.

based on theory and equally likely outcomes?

Probability is the likelihood of an event happening. It is expressed on a scale from 0 to 1. Where an event cannot happen, its probability is 0. Where it is certain its probability is 1. Probability can be expressed as a fraction, decimal or percentage. For example, the probability that a coin will land tails up is ½, 0.5 or 50%. Fifty-fifty chance is another way of expressing probability using percentages.

The theoretical probability of scoring 5 with a fair dice is

1

6

. The denominator expresses the total number of equally likely outcomes. The numerator expresses the number of outcomes that represent a ‘successful’ occurrence.

b.

from a set of experimental data?

In an experiment a fair dice is rolled 120 times. The number 5 appears 18 times. The experimental probability of scoring 5 is estimated as

18

120

, which cancels to

3

20

.

8.

How confident are you that you can explain:

1

2

3

4

a.

independent events?

Events are independent when the outcomes of one do not influence the outcomes of another.

Examples:

The gender of a first baby does not influence the gender of subsequent babies.

When a fair three-sided spinner is spun and a fair coin is tossed at the same time, the outcomes from spinning the spinner do not affect the outcomes from tossing the coin and vice versa.

9.

How confident are you that you can explain that:

1

2

3

4

a.

sometimes events have to be combined?

Events are combined when the outcome depends on separate outcomes of more than one independent event.

Examples include the likelihood that if you toss a coin and roll a die at the same time that you will get a head on the coin and a six on the die, or if you have twins, the likelihood that they will both be boys.

10.

How confident are you that you can explain how to combine events using:

Tables can be used to record all possible outcomes in order to work out the probabilities.

Example: What is the likelihood of getting a head on the toss of a coin at the same time as an even number on the roll of a die?

Outcome on the die

1

2

3

4

5

6

Outcome on coin

H

1, H

2, H

3, H

4, H

5, H

6, H

T

1, T

2, T

3, T

4, T

5, T

6, T

The table shows all possible outcomes, of which there are 12. Three of these have an even number with a head, so the probability of getting an even number and a head is 3 out of 12, or one quarter. This can be expressed as

Huan and her son Chen are playing a board game which uses two dice. You have to throw a double six to start. It takes them a very long time to get started and Huan is convinced that it is more difficulot to throw a double six than any other combination. Is she right?

Score on second die

1

2

3

4

5

6

Score on
first die

1

1, 1

1, 2

1, 3

1, 4

1, 5

1, 6

2

2, 1

2, 2

2, 3

4, 2

2, 5

2, 6

3

3, 1

3, 2

3, 3

4, 3

3, 5

3, 6

4

4, 1

4, 2

4, 3

4, 4

4, 5

4, 6

5

5, 1

5, 2

5, 3

5, 4

5, 5

5, 6

6

6, 1

6, 2

6, 3

6, 4

6, 5

6, 6

From looking at the table, there are 36 different possible combinations of scores on the two dice. Each double can only be thrown in one way, so a double six is equally likely as any other double. However, combinations of two different numbers can all be thrown in two ways (for example, 4,2 and 2,4 both give the same outcome) so these are all twice as likely as doubles.

A probability tree diagram shows all of the possible outcomes of more than one event by following all of the possible paths along the branches of the tree.

Example: A local football team need to win both its remaining matches to score maximum points. What is the likelihood of them winning both games?

This probability tree diagram shows all the possible outcomes.

It can be seen from the diagram that there are nine possible outcomes of the two matches and only one of these is win, win. Therefore, the likelihood of winning both games is 1 in 9 or

Baljinder has a CD player in his car that will hold 3 CDs. He puts CDs in by Coldplay (C), Radiohead (R) and Foo Fighters (F). He selects the option that randomly chooses the albums to play. Draw a tree diagram to show the possible albums the first two tracks will be from.
(a) What is the probability that both tracks are from the Radiohead album?
(b) What is the probability that one track will be from the Coldplay album and the other from the Foo Fighters album?
(c) What is the probability that both tracks are from the same album?

(a) There is only one outcome from 9 that both tracks will be from the Radiohead album (RR) so the probability is

1

9

.

(b) There are two outcomes in which one track is from Coldplay and the other from Foo Fighters (CF and FC) so the probability is

2

9

.

(c) There are three outcomes in which both tracks are from the same album (CC, RR and FF) so the probability is