The language of mathematics

I. Look at this map carefully and then describe the main properties of this language

II. Work in pairs

A. Say the well – known Pythagorean Property in words and then use symbols to represent it

B. Explain why mathematicians prefer to use symbols instead of words to represent this Property

III. There are more than 300 proofs of the Pythagorean Property. Role play the following situation: You are a teacher who should tell his pupils about the Pythagorean Property and then should prove it

Practice set 12

I. Use this mind-map to speak about Statistics and its application. Add more information

II. Read and analyze graphs that are commonly used in Statistics (Work in pairs)

1. Line graphs are useful in showing changes and trends (general tendencies or directions in the way a situation is changing or developing) involving quantities or amounts over time. It is important to look at the overall pattern on a line graph as well as at the significant features within it.

A. What information is being shown in the graph below?

B. Here are two simple descriptions of the graph:

The weight of this person has risen. OR

The graph shows an increase in the weight of this person.

C. Here are some words and phrases to help you describe trends:

Nouns	Adjectives and adverbs	Phrase
A rise	Sharp(ly) / dramatic(ally)	Remain the same
An increase	Considerable(ly)	Reach a plateau
A fall	Steady(ly)	Remain stable
A drop	Slight(ly) / gentle(ly)	Remain/ stay constant
A decline	Gradual(ly)	Reach a peak
A pick/dip	Relative(ly)	Hit/fall to the lowest point

D. Using some of the words and phrases above, describe the pattern in the graph above.

2. Pie Charts: A pie chart is a type of a circle graph normally used to show the relationship of each part to the whole. The whole quantity depicts entire sample space and the pieces of pie in the circle graph are called sectors. Rank the percentages from the greatest to the least.

Look at this pie chart below and read some information presented in it. For example: Two students out of six (in group) live in Makeevka. This numbers 40% out of 100%.

3. Bar Charts: This is a type of chart, which contains labeled horizontal or vertical bars showing a piece of information. The numbers along the side of bar graph compose the axis. This is also called a histogram; Bar Graph is useful when there is a numerical comparison. When analyzing information in a line or bar graph, note time periods and increases or decreases in amounts.

Fall semester (2011)

Look at the bar chart above and make some factual statements about the data. Try to use the following structures:

Number (e.g. one out of five students has got …

Percentage (e.g. 50 per cent of) students are good at solving …

General (e.g. the majority of / a large number of/ most / very few/ hardly any) students cope with solving…

4. Area Graphs: These graphs are used to show how something changes with respect to time. An area graph shows the contribution of each data series in the form of a picture.

Look at the graph below and make some factual statements. For example:

During the fall semester two students, Prashant and Santosh, are constantly improving their knowledge in Maths. Their marks are the highest ones.

4. Waterfall Chart: This is a type of chart, which shows an increase or decrease in an initial value. This contains floating vertical columns that show the increase or decrease in an initial value through a series of intermediate steps leading to a final value. An invisible column keeps the increase or decrease related to the heights of the previous columns.

Practise in describing this graph. For example: Rahul started working as a program designer three months ago. Each month his salary is increasing compared with his initial one. He is at the beginning of his work career.