Lesson 5 Sam and the newspaper

Episode 3

Reasoning Resources
Worksheet 3 on board or projector
Whole class or pair work on comparisons
On the board or OHT compare the results for the three samples: the first 20 words, the words from 21 to 60, and the words from 61 to 100.

Moving to look at summaries of samples and their comparisons.

The visual look of the distribution is more informative than numbers in a table of values.
Discuss the similarities and differences in the three samples and ways of combining them. In ‘other features’ include extreme values or double modes. You could use a different colour pen for each sample to create the combined tally chart for the 100-word samples. This visually shows the distribution for the whole 100 words as well as for each of the samples. You could actually draw the profile for each sample. The pupils should see that the profile shows that both texts are actually similar.

Sample Mode Range/spread Other features
First 20 Words
Middle 40 words
Last 40 words
Full 100 words together
End of Lesson Reflection
Different levels of reflection.

Appropriateness of using statistics to measure things depends on good hypothesis and good design.

Representative sample.

Difficulty of sample size overcome by computers.
Depending on how far the class has got in the activity the reflection can be on any of the following, often mixed up together: Did the test confirm the hypothesis? Is the hypothesis wrong? Typical responses may be: ‘no difference’, ‘little difference’, ‘the language is the same’, ‘it wasn’t a good hypothesis', ‘may be OK hypothesis for nursery but not for junior’, 'many adults are not good at reading’, ‘newspapers write for below average readers'.

Was it a good test? Is the length of words a good measure for comparing texts?Typical responses may be: ‘long words may be easy or names of things', 'while some short words are hard’, ‘it is the meaning not the word that is difficult’, ‘better to look at length of sentences’, ‘better to look at clauses’, ‘there are other tests for difficulty’, ‘maths is not the best test for language’, ‘maths is only useful if used with other things, like on meanings’, ‘some books for children are designed for specific age groups, so there must be ways of making language easier or harder to read’.

Were the samples representative? How important is it to choose a representative sample? Typical responses may be: ‘there is no representative sample’, ‘we can only approximate’.

How important is the size of sample? Typical responses maybe: ‘we need lots of books and newspapers’, 'computers do the stats easily for any number of words and for a lot of different texts’, ‘you need averages from a lot of different types of writing'.


Thinking Mathematics Lessons Copyright © by Michael Shayer and Mundher Adhami. All Rights Reserved.

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