Lesson 5 Sam and the newspaper

Episode 1

Reasoning Resources:
Worksheets 1 and 3. Enlarged extract from newspaper article (or Worksheet 2). Worksheet 4 on board or OHT.
Whole class preparation: story for a hypothesis
Start with a hypothesis.

Agreeing on the elements of a problem.

Deciding on a comparison of two samples.
You could start with a story about Sam, aged six, who is worried that he is no good at reading, and that books for older children have longer words. Allow a discussion about this argument, and whether they agree with Sam or not, perhaps even by voting. Pupils should agree on what ‘long’ and ‘short’ words mean, and give example of each type. Some pupils will note that the main issue is understanding rather than length of word, something you suggest the class discusses later and concentrate instead on length of words. Pose the question of how to test the hypothesis: Are words for grown-ups longer than for children? Typical ideas are: 'Get two books and check how long the words are', ‘Let's count the words in the book and the newspaper’.

Lead the class through their ideas towards looking at a text for 6-year-olds and comparing that with a grown-up novel or newspaper by looking at word length (number of letters).
Whole class collecting and recording data
Note: The main consideration is to avoid time-consuming work and pupils struggling with accurate tallying. Older or more able classes may be left to collate data on their own.

Collecting numeric data. ‘Word length’is in number of letters, not actual space the word takes on the page. Often different letters take different spaces. Apostrophe is best counted as a letter since it also needs attention.

Demonstrating the tally table with equal spacing and bundles of 5.

Finding patterns in grouped data.

Predictions as a good start for investigation, clarifying that the purpose is often to confirm or disconfirm ideas.
Draw the two-sided tally table (Worksheet 4) on the board or show on the OHP, explaining that we best compare things by putting them side by side and that you will act as a recorder. Give out Worksheet 1 and ask pupils quickly to count the first 20 words including title, and to pencil above each word how many letters it has. Tell them to count an apostrophe, a digit or a hyphen as a letter.

Then ask pupils in turn to tell you the lengths of the words, with others checking he/she is correct. You record the results on the left side of the table, thus demonstrating the process of 5 tallying, making clear you are using marks at equal sensible distance from each other, with each fifth mark crossing the 7 previous four. They could think of this as the thumb crossing 8 the other fingers of one hand. The batches of five allow for counting and should help to ensure equal spacing.

Once all the 20 word lengths are recorded, ask pairs to think for a minute or two about what they notice, and what they expect the results for an adult book, or newspaper, to show. What do you notice? What predictions can we make? Typical responses may be ‘more five letter words’; ‘five is the most common — the mode’; ‘there are not many long words’, ‘that’s about right for young children'.

Ask for descriptions for the length 5 (e.g. mode, most common, middle) and for the spread (between 2 and 8, more than 1, less than 9) noting in passing that in mathematics we sometimes use range as a single value to describe the spread around the middle value. Likely predictions for the newspaper would be along the lines of ‘will be more spread out and have longer words, ‘the mode will be more than 5‘.
Pair work- independent collection and recording
Now give out to each pair Worksheet 1, Worksheet 3 with the table with Jimmy’s story results for the first 20 words, and a copy of an enlarged extract from a well-recognised newspaper on some daily events (or Worksheet 2). They can now tally the word lengths of the first 20 words of the newspaper article before making rough notes on comparisons between the two texts.
Whole class sharing/discussion
A good description of a set of data uses an average or a single representative value (mode, mean, median) and a measure for the spread of values.

Fill in the newspaper side of the table on the board or OHT and collect pupils’ ideas on its main features, Somewhat counter-intuitive results may come from sampling any local newspaper. Pupils focus on the mode as the most useful way of describing what they see. Typical outcomes may be: ‘the mode is 3’; ‘it has shorter words’; ‘book for the 6-year-old looks harder’; ‘spread is wider’ Allow time for puzzlement, checking and speculation on reasons before moving on.


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

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