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Level Four > Number and Algebra

How many Words?

Purpose: 

This unit compares the frequencies of different parts of speech in different kinds of text.  This provides an opportunity to discuss and categorise parts of language, as well as a practical context in which to use percentages, and generate pie graphs.

Achievement Objectives:

Achievement Objective: NA4-3: Find fractions, decimals, and percentages of amounts expressed as whole numbers, simple fractions, and decimals.
AO elaboration and other teaching resources
Achievement Objective: S4-1: Plan and conduct investigations using the statistical enquiry cycle: determining appropriate variables and data collection methods; gathering, sorting, and displaying multivariate category, measurement, and time-series data to detect patterns, variations, relationships, and trends; comparing distributions visually; communicating findings, using appropriate displays.
AO elaboration and other teaching resources

Specific Learning Outcomes: 
  • identify parts of speech
  • calculate percentages from raw data
  • calculate angles and draw pie graphs using correct conventions
Description of mathematics: 

Percentages are an important part of the Number Strand. We encounter them frequently in our everyday life and it is important that students develop a good understanding of their meaning and use.  A percentage is often described as “a fraction over 100” and this can be a useful way to help students understand how to calculate them.

A pie graph is just like a piece of pizza pie divided up into sections. The size of the piece, that is the angle subtended at the centre of the pie, tells the relative magnitude of the object represented by that piece of pie.

Associated Achievement Objective

English; Listening, Reading, and Viewing - Language features - shows an increasing knowledge of how a range of text conventions can be used appropriately and effectively

Required Resource Materials: 
a variety of texts
highlighters or felt pens
Key Vocabulary: 

 percentages, decimals, convert, approximate, fraction, categories, predictions, sample, pie graph, wedge, angle, estimate, 

noun, verb, adjective, adverb, preposition, conjunction, genre

Activity: 

Session 1

In this session we discuss parts of language, especially nouns, verbs, and adjectives, and predict which we will find more of in a given piece of writing.  We check our predictions by counting, and then calculate percentages.

  1. Choose a piece of text to investigate – this may be the first page of a book you are currently reading the class, or a page from a familiar book (e.g. Harry Potter)
  2. Write the first sentence on the board.
    Ask students:
    Who can find a word in this sentence which is a noun?
    What is a noun?
  3. Discuss the fact that nouns are ‘naming’ words.  Find any other nouns in the sentence.  Ask for some examples of other nouns. 
  4. Discuss the ‘other’ nouns – proper nouns, and pronouns.  Proper nouns are nouns which describe a specific thing, rather than a member of a group.  For example while city is a noun, Dunedin is a proper noun.  Proper nouns start with a capital letter.  Pronouns are words which are used in place of a noun, usually to avoid repetition.  For example in the sentence “Johnny ran home because he was hungry.”, “he” is a pronoun which replaces the proper noun “Johnny”.
  5. Refer back to the sentence, ask students:
    Who can find a word in this sentence which is a verb?
    What is a verb?
  6. Discuss the fact that verbs are ‘doing’ words.  Find any other verbs in the sentence.  Ask for some examples of other verbs. 
  7. Ask students:
    Who can find a word in this sentence which is an adjective?
    What makes it an adjective?
  8. Discuss the fact that adjectives are ‘describing’ words.  Find any other adjectives in the sentence.  Ask for some examples of other adjectives. 
    Are all describing words adjectives?
  9. Discuss adverbs:
    What is an adverb?
    An easy way to remember what an adverb is, is to break it down to ad-verb.  So an adverb is an adjective for verbs, or a word which describes verbs.  In the sentence “The boy ran very fast.”, “fast” is an adverb which describes the verb “ran”. This is not a strictly accurate definition as an adverb can also describe or clarify adjectives.  In the sentence “The shirt was extremely clean”, “clean” is the adjective which describes “the shirt”, and extremely is an adverb describing the adjective “clean”.
  10. Ask students:
    Which do you think is more common in this piece of writing, nouns, verbs, or adjectives and adverbs?
    How could we find out?
    The obvious answer is to count and see.
  11. Give each student a copy of the text and ask them to go through it, highlighting nouns and pronouns one colour, verbs another colour, and adjectives and adverbs a third colour.  Students could use a dictionary to help categorise difficult words.  Not all words will be highlighted.
  12. Get students to count total numbers of each part of language in the text.  Compare results and discuss differences.  Discuss words that caused particular difficulty.
  13. Ask what would be the best way to tell someone else your results.  Hopefully students will realise that the raw data is less clear than converting to percentages.
    How can we convert these numbers to percentages?
    Percent means “per 100”, so we need to know how many per hundred are each type of word. 
    How many words are we counting altogether?
    You must count all the words, not just the highlighted ones.
  14. As an exercise try to work out the percentages without using a calculator.  There are likely to be a number of ways to approximate the percentages. Discuss which are most accurate, and then compare with the result from a calculator.  Make sure students understand how to convert a fraction to a percentage on a calculator.  They will need to convert to a decimal and then multiply by 100.
    How do we convert the fraction to a decimal? (Divide the top number by the bottom number.)
    Why do we multiply by 100?
    (Because percent means “per 100”, or divided by 100.  A percentage is like a fraction over 100 (you can describe the % as being the / and the 00 from /100), so to go from a decimal which is out of 1 to a percentage, you need to multiply by 100.)
  15. Compare the percentages of each type of word.  Discuss the results.

Session 2

In this session we investigate a second text, comparing the percentages of each part of language with those found in the first session.  We make pie graphs to display the results.

  1. Choose a second piece of text to investigate – this one should be of a different genre, so that you are more likely to get interesting results.  Possibly an article from the front page of the newspaper or a poem could be used.
  2. Ask students to predict the percentages of nouns, verbs, and adjectives/adverbs in this piece of text.  Record the predictions.
  3. Give each student a copy of the text and ask them to highlight as in the previous session.  Circulate and assist students who need help with categorising words.
  4. When students have finished, ask them to calculate percentages as previously, ensure calculations are carried out accurately.
  5. Compare the results with those from session 1 and with the predictions made at the start of the session.
    Why do you think there are more/less nouns in this sample?
    Why do you think there are more/less verbs in this sample?
    Why do you think there are more/less adjectives and adverbs in this sample?
  6. Discuss good ways to present these results.  Suggest pie graphs.
    How do we draw a pie graph?
    What information do we need to show?
    How do we know how big to make each wedge?

    If 100% is a full circle, how much will 50% be?  (half circle)
    How much will 25% be?
    (quarter circle)
    How much will 1% be?  (Students will need to know that there are 3600 in a circle – possibly this will need to be constructed from a right angle, or by measuring.  They can then easily discover that each 1% is equivalent to 3.60.)
    Also teach students conventions for correct pie graphs (start from a vertical radius and work clockwise from the biggest sector down, a key can be drawn to show what each sector represents, and sectors should be labelled with percentage not angle if at all).
  7. Create a table like the one below to convert from number to percentage to angle.
Type of word Number Percentage (Number/Total) Angle (Percentage x 3.60)

 

 

 

 

 

 

 

 

  1. Construct a pie graph of the percentages of each type of word for each text.  There will be a large sector of words that do not fit into any of the three categories being counted.  See whether students identify that this sector still needs to be included and labelled.
  2. Compare the pie graphs and discuss how well they show the differences between the results.

Session 3

In this session we discuss the ‘missing’ parts of language, and how we can categorise them. 

  1. Discuss the pie graphs drawn in the previous session.
    How could these be improved?
    What extra information could be collected?
  2. Suggest that some of the ‘other’ words could be categorised.  Depending on the ability of your students you could also count adjectives and adverbs separately, and have separate categories for proper nouns and pronouns.
  3. Other types of words that could be categorised include:
  • prepositions (‘placing’ words, such as ‘on’, ‘in’, ‘beside’, etc.)
  • conjunctions (‘joining’ words, such as ‘and’, ‘but’, ‘because’, etc.)
  1. Students to recategorise the two texts from the earlier sessions using the updated criteria, and draw new pie graphs.  There may still be some words categorised as ‘other’.
  2. Discuss again why there are differences between the two texts.  Students should have had experience with different genre before and should realise that the types of language used varies.
  3. Discuss whether there are other genre that could be explored.  Ask students to bring a sample of a piece of text that they would like to examine to the next class (of similar size to those already examined).

Session 4

In this session students work on individual investigations of texts.

  1. Explain to students that in the next session and a half they will be carrying out an investigation in which they will analyse the proportions of each type of word in at least three texts of different genre, and produce a display of their results, including pie graphs.
  2. Students should have brought at least one sample text from home, the teacher should provide a selection of other texts from a variety of genre, including at least poetry, formal letters, and non fiction.  Maybe some extras such as cartoons (a few would have to be combined to make up word numbers), or Shakespeare (for more able students) could be added.
  3. Students are to choose their texts, read them through, and estimate the proportions of each of at least nouns, verbs, and adjectives/adverbs.
  4. They should record these estimates and then analyse the texts according to the more detailed criteria used in session 3.
  5. They will be required to write up their findings and report back to the class.
  6. The teacher should circulate and provide support and feedback to students.  Check that students are accurately categorising words.
  7. Some students may move on to calculating percentages and angles in this session.  Again circulate and provide feedback.

Session 5

This session is devoted to completing displays and presenting them to the class.

  1. Students should be given the first part of this session to work on their pie graphs for their investigations.  Ensure that they are calculating the percentages and angles accurately. 
  2. Ask students to suggest a quick check that they could do to ensure that they have worked out the right percentages.  (Percentages should total to 100%)
  3. Ask students to suggest a quick check that they could do to ensure that they have worked out the right angles before graphing.  (Angles should total to 3600)
  4. When students have created their graphs they should produce a display with a few paragraphs discussing the differences between the texts.
  5. Some students could present their displays to the class.
  6. Discuss whether it seems like there is any pattern in the types of text that have more/less of each type of word.  (For example poetry is likely to have more adjectives and adverbs than other types.)