Scrabble stats

Stage 2 and 3 – A thinking mathematically targeted teaching opportunity focussed on recording and representing data to conduct a mathematical investigation

These videos were created with Lizz at Scone PS.

Syllabus

Syllabus outcomes and content descriptors from Mathematics K–10 Syllabus © NSW Education Standards Authority (NESA) for and on behalf of the Crown in right of the State of New South Wales, 2023

• MAO-WM-01
• MA2-DATA-01
• MA2-DATA-02

• MAO-WM-01
• MA3-DATA-01
• MA3-DATA-02

Collect resources

You will need:

• a book, magazine or newspaper

• paper and pens.

Watch

Watch the video (3:14) to learn about Scrabble stats!

Has letter frequency changed since 1930?

Transcript of Scrabble stats part 1

[White text on a navy-blue background reads ‘Scrabble Stats - reSolve’. Small white text at the bottom reads ‘NSW Mathematics Strategy Professional Learning team (NSWMS PL team)’. In the bottom right corner, a NSW Government red ‘waratah’ logo.]

Female speaker

Hi, mathematicians. Today we're going to conduct an investigation from reSolved, update the rules of Scrabble for the 21st century. Our first task is to investigate the frequency of letters in modern texts.

[Black text on a white background reads ‘You will need…’ Black text bullet points below (read by speaker). On the right in a still colour image, a silver pen sits on a sheet of lined notepaper as well as a book entitled ‘The Stolen Prince of Cloudburst by Jaclyn Moriarty’.]

For this you'll need a recent book, magazine or newspaper article, and paper and pens. If you're using a book, just select one page.

[A still colour image of a ‘Scrabble’ board. The letters on the board run perpendicular and spell ‘Lifelong Learning’.]

The game of Scrabble was invented in 1933. The inventor of Scrabble, Alfred Butts, chose the value of each letter by reviewing newspapers and other sources of text. He calculated the frequency of each letter. The frequency is how common or how often something happens. Letters that were used the most were worth fewer points and letters that were rarely used were worth more points. He did this in the 1930s. Do you think that since then, letter frequencies might have changed? Why do you think that? Let's look at the current Scrabble points system.

[2 tables side by side are divided into 2 columns each. A header at the top of each column reads ‘Tile’ and ‘Point Value’. Further details explained by speaker and highlighted by red circles. At the bottom, a yellow banner has a white ‘reSolve’ logo in it.]

So, what can we notice and wonder about these letters and their scores? Well, I've noticed that some letters like a, e and s have very low scores, while others like j and q have very high scores.

[White text on a blue background reads ‘Let’s investigate!’.]

To complete our investigation, we need to find out how often different letters are used in a modern text by recording how many times we see each letter. What do you think an efficient way to collect this data might be? I'm going to create a table as this will let me organise the information easily.

[The speaker places a lined sheet of paper onto a white desktop. At the top, blue handwriting reads ‘Scrabble Stats’ and it is divided into 3 columns – ‘letter’, ‘frequency (how often?)’ and ‘total’.]

You can see my table has 3 columns. The first column will have the letters of the alphabet. The second column will tell me how often I see each letter and then when I'm finished, I'll find the total.

[The book from earlier is placed alongside the notepaper. The ‘letter’ column on the sheet has now been filled from A to Z.]

Female speaker

Now, you need to find your text. Before we start, let's think about what we expect to find. Which letters do we think will appear most frequently, and which ones least?

[The speaker opens the book up and uses a pen to mark a tally of each letter (as explained).]

To get started, we're going to choose a page or a paragraph of our text, and then we're going to tally up the letters that we can see. So, my first word is ‘the’. So, I'll do a tally for t, the h, and for e. Stolen, s, t, o, l, e, n. Prince, p, r, i, n, c, e. I'll keep going now until I reach the end of the page. So, now it's over to you, mathematician!

[White text on a blue background reads ‘Over to you, mathematicians!’]

To investigate the frequency of each letter on a page from your text.

[The NSW Government waratah logo turns briefly in the middle of various circles coloured blue, red, white and black. A copyright symbol and small blue text below it reads ‘State of New South Wales (Department of Education), 2021.’]

[End of transcript]

Instructions

• Take a look at the current Scrabble points system. What do you notice? What do you wonder?
• Find a recent newspaper, magazine or book. Choose a paragraph or page to analyse.
• Create a table to record your findings.
• For each letter in the text you are analysing, record the frequency in your table using tally marks.
• How many times was each letter used in the text you investigated?

Watch

When you're ready, watch the next video (4:02).

Analyse and compare letter frequency data from a modern text.

Transcript of Scrabble stats part 2

[White text on a navy-blue background reads ‘Scrabble Stats 2 - reSolve’. Small white text at the bottom reads ‘NSW Mathematics Strategy Professional Learning team (NSWMS PL team)’. In the bottom right corner, a NSW Government red ‘waratah’ logo.]

Female speaker

Welcome back, mathematicians, to the second part of Scrabble Stats.

[A lined sheet of paper has blue handwriting at the top that reads ‘Scrabble Stats’ and it is divided into 3 columns – ‘letter’, ‘frequency (how often?)’ and ‘total’. On the right is a book entitled ‘The Stolen Prince of Cloudburst by Jaclyn Moriarty’.]

Earlier, we investigated the frequency of letters in a modern text by analysing a paragraph to tally how often each letter of the alphabet was used. Now, we're going to look at our table to update the rules of Scrabble for the 21st century. Let's take a look at Alfred Butts original table of letter scores.

[2 tables side by side are divided into 2 columns each. A header at the top of each column reads ‘Tile’ and ‘Point Value’. Further details explained by speaker and highlighted by red or green circles. At the bottom, a yellow banner has a white ‘reSolve’ logo in it.]

Female speaker

We know that when he designed the rules for Scrabble, high frequency letters, those that appear frequently in words, were given low scores, and low frequency letters, those we didn't see very often, were given higher scores. So what do we notice about the letters and the scores that they have? I can see that some letters like the 5 vowels, a, e, i, o, and u, as well as some other letters like r, s and t, must have been very common because their scores are very low. Other letters like j, q, x and z must have been very rarely used as they have very high scores. Now, let's see if our scores from our text match these frequencies or if we can see some differences.

[The lined sheet of paper, pen and book from earlier. The speaker begins to write in the ‘Total’ column. Further details explained.]

Female speaker

To calculate the total for each letter, we can use tally marks to help make our counting more efficient. We know that a group of tally marks always represents 5, so we don't need to count the individual tally marks. For the letter 'a', I can see that there are 6 groups of tally marks, which is 30, and then there are 4 more for a total of 34. Next, I can see 2 groups of 5 and 4 more, which we can rename as 14. And 2 groups of 5 and 2 more, which we know is 12.

[The ‘Total’ column is now completed.]

Female speaker

Now that I've found the total for each letter, let's see what we notice. Which are the most frequent letters? Which are the least frequent letters? Do these surprise you?

[A colour image of the lined sheet of paper recording the tally of letter frequency in the book. To the right of it, a blue table has a white text header that reads ‘Classic Scrabble’ and has the points value for each letter grouped accordingly in 2 columns.]

You might like to pause the video here to compare the frequencies that I found with the original Scrabble points scores, looking at what is the same and what might be different.

[White text on a blue background reads ‘Over to you!’]

Over to you now mathematicians! Find the total for each of the letters in your text and see how it compares to Alfred Butts original point score. Think about how might you need to adjust the scores for each letter based on what you found for your text.

If you want an extra challenge, think about this. If the rules were changed so the Scrabble winner was the player with the lowest score, how could you then change the individual letter scores to make that happen?

[White text on a blue background reads ‘What’s (some of) the mathematics?’]

So, what's some of the mathematics that we see in this activity?

[Black text on a white background reads ‘What’s (some of) the mathematics?’ Bullet points below (read by speaker) and a colour image of the lined notepaper with the tally of letter frequency.]

We are able to ask questions and make predictions about the frequency of letters in a text. For example, we predicted that vowels would have a higher frequency than consonants. By using a table and tally marks, we were able to efficiently collect and organise our data. Our table helps us to see which letters are the most and the least frequent. We noticed that the letter 'e' was the most frequent as it occurred 45 times, and the letters j, q, x and z were not used at all.

[The NSW Government waratah logo turns briefly in the middle of various circles coloured blue, red, white and black. A copyright symbol and small blue text below it reads ‘State of New South Wales (Department of Education), 2021.’]

[End of transcript]

Instructions

• What do you notice about the frequency of the letters on your tally sheet?

• Does anything surprise you?

• Which letters were you expecting to be used most? Or least?

• Look at the letters that are most frequent (have the highest number) and least frequent (have the lowest number.
• Compare your data with the original Scrabble scoring system?
• Are there any similarities?
• Are there any differences?
• Using your Scrabble Stats findings, identify which letters you think should now be given the highest and lowest scores.

• Represent the data you collected in a column graph or a different data display. You may like to use Excel.

• You can also repeat your investigation with a different text.

• Does the type of text we select change the letter frequencies?

• What are some similarities and differences between both data sets?