More activity ideas

Ideas for introducing, collecting and investigating your Reach for the Stars 2009 data are available for five different student age groups from the Core activity section.

Below are some additional suggestions you might like to explore. They are grouped into the following categories:

Shape and space	Games and puzzles	Letter usage and language patterns	Names
Codes and ciphers	Probability and combinations	Other ideas and links

Shape and space

“Make” your name (out of dough etc).

Look at letters with rotation, reflection and translation in mind. How many letters in your name have symmetrical properties? Does anyone in your class have a name that makes sense if you look at it upside down or in a mirror? Can you invent such a name? What if you manipulate each of the letters individually (e.g. by rotation or reflection)? Is it easier to do using upper case letters?

Can you find a name to “fit” in the net of a cube (e.g. illustration at right)? How many cube nets are there? Can you find a name for each of them?

Calculate the area of your name written in block letters on square grid paper. Is there a relationship between the total area and the number of letters? Can you construct your name on isometric paper? Is the area different?

Draw a plan for a 3D model of your name. What would be the volume and surface area of the finished product? Make the model, and investigate the number of faces, edges and vertices for each letter – how does what you find link to “Euler’s formula”?

Games and puzzles

Invent a game or song based on the names of people in your class.

Create a crossword using the names of everyone in your class.

Explore and/or invent some ways of determining “scores” for names (e.g. using Scrabble letter values, or a system such as A=1, B=2 etc.). Can you make up a scheme that will give your name the highest value in the class?

Play and/or investigate some games or puzzles in which letter usage frequencies play a role (e.g. Hangman, Scrabble, Wheel of Fortune, cryptograms…).

Can you fit all your class names so that they interconnect on a Scrabble board? What arrangement takes up the minimum possible area? What arrangement uses the maximum area?

Why are the letter scores in Scrabble allocated the way they are? If you wanted to play a version of Scrabble based on names, to which letter would you assign the highest value? How would you allocate the scores for other letters?

Letter usage and language patterns

Does your name have any ‘special’ letters or characters?

Create a class template sheet of letter cut-outs, so that if each person received a copy they could create their name from it (e.g. Theresa has two Es, so the sheet must have at least two Es). What is the smallest number of letters the sheet can have?

Investigate the number of syllables in different names. Is there any relationship between the number of syllables and the number of vowels or the length of the name?

Does the proportion of letters which are vowels change much from one name to another?

Explore mobile phone “texting” of names – how many “button presses” does it take to input your name? What would you expect the average number to be for a name of that length? Collect some data for your classmates’ names…

Why do we have “QWERTY” keyboards? (You could also investigate the Dvorak keyboard – why do you think most of us don’t use it?)

Are the frequencies of vowels and consonants different in other languages? Can you make a reasonable guess about what language a piece of text is written in by looking at the letter usage?

Investigate the use of mathematics in determining authorship of text (e.g. by comparisons of word usage, sentence length etc.).

Names

Identify and record as many characteristics about your name as you can.

Can you find names for which there are a variety of spellings? Which of them has the largest number of variations?

Investigate the origin and/or meaning of your name. Is there a particular reason your name was chosen for you?

Compare your name with a partner and find similarities and differences (e.g. both have repeated letters, one starts with a vowel but the other doesn’t, neither has any ‘silent’ letters…). How can you record this information? (e.g. Venn diagram)

Are names of students in Australian schools today the same length as when your parents or grandparents were at school? What other characteristics are the same or different (e.g. the proportion of names which are ‘unisex’)? Are these characteristics different in different countries or cultures?

Find some names in your class which ‘translate’ to names in other languages (e.g. Henry/Henri/Enrico/Henrik…). Find the countries in which those names are used on a map. Does anyone in your class have two names because they speak two languages or were born in a different country?

Research the first names of some famous mathematicians and find out about what they did.

Compare names that are available in shops on mugs, notepaper, birthday cards etc. with the names in your class/school. Do you think the manufacturers are producing an appropriate range?

Conduct some surveys to find out about people in your class or school, e.g.
- How many students use a preferred name that is different from the name on their school enrolment form?
- How were students given their names? (e.g. after a family member, according to a tradition; after a famous person or character etc.)
- How many classes have two or more people with the same name?
- What are the most common names? Are these related to the statistically popular names in your birth year?
- How many people have first names that are also used as surnames, or vice versa?
- What are students’ favourite names? Are the most popular names different among students of different ages? How do they compare with the most popular babies’ names now and/or when you were born?

Make “human bar graphs” based on the length and initial letters in surnames instead of first names. Who has to move? In what ways are the distributions similar to and different from those for first names? Do people with long first names tend to have long surnames?

Investigate popular names. Does anyone in your class have a name that was in the “Top 10” in the year you were born? How many were in the “Top 100”? Are any of these still in the lists of most popular names now? Why do you think this is? What names would you predict as the “Top 10” names for babies born in 2010?

Codes and ciphers

Find out how you would represent your name using various ‘codes’ (e.g. Braille, Morse code, or the international radiotelephony spelling alphabet – “Alfa”, “Bravo”, “Charlie” etc). You might like to explore the history and purpose of the codes, too. (A recent Australian novel which connects with the use of Morse code is Dianne Woolfer’s Lighthouse Girl).

The Black Chamber is an interactive section of mathematics and science writer and broadcaster Simon Singh’s website which explores codes and ciphers (includes a letter frequency analysis tool – look in the Contents for the section on cracking the substitution cipher).
http://simonsingh.net/The_Black_Chamber/home.html

Probability and combinations

How many ways can the letters of your name be rearranged? Do any of these make sense as words or names? (How is this different for a name of a particular length if there is/is not a repeated letter?)

If you have the letters from the whole class’s names in a bucket, what is the likelihood of randomly selecting an E? How many letters would you need to take out to be sure of being able to assemble the name of someone in the class?

If you have the letters of your name in a bag and take them out one at a time, what is the probability that they will be drawn in the order required to spell your name? What is the probability that the first 2, 3, or 4 letters will make a recognisable word or name? (Try it and compare the theory with an experiment!). Do your expectations change if you put the letters on a spinner or dice instead of drawing out of a bag?