Lesson 2 Text ‘n’ talk

# Episode 2

Reasoning Resources
Whole class preparation
Shift of attention to different variables in a similar real-life situation. Direct the class attention to mobile phone conversations rather than messages. If two people have a telephone conversation how many phone calls are made? What about three people?

Remember that each person must speak to everybody in the group and only two people can speak during a phone call. Talk to your group and think of a way to record this.

Briefly take feedback on the board. Pupils will readily recognise that they have to halve the number of messages to obtain the number of conversations. Discussion of the best terms to use is useful.
Pair and small group work
Intuitive predictions provide motivation and initial focus for pupils' attention to features of the problem. Working in pairs, or threes/fours, pupils should show their systematic workings for the following situations on large sheets of paper, or on OHT.

• Try to work out the number of phone calls made if there are four people in the group all needing to speak to each other. Be careful that you have not missed out any of the phone calls or counted any twice.
• Make a prediction for the number of phone calls made for five people and write down how you made your prediction. Check using your systematic method.
• Whole class sharing and discussion
Phone calls are half the number of text messages i.e. (n x (n-1))/2

Fraction line acts as brackets
Take feedback from the groups to show different methods of recording the numbers of phone calls. Sheets can be displayed on the wall for the example of five people. Some pupils may already write full sentences, part-word and part-symbols or algebraic expressions, all of which should be shared.

What are the similarities between the phone call and text message rules? How many texts for ten people? How could we work this out? What if all of the pupils in the class need to speak to each other (two at a time)? What if there were n people, what would the total number of phone calls made be

Work with the class on expressions to link the number of people with the total number of phone calls, leading to the conventional ways including the brackets and the fraction line which also acts as brackets.

Conduct a reflection discussion on which other real-life situations have similar differences between the two types of enumeration. For example, sending Christmas cards vs. handshakes or meetings, league table football games vs. cup tournaments. In each the same formula applies.