# 110 Years On

Pupils use mathematical reasoning to estimate the number of descendants a girl who lived 110 years ago might have today.

# Practical details

Suitability
National Curriculum levels 5 to 8
Time
Resources

# Key Processes involved

Representing
Simplify the information given, choose a model, then make assumptions to complete the model.
Analysing
Use their model to calculate the potential number of descendants.
Communicating and reflecting
Present arguments summarising their onclusions and reflect on the validity of their results.

# Teacher guidance

You may wish to show the task on a whiteboard and talk about the concept of descendants

• In this task, there is a photograph of a girl, about your age, who lived 110 years ago. She grew up, had children, who had their own children and so on.
• A family party is being planned for all her descendants. Your task is to make a good estimate of how many descendants you might expect her to have.
• You are given some facts – think about why there are there, and use them!
• Show your working so I can know what you did and how you reached your answer.

The task requires multiplicative calculations to represent changes over time.

The following probing questions may be helpful:

• What assumptions have you made?
• When you are thinking about all her descendants over the 110 years, are there any other factors you need to consider?
• Have you made sure you have thought of all her descendants?

There are several assumptions needed for the task:

• How many children the girl had and when.
• The average age of giving birth and whether this changes over time.
• When and how, during the 20th century, the birth rate changed.
• The proportion of her descendants that conformed to the average birth rates.
• At what age people die, and so how many descendants are still alive for the party.

Note: If pupils use more than 25 years between generations, they are likely to work with only 3 generations so may consider just counting. If so, they should be encouraged to consider a smaller number of years between generations.