### Number Detective

Follow the clues to find the mystery number.

### Six Is the Sum

What do the digits in the number fifteen add up to? How many other numbers have digits with the same total but no zeros?

### ABC

In the multiplication calculation, some of the digits have been replaced by letters and others by asterisks. Can you reconstruct the original multiplication?

# Becky's Number Plumber

## Becky's Number Plumber

This problem has been inspired by learners who were working on the Become Maths Detectives Project.

You may like to watch the video in the Become Maths Detective Project before having a go at this activity.

Becky created a number plumber which multiplies by $5$ and subtracts $4$.
Click on the picture to explore Becky's number plumber.

What do you notice about the units digit of the answer each time?
Can you explain why this happens?
Can you find any other numbers that work in a similar way?

### Why do this problem?

This month's NRICH site has been inspired by the way teachers at Kingsfield School in Bristol work with their students. Following an introduction to a potentially rich starting point, a considerable proportion of the lesson time at Kingsfield is dedicated to working on questions and ideas generated by children.

This problem is based on the Become Maths Detectives Project. It encourages children to notice and explain patterns, based on their understanding of the number system. It also gives them the freedom to choose their own questions to explore.

### Possible approach

Show the group the Becky's number plumber interactivity and drop in some different inputs so that everyone can see how to use the number plumber. Without saying much more at this stage, ask children to explore what happens when different numbers are multiplied by $5$ and then $4$ is subracted from the result. What do they notice?

Give them time to work in pairs, ideally using the interactivity. You may need to draw the whole class together briefly to discuss how they are recording what is happening. After a suitable length of time, bring everyone back together to talk about what they have noticed. Look out for children who can use what they know about multiples of $5$ and odd/even numbers to create good explanations.

You could then give more time for children to explore more for themselves. Can they find other numbers that behave in a similar way? (Each pair will have different ways of interpreting 'similar way', which is absolutely fine!) You could ask each pair to make a poster of their findings, including explanations and further questions.

For teachers who want to create their own alternatives to Become Maths Detectives for use in the classroom, Mike's blog Grumplet describes some instructions and rationale.