# Bob's Buttons Years 4 - 8

### Preparation

• About forty (40) objects such as buttons, plastic screw caps, pasta, tiny toy people, beads or pebbles
• Write the title of this challenge and today's date on a fresh page in your maths journal.

### Getting Started

• Click the photo on the right to play a video that will be Introducing Bob's Buttons.
You can play the video through again any time you like if you want to check anything.

The photo below is the Recorder's book from the video.

• Copy the picture into your journal.
• Play the clumps game with 17 pretend people five (5) more times.
Draw a new arrow on your page each time and write its number story.

Have fun exploring Bob's Buttons.

### The Teacher's Questions

(Answer in your journal.)
1. If I called out sixteen (16) what number of players would be left out?
2. If I called out three (3) what number of players would be left out?
3. If I called out seventeen (17), what number of players would be left out?
4. If I called out one (1), what number of players would be left out?
5. Five (5) players were left out, what numbers might I have called?
6. Four (4) players were left out, what numbers might I have called?
In your journal, draw a table like the one below for all the numbers I could call in the 17 clumps game. Fill in all the boxes.

 No. Called No. of Groups No. Left Out Equation 1 17 0 17 x 1= 17 2 8 1 (8 x 2) + 1 = 17 ... ... ... (5 x 3) + 2 = 17 ... ... ... ...

When you have recorded all the data write or draw about anything interesting in the table.

### Special Questions to Think About

(You don't even have to look at these if you don't want to.)

Mathematicians like to ask unusual questions just for the fun of thinking about them. Questions like these:

• What would happen if the teacher called eighteen (18)?
The players can't stand apart like they are social distancing, because that would be groups of 1.
What could they do?
What would the equation be?
• What if the teacher called any number greater than seventeen in the 17 game?
• What would happen if the teacher called zero (0)? Is there an answer?? Could we write an equation??

### More of the Teacher's Questions

Seventeen is a special number because it has exactly two ways of having zero left overs. If the teacher calls 1 or the teacher calls 17.
A number like this is called a Prime Number.
A Prime Number has exactly two ways it can make groups with zero left overs.
One way is its groups of 1.
The other way is the group made by the number itself.
1. Make a list of all the Prime Numbers up to twenty-five (25).
(Mathematicians say the number 1 is not a prime number. If you want to, you can try to explain why.)
2. Choose one number that is a prime number up to 25 and one that isn't.
For each of them draw an arrow picture or a table using a few 'call out' numbers.
If you want to, you can play the game as you do it, like on the video, but remember to check your number of players two ways.
3. Make up your own clumping game question and try it out.

### Bob's Buttons Question

This is the question Bob made up when he was working with buttons as his pretend people.
Find the answer to Bob's challenge and explain it in your journal.

### Bob's Extra Challenges

When you have worked out the answer to Bob's question and explained it, watch this video and see what you think of Jamie and Jack's explanation.
They were in Year 5 when they made the video.

 Hint: They start off with groups of 5 and 1 left over. One of the groups of 5 is on the left page. But what do they end with? It works, but is it Bob's question? Could you explain to them how they could change groups of 5 with 1 left over to make the other part of Bob's challenge?

Bob knew something extra and he has given us clues.

• Why does the challenge say 'the smallest number of buttons' instead of just 'the number of buttons'?
• Why does it say that he had '...more than 10 buttons'?
Explore ... and record your experiments.

If you aren't sure about Bob's clues, there is a photo in the Answers & Discussion section that explains what happens if he had less than 10 buttons. But don't look ... unless your really, really can't figure it out for yourself.

If you don't have to just find the smallest number of players (buttons), then Bob's challenge has many answers.
One answer for the number of players is even smaller than the one in the boys' video and all the other answers are bigger.
• Make a list of the first ten (10) answers to Bob's question.
• Describe the pattern.
• What happens if Bob's question was groups of 3 with 2 left over and groups of 5 with 1 left over.
• If there is a pattern of answers, describe the pattern.
Now we have two pieces of data:
• If the 'call out numbers' are 4 & 5 with left overs of 2 & 1 there are many answers to the number of players and there is a counting pattern of ... between the answers.
• If the 'call out numbers' are 3 & 5 with left overs of 2 & 1 there are many answers to the number of players and there is a counting pattern of ... between them.
There is a way to predict the counting pattern number from the 'call out' numbers.
What is it?
Explain in your journal.
Mathematicians love Bob's Buttons question because it has more than one answer. They love it more because the answers make a pattern. They love it even more because they can ask 'what if' questions and find even more patterns.

### A New Challenge

Your new challenge is to find out more about what happens to the counting patterns when you change the group numbers or left over numbers.

A school resource called Maths300 provides free software that helps you explore Bob's Buttons.

• Click the link, then scroll down the page to find the software download files.
• The software works on Windows and Mac computers and some Windows tablets.
It does not work on phones or iPads.
• Ask your parents' permission and help before you download and install.
• Download to your desktop then double click to install.
• Click the program icon (green dart) to start the app.
• Choose Bob's Buttons from the home screen.
Bob's Buttons software has three options:
• Option 1
...is like the small table in the first video. It has a drawing of a 'playground'. You enter the number of players and they run onto the playground (as red plugs). Then you enter the group size, which is the 'call out' number. Press the spacebar to make the players form groups and find out the number left over. Make sure you predict what will happen before you press the space bar.
• Option 2
...allows you to test any 'class size' with any call out numbers and left overs. The results of the your experiments are recorded in an on-screen journal which you can screen capture if you want to.
• Option 3
...allows you to enter any Bob's Button question and set the computer to work automatically to find the pattern of answers (if there is one).
There are at least two ways to explore and the Maths300 software can help with both of them. You might need to use your 'players' to help you too.

### Design Your Own Investigation

Try some more What happens if...? questions and record your experiments. These questions might get you started.
• Is it true that the counting pattern number can always be predicted from the 'call out' numbers?
• Is it true that any two group numbers with their remainders produces solutions?
If not, what can you learn about the numbers that do give solutions?

A mathematician must be able to explain their discoveries to other mathematicians, so when you have finished finding out stuff, prepare a report of your discoveries. You might write a report, or make a slide show, or a video, or a poster or explain in some other way.

Or instead you can do this Bob's Buttons Project from Maths300 which was designed by a Year 7 teacher. It also asks you to report on your answers.

### Use Investigation Guides

These guides also all come from Maths300. The first two links take you to the site. The other two are PDF files from the site that were designed by a Year 7 teacher. Do at least one of these. When you have explored as many of the guides as you want, do this Bob's Buttons Project from Maths300 which was designed by a Year 7 teacher. Report on your answers.

### Just Before You Finish

Read your Working Like A Mathematician page again and write three or more sentences explaining how you worked like a mathematician.

### Answers & Discussion

 This photo shows that there is another solution to Bob's question about groups of 4 with 2 left over and groups of 5 with 1 left over. Copy and complete this sentence in your journal: If there are 6 players playing Bob's game they can ... Answers: Investigation Guides 1 & 2 The PDF Guides are similar questions to these and will have similar answers. After you write your own answers to the Bob's Buttons Project, you might like to look at Juliana's report, which is also from Maths300. If you were her teacher: what mark would you give her? what comments would you make to encourage her and help her learn more? These notes were originally written for teachers. We have included them to support parents to help their child learn from Bob's Buttons. Notes for Bob's Buttons You can also read more teachers' notes in the Maths300 Bob's Buttons sample lesson plan.

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Maths At Home is a division of Mathematics Centre