The focus of this activity is on learning the steps a mathematician takes when they find a problem that interests them.
## PreparationG'day young mathematician.You are just starting this problem, so you really don't know what you need yet. Some stuff you could have around just in case might be: - Objects like a collection of plastic screw caps that can be used to represent things in the problem.
- Blank paper and markers for drawing and doodling as you think through the problem.
- A piece or two of this Square Line Paper.
always need when you are learning to work like a mathematician are:
- The Working Mathematically page. Printing it for this activity is probably best.
- Your Maths Journal with the name of the activity and today's date.
That's what happens in your Maths Journal.
These are the steps in solving
Have fun exploring The Farmer's Puzzle
while you are learning to work like a mathematician.
- What did she do?
*She bought some animals. Right?*- Sure, but what was special about how she spent her money?
## 2. Plan A StrategyIf you have a pen in your hand you will start doing something before you have planned what to do. Sit on your hands if you have to. - Read through the strategy toolbox on the Working Mathematically page.
- Which strategies do you think might work? - guess & check or make a model or draw a diagram or make a table or write an equation or ...?
- When you choose one, what will be the first thing you do when you are allowed to pick up a pen?
Okay. If you know where you are going to start... ## 3. Do ItPick up a pen or anything else you need and start.- Starting is all a mathematician can do.
- They know what they are aiming for
- buy 100 animals and spend $100 - but they don't know how they will get there or how long it will take to get there. - If they did ... it wouldn't be a problem.
## 4. Check & ReflectCheckSo you spent $100 and you know how many of each animal and there are a total of 100 animals. You should be right, but...
- Can you check your answer another way?
Reflect - Is there another solution? If not, how can you be sure? If so, how can you be sure you have found them all?
- What happens if the problem is still 100 animals and 100 dollars, but the prices are different?
- Is 100 such a special number? Could a similar problem be constructed with say 80 animals for $80. How about for other numbers?
## Just Before You FinishPrepare a report for your colleagues to explain what the problem is and how you solved it. Perhaps you could make a video with your phone.
## Answers & DiscussionHint: Is there anything special that must be true about the number of hens?That's it. That's all you get. If you haven't figured it out yet come back another time and have another go. Or work with a partner. Almost all the mathematics invented since the middle of last century has been by a team of two or more. Send any comments or photos about this activity and we can start a gallery here.
Maths At Home is a division of Mathematics Centre |