## Preparation- A large piece of paper or four A4 pieces and sticky tape
- At least ten (10) small objects like pebbles, pasta, blocks or...
- Write the title of this challenge and today's date on a fresh page in your maths journal.
## The StoryAinsley was asked to try this problem when she was home schooling with Grampa in Year 3.The story on the teacher's slides went something like this: - Dad's three (3) children liked to help in the garden.
- They were 7 years old, 6 years old and 5 years old.
- Dad thought they would learn more about gardening by looking after their own plants.
- He said he would buy them one (1) plant for each year of their age. The children thought that was a fun idea.
- So they packed a picnic lunch and went to a big plant nursery.
- At the nursery Dad discovered he only had enough money for ten plants.
"Mmm" said Dad. "Let's sit under that big gum tree over there and have our picnic while I think about what we can do." ## First Thoughts- Think about Dad's situation.
- He doesn't want to disappoint the kids.
- In your journal write or draw any suggestions that might help Dad.
## Aha! MomentAt the picnic spot the oldest child could see that Dad was a bit sad because he couldn't afford to keep his promise."It's okay Dad. We don't mind. Just get ten plants and we can share looking after them."That helped Dad relax a bit. He started thinking as he opened up the picnic backpack and began passing out the lunch.
## Challenge 2Grampa suggested to Ainsley (the real one) that a mathematician might start wondering if there was another way to do it."What do you mean?"Ainsley started moving the blocks around on the drawing. She tried other numbers of blocks in the middle. Each time the middle ones were the only ones shared. Your challenge is to: - Try 1, 2 and 3 in the middle as
__the only ones shared__. - Explain in your journal what Ainsley found out.
When she finished Grampa said, "But you only tried numbers less than four. What happens if you try numbers bigger than four in the middle and they are the only ones shared?"So she tried this one. Then she stopped.
## Challenge 4Ainsley's solution in Challenge 3 has two plants in the middle.There is another way to do it with two in the middle. Find a different solution with two in the middle. ## Challenge 5Now we have a problem with three correct answers so far:- 4 plants in the middle ... 1 answer
- 2 plants in the middle ... 2 answers
- How many solutions are there?
- How do I know that I have found them all?
Mathematicians don't expect to answer questions like this in one day. They would probably leave their drawing, blocks and some scribble paper on the table and come back to look for more answers when they could. Your challenge is to keep on looking for solutions until you know that there can't be more.
## Just Before You FinishThe only reason for tackling this problem is to practise working like a mathematician. And you can prove that you have been.It doesn't matter how many solutions you found, even if it was zero, follow these steps to discover how you were working like a mathematician. - Print this Working Like A Mathematician page.
- Read every line carefully and tick anything on the page that you were doing or thinking during the problem.
- When you have finished stick it in your journal with the heading:
**I worked like a mathematician when I...**
## Answers & DiscussionChallenge 1
Then the rest was easy. And she didn't need to use all the areas.
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