- How many different ways can your three cars be parked in your three garages?
- Record your ways in your journal.
- How do you know when you have found them all?
- Explain your thinking in words and pictures.
## The Next Challenge- Open this Cars In A Garage Starter. You can read it on screen or print it.
- You have already done Question 1.
Your challenge now is to try Question 2. - Remember to keep good notes and diagrams in your journal.
Have fun exploring Cars In A Garage.
When you have written your own journal you can look at some journals from the Year 4 class that made the videos.
Note: If your school is a member of Maths300, your teacher can provide software that will help you explore Cars In A Garage.You can stop the activity here if you want to ... or you can take yourself to the next level. ## The Big ChallengeThe challenge on the Starter has two parts.The first part is to try five cars in five garages. - Find a method to calculate the number of ways without having to draw them all?
- Explain your calculation to someone else.
- It might be too hard to find the exact number. It's pretty big.
- What the challenge really wants you to do is
*explain how*to do it.
## Digging DeeperCalculating the 100 Challenge- There are 100 cars that could go in the first garage.
- Choose 1, then there are 99 left that could go in the next garage.
- Choose 1, then there are 98 left that could go in the next garage.
- And so one until there is only one car left and that has to go in the last garage.
- In fact the first car could be different 100 times.
- Which means the second car could be different 99 times.
- And the third car could be different 98 times.
- And so on...
100 x 99 x 98 x 97 ... 4 x 3 x 2 x 1 = ???Try it on your ordinary calculator. Can you get all the way? - Describe what happens.
- Describe what happens.
A mathematician is never finished with a problem. - What happens if there are 3 cars and 4 garages? How many ways to park?
- What happens if there are 4 cars and 4 garages, but the green car
*must always be*in the left garage? - What happens if there are 4 cars and 4 garages, but the red and the blue
*must not be*beside each other?
## Just Before You Finish- In your journal explain what parts of this activity you liked and why you liked those parts.
- Does this activity make you think of something you want to learn better, or perhaps something new you want to know?
## Answers & DiscussionThese journals are all answering Questions 1 & 2 about three cars and four cars.These notes were originally written for teachers. We have included them to support parents to help their child learn from Cars In A Garage. - Notes for Cars In A Garage.
Send any comments or photos about this activity and we can start a gallery here.
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