### Circle Fireworks

Lets start this maths lesson with a game. Play Circle Fireworks a few times and see how many points you can score. Good luck!

### How Scoring Works

What did you notice about the game? Did you notice that circles leave the screen after 8 wall bounces? Did you notice that larger circles score more points than smaller ones? Did you notice that hitting a circle makes it score more points afterwards?

To improve your score, you really need to fully understand how the scoring system works. There are five sizes, 1 is the smallest and 5 is the largest. When a size 1 cirlce hits a wall it scores 1 point and when a size 5 circle hits a wall it scores... 5 points!

Pretty simple huh? But wait, there's more! If you hit a cirlce with your beachball, then all it's future wall bounces get ** double** points. If you hit it again than all future bounces get

**points etc.**

*triple*### How Many Points?

Look at the first example. How many points would this size 3 circle score for you? First it hits the wall (3 points), next it hits the beachball (x2 bonus), and finally it hits the top wall (2x3 points).

Let's write this as a number sentence: 3 + 2 x 3 = ? With number sentences, we have to be careful and always do multiplication and division before addition and subtraction (otherwise we will get the wrong answer - check for yourself!) So it becomes 3 + 6 = 9 points.

Can you work out the score of the next two pictures?

### Winning Strategy

Now you understand the scoring. What sort of strategy would score the highest? Play the game agian to test out your thinking. You can also compete against your friends.

### Night Version

Time to make the game even better. For starters the game will take place at night. Secondly, to give you more reward for keeping a circle on the screen, a circle's value now increases by 1 every time it touches the wall. So, to show the same example as before, it becomes 3 + 2 x (3 + 1). Notice how we had to add brackets around addion we wanted done ** before** the multiplication. Another way we could write this would be 3 + 2 x 3 + 2 x 1, because we want to double both the circles value (2) and the bonus score (1). Can you work out what the three earlier examples would score now? You can play the new version here.

### How Many Circles?

Have you noticed that each set of circles in the game is bigger than the last? Look at the example sets in the diagram. Can you work out what the pattern is?

The game code calculates how many circles are needed in each set using the formula ** setNumber x ? + ?**, can you work out what numbers to replace the question marks with?

There are 8 sets of circles in the game. How many circles appear in total?

### Final Challenge

If you are really feeling confident, your final challenge is to work out the highest possible score that could * ever* be achieved (your choice which version of the game). Imagine a game where every piece of luck went your way. All the balls were size 5, and you somehow managed to get the maximum score from each ball (remember balls leave the playing area after 8 wall bounces). What would your score be?