## Billiard Ball Maths Project

Over the last few weeks in project maths we have done the billiard ball activity.

In this activity you are on a pool table and there is no middle pockets. The ball will always start from the bottom left corner. The first thing that we had to do was guess how many times the ball would bounce before going in, but with a twist each bounce has to be on a 45 degree angle. Sometimes this could be quite challenging because if you did not quite get it straight then your whole grid would be stuffed up and you will most likely not get the correct answer.

This was very hard to just guess the exact pocket that it would go into so we started to look for patterns and strategy’s. I found a lot of different patterns but they were only to predict one number such as a 1 by 1 grid or a 5 by 8 grid size. Some of my patterns were…..

3 by …..= The answer is one more then the second number except for 3 by 3 because for every 1st and 2nd number that is the same it will always equal 0. And much more

After having a think about different patterns we then started to think about one formula that will work to predict every single pocket! This was very challenging. I started to do this by guessing and checking. I then checked with the teacher and he said that I got the two part correct. I just did not know what to do with the 2, I just knew to use one in the end formula.

This helped me a lot because then I started to think about everything I could do with a 2.

After re grouping with the class I worked out what the formula was…..

You need to simplify both numbers or half them as much as you can but both the same amount. You can also not go into minus numbers or decimals. Once you have done that the most that you can you add the width and the length together and -2. For example……

10 by 8= simplify down to 5 by 4 is the most you can do now 5+4=9-2=7 which is your answer.

I think this was challenging to find the formula because you needed to test so many different things and then you would finally get it. Below is some of my working out.

## Building views

This term in maths we have been working on building little buildings with blocks and then we had to look at them from the side, front and record it.

Sheet 1:

This is the 1st sheet that we got given. It has one big 4 by 4 grid to make the buildings on and below it had the example shape [floor plan] that you had to make.

To make it you had to put the same amount of blocks stacked up on each other as it said, that’s what the numbers mean. Then look at number one and make it on the 4 by 4 grid. We needed to kneel down to see it from the same level just to be sure i then drew the pattern made out of blocks, you just drew the biggest amount of blocks stacked up on each other for each row. Which looked like this.

We did this for 4 buildings. There is 5 buildings.  For the last building we did not make it we just had to visualise it in our head. I thought both were quite easy because you just had to look at the side and front then record it. It did take a while.

Sheet 2:

Next we were given sheet 2. Sheet 2 looks like this. You got the option to make it with blocks or you could just visualise it, but I made some of them.

It already showed us what the blocks looked like so we had to map out where they were using a [floor plan]. We had to make each one with 15 blocks. This was a lot more challenging because it was reversed so we had to make the map of where they went and that showed us what the patter was. My strategy was to start with how ever many blocks were in the left column then just put them in the front row then I would do the same for all rows. I then looked at the side view and moved some back according to the biggest number in both the side and front view. Next I just added in some more blocks where ever, making sure that they were no higher than the highest stacked up row. I made this equal 15. This is what I did for all four buildings.

I continued doing this except we had to put as many blocks as we could and the least amount of blocks. I found the least amount of blocks hardest because you had to take blocks away while moving them so they could become less.

Then we had to start back at 15 blocks and move as many blocks as we could, these are called variations. This was very had because sometimes I forget if I had already put one some where. To record this I just had a tally at the bottom of my page instead of drawing them all.

Finally we played around with this on our laptops using maths 300 soft wear. Using maths 300 we could do the same thing. Here is a photo of it.

Overall I liked doing this activity and it got more challenging as we went through the different sheets.

## Win at the fair Maths

Lesson 1

Today in project maths we started a new unit/game. It is called Win at the fair. The original game board looks like this…

The game has different vales of money that you can win. You roll 2 dies and you either go up, left or right. The aim of the game is to obviously win as much money as you can.

Our first job was just to play the original game. We did this for at least half of the session. But we did not just keep playing for no reason we recorded all of the results from every game as a class. As a class we ended up playing 83 games. We then made a little tally. To play the game it costed one dollar so we had already made \$83 but then this happened.

We ended up losing lots of money, we did not earn any money we lost money. We lost \$117.00 witch is way way to much. We then had a group chat about every thing we could change to inshore we would make money not lose money. We worked out that the original game board was losing money but we wanted to pull in money.

In one day we want 1,000 games to be played. We want to give out \$700 and make at least \$300. We then brainstormed a list of everything that we could change to make sure we did not lose money. Below is the list.

• Less difference between the prizes
• Lower the jackpot.
• Switch some of the prize locations.
• Expand the size of the board.
• Change the playing price.
• Remove some prize tiles / no prizes for some spaces?
• Special moves like ‘snake eyes moves two spaces’ or a tile that makes you go backwards.
• Change the rules of the dice
• Dramatic money change!

Lesson 2

Today we started to make our own new and improved game board. My first game board looks like this.

As you can see I changed…

•  Money prizes
• I changed the direction of the numbers when you roll them. For example if 4 was going left I changed it to straight up.
• I lowed the jackpot
• I switched some of the prize locations
• I removed some of the prize tiles, so that you don’t get any prize money

I then tested my 1st changed game board and these were the results…

As you can see in my results I made \$546.50 exactly, and I played 1,000 games. Well I didn’t the computer did it for me I then wanted to test it again with exactly the same game board. Below the 2nd results are…

In the 2nd lot of results I made \$561.40. The second time I made more money witch is a good thing. I then decided to test it one more time and these were the results…

In the last test I did I made \$550.4. So that means that my second test I made the most money. I then decided to make another game board, it is below.

As you can see I changed…

• The money values so that you always got some money

I will now show the results.

As you can see in the results I made \$424.3. Sadly I did not take a picture of my second test for that game board. I did not earn more money with that game board but I think more people would want to play that game because you can not get no prize. Below is my final game board.

In this game board I kept the arrows the same but I changed the 10c and the 30c so that you would still win money but I would win more. Here are the first lot of results

As my results show I made \$581.9. So far this is the most amount of money that I have made. I also think that this game board looks inserting and people would want to play it. Below are my last results.

As you can see above I made \$546.4. This is a good amount but not very consistent compared to the other results.

The second last game is the game that I being the game owner earned the most money. I think I should go with the last game board. Overall I liked this activity it was challenging but also fun.

## Magic Squares

The last two lessons we have been working on magic squares. The first thing we did was try to guess what they are, according to the picture above. After a little while of thinking we worked out that each line up and down, diagonal and across all equal the same thing in this case they equal 34. These magic numbers also are a four by four grid.

Our first challenge was to make our own magic numbers using a three by three grid,  and we were only allowed to use the numbers 1, 2, 3, 4, 5, 6, 7, 8 and 9.  We also worked with a partner. One of the first things we did was the equation 45÷3 = 15.

We did this because 1 through to 9 equals 45. We then divided it into  three parts because there are three rows up and down. The answer was 15.  This means that each column has to add up to 15 in total. After that we just played around with making each coloum equal 15. When we were playing around with having 15 in each row we noticed a pattern that you couldn’t have 1, 7 and 4 in the same line if you did it did not work, but we’re still not sure why it didn’t work.

I think the most challenging thing was when we made the up-and-down columns equal 15 but the diagonal rows did not work. Also the opposite way round happened as well.

The main strategy that we used in the past few lessons were guess and check, break it into smaller problems so that we could find the answer to the bigger problem. After this we regrouped as a class and talked about the problem. Someone said that they found the answer when they had a five in the middle. We then went back and tried this idea and we found the answer. Although we have only found one answer there are seven more.

Myself and my partner where only looking for unique solutions because we did not know that you are allowed to have the same answer just in different places so in the end we ended up getting three answers one was unique and the other two were not. If you look in my book there is more info about my awnsers. Over all I really enjoyed this problem because it was changeling, but when we got the awnsers it was fun.

## Maths Spinner B

Today in Maths we were focusing on spinner B. Above is a picture of spinner B. In spinner B, B has half and all of the other letters have an equal amount. We had to spin spinner B forty times. Below is a picture of my results.

In this picture it shows my results. I then made a pie chart with my results. My pie chart does not really look like the original spinner. This is not because I did not spin it correctly it is because the mathematic probability is not always the same as the experimental probability. We then combined the whole classes results and made a pie chart.

Overall there were 721 spins. There was only supposed to be 720 spins, this means someone did one extra spin. Because I only did 40 spins it did not show the overall result. The more spins that we did the closer and even it got to looking like the real spinner or pie chart. This is because people did not all have the same spins. When we combined all of the results I was quite surprised because I did not think it would look similar. Mine was very different compared to the class results.

Overall I really liked doing this activity because we got to spin spinners lots of times and we also got to make pie charts. I really like pie charts.

## Spinners

Today in maths we started a new topic. We were given three little circles/ spinners. On the back they said: Fair, Unfair and Unfair copy.

We then had to get a green pencil and colour and rule the fair spinner into how ever many parts we wanted. We had to make sure that they were all even. Then we coloured in some of those parts, making sure that there was an even amount of parts coloured in. Then we cut it out neatly. Here is a picture of my fair spinner.

In this picture there is a 50 percent chance of getting each colour. That means that there is an even chance of the spinner landing on the green or the white. We then did the unfair circle. Here is a picture of my Unfair spinner.

In this picture there is a 80 percent chance that the spinner will land on the white and there is only 20 percent chance of green. Our next task was to make another copy of our unfair spinners because one will go up on the wall.

Before we could do anything else we had to write a guess down about how many times we thought our spinner would land on each colour. I thought there was a one in 9 chance of the spinner landing on green. We then had to find a spinner and put our unfair spinner inside it. We then had to spin it 10 times and see if your guess was correct.

My guess was correct. If you spin your spinner a few times it could change the outcome. We then had to do the same thing again so that we could see if there was any difference. The second time I tested it, it did not even land on the green at all. Below is a picture of my book and the chart I made

The top chart is my first try and the bottom chart is my second try. Once we had done that we were given two spinner circles. Below is a picture of spinner A and B.

We than had to think about all of the different things about spinner A and spinner B. Here is a picture of what we thought about the spinners.

It was quite hard to think of all of those ideas. But some were easy. We then thought about how many times A, B,C ,D and E will come up. On spinner A I thought: A= 10, B= 10, C= 10, D= 5 and E= 5. For spinner B I thought: A= 10, B= 20, C= 5, D= 4 and E= 1. We then had to spin each spinner 40 times and make a graph so we knew the results. Below are pictures of graph A and B.

In graph A: A= 8, B= 7, C= 10, D= 9 and E= 6. This is not what I thought would happen but it was around 8 most of the time so I was close. In graph B: A= 5, B= 23, C= 4, D= 5 and E= 3. I was very surprised with some of these results because they we very different compared to the other results I got in graph A.

We then combined all of our results together for graph A and also made a pie chart.

Overall I have really enjoyed this maths task and I learnt a lot. I have also done a lot of thinking that I would have not normally done. I hope that in the future we will get to do more of this kind of maths.

## Why we should not leave kids or pets in cars on hot days

In maths we have been learning about the surface area, volume and square meters. By doing this we made mathematic models of child named [little Jo]. We made him out of square blocks. Below is a picture of little Jo.

We then had to work out what his volume was. Volume= 10. I knew there is ten because I counted the legs= 4, then the arms= 2, then the body= 3 and the head 1. 4+2+3+1= 10. We then did the surface area. Surface area= 42. I know this because there is ten faces on the front and back. 10+10= 20. Then I counted the sides there was 10. 10+10=20. Plus the top of the head and the bottom =2. 20+20=2= 42.

We then made a bigger Jo below is a picture of him and the Little Jo.

For each of Little Jo’s unit of volume there is two times as much surface area for evaporation than big Jo. That is why we should not leave babies\kids and pets in the car for too long. Below is a table that tells you the exact measurements.

 Headings Volume Surface Area Comparison Little Jo 10 42 1 to 4 Big Jo 80 168 1   to 2

## Usain Bolt

Today in maths we watched a video of a race in Rio. It was the 100m Mens race.

We were trying to calculate the length of one of Usain Bolts steps in the 100 metre race. Above is a video of the race. When Usain Bolt runs he does not breath! Usain Bolt only takes 41 steps. Below is a picture of one step. He takes 41 of these steps.

It takes me two big steps just to do his one step. We calculated the distance of his step. It was

metres

We got to use the calculator and entered the distance of the race, divided by 41 steps and got the answer. It would take me about 82 steps to run this race and I would have the breathe.

## Four Cube Houses

In maths we have been making four cube houses. These were the rules we were given.

We had to find out how many houses we could make. I think there are 15 possible answers or houses.

To find all the possible answers we had to flip houses in diffrent directions. Once you had thought about all of the possible answers you needed to look closer. By doing this you had to flip houses. If you did this it could make another house or it might not. Here is a picture of all 15 houses that we made.

The houses are in groups. The groups mean we have flipped all of them or turned them upside down. Most of the houses are in twos but there is one house with one and four houses with four. From doing this activity I have leant alot. You need to see or look at the individual houses to see if they can be flipped or made in other ways. Sometimes you need to look harder you might need to turn it around our flip it.