# Probability

How do weathermen and women predict the weather? How can you tell if an earthquake is going to happen soon?

There is no exact way to do any of these things. But there is a way to make an educated guess. You have to watch and observe collected data over a period of time to see if you can spot any patterns, and then try to predict what will happen next.

You will now need your math journal and a pencil.

To warm up your brain into a pattern finding mode, find the next few numbers in these number pattern problems. Copy each problem into your journal, and fill in the blanks. Write down at the very end of your pattern what the rule is for each problem.

E.g. – 1, 3, 5, 7, 9, 11, 13,   15   ,   17  ,    19    .  ( +2)

1)  1, 5, 9, 13, 17, 21, 25, ______ , ______ , ______ .
2)  88, 108, 128, 148, 168, 188, 208, ______ , ______ , ______.
3)  115, 109, 103, 97, 91, 85, 79, ______ , ______ , ______.
4)  6, 10, 14, 18, 22, 26, 30, ______ , ______ , ______.
5)  672, 622, 572, 522, 472, 422, 372, ______ , ______ , ______.
6)  23, 34, 45, 56, 67, 78, 89, ______ , ______ , ______.
7)  1, 3, 7, 15, 31, 63, 127, ______, ________, _________.

# Probability – using die

You will now have a go at watching and observing collected data to see if you can spot any patterns.

First you need to collect some data!

You will need two dice, a pencil, and a copy of this sheet (also below)  Rolling dice game chart

You will be rolling the dice 20 times. You will be recording how many of each number (the total of both dice) you get using tally marks. You will do this a total of four times. The objective is to notice an patterns and trends, and see if you get better at predicting the numbers you will roll in only 20 rolls.

Make some agreements as to how you will proceed if you are working in pairs (e.g. how many rolls you will each take, who will record, etc… ). Then :-

• In the first grey column predict how many of each number you think you will get
• Then actually roll the dice 20 times. Record what you get using tally marks.

When you are done, see how good you were at predicting by comparing your prediction and the actual numbers you got. Try to get better in the next three times you do this. Here is the second half of the ‘Rolling dice game chart’.

Reflection

1. How easy was it to learn from the data?
2. How good were you at predicting? Did you get any better in the 2nd, 3rd, and 4th roll? Why/why not?
3. What were some of the problems you had while doing this activity?
4. If you had to do this again, how would you improve it?

# The Brownie Conundrum

‘Here they all are!’ I shouted. I saw my nine friends coming up the drive way. It was my very first sleepover that night, and Mum and me had made lots of delicious snacks to eat.

Everyone piled in and we immediately went to the kitchen and demanded food.

Mum put a tray of brownies on the table. She had already cut the tray of brownies into nine perfect pieces (about 7cm x 7cm / 3″ x 3″). We all immediately saw the problem.

‘Mum! There are ten of us!’ I said.

‘Ooops!’ she said. ‘I don’t have anymore ingredients to bake another one, and all the shops are closed now.’

After a while she said, ‘How can we fix this so that everyone gets a fair share of brownies?’

We all thought about it, and couldn’t figure it out, so we decided to ask YOU for help. How would you make sure that everyone got an equal share of brownies?

Remember… it is very important that everyone gets AN EQUAL share of the brownies, otherwise someone will cry about it!

1. Work in pairs – you have to prove that your idea works!
2. Use any manipulatives or pieces of paper you need to help you prove your thinking  to work out this conundrum .
3. Use the correct language of fractions and mathematics when explaining what you and your partner did.
4. Make a new post on your blog. Give it the title ‘The Brownie Conundrum’. Put it in the Mathematics category. Tag it as fractions and brownies
5. Your post must include a written explanation, and a conclusion that begins with the sentence – ‘Each person gets ….. of a brownie’.
6. As you are working it all out take photos of your work, and include them in your blog post

# Fractions in action

You will need: –

1. Several cubes
3. a pencil
4. coloured pencils

# Fraction vocabulary

Ha! I bet you thought that you should only learn spelling and do vocabulary words when writing stories, hey?

Well…. WRONG!!!!

LOL

You will need your math journals, a pencil to write with, your ruler, and some coloured pencils.

LIST OF WORDS

half      halves     thirds      quarters      fifths       sixths      eighths      tenths twelfths    sixteenths     numerator       denominator   whole

1. Use the PYRAMID WORD strategy to learn the above fraction vocabulary
2. Next to each pyramid, draw a quick sketch that clearly shows the fraction word you are working with
3. Write this work in your journal in a list
4. Draw a line using your ruler after each one.

E. g.

# Ben the Gardner wants to make more money! – Part 1

Ben the Gardner leaned on his shovel and looked at his garden. He recently had made quite a lot of money by selling the beautiful flowers he grew in his garden. In fact, he had made 2,130 rmb. It had been his friend’s Bill the Baker’s advice.

Now Ben wondered if he could make even more money! But he didn’t quite know how to organize his garden. He still had his garden split into 100 squares like this.

He wanted to earn about four times as much as he did last time. His friend Bill came over and sat beside him. They talked for a few minutes, and then Bill gave Ben an idea how to solve his problem.

What do you think? How would you solve this problem? What advice do you think Bill gave Ben?

When you are good to go…. click the arrow….

# Ben the Gardner wants to make more money! – Part 2

This is what Bill and Ben came up with. Ben would plant four flowers in each square. This would give him 400 flowers! Of course he had no way of knowing what colour the flowers would be when they grew.

This is what happened.

You will need to work in pairs for this next part. You will need an A3 sheet of paper, and some pencils. NO calculators!

1. How many red flowers are there?
2. How many orange flowers are there?
3. How many yellow flowers are there?
4. How many pink flowers are there?
5. How many purple flowers are there?
6. How many blue flowers are there?
7. If you add all these flowers up, what is your total? Is that correct?

If you’re good to go…. click the arrow……

# Ben the Gardner wants to make more money! – Part 3

Are you ready to talk fractions?

1. What fraction of the garden are 400 flowers? Do you know of any other way to write this?
2. What fraction of the flowers are blue? Do you know of any other way to write this?
3. What fraction of the flowers are orange? Do you know of any other way to write this?
4. What fraction of the flowers are yellow? Do you know of any other way to write this?
5. What fraction of the flowers are purple? Do you know of any other way to write this?
6. What fraction of the flowers are pink? Do you know of any other way to write this?
7. What fraction of the flowers are red? Do you know of any other way to write this?

Now write your thoughts about what you have just done and what you have just found out about fractions.

If Ben sells each flower for the following prices, how much does he earn altogether?

1 red flower = 15 rmb

1 yellow flower = 25 rmb

1 purple flower = 37 rmb

1 orange flower = 24 rmb

1 pink flower – 18 rmb

1 blue flower – 12.50 rmb

# The gardener and the mixed up flowers.

Ben the Gardener looked at his garden. He always managed to grow beautiful flowers and plants. He had a Talent for this. A friend of his, Bill the Baker, suggested that he grow flowers and sell them to people. Ben thought this would be a good idea. So he planned how many flowers to grow.

He had a large growing garden that he could use to grow the plants from seeds.

He split this garden into 100 equal boxes.

In each box he planted a flower. But he had no way of knowing what colour the flowers would be when the grew! This is what he saw when the flowers grew.

Bill the Baker asked what fraction of the garden each colour was. But Ben could not answer him! He knew he had 100/100 flowers. (He also knew that this was 100%, or a whole garden)

He stood in front of his flowers and wondered how to answer Bill. How would you answer Bill? Work with a partner to figure out what fraction of the garden Ben had grown of each colour.

———————————————————–

If Ben sells each flower for the following prices, how much does he earn altogether?

1 red flower = 15 rmb

1 yellow flower = 25 rmb

1 purple flower = 37 rmb

1 orange flower = 24 rmb

1 pink flower – 18 rmb