Purpose

In this unit we have a first look at uncertainty and chance. We begin to develop an intuitive sense of what chance and possibilities are about through games that involve following rules, making predictions and seeing what happens.

Specific Learning Outcomes

- Use everyday language to talk about chance.
- List outcomes of simple events.

Description of Mathematics

Although students at this level won't be ready to fully grasp the idea of chance they will develop some valuable intuitive notions. Underlying the activities is the idea that some events can be influenced by information, whereas others rely largely on luck. This provides the basis for the two ways of determining probabilities: theoretically and experimentally. Later on we explore certain situations such as rolling dice, using spinners, choosing cards to determine precise values of probability. This is the theoretical aspect. Ideally you would always like to do this as you are then sure exactly what the probability is. However, in other situations we have to rely on a series of experiments and deduce the likely probability of an event through the long-term frequency of its occurrence. This applies to the kind of events that insurance companies are interested in such as the likelihood of an accident or the length of life of a 30 year old male.

Required Resource Materials

- Resealable sandwich-size plastic bags to store cards
- Animal cards

Activity

Today we make our own set of cards using pictures of cats and dogs.

- Give each pair of students 20 cards. You might like to use the cats and dogs from Copymaster 1. Otherwise you will need to direct the students to draw cats on 10 of the cards and dogs on the other 10.
- When the students have completed their pack of cards demonstrate a game of Cats and Dogs.
**Rules**

Shuffle the cards.

Put the cards face down in one pile.

Players decide who will collect same pairs and who will collect different pairs.

Take turns turning a card from the top of the pile.

Compare the two cards. If they are the same, the player collecting same pairs takes them. If they are different, the other player takes them.

The game continues until all cards are used.

The winner is the player who collects the most cards.- After the students have played a few games lead a discussion highlighting their observations about the chances of winning.
*Was one of the players luckier than the other one? What made you think this?*

How many times did you win?

How many times did your partner win?

Was it better to be a same or a different? Why?

(note: The probability of different pairs is slightly greater than that of same pairs.)

Today we add 6 mice to our pack of cat and dog cards and play the game again.

- Give the pairs 6 blank cards to draw the mice or use the mice from Copymaster 1. Add the mice to the pack of 20 cats and dogs used in session one.
- Play the same pairs and different pairs game from yesterday.
- After the students have played a few games lead a discussion highlighting their observations about the chances of winning.
*Was one of the players luckier than the other one? What made you think this?*

How many times did you win?

How many times did your partner win?

Was it better to be a same or a different? Why?

Was it easier to win today? Why/Why not?

Today we add one pig to our pack of cats, dogs and mice and play a new game.

- Give each pair one pig card to add to their set.
- Explain that today we are using the cards to play animal memory.

Rules

Spread the cards out face down.

Players take turns to turn over two cards.

If the cards are the same the player keeps the pair of cards but does not have another turn.

If the cards are different the cards are turned back face down.

Continue taking turns until all the cards (except the pig) are collected. - As the students play the game ask questions that focus on the likelihood of finding pairs.
*What card do you think you will turn up next? Why do you think that?*

Which cards do you think will be last?

Which are the hardest pairs to find? Why?

Which are the easiest pairs to find?

What can you tell me about the pig?

Why do you think the game is called The little lost pig?

Can you think of another name for our game?

- Wooden cubes with two of the faces red, two blue and two green (dot stickers work well)
- Pictures of 3 cats from Copymaster 2
- Pictures of fish cut outs from Copymaster 3 (30 per page)
- Felt pens (colours to match the dots)

In this activity the students roll a dice to feed fish to our three cats. The students will investigate the chance of giving a fish to their cat.

- Give groups of 3 students the three cat pictures, a prepared dice and 30 fish.
- Each student chooses one of the three colours for their cat and colours it in (single colour only).
- The students play Greedy cat

Rules

The students take turns rolling the dice.

The student whose colour shows gives their cat a fish.

The game continues with players taking turns until all the fish are eaten. - After allowing the students to play the game(s), discuss:
*Which coloured cat got the most fish?*

Was there a lucky colour in your group?

Was it lucky in all the groups? Why/Why not?

- Dice 1: 5 blue faces representing the greedy cat, one red face for the second cat.
- Dice 2: 3 blue faces, 3 red faces.
- Copymaster 3 of Fish Cut Outs (30 per page)
- Copymaster 4 of blue greedy cat and red greedy cat

In this game the students experiment with different dice.

- Read the book
*Greedy Cat is Hungry*(from the Ready to Read series) - Discuss Greedy Cat’s need for food.
- Give pairs the two cat pictures, the prepared dice and 20 fish.

Rules

The students take turns first selecting and then rolling one of the dice.

They give a fish to the cat whose colour is shown.

The game continues with players taking turns until all the fish are eaten. - After allowing the students to play the game(s), discuss:
*Which cat got the most fish?*

Was there a lucky colour in your group? Why?

Was it lucky in all the groups? Why/Why not? - Now pose a problem for the students.
*In the game we want to stop Greedy Cat from yowling for food. What should we do?*(Check that the students understand that they need to feed Greedy Cat to stop him yowling.) - Send the students away to explore the problem as they play the game.
- After allowing the pairs time to explore the solution and share their thinking about the problem.

Home Link

Dear Parents and Whānau,

This week we have been learning about probability by playing games. As we have played the games we have thought about how likely it is to get certain things. Your child will bring home one of our copies of * Little Lost Pig.* As you play the game you could help your child by asking questions that focus on the likelihood or chance of finding pairs. What card do you think you will turn up next? Why do you think that? Which cards do you think will be last? Which are the hardest pairs to find? Why? Which are the easiest pairs to find? What can you tell me about the pig? Why do you think the game is called The little lost pig? Can you think of another name for our game?

Rules for * Little Lost Pig*.

- Spread the cards out face down.
- Players take turns to turn over two cards. If the cards are the same the player keeps the pair of cards but does not have another turn. If the cards are different the cards are turned back face down.
- Continue taking turns until all the cards (except the pig) are collected.

We hope that together you enjoy playing * Little Lost Pig*.

Attachments

lonely-pig-1.pdf344.75 KB

lonely-pig-2.pdf97.95 KB

lonely-pig-3.pdf193.61 KB

lonely-pig-4.pdf86.93 KB