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# Probability

Children
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## An Investigation of Random Processes

This unit aims to provide students with an experience of randomness. This is done by a related set of activities that link large sequences of tossing coins, random walks, Pascal's Triangle, and probabilities that are a little too complicated for probability trees.

Children
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## Another Dartboard

Predict probabilities of an event involving area

Make deductions from probabilities

Devise and use problem solving strategies to explore situations mathematically (guess and check, be systematic, look for patterns, draw a diagram, make a table, think, use algebra).

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## Lara's Equiprobable Dice I

Find certain probabilities relating to rolling two dice

Devise and use problem solving strategies to explore situations mathematically (be systematic)

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## Probability Distributions

This unit aims to introduce students to concepts that are important in probability.The emphasis should be on working slowly taking the time to let the students grasp the ideas that underlie the activities presented. All the ideas are important as a base for future learning in this area of mathematics.

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## Slater Mazes

This is a level 5 statistics activity from the Figure It Out series.

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## Rough Justice

This is a level 5 statistics activity from the Figure It Out series.

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## Card Sharp

This is a level 5 statistics activity from the Figure It Out series.

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## Birth Months

This is a level 5 statistics activity from the Figure It Out series.

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## Fair Games

Many games of chance and activities in maths text books involve rolling two dice and combining the scores, usually by addition. Students often find the probabilities of such events difficult to calculate as they are confused between events (for example a score of 4) and outcomes (for example 3 and 1, 2 and 2, 1 and 3). This unit makes use of a variety of activities where the number of outcomes in the sample space is clearly different from the number of events.

Children
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## Make the Highest Total

theoretically and experimentally examine the probabilities of games of chance

devise and use problem solving strategies to explore situations mathematically (be systematic, use a table).

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## Probability Distributions

This unit aims to introduce students to concepts that are important in probability.The emphasis should be on working slowly taking the time to let the students grasp the ideas that underlie the activities presented. All the ideas are important as a base for future learning in this area of mathematics.

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## Number in Probability 1

These exercises, activities and games are designed for students to use independently or in small groups to practise number properties. Some involve investigation (see copymaster of investigation write up) and may become longer and more involved tasks with subsequent recording/reporting. Typically an exercise is a 10 to 15 minute activity.

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## Fair Games

Many games of chance and activities in maths text books involve rolling two dice and combining the scores, usually by addition. Students often find the probabilities of such events difficult to calculate as they are confused between events (for example a score of 4) and outcomes (for example 3 and 1, 2 and 2, 1 and 3). This unit makes use of a variety of activities where the number of outcomes in the sample space is clearly different from the number of events.

Children
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## Greedy Pig

This activity provides students with a fun game context in which to practice their addition skills. It also introduces concepts of probability.

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## Beat It

The purpose of this unit is to use games to gather and present data in a systematic way in order to determine the likely outcomes of some everyday events.

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## The Coloured Cube Question

Two red and two blue multi-link cubes are placed in a bag. The player takes out two cubes. If the player gets two red cubes they win. The unit looks at, analyses, and extends, this game of chance.

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Three coins are tossed. A player wins if two heads and a tail come up. The unit looks at, analyses, and extends, this game of chance.

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## Murphy's Law

In this unit, students will explore the commonly held belief that if anything bad can possibly happen it will and at the most inopportune time. They will be encouraged to look at events involving chance and predict the likelihood of certain outcomes by both trialling the event and analysing it theoretically. There is a lot of work in this unit so you might like to spread it over more than one week or do different parts at different times of the year. Some of the simulations are reasonably complicated so it may take students most of a lesson until they have come to grips with the rules involved.

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## Gambling- Who Really Wins?

In this unit we investigate the link between experimental and theoretical probability and learn about short run variability. We then take part in sports betting simulations designed to illustrate how damaging gambling can be.

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## Penny's Pizza

Make a list of possible outcomes as a method of finding probability

Express the outcome as a fraction

Devise and use problem–solving strategies to explore situations mathematically (make an organised list)

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## Wallowing Whales

This is a level 4 statistics activity from the Figure It Out series.

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## What's the Chance?

This is a level 4 statistics activity from the Figure It Out series.

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## Unlucky Lines

This is a level 4 statistics activity from the Figure It Out series.

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## Paper, Scissors, Rock

This is a level 4 statistics activity from the Figure It Out series.

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## Orders

This is a level 4 probability activity from the Figure It Out theme series.

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## Scratch, Text, and Win

This is a level 4 statistics activity from the Figure It Out series.

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## Gaming Choices

This is a level 4 statistics activity from the Figure It Out series.

Children
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## Top Drop

In this unit students play the game "Top Drop" which has them predicting the outcome of dropping a plastic drink bottle top. The outcome of each drop is recorded and used to develop an understanding of relative frequency and probability and to increase the likelihood of winning. The unit culminates in a "Top Drop" tournament where students use the knowledge and understanding they have gained during the unit.

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## Greedy Pig

This activity provides students with a fun game context in which to practice their addition skills. It also introduces concepts of probability.

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## Beat It

The purpose of this unit is to use games to gather and present data in a systematic way in order to determine the likely outcomes of some everyday events.

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## The Coloured Cube Question

Two red and two blue multi-link cubes are placed in a bag. The player takes out two cubes. If the player gets two red cubes they win. The unit looks at, analyses, and extends, this game of chance.

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## Gambling- Who Really Wins?

In this unit we investigate the link between experimental and theoretical probability and learn about short run variability. We then take part in sports betting simulations designed to illustrate how damaging gambling can be.

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## Bubblegum balls

Identify the possible outcomes of an event

Write a rule for the pattern

Interpret information and results in context (logic, be systematic)

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## Dominoes

Apply counting strategies to the case of dominoes

Write an explanation of what they have done

Devise and use problem solving strategies to explore situations mathematically (be systematic, make a list, use a diagram).

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## The Clumsy Tiler S

Use a pattern to count in a geometrical situation.

Devise and use problem solving strategies to explore situations mathematically (make a drawing, use equipment).

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## Breakfast Biscuits

This unit seeks to connect learning outcomes across all five content strands, number, geometry, statistics, and measurement. However the context lends itself strongly to use of measurement and statistics. In the unit students investigate questions that involve them in experiment design, data collection and display, and drawing conclusions from data. Students investigate the measurements of breakfast biscuits, how much milk they absorb, how strong they are and the hidden truth about collecting cards.

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## Random Numbers

These exercises, activities and games are designed for students to use independently or in small groups to practise random number properties. Some involve investigation (see Related Resources) and may become longer and more involved tasks with subsequent recording/reporting. Typically an exercise is a 10 to 15 minute independent activity.

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## More No three in a line

This activity has a logic and reasoning focus.

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## Thirsty Work

These are level 4 number, algebra and statistics problems from the Figure It Out series.

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## Lining Up

These are level 4 number and statistics problems from the Figure It Out series.

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## Left to Chance

This is a level 4 statistics activity from the Figure It Out series.

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## Take Five

This is a level 3 and 4 statistics activity from the Figure It Out series.

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## Picking Pocket Money

This is a level 3 and 4 statistics activity from the Figure It Out series.

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## Crossing the Line

This is a level 3 and 4 statistics activity from the Figure It Out series.

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## The Unit Fraction Game

This is a level 3 and 4 statistics activity from the Figure It Out series.

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## Dylan's Dominoes

This is a level 3 and 4 statistics activity from the Figure It Out series.

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## Monster Munch

This is a level 4 statistics activity from the Figure It Out series.

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## Catch of the Match

This is a level 4 statistics activity from the Figure It Out series.

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## Across the River

This is a level 4 statistics activity from the Figure It Out series.

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## Wallowing Whales

This is a level 4 statistics activity from the Figure It Out series.

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## Dodgy Dice

This is a level 4 statistics activity from the Figure It Out series.

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## What's the Chance?

This is a level 4 statistics activity from the Figure It Out series.

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## Game Show

This is a level 4 statistics activity from the Figure It Out series.

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## On a Plate

This is a level 4 statistics activity from the Figure It Out series.

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## Paper, Scissors, Rock

This is a level 4 statistics activity from the Figure It Out series.

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This is a level 4 probability and masurement activity from the Figure It Out theme series.

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## Free CD!

This is a level 4 statistics activity from the Figure It Out series.

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## Pedal Power

This is a level 4 activity from the Figure It Out series.

Children
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## What's in the bag?

In this unit we experiment with cubes to make predictions about likelihood based on our observations. With these experiences the students find out that with probability there is no way of knowing for sure that will happen.

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## I'm Spinning

This week we use spinners to develop our understanding of the probability of simple events occurring.

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## Counting on Probability

This week we investigate ways of systematically counting all the possible outcomes of an event. One approach that we focus on is the use of tree diagrams.

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## Predict away

In this unit we take samples of blocks from a bag and use them to make predictions about the blocks that the bag actually contains. The students learn that although we can't be 100% certain we can use the information that we gather from sampling to make reasonable predictions.

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## Long Running

In this unit we take samples of blocks from a bag and use them to make predictions about the blocks that the bag actually contains. We discuss the difference between theoretical and experimental probabilities.

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## Spinners

This unit uses one of the digital learning objects, Spinners, to support students as they explore probability. It includes problems and questions that can be used by the teacher when working with a group of students on the learning object, and ideas for independent student work.

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Three coins are tossed. A player wins if two heads and a tail come up. The unit looks at, analyses, and extends, this game of chance.

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## Murphy's Law

In this unit, students will explore the commonly held belief that if anything bad can possibly happen it will and at the most inopportune time. They will be encouraged to look at events involving chance and predict the likelihood of certain outcomes by both trialling the event and analysing it theoretically. There is a lot of work in this unit so you might like to spread it over more than one week or do different parts at different times of the year. Some of the simulations are reasonably complicated so it may take students most of a lesson until they have come to grips with the rules involved.

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## Dressing In The Dark

Work systematically to identify all the possible outcomes.

Describe events using everyday language.

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## Grabbing CDs

Systematically count outcomes

Compare the likelihood of events

Devise and use problem solving strategies to explore situations mathematically (systematic list, draw a picture, use equipment).

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## Coin Shake-Up

Predict the likelihood of an event based on data collected

Use a systematic approach to find all possible outcomes

Effectively plan mathematical exploration

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## Houses

This unit seeks to connect learning outcomes across all five content strands, number, geometry, statistics, algebra, and measurement.  The context of houses is used to develop concepts such as drawing and modelling 3-dimensional objects, using co-ordinate systems to locate position, finding all the possibilities of events, and identifying paths through simple networks.  The unit provides an excellent vehicle for students to use a broad range of problem solving strategies.

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## No Three In a Line

This activity has a logic and reasoning focus.

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## Join the Queue

These are level 3 number and statistics problems from the Figure It Out series.

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## Home Sweet Home

These are level 3 number, algebra, and statistics problems from the Figure It Out series.

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## Teething Problems

These are level 3 number, geometry, and statistics problems from the Figure It Out series.

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## Numbers in Disarray

These are level 3 number, measurement, and statistics problems from the Figure It Out series.

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## Power to the People

These are level 3 statistics problems from the Figure It Out series.

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## Slippery Solutions

These are level 3 number and statistics problems from the Figure It Out series.

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## All Sorts

These are level 3 x problems from the Figure It Out series.

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## Darting for Cover

These are level 3 number and statistics problems from the Figure It Out series.

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## Over a Barrel

These are level 3 algebra and statistics problems from the Figure It Out series.

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## Mixing Fruit

These are level 3 statistics, geometry, algebra, and number problems from the Figure It Out series.

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## To the Wire

These are level 3 number, geometry, and statistics problems from the Figure It Out series.

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These are level 3 number and statistics problems and level 4 algebra problems from the Figure It Out series.

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## Out for the Count

These are level 3 statistics, geometry, algebra, and number problems from the Figure It Out series.

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## Going Around

These are level 3 number, statistics, and algebra problems from the Figure It Out series.

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## Round Robins

These are level 3 number and statistics problems and level 5 number problems from the Figure It Out series.

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## Waste Not ...

These are level 3 probability and level 4 number problems from the Figure It Out series.

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## Investment Choices

This is a level 4 number activity from the Figure It Out series. It relates to Stage 7 of the Number Framework. It is also a level 3 statistics activity.

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## Investing on the Share Market

This is a level 4 number activity from the Figure It Out series. It relates to Stage 7 of the Number Framework. It is also a level 3 statistics activity.

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## Alana, the Online Entrepreneur

This is a level 3 number and statistics activity from the Figure It Out series. It relates to Stage 6 of the Number Framework.

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## Savings Ups and Downs

This is a level 3 number, algebra, and statistics activity from the Figure It Out series. It relates to Stage 6 of the Number Framework.

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## Spending Spurge

This is a level 3 number activity from the Figure It Out series. It relates to Stage 6 of the Number Framework.

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## Sneaky Snakes

This is a level 3 statistics activity from the Figure It Out series.

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## Which When?

This is a level 3 statistics activity from the Figure It Out series.

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## Scratch 'n' Win

This is a level 3 statistics activity from the Figure It Out series.

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## Superbeans

This is a level 3 statistics activity from the Figure It Out series.

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## Dicey Differences

This is a level 3 statistics activity from the Figure It Out series.

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## Take Five

This is a level 3 and 4 statistics activity from the Figure It Out series.

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## Picking Pocket Money

This is a level 3 and 4 statistics activity from the Figure It Out series.

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## Crossing the Line

This is a level 3 and 4 statistics activity from the Figure It Out series.

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## The Unit Fraction Game

This is a level 3 and 4 statistics activity from the Figure It Out series.

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## Dylan's Dominoes

This is a level 3 and 4 statistics activity from the Figure It Out series.

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## Fish Fair

This is a level 3 probability activity from the Figure It Out theme series.

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## Horse Racing

This is a level 3 probability and level 2 number activity from the Figure It Out theme series.

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## Pick the Place

This is a level 3 probability activity from the Figure It Out theme series.

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## Luck of the Draw

This is a level 3 probability activity from the Figure It Out theme series.

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## Pass it On!

This is a level 3 statistics activity from the Figure It Out theme series.

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## Spin to Win!

This is a level 3 statistics activity from the Figure It Out series.

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## Using Resources and Classifying Resources

This is a level (3+ to 4+) mathematics in science contexts activity from the Figure It Out series.

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## A Very Improbable Story

This is an activity based on the picture book A Very Improbable Story

Children
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## The Cube and Coin Challenges

In this unit we play several games based on coloured cubes and coins. The idea is to get some idea of the relative rate at which things happen and think about the concept of a fair game.

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## That's not fair!

In this unit we play probability games and learn about sample space and a sense of fairness

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## Three Coins on a Table

Distinguish between more and less likely events

List the possible outcomes

Devise and use problem solving strategies to explore situations mathematically (be systematic, draw a diagram).

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## Tony's Spelling Troubles

Describe in their own words the situation represented in a bar chart and tally chart

Use a bar chart and tally chart to make sensible predictions.

Interpret information and results in context

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## How Many Ice Creams?

Find all the possible outcomes of a simple event using a problem solving strategy (draw, act with objects, list)

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## Three In A Line

This activity has a logic and reasoning focus

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## Money-making Mice

This is a level 2 number and statistics and level 3 algebra activity from the Figure It Out series. It relates to Stage 5 of the Number Framework.

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## Way to Go

This is a level 2 statistics activity from the Figure It Out series.

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## In Between

This is a level 2 statistics activity from the Figure It Out series.

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In this unit students make spinners to show the probability of events. They will make statements about probabilities shown on spinners and evaluate statements made by other classmates.

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This is a level 2 statistics activity from the Figure It Out series.

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## Patent Problems

This is a level 2 activity from the Figure It Out series.

Children
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## No way Jose

In this unit we develop the language of probability by considering events which are likely or unlikely. We do this using the context of children's stories.

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## Lonely Pig

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. The activities in this unit are games that involve following rules, making predictions and seeing what happens.

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## Who Plays What?

Use words to describe the likelihood of events.

Use logical reasoning to solve a problem.

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## Strawberry Milk

This unit has a logic and reasoning focus.

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## Strawberry Milk

This activity has a logic and reasoning focus.

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## Strawberry and Chocolate Milk

This activity has a logic and reasoning focus.

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## Probably Pistachio

This is an activity based on the picture book Probably Pistachio