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# Probability

## S6-3: Investigate situations that involve elements of chance: comparing discrete theoretical distributions and experimental distributions, appreciating the role of sample size; calculating probabilities in discrete situations.

Teaching resources for this Achievement Objective:

## An Investigation of Random Processes

• Units of Work
• Statistics
• Level Six

In this unit students are provided with experiences 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.

## S5-4: Calculate probabilities, using fractions, percentages, and ratios.

Elaboration on this Achievement Objective:

This means that students will calculate probabilities for probability situations that involve two or more events.  These events may be independent (for example rolling two dice, or tossing two coins) or dependent (for example drawing two cards from a deck of cards without replacement, or choosing to students from the class at random).  They will be able to model these situations using models such as tree diagrams, tables and systematic lists and assign theoretical probabilities as proportions using fractions, percentages and ratios, for example the odds of winning the game are 2:3.

Students should also be able to estimate probabilities given results of sufficient trials. Such estimates are always approximate, and require use of equivalent proportions, for example an experiment results in a ratio of 43 blue: 79 red. An estimate of the probability of red is 2/3 or 67%.

Teaching resources for this Achievement Objective:

## Another dartboard

• Problem solving activities
• Statistics
• Level Five
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).

## Lara's equiprobable dice I

• Problem solving activities
• Statistics
• Level Five
Find certain probabilities relating to rolling two dice
Devise and use problem solving strategies to explore situations mathematically (be systematic)

## Probability Distributions

• Units of Work
• Statistics
• Level Five

This unit introduces students to concepts that are important in probability, including the probability function. All the ideas are important as a base for future learning in this area of mathematics.

## Slater Mazes

• Figure It Out activities
• Statistics
• Level Five

This is a level 5 statistics activity from the Figure It Out series.
A PDF of the student activity is included.

## Rough Justice

• Figure It Out activities
• Statistics
• Level Five

This is a level 5 statistics activity from the Figure It Out series.
A PDF of the student activity is included.

## Card Sharp

• Figure It Out activities
• Statistics
• Level Five

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

## Birth Months

• Figure It Out activities
• Statistics
• Level Five

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

## Fair Games

• Units of Work
• Statistics
• Level Five

This unit explores a variety of activities where the number of outcomes in the sample space is clearly different from the number of events. Students learn to see the difference between events (for example a score of 4) and outcomes (for example 3 and 1, 2 and 2, 1 and 3).

## That's the way the cookie crumbles

• Rich learning activities
• Statistics
• Level Five

The purpose of this multi-level task is to engage students in an investigation that leads to the comparison of experimental probability, with a theoretical probability.

## Risk it for a Ticket?

• Rich learning activities
• Statistics
• Level Five

The purpose of this task is to engage students in calculating a combined probability and using this to solve a problem.

## Probability Distributions

• Units of Work
• Statistics
• Level Five

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.

## Flooding likely?

• Number and Algebra
• Level Five

The purpose of this unit is to integrate student learning in the mathematics and social sciences learning areas.

## S5-3: Compare and describe the variation between theoretical and experimental distributions in situations that involve elements of chance.

Elaboration on this Achievement Objective:

Students at Level Five understand that elements of chance have an effect on the certainty of results from surveys or experiments. Through examples from real life they should understand that statistics usually involves situations where the actual probabilities are not known, for example, probability of catching a disease. They should recognise situations where deterministic theoretical models are not possible, for example chance of a bus being early, and distinguish them from situations where probabilities can be reasoned from all the possibilities.
This means that students will identify the theoretical probabilities for situations involving chance by using proportions of possible outcomes.  For example, they will recognise that the probability of rolling an even number on a standard die is 1/2 because there are 6 possible outcomes and 3 of them are even, 3/6 = 1/2.

They will carry out experiments to test the probability of events and compare their results with theoretical probabilities. They will understand that some variation between experimental estimates of probability and theoretical probabilities is normal, for example, when rolling a die 10 times they will not usually roll an even number 5 of the times.  They will understand that a larger sample is likely to provide a more accurate theoretical probability, proportionally speaking, than a small one.

Students will also understand that the results of past trials in probability experiments do not impact on future events, for example the fact that an even number has been rolled three times in a row does not make it more likely that the fourth roll will be an odd number.

Teaching resources for this Achievement Objective:

## Make the highest total

• Problem solving activities
• Statistics
• Level Five
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).

## Probability Distributions

• Units of Work
• Statistics
• Level Five

This unit introduces students to concepts that are important in probability, including the probability function. All the ideas are important as a base for future learning in this area of mathematics.

## Number in Probability 1

• Secondary activities
• Statistics
• Level Five

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.

## Fair Games

• Units of Work
• Statistics
• Level Five

This unit explores a variety of activities where the number of outcomes in the sample space is clearly different from the number of events. Students learn to see the difference between events (for example a score of 4) and outcomes (for example 3 and 1, 2 and 2, 1 and 3).

## That's the way the cookie crumbles

• Rich learning activities
• Statistics
• Level Five

The purpose of this multi-level task is to engage students in an investigation that leads to the comparison of experimental probability, with a theoretical probability.

## Probability Distributions

• Units of Work
• Statistics
• Level Five

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.

## Flooding likely?

• Number and Algebra
• Level Five

The purpose of this unit is to integrate student learning in the mathematics and social sciences learning areas.

## S4-4: Use simple fractions and percentages to describe probabilities.

Elaboration on this Achievement Objective:

Simple fractions and percentages in this objective are common benchmarks like one half (50%), thirds (33.3% and 66.6%), quarters (25% and 75%), fifths (20%, 40%, 60%, 80%), tenths (10%, 30%, etc). Students should know that outcomes that are certain are described by fractions equalling one, including 100%, and outcomes that are impossible are described by fractions equalling zero, including 0%. In contrived situations involving elements of chance, for example totalling two dice, students should know that the count of all possible outcomes gives the denominator of a probability fraction, for example 36 possible outcomes, and the number of desired outcomes gives the numerator, for example there are 9 ways to get a total of either 2,4 or 6 so the probability is 9/36 or 1/4 . In realistic situations where probabilities are estimated, for example the chance of a drawing pin landing safe, students are expected to accept variation from an exact fraction, for example 37 out of 100 were safe which is about or 33.3%.

Teaching resources for this Achievement Objective:

## Greedy Pig

• Units of Work
• Statistics
• Level Four

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

## Beat It

• Units of Work
• Statistics
• Level Four

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.

## The Coloured Cube Question

• Units of Work
• Statistics
• Level Four

This unit looks at, analyses and extends a game of chance. 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.

• Units of Work
• Statistics
• Level Three

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

## Murphy's Law

• Units of Work
• Statistics
• Level Three

In this unit, students explore the commonly held belief that if anything bad can possibly happen it will and at the most inopportune time. They are encouraged to look at events involving chance and predict the likelihood of certain outcomes by both trialling the event and analysing it theoretically.

## Gambling- Who Really Wins?

• Units of Work
• Statistics
• Level Four

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

## Penny's Pizza

• Problem solving activities
• Statistics
• Level Four
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)

## Wallowing Whales

• Figure It Out activities
• Statistics
• Level Four

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

## What's the Chance?

• Figure It Out activities
• Statistics
• Level Four

This is a level 4 statistics activity from the Figure It Out series.
A PDF of the student activity is included.

## Unlucky Lines

• Figure It Out activities
• Statistics
• Level Four

This is a level 4 statistics activity from the Figure It Out series.
A PDF of the student activity is included.

## Paper, Scissors, Rock

• Figure It Out activities
• Statistics
• Level Four

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

## Orders

• Figure It Out activities
• Statistics
• Level Four

This is a level 4 probability activity from the Figure It Out theme series.
A PDF of the student activity is included.

## Scratch, Text, and Win

• Figure It Out activities
• Statistics
• Level Four

This is a level 4 statistics activity from the Figure It Out series.
A PDF of the student activity is included.

## Gaming Choices

• Figure It Out activities
• Statistics
• Level Four

This is a level 4 statistics activity from the Figure It Out series.
A PDF of the student activity is included.

## Deliveries

• Rich learning activities
• Statistics
• Level Four

The purpose of this activity is to engage students in solving a problem involving probability, proportional reasoning and expected number, within context.

## New Turf

• Rich learning activities
• Statistics
• Level Four

The purpose of this activity is to engage students in solving a probability problem using both theoretical and experimental (modelling) methods.

## Cubic Conundrums

• Number and Algebra
• Level Four

To provide a set of learning tasks that integrate across the strands of the New Zealand Mathematics Curriculum and provide opportunities for assessment of student achievement across those strands. Each session may involve more than one lesson, especially if students need more time to become proficient at the tasks.

## Figure me out

• Units of Work
• Number and Algebra
• Level Four

This unit is designed to engage your class for at least the first week of the school year. It provides students an opportunity to work collaboratively and independently on challenging mathematical tasks. It also provides you, their teacher, with opportunities for you to learn about their current level of achievement.

## S4-3: Investigate situations that involve elements of chance by comparing experimental distributions with expectations from models of the possible outcomes, acknowledging variation and independence.

Elaboration on this Achievement Objective:

This means students will understand that probability is about the chance of outcomes occurring. At Level Four students should recognise that it is not possible to know the exact probability of something occurring in most everyday situations, for example the probability of someone being left-handed. They should understand that trialling must be used to gain information about the situation and that the results of trial samples vary, for example different samples of 100 people will have different proportions. Contrived chance events are used to highlight the variation between expected outcomes from models, and experimental outcomes from trialling. Level Four students are expected to use systematic methods such as listing, tree or network diagrams with equally likely outcomes, and tables to find all the possible outcomes of simple one or two stage situations such as tossing two coins, drawing counters from a bag, or rolling two dice. Students should compare the distributions they get from trialling with the expectations obtained from models, accepting variation between samples and that the results of one sample do not impact on the next (independence), for example take samples of twenty counters, with replacement, from a bag that has one-half red, one-third blue and one-sixth yellow. Accept that an eight red, seven blue, and five yellow result is natural and that it will not be compensated by the next sample.

Teaching resources for this Achievement Objective:

## Top Drop

• Units of Work
• Statistics
• Level Four

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.

## Greedy Pig

• Units of Work
• Statistics
• Level Four

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

## Beat It

• Units of Work
• Statistics
• Level Four

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.

## The Coloured Cube Question

• Units of Work
• Statistics
• Level Four

This unit looks at, analyses and extends a game of chance. 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.

## Gambling- Who Really Wins?

• Units of Work
• Statistics
• Level Four

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

## Bubblegum

• Problem solving activities
• Statistics
• Level Four
Identify the possible outcomes of an event
Write a rule for the pattern
Interpret information and results in context (logic, be systematic)

## Dominoes

• Problem solving activities
• Statistics
• Level Four
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).

## The clumsy tiler C

• Problem solving activities
• Statistics
• Level Four
Use a pattern to count in a geometrical situation.
Devise and use problem solving strategies to explore situations mathematically (make a drawing, use equipment).

## Breakfast Biscuits

• Units of Work
• Geometry and Measurement
• Level Four

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.

## Random Numbers

• Secondary activities
• Statistics
• Level Four

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.

## More no three in a line

• Problem solving activities
• Geometry and Measurement
• Level Four

This activity has a logic and reasoning focus.

## Thirsty Work

• Figure It Out activities
• Number and Algebra
• Level Four

These are level 4 number, algebra and statistics problems from the Figure It Out series.
A PDF of the student activity is included.

## Lining Up

• Figure It Out activities
• Number and Algebra
• Level Four

These are level 4 number and statistics problems from the Figure It Out series.
A PDF of the student activity is included.

## Left to Chance

• Figure It Out activities
• Statistics
• Level Four

This is a level 4 statistics activity from the Figure It Out series.
A PDF of the student activity is included.

## Take Five

• Figure It Out activities
• Statistics
• Level Three

This is a level 3 and 4 statistics activity from the Figure It Out series.
A PDF of the student activity is included.

## Picking Pocket Money

• Figure It Out activities
• Statistics
• Level Three

This is a level 3 and 4 statistics activity from the Figure It Out series.
A PDF of the student activity is included.

## Crossing the Line

• Figure It Out activities
• Statistics
• Level Three

This is a level 3 and 4 statistics activity from the Figure It Out series.
A PDF of the student activity is included.

## The Unit Fraction Game

• Figure It Out activities
• Number and Algebra
• Level Three

This is a level 3 and 4 statistics activity from the Figure It Out series.
A PDF of the student activity is included.

## Dylan's Dominoes

• Figure It Out activities
• Statistics
• Level Three

This is a level 3 and 4 statistics activity from the Figure It Out series.
A PDF of the student activity is included.

## Monster Munch

• Figure It Out activities
• Statistics
• Level Four

This is a level 4 statistics activity from the Figure It Out series.
A PDF of the student activity is included.

## Catch of the Match

• Figure It Out activities
• Statistics
• Level Four

This is a level 4 statistics activity from the Figure It Out series.
A PDF of the student activity is included.

## Across the River

• Figure It Out activities
• Statistics
• Level Four

This is a level 4 statistics activity from the Figure It Out series.
A PDF of the student activity is included.

## Wallowing Whales

• Figure It Out activities
• Statistics
• Level Four

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

## Dodgy Dice

• Figure It Out activities
• Statistics
• Level Four

This is a level 4 statistics activity from the Figure It Out series.
A PDF of the student activity is included.

## What's the Chance?

• Figure It Out activities
• Statistics
• Level Four

This is a level 4 statistics activity from the Figure It Out series.
A PDF of the student activity is included.

## Game Show

• Figure It Out activities
• Statistics
• Level Four

This is a level 4 statistics activity from the Figure It Out series.
A PDF of the student activity is included.

## On a Plate

• Figure It Out activities
• Statistics
• Level Four

This is a level 4 statistics activity from the Figure It Out series.
A PDF of the student activity is included.

## Paper, Scissors, Rock

• Figure It Out activities
• Statistics
• Level Four

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

• Figure It Out activities
• Statistics
• Level Four

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

## Free CD!

• Figure It Out activities
• Statistics
• Level Four

This is a level 4 statistics activity from the Figure It Out series.
A PDF of the student activity is included.

## Pedal Power

• Figure It Out activities
• Statistics
• Level Four

This is a level 4 activity from the Figure It Out series.
A PDF of the student activity is included.

## Family Feast

• Figure It Out activities
• Statistics
• Level Four

This is a level 4 statistics activity from the Figure It Out series.
A PDF of the student activity is included.

## New Turf

• Rich learning activities
• Statistics
• Level Four

The purpose of this activity is to engage students in solving a probability problem using both theoretical and experimental (modelling) methods.

## Lucky Sausages

• Rich learning activities
• Statistics
• Level Four

The purpose of this activity is for students to set up and run a simple probability simulation and to compare their experimental value of probability with the theoretical value.

## Cubic Conundrums

• Number and Algebra
• Level Four

To provide a set of learning tasks that integrate across the strands of the New Zealand Mathematics Curriculum and provide opportunities for assessment of student achievement across those strands. Each session may involve more than one lesson, especially if students need more time to become proficient at the tasks.

## Figure me out

• Units of Work
• Number and Algebra
• Level Four

This unit is designed to engage your class for at least the first week of the school year. It provides students an opportunity to work collaboratively and independently on challenging mathematical tasks. It also provides you, their teacher, with opportunities for you to learn about their current level of achievement.

## S3-3: Investigate simple situations that involve elements of chance by comparing experimental results with expectations from models of all the outcomes, acknowledging that samples vary.

Elaboration on this Achievement Objective:

This means students will understand that probability is about the chance of outcomes occurring. At Level Three students should recognise that it is not possible to know the exact probability of something occurring in most everyday situations, for example the chance of a day in March being fine. They should understand that trialling must be used to gain information about the situation and that the results of trial samples vary, for example March 2008 is likely to be different from March 2009. Contrived chance events are used to highlight the variation between expected outcomes from models, and experimental outcomes from trialling. Level Three students are expected to use systematic methods such as listing, tree diagrams with equally likely outcomes, or tables to find all the possible outcomes of simple situations such as tossing coins, drawing cards, or rolling dice. They should accept that experimental samples from those situations, for example tossing a coin ten times, vary from one another, and from the proportions expected from a model, that is, most times five heads do not come up.

Teaching resources for this Achievement Objective:

## What's in the bag?

• Units of Work
• Statistics
• Level Three

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.

## I'm Spinning

• Units of Work
• Statistics
• Level Three

In this unit we use spinners to develop our understanding of the probability of simple events occurring.

## Counting on Probability

• Units of Work
• Statistics
• Level Three

In this unit we investigate ways of systematically counting all the possible outcomes of an event. One approach is to use tree diagrams.

## Predict away

• Units of Work
• Statistics
• Level Three

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.

## Long Running

• Units of Work
• Statistics
• Level Three

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 probability and experimental estimates of probability.

• Units of Work
• Statistics
• Level Three

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

## Murphy's Law

• Units of Work
• Statistics
• Level Three

In this unit, students explore the commonly held belief that if anything bad can possibly happen it will and at the most inopportune time. They are encouraged to look at events involving chance and predict the likelihood of certain outcomes by both trialling the event and analysing it theoretically.

## Dressing in the dark

• Problem solving activities
• Statistics
• Level Three
Work systematically to identify all the possible outcomes.
Describe events using everyday language.

## Grabbing CDs

• Problem solving activities
• Statistics
• Level Three
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).

## Coin shake-up

• Problem solving activities
• Statistics
• Level Three
Predict the likelihood of an event based on data collected
Use a systematic approach to find all possible outcomes
Effectively plan mathematical exploration

## Houses

• Units of Work
• Geometry and Measurement
• Level Three

This unit seeks to connect learning outcomes, and provide problem solving opportunities 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.

## No three in a line

• Problem solving activities
• Geometry and Measurement
• Level Three

This activity has a logic and reasoning focus.

## Join the Queue

• Figure It Out activities
• Number and Algebra
• Level Three

These are level 3 number and statistics problems from the Figure It Out series.
A PDF of the student activity is included.

## Home Sweet Home

• Figure It Out activities
• Number and Algebra
• Level Three

These are level 3 number, algebra, and statistics problems from the Figure It Out series.
A PDF of the student activity is included.

## Teething Problems

• Figure It Out activities
• Statistics
• Level Three

These are level 3 number, geometry, and statistics problems from the Figure It Out series.
A PDF of the student activity is included.

## Numbers in Disarray

• Figure It Out activities
• Statistics
• Level Three

These are level 3 number, measurement, and statistics problems from the Figure It Out series.
A PDF of the student activity is included.

## Power to the People

• Figure It Out activities
• Statistics
• Level Three

These are level 3 statistics problems from the Figure It Out series.
A PDF of the student activity is included.

## Slippery Solutions

• Figure It Out activities
• Number and Algebra
• Level Three

These are level 3 number and statistics problems from the Figure It Out series.
A PDF of the student activity is included.

## All Sorts

• Figure It Out activities
• Geometry and Measurement
• Level Three

These are level 3 x problems from the Figure It Out series.
A PDF of the student activity is included.

## Darting for Cover

• Figure It Out activities
• Number and Algebra
• Level Three

These are level 3 number and statistics problems from the Figure It Out series.
A PDF of the student activity is included.

## Over a Barrel

• Figure It Out activities
• Number and Algebra
• Level Three

These are level 3 algebra and statistics problems from the Figure It Out series.
A PDF of the student activity is included.

## Mixing Fruit

• Figure It Out activities
• Statistics
• Level Three

These are level 3 statistics, geometry, algebra, and number problems from the Figure It Out series.
A PDF of the student activity is included.

## To the Wire

• Figure It Out activities
• Number and Algebra
• Level Three

These are level 3 number, geometry, and statistics problems from the Figure It Out series.
A PDF of the student activity is included.

• Figure It Out activities
• Number and Algebra
• Level Three

These are level 3 number and statistics problems and level 4 algebra problems from the Figure It Out series.
A PDF of the student activity is included.

## Out for the Count

• Figure It Out activities
• Statistics
• Level Three

These are level 3 statistics, geometry, algebra, and number problems from the Figure It Out series.
A PDF of the student activity is included.

## Going Around

• Figure It Out activities
• Number and Algebra
• Level Three

These are level 3 number, statistics, and algebra problems from the Figure It Out series.
A PDF of the student activity is included.

## Round Robins

• Figure It Out activities
• Number and Algebra
• Level Three

These are level 3 number and statistics problems and level 5 number problems from the Figure It Out series.
A PDF of the student activity is included.

## Waste Not ...

• Figure It Out activities
• Statistics
• Level Three

These are level 3 probability and level 4 number problems from the Figure It Out series.
A PDF of the student activity is included.

## Investment Choices

• Figure It Out activities
• Number and Algebra
• Level Four

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.
A PDF of the student activity is included.

## Investing on the Share Market

• Figure It Out activities
• Number and Algebra
• Level Four

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.
A PDF of the student activity is included.

## Alana, the Online Entrepreneur

• Figure It Out activities
• Number and Algebra
• Level Three

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

## Savings Ups and Downs

• Figure It Out activities
• Number and Algebra
• Level Three

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.
A PDF of the student activity is included.

## Spending Spurge

• Figure It Out activities
• Number and Algebra
• Level Three

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

## Sneaky Snakes

• Figure It Out activities
• Statistics
• Level Three

This is a level 3 statistics activity from the Figure It Out series.
A PDF of the student activity is included.

## Which When?

• Figure It Out activities
• Statistics
• Level Three

This is a level 3 statistics activity from the Figure It Out series.
A PDF of the student activity is included.

## Scratch 'n' Win

• Figure It Out activities
• Statistics
• Level Three

This is a level 3 statistics activity from the Figure It Out series.
A PDF of the student activity is included.

## Superbeans

• Figure It Out activities
• Statistics
• Level Three

This is a level 3 statistics activity from the Figure It Out series.
A PDF of the student activity is included.

## Dicey Differences

• Figure It Out activities
• Statistics
• Level Three

This is a level 3 statistics activity from the Figure It Out series.
A PDF of the student activity is included.

## Take Five

• Figure It Out activities
• Statistics
• Level Three

This is a level 3 and 4 statistics activity from the Figure It Out series.
A PDF of the student activity is included.

## Picking Pocket Money

• Figure It Out activities
• Statistics
• Level Three

This is a level 3 and 4 statistics activity from the Figure It Out series.
A PDF of the student activity is included.

## Crossing the Line

• Figure It Out activities
• Statistics
• Level Three

This is a level 3 and 4 statistics activity from the Figure It Out series.
A PDF of the student activity is included.

## The Unit Fraction Game

• Figure It Out activities
• Number and Algebra
• Level Three

This is a level 3 and 4 statistics activity from the Figure It Out series.
A PDF of the student activity is included.

## Dylan's Dominoes

• Figure It Out activities
• Statistics
• Level Three

This is a level 3 and 4 statistics activity from the Figure It Out series.
A PDF of the student activity is included.

## Fish Fair

• Figure It Out activities
• Statistics
• Level Three

This is a level 3 probability activity from the Figure It Out theme series.
A PDF of the student activity is included.

## Horse Racing

• Figure It Out activities
• Statistics
• Level Three

This is a level 3 probability and level 2 number activity from the Figure It Out theme series.
A PDF of the student activity is included.

## Pick the Place

• Figure It Out activities
• Statistics
• Level Three

This is a level 3 probability activity from the Figure It Out theme series.
A PDF of the student activity is included.

## Luck of the Draw

• Figure It Out activities
• Statistics
• Level Three

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

## Pass it On!

• Figure It Out activities
• Statistics
• Level Three

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

## Spin to Win!

• Figure It Out activities
• Statistics
• Level Three

This is a level 3 statistics activity from the Figure It Out series.
A PDF of the student activity is included.

## Using Resources and Classifying Resources

• Figure It Out activities
• Number and Algebra
• Level Four

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

## A Very Improbable Story

• Picture book activities
• Statistics
• Level Three

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

## Penalty shoot-out

• Rich learning activities
• Statistics
• Level Three

The purpose of this activity is to engage students in running an experiment to determine a probability and compare this with the results of similar practical situations.

## 5+ a Day

• Statistics
• Level Three

The purpose of this activity is to engage the students in finding an experimental probability and using this to model the outcome of a given scenario.

## Combos

• Units of Work
• Number and Algebra
• Level Three

This unit introduces students to combinations as a situation type that multiplicative thinking can be applied to.

## S2-3: Investigate simple situations that involve elements of chance, recognising equal and different likelihoods and acknowledging uncertainty.

Elaboration on this Achievement Objective:

This means students will recognise that probability is about the chance of outcomes occurring. Through activities that involve them personally, students at Level Two are expected to consider the possible outcomes of events in predicting what might occur. Through carrying out experiments, for example playing a game of chance, and making simple models of all the outcomes, for example lists or tables, students should recognise when outcomes appear to be equally likely, for example getting an even number when tossing a dice. Students should also recognise that where an event has more than one possible outcome they cannot predict the outcome with certainty, for example "it probably won’t be a six but it might be" when rolling a dice. Students should relate probability to events in their daily life, for example "it is very likely to rain today".

Teaching resources for this Achievement Objective:

## The Cube and Coin Challenges

• Units of Work
• Statistics
• Level Two

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

## That's not fair!

• Units of Work
• Statistics
• Level Two

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

## Three coins on a table

• Problem solving activities
• Statistics
• Level Two
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).

## Tony's spelling troubles

• Problem solving activities
• Statistics
• Level Two
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

## How Many Ice Creams?

• Problem solving activities
• Statistics
• Level Two
Find all the possible outcomes of a simple event using a problem solving strategy (draw, act with objects, list)

## Three in a line

• Problem solving activities
• Geometry and Measurement
• Level Two

This activity has a logic and reasoning focus

## Money-making Mice

• Figure It Out activities
• Number and Algebra
• Level Two

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.
A PDF of the student activity is included.

## Way to Go

• Figure It Out activities
• Statistics
• Level Two

This is a level 2 statistics activity from the Figure It Out series.
A PDF of the student activity is included.

## In Between

• Figure It Out activities
• Statistics
• Level Two

This is a level 2 statistics activity from the Figure It Out series.
A PDF of the student activity is included.

• Units of Work
• Statistics
• Level Two

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.

• Figure It Out activities
• Statistics
• Level Two

This is a level 2 statistics activity from the Figure It Out series.
A PDF of the student activity is included.

## Patent Problems

• Figure It Out activities
• Statistics
• Level Two

This is a level 2 activity from the Figure It Out series.
A PDF of the student activity is included.

## Rolling Dice

• Rich learning activities
• Statistics
• Level Two

The purpose of this activity is to engage students in finding an expected number that is based on equally likely outcomes.

## Where's bunny now?

• Rich learning activities
• Statistics
• Level Two

The purpose of this activity is to engage students in evaluating another’s judgement about the fairness of a game of chance and investigating the fairness of their own game.

## Mathematical Magic

• Units of Work
• Number and Algebra
• Level Two

This unit provides you with a range of opportunities to assess the entry level of achievement of your students.

## S1-3: Investigate situations that involve elements of chance, acknowledging and anticipating possible outcomes.

Elaboration on this Achievement Objective:

This means students will consider the possible outcomes of events. Possible outcomes can be listed, for example when tossing a coin the outcomes are heads and tails. The possible outcomes should be the basis for predictions rather than perceptions of luck.

Teaching resources for this Achievement Objective:

## No way Jose

• Units of Work
• Statistics
• Level One

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.

## Lonely Pig

• Units of Work
• Statistics
• Level One

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.

## Who plays what?

• Problem solving activities
• Statistics
• Level One
Use words to describe the likelihood of events.
Use logical reasoning to solve a problem.

## Strawberry Milk

• Problem solving activities
• Geometry and Measurement
• Level One

This activity has a logic and reasoning focus.

## Strawberry Milk

• Problem solving activities
• Geometry and Measurement
• Level One

This activity has a logic and reasoning focus.

## Strawberry and Chocolate Milk

• Problem solving activities
• Geometry and Measurement
• Level One

This activity has a logic and reasoning focus.

## Probably Pistachio

• Picture book activities
• Statistics
• Level One

This is an activity based on the picture book Probably Pistachio

## What's next?

• Rich learning activities
• Statistics
• Level One

The purpose of this activity is to engage students in identifying possible outcomes in a given situation and describing the chance of an outcome occurring in broad terms.

## Odd socks

• Statistics
• Level One

The purpose of this activity is to engage students in identifying possible outcomes in a given situation.