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# 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.