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

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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
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Another dartboard

Level Five
Statistics
Problem solving activities
This problem solving activity has a statistics focus.
  • 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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Birth Months

Level Five
Statistics
Figure It Out activities
This is a level 5 statistics activity from the Figure It Out series.

explore the outcomes of a probability activity

find theoretical probabilities

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Card Sharp

Level Five
Statistics
Figure It Out activities
This is a level 5 statistics activity from the Figure It Out series.

calculate theoretical probabilities

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Fair Games

Level Five
Statistics
Units of Work
This unit explores a variety of activities (games of chance) 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).
  • Use long-run frequencies to estimate probabilities.
  • Compare the results of theoretical and experimental approaches to games of chance.
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Flooding likely?

Level Five
Integrated
The purpose of this unit, which provides an integrated social sciences/statistics and probability context, is develop students' understandings of skills and knowledge of interpreting statistical and chance situations. Within this, students investigate flooding as an example of a natural catastrophe.
  • Combine probabilities to find the probability of an outcome from a complex chance situation.
  • Run a simulation to find an experimental probability
  • Understand and describe the differences and advantages between theoretical and experimental probabilities.
  • Find a theoretical probability and express it as a300
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Greedy Pig

Level Five
Statistics
Units of Work
This unit provides students with the opportunity to explore concepts of probability in the context of a fun game - Greedy Pig.
  • Calculate the probabilities for outcomes of a dice roll.
  • Draw a dot plot of results.
  • Interpret dot plots in terms of centre and variation.
  • Calculate averages and expected values.
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Lara's equiprobable dice I

Level Five
Statistics
Problem solving activities
This problem solving activity has a statistics focus.
  • 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

Level Five
Statistics
Units of Work
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.
  • Explain what a probability distribution is.
  • Explain how probabilities are distributed.
  • Calculate what happens to the distribution when variables are summed.
  • Calculate expected number from theoretical probabilities.
  • Appreciate the difference between theoretical and experimental probabilities.
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Risk it for a Ticket?

Level Five
Statistics
Rich learning activities
The purpose of this activity is to engage students in calculating a combined probability and using this to solve a problem.
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Rough Justice

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

calculate the probabilities of events occurring using fractions

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Slater Mazes

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

calculate the probabilities of events occurring using fractions

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That's the way the cookie crumbles

Level Five
Statistics
Rich learning activities
The purpose of this activity is to engage students in an investigation that leads to the comparison of experimental probability, with a theoretical probability.