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

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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

Beat It

Level Four

Statistics

Units of Work

The purpose of this unit is for students to use games to gather and present data in a systematic way. In turn, this allows them to determine the likely outcomes of some everyday events.

Investigate, state and justify the probability of events in common situations.
Theoretically and experimentally examine the probabilities of games of chance.

Cubic Conundrums

Level Four

Integrated

Units of Work

This unit provides a set of learning tasks that integrate across the strands of the Mathematics and Statistics learning area of the New Zealand Curriculum and provide opportunities for assessment of student achievement across those strands. Each session may involve more than one lesson, especially...

Session One
Use systematic approaches to find all the possible outcomes, e.g. tree diagrams, organised lists.

Session Two
Use tables, graphs, and word rules to represent growing patterns.

Session Three
Draw cube models using plan views.

Session Four
Draw cube models using isometric projections.

Session Five300

Flip and roll

Level Four

Statistics

Units of Work

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.

Calculate the theoretical probability of an event by finding all the possible outcomes.
Use more than one way to find a theoretical probability.
Check theoretical probabilities using trials.
Identify what a fair game is and how to make an unfair game fair.

Gaming Choices

Level Four

Statistics

Figure It Out activities

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

use tables to explore probabilities

Murphy's Law

Level Four

Statistics

Units of Work

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...

Use simulations to investigate probability in common situations.
Predict the likelihood of outcomes on the basis of an experiment.
Determine the theoretical probability of an event.

New Turf

Level Four

Statistics

Rich learning activities

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

Orders

Level Four

Statistics

Figure It Out activities

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

use problem solving strategies to solve ordering problems

find all possible probability outcomes

describe an outcome as a fraction

Paper, Scissors, Rock

Level Four

Statistics

Figure It Out activities

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

explore the outcomes in a probability game

list all possible outcomes

decide if a game is fair

calculate the theoretical probabilities

Penny's Pizza

Level Four

Statistics

Problem solving activities

This problem solving activity has a statistics focus.

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).

Scratch, Text, and Win

Level Four

Statistics

Figure It Out activities

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

calculate probabilities

The Coloured Cube Question

Level Four

Statistics

Units of Work

This unit analyses and extends a game of chance using both experimental and theoretical probability.

Find the theoretical probability of an event occuring.
Use more than one way to find a theoretical probability.
Check theoretical probabilities by trials.
Identify what a fair game is and how to make an unfair game fair.

Unlucky Lines

Level Four

Statistics

Figure It Out activities

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

describe a probability using fractions

Wallowing Whales

Level Four

Statistics

Figure It Out activities

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

find all possible outcomes using a table

find the probability of an event occurring

evaluate a statement about a probability event

Whakataukī

Level Four

Integrated

Units of Work

This unit requires students to find relationships between variables and calculate probabilities. It is set in the context of exploring ideas related to whakataukī (proverbs).

Find simple exponential number patterns.
Use exponential patterns to make predictions about further members of the pattern.
Use tables and graphs to identify relationships between two variables.
Create rules for relationships between two variables.
Use fractions to measure probabilities.

What are the chances?

Level Four

Statistics

Units of Work

In this unit students investigate the link between experimental estimates of probability and theoretical probability. They also learn about short run variability and independence/dependence of events.

Explore the theoretical and experimental probabilities of situations involving chance
Recognise variability from theoretical expectations, especially with small numbers of trials
Estimate and find the relative frequencies of events
Distinguish between events and the outcomes that lead to those events
Di300

What's the Chance?

Level Four

Statistics

Figure It Out activities

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

place probability of events on a continuum