Resources for Mathematics

Clarification of Unit Standards in Mathematics - EXCEPT for 8000-series standards

Level 1

The following notes provide clarification of the assessment requirements for the commonly used level one unit standards and must be read in conjunction with the unit standard.

5223 Version 3 Use formulae and equations to solve problems

• Questions must be set in context.
• Choosing the method implies going through the process of solving and finding the answer.
• It is helpful if the formulae are familiar to students. Suitable formulae could include area, perimeter and volume formulae.
• A suitable formula question might be:

Calamity Catering use the rule C = 12 n + 70 to calculate its catering costs for lunches where C stands for the cost and n is the number of people being catered for. Calculate the total cost of a lunch for 25 people.

• A suitable equation question might be:

The perimeter of a rectangle is 50 cm and its length is 18 cm. Solve the equation

50 = 36 + 2w to find its width.

• Equations should not involve fractions.
• Any method of solution, including guess and check, is acceptable.
• At least three questions should be given for each situation with students correctly answering at least two.

5224 Version 4 Use decimals and percentages to solve problems

• Problems need to be in context and involve one step of calculation in their solution.
• More than one decimal operation is required and at least two of: expressing one quantity as a percentage of another, finding a percentage of a quantity, increasing or decreasing quantities by a given percentage.

5225 Version 4 Use fractions, ratio and proportion to solve problems

• Problems need to be in context and involve one step of calculation in their solution.
• For increasing or decreasing by a factor, questions involving recipes are a suitable context or a question like 'In a bag of Canterbury Mix wine gums the ratio of red wine gums to black wine gums is 5:3. If a bag contains 30 red wine gums, how many black ones will there be?'
• For comparing using ratios, "best buys" problems are suitable or a question like 'Two pots of green paint are made by mixing blue and yellow paint. In the first tin the ratio of blue to yellow is 3:5 and in the second tin 4:6. Which tin is the darker shade of green?'

5226 Version 3 Construct and use tables and graphs

More than one table and one graph are expected for each element. It is expected that the tables and the graphs will be different types.

Element one

• Students must construct (not complete) tables and graphs from given data.
• Students may be told what type of graph to draw.

Element two

• These may involve using their own tables and graphs or given tables and graphs. It is necessary for the student to use the data from the tables and graphs. Interpretation requires more than straight reading of values.

5227 Version 4 Solve problems involving money

• Problems need to be in context and in most cases more than one step will be involved in getting the solution.
• For wage calculations students must be able to calculate both gross and net wages.

5228 Version 4 Take measurements and use calculations to solve measurement problems

Element one

• A list of formulae should be supplied.
• Students select what measurements they need to take and what formulae to use.
• Students must use their own measurements in the calculations.
• Shapes for area calculations should be more difficult than just a rectangle.
• Students are expected to know that units are part of the answer in measurement. It is not acceptable to instruct them to include units with their answers or to give the units in the task.
• An acceptable range of measurements and answers needs to be included in the schedule.

Element two

• A calculation of time is required. The calculation must involve base 60 knowledge. It is more than reading times from clocks and determining the difference between them.

5229 Version 3 Use geometry to describe situations and solve problems

Element one

• The object and the image should be identified in the diagrams given to students.
• For the description of the transformations students need to specify for:

  Reflection: the mirror line
  Rotation: centre and angle
  Translation: distance and direction
  Enlargement: centre and scale factor.

Element two

• One step problems for angle properties are acceptable and the reason must be given.

5230 Version 4 Carry out a statistical investigation and interpret data

Element one

• The investigation must address the question that is posed.
• The question or a list of questions from which students could choose may be given.
• The question needs to be at least as complex as involving a single variable associated with different categories. For example the single variable could be hours of sleep and the different categories could be owning or not owning a cell phone.
• It is appropriate to provide data from which students could choose a sample.
• It would be appropriate to specify which measures/graphs are expected.
• The question posed must be answered by correct interpretation of the statistical analysis.

Element two

• At least three situations need to be given with students accurately interpreting at least two.
• Questions must be answered with reference to the features of the data analysis.
• Data must be interpreted. It is insufficient to just read a value from a graph/table.

5232 Version 3 Determine probabilities in practical situations

• Probabilities can be expressed as fractions, decimals or percentages. The solution does not need to be rounded or simplified. A solution expressed as a ratio is not acceptable.
• For long-run relative frequency students are expected to carry out a probability experiment and use their results to determine probabilities.

5234 Version 4 Use calculations in money situations

• The result of the calculation needs to be used.
• Calculations of more than one step are expected.
• For GST calculations students must be able to calculate both the GST inclusive and GST exclusive amounts.
• For exchange rates students must be able to calculate both ways.

5235 Version 4 Use strategies to solve number problems

• Solution of the problem must require more than one step.
• The strategies used must involve all of fractions, decimals, percentages, ratio and proportion.
• Percentage problems could involve finding a percentage change or the original amount.
• Finding a percentage of a quantity and increasing or decreasing by a percentage is part of Unit Standard 5224.

5236 Version 4 Use Pythagoras' Theorem and trigonometry to find unknowns in right-angled triangles

• A correct solution will imply the correct use of Pythagoras' theorem or trigonometry even if correct mathematical statements are not used.
• It is expected that students will know the trigonometry and Pythagoras formulae that are needed.
• Units requirements: in the external AS the units tend to be given in the answer space. While units should be given with the answers, students should not be penalised for omitting them.

5239 Version 3 Describe patterns and solve problems and equations

Solutions should be interpreted in context.

Element one

• Students must describe patterns in words or symbols and use them to solve problems.
• Quadratic patterns should be no more complicated than ax², x(x + b) or x² + c.
• There should be more than one pattern described.

Element two

• Quadratic equations with a coefficient of x² equal to 1.
• Guess and check is acceptable for solving equations.

5242 Version 3 Determine probabilities

• Probabilities can be expressed as fractions, decimals or percentages. The solution does not need to be rounded or simplified. A solution expressed as a ratio is not acceptable.
• Combinations of probabilities could include probability trees. It could involve AND (multiplication) and/or OR (sum) situations.
• Could include simple conditional probability from probability trees or tables. The tree diagram may be given or partially completed.

20659 Version 1 Demonstrate basic algebra skills

• Calculators are not allowed.
• Both multiplying and dividing algebraic terms are required.
• For factorising with common factors, one variable and possibly a constant are required, not just a constant.
• Expressions need to be fully factorised so for an expression like 5ab + 15a² the common factor is 5a.
• For factorising and expanding quadratics, a coefficient of x² equal to 1 is sufficient
• It is not essential to simplify the answer to an expansion. If the expression is simplified this can provide further evidence for collecting like terms.

20662 Version 1 Make estimates of measurements with common units

• Calculators are not allowed.
• Units must not be included in the task but must form part of the student's answer.
• Measurements must not be marked on the object.
• It is inappropriate to use items that have a known measurement such as ice cream containers and drink bottles.
• A range of acceptable measurements for the objects needs to be given in the schedule.

20663 Version 1 Use a strategy to estimate the solution to number problems

• Calculators are not allowed.
• Questions will be in text format and will involve one step of calculation in the solution.
• Evidence of the strategy is required. This will include the approximated numbers and the approximate answer.

23738 Version 1 Use numeracy strategies to solve problems involving whole numbers

• Calculators are not allowed.
• Evidence of strategy is required, which may be described or shown.
• At least three different strategies are required in a range of problems.
• Problems will involve one step of calculation to solve but in demonstrating the strategy there will be more than one step in the solution. For example, some ways of solving 156 ÷ 4 could be:

160 ÷ 4 - 4 ÷ 4 = 40 - 1 = 39
120 ÷ 4 + 36 ÷ 4 = 30 + 9 = 39
78 ÷ 2 = 39

23739 Version 1 Use numeracy strategies to solve number problems involving decimals, percentages and fractions

• Calculators are not allowed.
• Evidence of strategy is required, which may be described or shown.
• At least three different strategies are required in a range of problems. All of decimals, percentages and fractions are required.
• Problems will involve one step of calculation to solve but in demonstrating the strategy there will be more than one step in the solution.

Last updated: 21 July 2009