Resources for Mathematics

Clarifications for 8000-number Unit Standards in Mathematics

For Mathematics standards levels 1-4 considerable detail is included in the special notes that will assist in the development of assessment tools.

Before assessing these unit standards all assessors should:

• be aware of the existence of the Mathematics in the New Zealand Curriculum document available from Ministry of Education website
• read the special notes for these unit standards
• ensure they are using the current versions of these unit standards.

See the Maths page for links to other online resources

Unit Standard 8489 version 3, level 1, Solve problems which require calculation with whole numbers

This standard is an introductory level number standard and requires learners to solve problems which involve calculation with whole numbers.

• Calculators must NOT be used.
• Addition, subtraction, multiplication and division of whole numbers are all required.
• All problems must be written as questions in text format. For example, 64 + 32= does NOT meet the requirements of the unit standard.
• All problems should involve only one step of calculations in the solution.
• Learners must decide on the operation to be used to solve the problem.
• Questions for each operation should be spread throughout the task.
• Problems should involve :
  • addition and subtraction of two whole numbers of 2 or 3 digits
  • multiplication and division by a 1 digit number.

Unit Standard 8490 version 3, level 1, Solve problems using calculations with numbers expressed in different forms

This standard is an introductory level number standard and requires the learners to convert between fractions, decimals and percentages; and solve problems involving conversions between percentages and fractions.

• Calculators and/or computers may be used.
• Assessment tasks should not require rounding or truncating to find the answer.

Element 1

• Conversion is between all forms: fractions, decimals and percentages. The learner must show competency in the SIX types of conversion.
  Decimal –> Percentage
  Percentage –> Decimal
  Fraction –> Percentage
  Percentage –> Fraction
  Decimal –> Fraction
  Fraction –> Decimal

• Questions do NOT have to be set in context.

Element 2

• Problems MUST be set in context.
• Problems should involve one step of calculation in their solution.
• All problems should be written as questions in text format.
• The assessment task must include solving problems involving ONLY the conversion between fractions to percentages and percentages to fractions. For example Tom got 17/20 in his test. What percentage did he get?
• This unit standard does NOT require the learner to find fractions or percentages of quantities.
• Three questions for each type of conversion is sufficient. The learner should be expected to solve at least two of the three questions for each type of conversion correctly.

Unit Standard 8491 version 3 level 1, Read and interpret information presented in tables and graphs

This standard is an introductory level number standard and requires the learners to read and interpret information presented in tables and graphs.

Calculators and/or computers may be used.

Element 1

• The standard must be met for at least three different types of tables. These could include but are not limited to: timetables, tables of statistical information. Three questions for each table is sufficient. The learner should be expected to solve at least two of the three questions for each type of table correctly

Element 2

• The standard must be met for at least three different types of graphs. These could include but are not limited to: bar graph, pictograph, line graph, pie graph, box-and-whisker graph, stem and leaf graph. Three questions for each table is sufficient. The learner should be expected to solve at least two of the three questions for each type of graph correctly

Interpretation could include but is not limited to significant features of the graphs such as: greatest and least values, trends, finding totals of values greater or less than a given value. This sets the frame for the level and type of questions that should be set.

Unit Standard 8492 version 4, level 1, Use standard units of measurement

This standard is the introductory level measurement standard and requires the learners to take measurements, and perform measurement calculations.

The assessment schedule needs to specify the acceptable range of measurement and solutions for practical problems.

Units must not be stated, indicated in the question or asked for. Learners are required to know that units form part of the solution to a measurement problem.

Calculators and/or computers may be used.

Element 1

• The standard must be met for at least five of the nine units of measurement listed. The nine units of measurement are: metres, centimetres, millimetres, kilograms, grams, litres, millilitres, minutes and seconds. However, assessment must cover the range of each of the types of measurement- at least one from length, at least one from mass, at least one from volume (capacity) and at least one from time.

• Learners must select the appropriate measurement tool and then measure to an appropriate accuracy to establish that the learner can "use measurement devices to measure quantities". Assessors must NOT tell the learner what measuring tool to use. The learner does not have to state what measuring tool they used as the correct answer will demonstrate competency. However, the numerical values of measurement of the tool the learner uses needs be to be recorded in the learner's answers with the units for the measurement. This will assist in verifying the assessor's decision.

• Assessors must NOT give the learner standard objects to measure where the measurement is already known. For example a 2 litre milk or ice-cream container.

• Measurement must be made to the appropriate degree of accuracy. This will depend on the type of measurement and the measuring device used by the learner. The Judgement Statement in the Assessment Schedule should include the degree of accuracy required.

• When measuring time it is NOT about telling the time or converting time measurements from one form to another. For example: measuring time could be done by reading the start and finish times for a piece of music from a watch.

• Assessment tasks should be as realistic as possible and relate to everyday and/or workplace situations. Asking the learner to measure straight lines on a page in a test is inappropriate.

• Multi-choice questions in a test are inappropriate as the learner must be able to perform certain skills.

Element 2

• The standard must be reached for calculations of three of the four quantities as listed in Special Note 2. This means three from the four quantities listed- area, volume, speed and time.

• Learners are required to perform calculations involving a range of aspects as stated in Special Note 2. The learner must choose the method to use and perform the required calculation. This means that the learner correctly calculates the measurement. In maths it is expected that the learner would get the majority of the problems correct. For example, if the learner was given three problems involving area, then it would be expected that the learner would be able to solve two of the three problems correctly. This should be stated in the Judgement Statements in the Assessment Schedule.

Last updated: 12 May 2009