New Zealand

The Mathematics Curriculum in Primary and Lower Secondary Grades

The mathematics learning area for both English- and Māori-medium education has three strands: Number and Algebra, Measurement and Geometry, and Statistics. New Zealand only assessed students in English-medium settings in TIMSS 2015, therefore the following summary details Level 3 of the English-medium curriculum, with additional details provided by the National Standards.^k

The majority of students should have been introduced to or taught each of the following topics or skills by the end of Year 5:

• Number and Algebra—Use a range of additive and simple multiplicative strategies with whole numbers, fractions, decimals (simple), and percentages; know basic multiplication and division facts; know counting sequences for whole numbers; know how many ones, tens, hundreds, and thousands are in whole numbers; know fractions and percentages in everyday use; find fractions of sets, shapes, and quantities; record and interpret additive and simple multiplicative strategies using words, diagrams, and symbols, with an understanding of equality; generalize the properties of addition and subtraction with whole numbers; and connect members of sequential patterns with their ordinal position and use tables, graphs, and diagrams to find relationships between successive elements of number and spatial patterns
• Geometry and Measurement—Use linear scales and whole numbers of metric units for length, area, volume and capacity, weight (mass), angle, temperature, and time; find areas of rectangles and volumes of cuboids by applying multiplication; classify plane shapes and prisms by their spatial features; represent objects with drawings and models (nets for rectangular prisms and plans); use a coordinate system or the language of direction and distance to specify locations and describe paths; and describe transformations (reflection, rotation, or translation) that have mapped one object onto another
• Statistics—Gather, sort, and display multivariate categorical and whole-number data and simple time-series data to answer questions; identify patterns and trends in context, within and between data sets; communicate findings using data displays; evaluate the effectiveness of different data displays; and investigate simple situations involving elements of chance by comparing experimental results with expectations from models of all outcomes, acknowledging that samples vary

The following summary details Level 5 of the English-medium document.^l Note that there are no National Standards for mathematics for Year 9 students. The majority of students should have been introduced to or taught each of the following topics or skills by the end of Year 9:

• Number and Algebra—Reason with linear proportions; use prime numbers, common factors and multiples, and powers (including square roots); understand operations on fractions, decimals, percentages, and integers; use rates and ratios; know commonly used fraction, decimal, and percentage conversions; know and apply standard form, significant figures, rounding, and decimal place value; form and solve linear equations; generalize the properties of operations with fractional numbers and integers; and relate tables, graphs, and equations to linear relationships found in number and spatial patterns
• Geometry and Measurement—Select and use appropriate metric units for length, area, volume and capacity, weight (mass), temperature, angle, and time, with awareness that measurements are approximate; convert between metric units using decimals; deduce and use formulas to find perimeters and areas of polygons and volumes of prisms; find perimeters and areas of circles and composite shapes; deduce angle properties of intersecting and parallel lines and angle properties of polygons and apply these properties; create accurate nets for simple polyhedra and connect three-dimensional solids with different two-dimensional representations; construct and describe simple loci; interpret points and lines in coordinate planes, including scales and bearings on maps; define and use transformations and describe the invariant properties of figures and objects under these transformations; and apply trigonometric ratios and the Pythagorean theorem in two dimensions
• Statistics—Determine appropriate variables and measures; consider sources of variation; gather and clean data; use multiple displays, and recategorize data to find patterns, variations, relationships, and trends in multivariate data sets; compare sample distributions visually, using measures of center, spread, and proportion; present a report of findings; evaluate statistical investigations or probability activities undertaken by others, including data collection methods, choice of measures, and validity of findings; compare and describe the variation between theoretical and experimental distributions in situations involving elements of chance; and calculate probabilities, using fractions, percentages, and ratios