Mathematics
Mathematics and statistics are an investigation of patterns and relationships in quantities, space, and time relationships in data. The two disciplines are associated however there are different ways of thinking and resolving problems. Both supply students with effective means for investigating, interpreting, explaining, and making sense of the world they live in (Ministry of Education. 2007).
Search for resources that line up directly with the New Zealand Curriculum's learning intentions. Some resources may be relevant to more than one learning intention or level.
Level 1 Mathematics
Number and Algebra |
Geometry and Measurement |
Statistics |
Number strategies • Use a range of counting, grouping, and equal-sharing strategies with whole numbers and fractions. |
Measurement • Order and compare objects or events by length, area, volume and capacity, weight (mass), turn (angle), temperature, and time by direct comparison and/or counting whole numbers of units. |
Statistical investigation • Conduct investigations using the statistical enquiry cycle:– posing and answering questions;– gathering, sorting and counting, and displaying category data;– discussing the results. |
Number knowledge • Know the forward and backward counting sequences of whole numbers to 100. • Know groupings with five, within ten, and with ten. |
Shape • Sort objects by their appearance. |
Statistical literacy • Interpret statements made by others from statistical investigations and probability activities. |
Equations and expressions • Communicate and explain counting, grouping, and equal-sharing strategies, using words, numbers, and pictures. |
Position and orientation • Give and follow instructions for movement that involve distances, directions, and half or quarter turns. • Describe their position relative to a person or object. |
Probability • Investigate situations that involve elements of chance, acknowledging and anticipating possible outcomes. |
Patterns and relationships • Generalise that the next counting number gives the result of adding one object to a set and that counting the number of objects in a set tells how many. • Create and continue sequential patterns. |
Transformation • Communicate and record the results of translations, reflections, and rotations on plane shapes. |
Level 2
Number and Algebra |
Geometry and Measurement |
Statistics |
Number strategies • Use simple additive strategies with whole numbers and fractions. |
Measurement • Create and use appropriate units and devices to measure length, area, volume and capacity, weight (mass), turn (angle), temperature, and time. • Partition and/or combine like measures and communicate them, using numbers and units. |
Statistical investigation • Conduct investigations using the statistical enquiry cycle:– posing and answering questions;– gathering, sorting, and displaying category and whole-number data; – communicating findings based on the data. |
Number knowledge • Know forward and backward counting sequences with whole numbers to at least 1000.• Know the basic addition and subtraction facts. • Know how many ones, tens, and hundreds are in whole numbers to at least 1000. • Know simple fractions in everyday use. |
Shape • Sort objects by their spatial features, with justification. • Identify and describe the plane shapes found in objects. |
Statistical literacy • Compare statements with the features of simple data displays from statistical investigations or probability activities undertaken by others. |
Equations and expressions • Communicate and interpret simple additive strategies, using words, diagrams (pictures), and symbols. |
Position and orientation • Create and use simple maps to show position and direction. • Describe different views and pathways from locations on a map. |
Probability • Investigate simple situations that involve elements of chance, recognising equal and different likelihoods and acknowledging uncertainty. |
Patterns and relationships • Generalise that whole numbers can be partitioned in many ways. • Find rules for the next member in a sequential pattern. |
Transformation • Predict and communicate the results of translations, reflections, and rotations on plane shapes. |
Level 3
Number and Algebra |
Geometry and Measurement |
Statistics |
Number strategies • Use a range of additive and simple multiplicative strategies with whole numbers, fractions, decimals, and percentages. |
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. |
Statistical investigation • Conduct investigations using the statistical enquiry cycle:– gathering, sorting, and displaying multivariate category and whole-number data and simple time-series data to answer questions;– identifying patterns and trends in context, within and between data sets;– communicating findings, using data displays. |
Number knowledge • Know basic multiplication and division facts.• Know counting sequences for whole numbers. • Know how many tenths, tens, hundreds, and thousands are in whole numbers. • Know fractions and percentages in everyday use. |
Shape • Classify plane shapes and prisms by their spatial features. • Represent objects with drawings and models. |
Statistical literacy • Evaluate the effectiveness of different displays in representing the findings of a statistical investigation or probability activity undertaken by others. |
Equations and expressions • Record and interpret additive and simple multiplicative strategies, using words, diagrams, and symbols, with an understanding of equality. |
Position and orientation • Use a co-ordinate system or the language of direction and distance to specify locations and describe paths. |
Probability • Investigate simple situations that involve elements of chance by comparing experimental results with expectations from models of all the outcomes, acknowledging that samples vary. |
Patterns and relationships • Generalise the properties of addition and subtraction with whole numbers. • 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. |
Transformation • Describe the transformations (reflection, rotation, translation, or enlargement) that have mapped one object onto another. |
Level 4
Number and Algebra |
Geometry and Measurement |
Statistics |
Number strategies and knowledge • Use a range of multiplicative strategies when operating on whole numbers. • Understand addition and subtraction of fractions, decimals, and integers. • Find fractions, decimals, and percentages of amounts expressed as whole numbers, simple fractions, and decimals. • Apply simple linear proportions, including ordering fractions. • Know the equivalent decimal and percentage forms for everyday fractions. • Know the relative size and place value structure of positive and negative integers and decimals to three places. |
Measurement • Use appropriate scales, devices, and metric units for length, area, volume and capacity, weight (mass), temperature, angle, and time. • Convert between metric units, using whole numbers and commonly used decimals. • Use side or edge lengths to find the perimeters and areas of rectangles, parallelograms, and triangles and the volumes of cuboids. • Interpret and use scales, timetables, and charts. |
Statistical investigation • Plan and conduct investigations using the statistical enquiry cycle:– determining appropriate variables and data collection methods; – gathering, sorting, and displaying multivariate category, measurement, and time-series data to detect patterns, variations, relationships, and trends;– comparing distributions visually;– communicating findings, using appropriate displays. |
Equations and expressions • Form and solve simple linear equations. |
Shape • Identify classes of two- and three-dimensional shapes by their geometric properties. • Relate three-dimensional models to two-dimensional representations, and vice versa. |
Statistical literacy • Evaluate statements made by others about the findings of statistical investigations and probability activities. |
Patterns and relationships • Generalise properties of multiplication and division with whole numbers. • Use graphs, tables, and rules to describe linear relationships found in number and spatial patterns. |
Position and orientation • Communicate and interpret locations and directions, using compass directions, distances, and grid references. |
Probability • Investigate situations that involve elements of chance by comparing experimental distributions with expectations from models of the possible outcomes, acknowledging variation and independence. • Use simple fractions and percentages to describe probabilities. |
Transformation • Use the invariant properties of figures and objects under transformations (reflection, rotation, translation, or enlargement). |
Level 5
Number and Algebra |
Geometry and Measurement |
Statistics |
Number strategies and knowledge • 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. |
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 formulae to find the perimeters and areas of polygons and the volumes of prisms. • Find the perimeters and areas of circles and composite shapes and the volumes of prisms, including cylinders. |
Statistical investigation • Plan and conduct surveys and experiments using the statistical enquiry cycle:– determining appropriate variables and measures;– considering sources of variation;– gathering and cleaning data; – using multiple displays, and re-categorising data to find patterns, variations, relationships, and trends in multivariate data sets;– comparing sample distributions visually, using measures of centre, spread, and proportion;– presenting a report of findings. |
Equations and expressions • Form and solve linear and simple quadratic equations. |
Shape • Deduce the angle properties of intersecting and parallel lines and the angle properties of polygons and apply these properties. • Create accurate nets for simple polyhedra and connect three-dimensional solids with different two-dimensional representations. |
Statistical literacy • Evaluate statistical investigations or probability activities undertaken by others, including data collection methods, choice of measures, and validity of findings |
Patterns and relationships • Generalise the properties of operations with fractional numbers and integers. • Relate tables, graphs, and equations to linear and simple quadratic relationships found in number and spatial patterns. |
Position and orientation • Construct and describe simple loci. • Interpret points and lines on co-ordinate planes, including scales and bearings on maps. |
Probability • Compare and describe the variation between theoretical and experimental distributions in situations that involve elements of chance. • Calculate probabilities, using fractions, percentages, and ratios. |
Transformation • Define and use transformations and describe the invariant properties of figures and objects under these transformations. • Apply trigonometric ratios and Pythagoras’ theorem in two dimensions. |
References:
Ministry of Education. (2007). The New Zealand Curriculum. Ministry of Education.
Ministry of Education. (2007). The New Zealand Curriculum. Ministry of Education.