New Zealand Schools OER Portal/NZ OERs/Mathematics Levels 1-4

=Mathematics and Statistics=

Level 1
'''In a range of meaningful contexts, students will be engaged in thinking mathematically and statistically. They will solve problems and model situations that require them to:'''

Number and Algebra
Number strategies Number knowledge Equations and expressions Patterns and relationships
 * Use a range of counting, grouping, and equal-sharing strategies with whole numbers and fractions.
 * Know the forward and backward counting sequences of whole numbers to 100.
 * Know groupings with five, within ten and with ten.
 * Communicate and explain counting, grouping, and equal-sharing strategies, using words, numbers, and pictures.
 * 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.

Geometry and Measurement
Measurement Shape Transformation
 * 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.
 * Sort objects by their appearance.
 * Position and Orientation
 * Give and follow instructions for movement that involves distances, directions, and half or quarter turns.
 * Describe their position relative to a person or object.
 * Communicate and record the results of translations, reflections, and rotations on plane shapes.

Statistics
Statistical Investigation Statistical Literacy Probability
 * Conduct investigations using the statistical enquiry cycle:
 * posing and answering questions;
 * gathering, sorting and counting, and displaying category data;
 * discussing the results.
 * Interpret statements made by others from statistical investigations and probability activities.
 * Investigate situations that involve elements of chance, acknowledging and anticipating possible outcomes.

Level 2
'''In a range of meaningful contexts, students will be engaged in thinking mathematically and statistically. They will solve problems and model situations that require them to:'''

Number and Algebra
Number strategies Number knowledge Equations and expressions Patterns and relationships
 * Use simple additive strategies with whole numbers and fractions.
 * 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.
 * Communicate and interpret simple additive strategies, using words, diagrams (pictures), and symbols.
 * Generalise that whole numbers can be partitioned in many ways.
 * Find rules for the next member in a sequential pattern.

Geometry and Measurement
Measurement Shape Position and orientation Transformation
 * 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.
 * Sort objects by their spatial features, with justification.
 * Identify and describe the plane shapes found in objects.
 * Create and use simple maps to show position and direction.
 * Describe different views and pathways from locations on a map.
 * Predict and communicate the results of translations, reflections, and rotations on plane shapes.

Statistics
Statistical investigation Statistical literacy Probability
 * 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.
 * Compare statements with the features of simple data displays from statistical investigations or probability activities undertaken by others.
 * Investigate simple situations that involve elements of chance, recognising equal and different likelihoods and acknowledging uncertainty.

Level 3
'''In a range of meaningful contexts, students will be engaged in thinking mathematically and statistically. They will solve problems and model situations that require them to:'''

Number and Algebra
Number strategies Number knowledge Equations and expressions Patterns and relationships
 * Use a range of additive and simple multiplicative strategies with whole numbers, fractions, decimals, and percentages.
 * 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.
 * Record and interpret additive and simple multiplicative strategies, using words, diagrams, and symbols, with an understanding of equality.
 * 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.

Geometry and Measurement
Measurement Shape Position and orientation Transformation
 * 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.
 * Use a co-ordinate system or the language of direction and distance to specify locations and describe paths.
 * Describe the transformations (reflection, rotation, translation, or enlargement) that have mapped one object on to another.

Statistics
Statistical investigation Statistical literacy Probability
 * 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.
 * Evaluate the effectiveness of different displays in representing the findings of a statistical investigation or probability activity undertaken by others.
 * Investigate simple situations that involve elements of chance by comparing experimental results with expectations from models of all the outcomes, acknowledging that samples vary.

Level 4
'''In a range of meaningful contexts, students will be engaged in thinking mathematically and statistically. They will solve problems and model situations that require them to:'''

Number and Algebra
Number strategies and knowledge Equations and expressions Patterns and relationships
 * 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.
 * Form and solve simple linear equations.
 * Generalise properties of multiplication and division with whole numbers.
 * Use graphs, tables, and rules to describe linear relationships found in number and spatial patterns.

Geometry and Measurement
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.

Shape
Position and orientation Transformation
 * Identify classes of two- and three-dimensional shapes by their geometric properties.
 * Relate three-dimensional models to two-dimensional representations, and vice versa.
 * Communicate and interpret locations and directions, using compass directions, distances, and grid references.
 * Use the invariant properties of figures and objects under transformations (reflection, rotation, translation, or enlargement).

Statistics
Statistical investigation Statistical literacy Probability
 * 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.
 * Evaluate statements made by others about the findings of statistical investigations and probability activities.
 * 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.