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

• Use a range of counting, grouping, and equal-sharing strategies with whole numbers and fractions.

Number knowledge

• Know the forward and backward counting sequences of whole numbers to 100.
• Know groupings with five, within ten and with ten.

Equations and expressions

• Communicate and explain counting, grouping, and equal-sharing strategies, using words, numbers, and pictures.

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.

Geometry and Measurement

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.

Shape

• 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.

Transformation

• Communicate and record the results of translations, reflections, and rotations on plane shapes.

Statistics

Statistical Investigation

• Conduct investigations using the statistical enquiry cycle:
  • posing and answering questions;
  • gathering, sorting and counting, and displaying category data;
  • discussing the results.

Statistical Literacy

• Interpret statements made by others from statistical investigations and probability activities.

Probability

• 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

• Use simple additive strategies with whole numbers and fractions.

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.

Equations and expressions

• Communicate and interpret simple additive strategies, using words, diagrams (pictures), and symbols.

Patterns and relationships

• Generalise that whole numbers can be partitioned in many ways.
• Find rules for the next member in a sequential pattern.

Geometry and Measurement

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.

Shape

• Sort objects by their spatial features, with justification.
• Identify and describe the plane shapes found in objects.

Position and orientation

• Create and use simple maps to show position and direction.
• Describe different views and pathways from locations on a map.

Transformation

• Predict and communicate the results of translations, reflections, and rotations on plane shapes.

Statistics

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.

Statistical literacy

• Compare statements with the features of simple data displays from statistical investigations or probability activities undertaken by others.

Probability

• 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

• Use a range of additive and simple multiplicative strategies with whole numbers, fractions, decimals, and percentages.

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.

Equations and expressions

• Record and interpret additive and simple multiplicative strategies, using words, diagrams, and symbols, with an understanding of equality.

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.

Geometry and Measurement

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.

Shape

• Classify plane shapes and prisms by their spatial features.
• Represent objects with drawings and models.

Position and orientation

• Use a co-ordinate system or the language of direction and distance to specify locations and describe paths.

Transformation

• Describe the transformations (reflection, rotation, translation, or enlargement) that have mapped one object on to another.

Statistics

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.

Statistical literacy

• Evaluate the effectiveness of different displays in representing the findings of a statistical investigation or probability activity undertaken by others.

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.

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

• 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.

Equations and expressions

• Form and solve simple linear equations.

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.

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

• Identify classes of two- and three-dimensional shapes by their geometric properties.
• Relate three-dimensional models to two-dimensional representations, and vice versa.

Position and orientation

• Communicate and interpret locations and directions, using compass directions, distances, and grid references.

Transformation

• Use the invariant properties of figures and objects under transformations (reflection, rotation, translation, or enlargement).

Statistics

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.

Statistical literacy

• Evaluate statements made by others about the findings of statistical investigations and probability activities.

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.