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

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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.