# 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

### 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.