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Skills available for New Zealand year 6 maths curriculum

Objectives are in black and IXL maths skills are in dark green. Hold your mouse over the name of a skill to view a sample question. Click on the name of a skill to practise that skill.

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New Zealand Curriculum (updated for 2025): Year 6 New Zealand Curriculum (updated for 2025): Year 6
New Zealand National Standards (2009) New Zealand National Standards (2009)
New Zealand Curriculum (2007): Level 3 New Zealand Curriculum (2007): Level 3

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Number

Number structure
- identify, read, write, compare, and order whole numbers up to 1,000,000, and represent them using base 10 structure
- identify square numbers and factors of numbers up to 125
Operations
- use rounding, estimation, and inverse operations to predict results and to check the reasonableness of calculations
- round whole numbers to a specified power of 10, and round tenths and hundredths to the nearest whole number or one decimal place
  - Rounding (6-A.7)
  - Round decimals (6-P.8)
- add and subtract any whole numbers
- recall multiplication facts to at least 10 × 10 and corresponding division facts
- multiply multi-digit whole numbers (e.g., 54 × 112)
- divide up to four-digit whole number by a one-digit divisor, with a remainder (e.g., 198 ÷ 7; 4154 ÷ 8)
- use the order of operations rule with grouping, addition, subtraction, multiplication, and division
Rational numbers
- identify, read, write, and represent fractions, decimals (to two places), and related percentages
- compare and order fractions, decimals (to two places), and percentages, and convert decimals and percentages to fractions
- multiply and divide numbers by 10 and 100 to make decimals and whole numbers (e.g., 1.3 × 10 = 13)
- for fractions with denominators 2, 3, 4, 5, 6, 8, 10, 12, or 100:
  - compare and order the fractions
    - Graph and compare fractions on number lines (6-M.1)
    - Put fractions in order (6-M.3)
  - identify when two fractions are equivalent
    - Equivalent fractions (6-L.4)
  - represent the fractions in their simplest form
    - Write fractions in lowest terms (6-L.6)
- convert between mixed numbers and improper fractions
  - Convert between improper fractions and mixed numbers (6-L.8)
- find a fraction or percentage of a whole number where the answer is a whole number (e.g., ³/₈ of 48; 30% of $150)
- identify, from a fractional part of a set, the whole set
- add and subtract fractions with the same or related denominators (e.g., ¹/₄ + ¹/₈)
- add and subtract whole numbers and decimals to two decimal places (e.g., 250.11 + 135.29 = 385.4)
- use known multiplication and division facts to scale a quantity
Financial mathematics
- solve problems involving purchases (e.g., ensuring they have enough money)
- create simple financial plans (e.g., shopping lists, a family budget)
- create 10%, 25%, and 50% of whole-dollar amounts (e.g., 50% of $280)

Algebra

Equations and relationships
- form and solve true or false number sentences and open number sentences involving all four operations, using an understanding of equality or inequality (e.g., 8 × 7 < 8 × 5 + 8 (T or F?))
- use tables, XY graphs, and diagrams to recognise relationships in a linear pattern, develop a rule for the pattern in words (i.e., that there is a constant amount of change between consecutive elements or terms), and make conjectures about further elements in the pattern
  - Complete a table for a two-variable relationship (6-BB.5)
  - Complete a table from a graph (6-BB.6)
Algorithmic thinking
- create and use algorithms for making decisions that involve clear choices

Measurement

Measuring
- estimate and then accurately measure length, mass (weight), capacity, temperature, and duration, using appropriate metric or time-based units or a combination of units
  - Choose the more reasonable temperature (6-GG.11)
- select and use the appropriate tool for a measurement and the appropriate unit for the attribute being measured
  - Choose the appropriate metric unit of measure (6-GG.1)
- convert between common metric units for length, mass (weight), and capacity, and use decimals to express parts of wholes in measurements
- visualise, measure, and draw (to the nearest degree) the amount of turn in angles up to 360 degrees
  - Measure angles with a protractor (6-HH.6)
- convert between units of time and solve duration-of-time problems, in both 12- and 24-hour time systems
Perimeter, area, and volume
- visualise, estimate, and calculate the area of rectangles and right-angled triangles (in cm² and m²) and the volume of rectangular prisms (in cm³), by applying multiplication

Geometry

Shapes
- identify, classify, and explain similarities and differences between:
  - 2D shapes, including different types of triangles
  - prisms and pyramids
    - Identify three-dimensional figures (6-JJ.1)
- identify and describe the interior angles of triangles and quadrilaterals
  - Types of angles (6-HH.5)
  - Find missing angles in triangles and quadrilaterals (6-HH.7)
Spatial reasoning
- visualise and draw nets for rectangular prisms
  - Nets of three-dimensional figures (6-JJ.4)
- visualise, create, and describe 2D geometric patterns and tessellations, using rotation, reflection, and translation and identifying the properties of shapes that do not change
  - Reflection, rotation and translation (6-II.3)
Pathways
- interpret and create grid references and simple scales on maps
  - Objects on a coordinate plane (6-DD.1)
  - Coordinate planes as maps (6-DD.2)
- use directional language, including the four main compass points, turn (in degrees), and distance (in m, km) to locate and describe positions and pathways
  - Follow directions on a coordinate plane (6-DD.3)

Statistics

Problem
- use multivariate data to investigate summary, comparison, and time-series situations, by:
  - posing an investigative question that can be answered with data
    - Identify statistical questions (6-EE.1)
  - making conjectures or assertions about expected findings
Plan
- plan how to collect primary data or how to use provided data, including identifying the variables of interest and for provided data:
  - identifying who the data was collected from
  - identifying the original investigator's purpose for collecting the data
  - deciding if the source is reliable (e.g., by checking if survey questions appear to be biased towards a particular point of view)
Data
- collect primary data and check for errors, and provide information about variables in secondary data (e.g., how data was collected for them and possible outcomes for them)
  - Frequency tables (6-CC.12)
Analysis
- create and describe a variety of data visualisations to make meaning from the data, identifying features, patterns, and trends in context, and including the variable and group of interest
Conclusion
- answer the investigative question, comparing findings with initial conjectures or assertions and their existing knowledge of the world
Statistical literacy
- identify, explain, check, and, if necessary, improve features in others' data investigations (e.g., biased survey questions, misleading information or statements)

Probability

Probability investigations
- engage in chance-based investigations, including those with not equally likely outcomes, by:
  - posing an investigative question
  - anticipating and then identifying possible outcomes for the investigative question
  - generating all possible ways to get each outcome (a theoretical approach), or undertaking a probability experiment and recording the occurrences of each outcome
    - Experimental probability (6-EE.8)
  - creating data visualisations for possible outcomes
  - describing what these visualisations show
  - finding probabilities as fractions
    - Find the probability (6-EE.7)
  - answering the investigative question
  - reflecting on anticipated outcomes
    - Make predictions (6-EE.9)
  - comparing findings from the probability experiment and associated theoretical probabilities, if the theoretical model exists
Critical thinking in probability
- identify, explain, and check others' statements about chance-based investigations, referring to evidence

New Zealand

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Actions

Number

Number structure

identify, read, write, compare, and order whole numbers up to 1,000,000, and represent them using base 10 structure

identify square numbers and factors of numbers up to 125

Operations

use rounding, estimation, and inverse operations to predict results and to check the reasonableness of calculations

round whole numbers to a specified power of 10, and round tenths and hundredths to the nearest whole number or one decimal place

add and subtract any whole numbers

recall multiplication facts to at least 10 × 10 and corresponding division facts

multiply multi-digit whole numbers (e.g., 54 × 112)

divide up to four-digit whole number by a one-digit divisor, with a remainder (e.g., 198 ÷ 7; 4154 ÷ 8)

use the order of operations rule with grouping, addition, subtraction, multiplication, and division

Rational numbers

identify, read, write, and represent fractions, decimals (to two places), and related percentages

compare and order fractions, decimals (to two places), and percentages, and convert decimals and percentages to fractions

multiply and divide numbers by 10 and 100 to make decimals and whole numbers (e.g., 1.3 × 10 = 13)

for fractions with denominators 2, 3, 4, 5, 6, 8, 10, 12, or 100:

compare and order the fractions

identify when two fractions are equivalent

represent the fractions in their simplest form

convert between mixed numbers and improper fractions

find a fraction or percentage of a whole number where the answer is a whole number (e.g., 3/8 of 48; 30% of $150)

identify, from a fractional part of a set, the whole set

add and subtract fractions with the same or related denominators (e.g., 1/4 + 1/8)

add and subtract whole numbers and decimals to two decimal places (e.g., 250.11 + 135.29 = 385.4)

use known multiplication and division facts to scale a quantity

Financial mathematics

solve problems involving purchases (e.g., ensuring they have enough money)

create simple financial plans (e.g., shopping lists, a family budget)

create 10%, 25%, and 50% of whole-dollar amounts (e.g., 50% of $280)

Algebra

Equations and relationships

form and solve true or false number sentences and open number sentences involving all four operations, using an understanding of equality or inequality (e.g., 8 × 7 < 8 × 5 + 8 (T or F?))

use tables, XY graphs, and diagrams to recognise relationships in a linear pattern, develop a rule for the pattern in words (i.e., that there is a constant amount of change between consecutive elements or terms), and make conjectures about further elements in the pattern

Algorithmic thinking

create and use algorithms for making decisions that involve clear choices

Measurement

Measuring

estimate and then accurately measure length, mass (weight), capacity, temperature, and duration, using appropriate metric or time-based units or a combination of units

select and use the appropriate tool for a measurement and the appropriate unit for the attribute being measured

convert between common metric units for length, mass (weight), and capacity, and use decimals to express parts of wholes in measurements

visualise, measure, and draw (to the nearest degree) the amount of turn in angles up to 360 degrees

convert between units of time and solve duration-of-time problems, in both 12- and 24-hour time systems

Perimeter, area, and volume

visualise, estimate, and calculate the area of rectangles and right-angled triangles (in cm2 and m2) and the volume of rectangular prisms (in cm3), by applying multiplication

Geometry

Shapes

identify, classify, and explain similarities and differences between:

2D shapes, including different types of triangles

prisms and pyramids

identify and describe the interior angles of triangles and quadrilaterals

Spatial reasoning

visualise and draw nets for rectangular prisms

visualise, create, and describe 2D geometric patterns and tessellations, using rotation, reflection, and translation and identifying the properties of shapes that do not change

Pathways

interpret and create grid references and simple scales on maps

use directional language, including the four main compass points, turn (in degrees), and distance (in m, km) to locate and describe positions and pathways

Statistics

Problem

use multivariate data to investigate summary, comparison, and time-series situations, by:

posing an investigative question that can be answered with data

making conjectures or assertions about expected findings

Plan

plan how to collect primary data or how to use provided data, including identifying the variables of interest and for provided data:

identifying who the data was collected from

identifying the original investigator's purpose for collecting the data

deciding if the source is reliable (e.g., by checking if survey questions appear to be biased towards a particular point of view)

Data

collect primary data and check for errors, and provide information about variables in secondary data (e.g., how data was collected for them and possible outcomes for them)

Analysis

create and describe a variety of data visualisations to make meaning from the data, identifying features, patterns, and trends in context, and including the variable and group of interest

Conclusion

answer the investigative question, comparing findings with initial conjectures or assertions and their existing knowledge of the world

Statistical literacy

identify, explain, check, and, if necessary, improve features in others' data investigations (e.g., biased survey questions, misleading information or statements)

Probability

Probability investigations

find a fraction or percentage of a whole number where the answer is a whole number (e.g., ³/₈ of 48; 30% of $150)

add and subtract fractions with the same or related denominators (e.g., ¹/₄ + ¹/₈)

visualise, estimate, and calculate the area of rectangles and right-angled triangles (in cm² and m²) and the volume of rectangular prisms (in cm³), by applying multiplication