ai.page · roadmaps

How to learn Year 6: Mathematics

The New Zealand Curriculum (Ministry of Education): Mathematics, Year 6

0 of 47 concepts ready to learn · Markdown, for your AI

1. Number · Number structures

  1. Factors, multiples, and primes: Find all factor pairs for a whole number in the range 1–100; identify common factors and common multiples of two numbers; use these concepts to solve problems
  2. Rounding Large Numbers: Round any whole number up to 1,000,000 to the nearest 10, 100, 1,000, 10,000, or 100,000 using place-value understanding
  3. Rounding Answers: Solve problems which require answers to be rounded to specified degrees of accuracy
  4. Reading and writing numbers (age 9+): Read, write, order, and compare whole numbers up to at least 1,000,000 using base-ten numerals, number names, expanded form, and place-value understanding
  5. Negative numbers in context: Interpret negative numbers in context (temperature, sea level, bank balance); count forwards and backwards with positive and negative whole numbers, including through zero

2. Number · Operations

  1. Adding and subtracting mixed numbers: Add and subtract mixed numbers with like denominators, including by converting to improper fractions or using properties of operations
  2. Order of operations: Understand and apply the conventional order of operations (PEMDAS/BODMAS) to carry out calculations involving the four operations
  3. Written Multiplication: Multiply two-digit and three-digit numbers by a one-digit number using formal written layout

3. Number · Rational numbers

  1. Adding fractions (different denominators): Add and subtract fractions with denominators that are multiples of the same number by finding a common denominator
  2. Simplifying Fractions: Use common factors to simplify fractions to their simplest form; use common multiples to express fractions with a common denominator
  3. Percentages as Fractions: Define percentage as 'number of parts per hundred'; interpret percentages and percentage changes as a fraction or a decimal; express one quantity as a percentage of another; compare quantities using percentages; work with percentages greater than 100%
  4. Percentage and decimal equivalents: Solve problems requiring knowledge of percentage and decimal equivalents of 1/2, 1/4, 1/5, 2/5, 4/5 and fractions with denominators that are multiples of 10 or 25
  5. Decimals and fractions (age 10+): Associate a fraction with division and calculate decimal fraction equivalents for simple fractions (e.g. 3/8 = 0.375); recall and use equivalences between simple fractions, decimals, and percentages in different contexts
  6. Decimals for Tenths & Hundredths: Use decimal notation for fractions with denominators 10 or 100; read and write decimal numbers as fractions (e.g. 0.62 = 62/100, 0.71 = 71/100)
  7. Comparing Decimals: Compare two decimals to hundredths (or up to three decimal places) by reasoning about size using place-value understanding; record with >, =, <
  8. Reading and writing numbers (age 10+): Read, write, and compare decimals to thousandths using base-ten numerals, number names, and expanded form; compare using >, =, < based on place-value meaning
  9. Comparing fractions (age 10+): Compare and order fractions including fractions greater than 1, by converting to common denominators or using benchmarks
  10. Multiplying and dividing: Multiply and divide whole numbers and those involving decimals by 10, 100, and 1000

4. Algebra · Equations and relationships

  1. Expressions & Equations Vocabulary: Understand and use the concepts and vocabulary of expressions, equations, inequalities, terms, and factors; distinguish between an expression (no equals sign), an equation (equals sign), and an inequality (inequality sign)
  2. Checking Answers by Rounding: Use rounding to check answers to calculations and determine appropriate levels of accuracy in context
  3. Numbers on a number line: Understand inequalities as statements comparing expressions, represent solutions on a number line, and solve simple linear inequalities using the same inverse-operation methods as equations

5. Algebra · Growing patterns

  1. Shape patterns: Generate a number or shape pattern that follows a given rule; identify apparent features of the pattern not explicit in the rule and explain informally why they occur

6. Algebra · Coordinate plane

  1. Number Pattern Relationships: Generate two numerical patterns using two given rules; identify relationships between corresponding terms; form ordered pairs and graph them on a coordinate plane

7. Measurement · Measuring

  1. Comparing lengths by measuring: Measure to determine how much longer one object is than another, expressing the length difference in terms of a standard length unit
  2. Measurement Conversions: Solve problems involving the calculation and conversion of units of measure, using decimal notation and multi-step reasoning in real-world contexts
  3. Calculating with measurements: Measure, compare, add, and subtract lengths (m/cm/mm), mass (kg/g), and volume/capacity (l/ml) using standard units
  4. Converting measurement units (age 9+): Know relative sizes of measurement units within one system (km/m/cm/mm, kg/g, l/ml, hr/min/sec); convert between different metric units and express measurements in terms of a smaller unit; record equivalents in conversion tables

8. Measurement · Area and Volume

  1. Counting Unit Cubes: Measure volumes by counting unit cubes using cubic cm, cubic in, cubic ft, and other units
  2. Angles in triangles (age 11+): Derive and apply formulae for the area of triangles, parallelograms, and trapezia, and for the volume of cuboids and other prisms (including cylinders), connecting each formula to its geometric reasoning
  3. Measuring Perimeters: Measure the perimeter of simple 2-D shapes
  4. Perimeter (age 10+): Recognise that shapes with the same area can have different perimeters and vice versa; explore this relationship systematically

9. Measurement · Angles

  1. Angle Sum Rules: Know that angles at a point sum to 360° (one whole turn), angles on a straight line sum to 180°, and vertically opposite angles are equal; use these facts to find missing angles
  2. Measuring angles: Measure angles in whole-number degrees using a protractor; draw given angles and sketch angles of specified measure
  3. Measuring angles (age 9+): Recognise angle measure as additive; find unknown angles by adding or subtracting on a diagram using equations with a symbol for the unknown
  4. Understanding angles (age 10+): Recognise angles where they meet at a point, are on a straight line, or are vertically opposite; find missing angles using these properties
  5. Understanding angles (age 11+): Apply the properties of angles at a point (360°), on a straight line (180°), and vertically opposite angles to find unknown angles in multi-step problems

10. Measurement · Time

  1. Telling time to the minute (age 9+): Solve problems involving converting between units of time (hours↔minutes, minutes↔seconds, years↔months, weeks↔days)
  2. 12-hour and 24-hour time: Read, write, and convert time between analogue and digital 12-hour and 24-hour clocks
  3. Reading tables: Complete, read, and interpret information in tables, including timetables

11. Geometry · Shapes

  1. Classifying shapes by properties: Compare and classify geometric shapes based on their properties and sizes; understand that attributes belonging to a category also belong to all subcategories; classify two-dimensional figures in a hierarchy based on properties
  2. Properties of triangles and quadrilaterals: Derive and illustrate properties of triangles, quadrilaterals, and circles using appropriate language, including interior angles, diagonals, symmetry, and relationships between side lengths
  3. Degrees and turns: Know that angles are measured in degrees, where one degree is 1/360 of a full turn; understand that an angle turning through n one-degree angles has a measure of n degrees

12. Geometry · Spatial reasoning

  1. Transformations on a Grid: Identify, describe, and represent the position of a shape following a reflection or translation using appropriate language; know that the shape has not changed
  2. Coordinate Transformations: Identify properties of translations, rotations, and reflections; describe and perform these transformations on given figures, and understand that the image is congruent to the original

13. Geometry · Pathways

  1. Transformations on a grid: Represent and carry out geometric transformations on squared paper or a coordinate grid: reflections (in horizontal, vertical, and diagonal mirror lines, including the axes), translations (described as a vector or as left/right/up/down moves), and rotations (90° or 180° about a stated centre point); describe each transformation precisely using the correct language; identify which transformation maps one shape onto its image by comparing position, orientation, and size

14. Statistics · Visualisation of data

  1. Line graphs (age 10+): Interpret and construct pie charts and line graphs; use these to solve problems

15. Probability · Experimental probability

  1. Experimental probability: Record, describe, and analyse the frequency of outcomes from probability experiments to develop an understanding of relative frequency as an estimate of probability