# Year 6: Mathematics A course roadmap (maths). Language: en. By @si. Licence: CC BY-SA 4.0. 0 of 47 concepts ready. In the app: https://ai.page/roadmap/nz-moe-year-6 Part of: [New Zealand Curriculum: Mathematics](https://ai.page/roadmap/nz-moe.md) Goal: The New Zealand Curriculum (Ministry of Education): Mathematics, Year 6 ## 1. Number · Number structures - [Factors, multiples, and primes](https://ai.page/c/factors-multiples-and-primes/index.md): 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 - [Rounding Large Numbers](https://ai.page/c/rounding-large-numbers/index.md): 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 - [Rounding Answers](https://ai.page/c/rounding-answers/index.md): Solve problems which require answers to be rounded to specified degrees of accuracy - [Reading and writing numbers (age 9+)](https://ai.page/c/reading-and-writing-numbers-age-9/index.md): 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 - [Negative numbers in context](https://ai.page/c/negative-numbers-in-context/index.md): 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 - [Adding and subtracting mixed numbers](https://ai.page/c/adding-and-subtracting-mixed-numbers/index.md): Add and subtract mixed numbers with like denominators, including by converting to improper fractions or using properties of operations - [Order of operations](https://ai.page/c/order-of-operations/index.md): Understand and apply the conventional order of operations (PEMDAS/BODMAS) to carry out calculations involving the four operations - [Written Multiplication](https://ai.page/c/written-multiplication/index.md): Multiply two-digit and three-digit numbers by a one-digit number using formal written layout ## 3. Number · Rational numbers - [Adding fractions (different denominators)](https://ai.page/c/adding-fractions-different-denominators/index.md): Add and subtract fractions with denominators that are multiples of the same number by finding a common denominator - [Simplifying Fractions](https://ai.page/c/simplifying-fractions/index.md): Use common factors to simplify fractions to their simplest form; use common multiples to express fractions with a common denominator - [Percentages as Fractions](https://ai.page/c/percentages-as-fractions/index.md): 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% - [Percentage and decimal equivalents](https://ai.page/c/percentage-and-decimal-equivalents/index.md): 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 - [Decimals and fractions (age 10+)](https://ai.page/c/decimals-and-fractions-age-10/index.md): 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 - [Decimals for Tenths & Hundredths](https://ai.page/c/decimals-for-tenths-and-hundredths/index.md): 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) - [Comparing Decimals](https://ai.page/c/comparing-decimals/index.md): Compare two decimals to hundredths (or up to three decimal places) by reasoning about size using place-value understanding; record with >, =, < - [Reading and writing numbers (age 10+)](https://ai.page/c/reading-and-writing-numbers-age-10/index.md): Read, write, and compare decimals to thousandths using base-ten numerals, number names, and expanded form; compare using >, =, < based on place-value meaning - [Comparing fractions (age 10+)](https://ai.page/c/comparing-fractions-age-10/index.md): Compare and order fractions including fractions greater than 1, by converting to common denominators or using benchmarks - [Multiplying and dividing](https://ai.page/c/multiplying-and-dividing/index.md): Multiply and divide whole numbers and those involving decimals by 10, 100, and 1000 ## 4. Algebra · Equations and relationships - [Expressions & Equations Vocabulary](https://ai.page/c/expressions-and-equations-vocabulary/index.md): 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) - [Checking Answers by Rounding](https://ai.page/c/checking-answers-by-rounding/index.md): Use rounding to check answers to calculations and determine appropriate levels of accuracy in context - [Numbers on a number line](https://ai.page/c/numbers-on-a-number-line-maths/index.md): 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 - [Shape patterns](https://ai.page/c/shape-patterns-maths/index.md): 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 - [Number Pattern Relationships](https://ai.page/c/number-pattern-relationships/index.md): 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 - [Comparing lengths by measuring](https://ai.page/c/comparing-lengths-by-measuring/index.md): Measure to determine how much longer one object is than another, expressing the length difference in terms of a standard length unit - [Measurement Conversions](https://ai.page/c/measurement-conversions/index.md): Solve problems involving the calculation and conversion of units of measure, using decimal notation and multi-step reasoning in real-world contexts - [Calculating with measurements](https://ai.page/c/calculating-with-measurements/index.md): Measure, compare, add, and subtract lengths (m/cm/mm), mass (kg/g), and volume/capacity (l/ml) using standard units - [Converting measurement units (age 9+)](https://ai.page/c/converting-measurement-units-age-9/index.md): 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 - [Counting Unit Cubes](https://ai.page/c/counting-unit-cubes/index.md): Measure volumes by counting unit cubes using cubic cm, cubic in, cubic ft, and other units - [Angles in triangles (age 11+)](https://ai.page/c/angles-in-triangles-age-11/index.md): 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 - [Measuring Perimeters](https://ai.page/c/measuring-perimeters/index.md): Measure the perimeter of simple 2-D shapes - [Perimeter (age 10+)](https://ai.page/c/perimeter-age-10/index.md): Recognise that shapes with the same area can have different perimeters and vice versa; explore this relationship systematically ## 9. Measurement · Angles - [Angle Sum Rules](https://ai.page/c/angle-sum-rules/index.md): 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 - [Measuring angles](https://ai.page/c/measuring-angles/index.md): Measure angles in whole-number degrees using a protractor; draw given angles and sketch angles of specified measure - [Measuring angles (age 9+)](https://ai.page/c/measuring-angles-age-9/index.md): Recognise angle measure as additive; find unknown angles by adding or subtracting on a diagram using equations with a symbol for the unknown - [Understanding angles (age 10+)](https://ai.page/c/understanding-angles-age-10/index.md): Recognise angles where they meet at a point, are on a straight line, or are vertically opposite; find missing angles using these properties - [Understanding angles (age 11+)](https://ai.page/c/understanding-angles-age-11/index.md): 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 - [Telling time to the minute (age 9+)](https://ai.page/c/telling-time-to-the-minute-age-9/index.md): Solve problems involving converting between units of time (hours↔minutes, minutes↔seconds, years↔months, weeks↔days) - [12-hour and 24-hour time](https://ai.page/c/12-hour-and-24-hour-time/index.md): Read, write, and convert time between analogue and digital 12-hour and 24-hour clocks - [Reading tables](https://ai.page/c/reading-tables/index.md): Complete, read, and interpret information in tables, including timetables ## 11. Geometry · Shapes - [Classifying shapes by properties](https://ai.page/c/classifying-shapes-by-properties/index.md): 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 - [Properties of triangles and quadrilaterals](https://ai.page/c/properties-of-triangles-and-quadrilaterals/index.md): Derive and illustrate properties of triangles, quadrilaterals, and circles using appropriate language, including interior angles, diagonals, symmetry, and relationships between side lengths - [Degrees and turns](https://ai.page/c/degrees-and-turns/index.md): 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 - [Transformations on a Grid](https://ai.page/c/transformations-on-a-grid-maths/index.md): Identify, describe, and represent the position of a shape following a reflection or translation using appropriate language; know that the shape has not changed - [Coordinate Transformations](https://ai.page/c/coordinate-transformations/index.md): 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 - [Transformations on a grid](https://ai.page/c/transformations-on-a-grid/index.md): 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 - [Line graphs (age 10+)](https://ai.page/c/line-graphs-age-10/index.md): Interpret and construct pie charts and line graphs; use these to solve problems ## 15. Probability · Experimental probability - [Experimental probability](https://ai.page/c/experimental-probability/index.md): Record, describe, and analyse the frequency of outcomes from probability experiments to develop an understanding of relative frequency as an estimate of probability ## Health: 0 of 100 Of its 47 own concepts: 0 have an explanation, 0 have practice, 0 have a measurement question, 0 have a checked version. Findings (each is a task for anyone's AI): - Factors, multiples, and primes has no explanation yet - Rounding Large Numbers has no explanation yet - Rounding Answers has no explanation yet - Reading and writing numbers (age 9+) has no explanation yet - Negative numbers in context has no explanation yet - Adding and subtracting mixed numbers has no explanation yet - Order of operations has no explanation yet - Written Multiplication has no explanation yet - Adding fractions (different denominators) has no explanation yet - Simplifying Fractions has no explanation yet - Percentages as Fractions has no explanation yet - Percentage and decimal equivalents has no explanation yet - Decimals and fractions (age 10+) has no explanation yet - Decimals for Tenths & Hundredths has no explanation yet - Comparing Decimals has no explanation yet - Reading and writing numbers (age 10+) has no explanation yet - Comparing fractions (age 10+) has no explanation yet - Multiplying and dividing has no explanation yet - Expressions & Equations Vocabulary has no explanation yet - Checking Answers by Rounding has no explanation yet - Numbers on a number line has no explanation yet - Shape patterns has no explanation yet - Number Pattern Relationships has no explanation yet - Comparing lengths by measuring has no explanation yet - Measurement Conversions has no explanation yet - Calculating with measurements has no explanation yet - Converting measurement units (age 9+) has no explanation yet - Counting Unit Cubes has no explanation yet - Angles in triangles (age 11+) has no explanation yet - Measuring Perimeters has no explanation yet - Perimeter (age 10+) has no explanation yet - Angle Sum Rules comes before Degrees and turns, which it needs - Angle Sum Rules has no explanation yet - Measuring angles comes before Degrees and turns, which it needs - Measuring angles has no explanation yet - Measuring angles (age 9+) has no explanation yet - Understanding angles (age 10+) has no explanation yet - Understanding angles (age 11+) has no explanation yet - Telling time to the minute (age 9+) has no explanation yet - 12-hour and 24-hour time has no explanation yet - Reading tables has no explanation yet - Classifying shapes by properties has no explanation yet - Properties of triangles and quadrilaterals has no explanation yet - Degrees and turns has no explanation yet - Transformations on a Grid comes before Transformations on a grid, which it needs - Transformations on a Grid has no explanation yet - Coordinate Transformations has no explanation yet - Transformations on a grid has no explanation yet - Line graphs (age 10+) has no explanation yet - Experimental probability has no explanation yet Credit: The structure of The New Zealand Curriculum (Ministry of Education): Mathematics (https://nzcurriculum.tki.org.nz/the-nzc/learning-areas/mathematics-and-statistics); concepts from the Marble Skill Taxonomy (v1), © Generative Spark, Inc. (withmarble.com), text CC BY-SA 4.0, database ODbL 1.0: https://github.com/withmarbleapp/os-taxonomy, mapped to its standards by Marble.