# Year 8: Mathematics A course roadmap (maths). Language: en. By @si. Licence: CC BY-SA 4.0. 0 of 46 concepts ready. In the app: https://ai.page/roadmap/nz-moe-year-8 Part of: [New Zealand Curriculum: Mathematics](https://ai.page/roadmap/nz-moe.md) Goal: The New Zealand Curriculum (Ministry of Education): Mathematics, Year 8 ## 1. Number · Rational numbers - [Dividing Quantities by Ratio](https://ai.page/c/dividing-quantities-by-ratio/index.md): Divide a given quantity into two parts in a given part:part or part:whole ratio, and express the division as a fraction of the whole - [Number Sets & Infinity](https://ai.page/c/number-sets-and-infinity/index.md): Appreciate the infinite nature of the sets of integers, real numbers, and rational numbers; position integers on a number line and distinguish between rational and irrational 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 - [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% - [Ratio (age 11+)](https://ai.page/c/ratio-age-11/index.md): Use conventional notation for the priority of operations including brackets, powers, roots, and reciprocals; apply BIDMAS/BODMAS consistently to evaluate complex numerical expressions ## 2. Number · Financial mathematics - [Compound Units](https://ai.page/c/compound-units/index.md): Use compound units such as speed (distance ÷ time), unit pricing (cost ÷ quantity), and density (mass ÷ volume); solve problems involving compound units - [Calculating Percentages](https://ai.page/c/calculating-percentages/index.md): Solve problems involving the calculation of percentages of amounts (e.g. 15% of 360) and the use of percentages for comparison ## 3. Algebra · Equations and relationships - [Expanding Single Brackets](https://ai.page/c/expanding-single-brackets/index.md): Expand (multiply out) a single term over a bracket using the distributive property, e.g., 3(2x + 5) = 6x + 15; expand expressions involving negative multipliers - [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 - [Substituting into Formulae](https://ai.page/c/substituting-into-formulae/index.md): Substitute numerical values into formulae and expressions including scientific formulae; evaluate expressions by replacing variables with given values and computing the result using correct order of operations - [Solving Linear Equations](https://ai.page/c/solving-linear-equations/index.md): Use algebraic methods to solve linear equations in one variable, including equations that require rearrangement, expanding brackets, and collecting terms on both sides; solve equations with rational number coefficients ## 4. Algebra · Algorithmic - [Algebraic Transformations](https://ai.page/c/algebraic-transformations/index.md): Model situations or procedures by translating them into algebraic expressions or formulae and by using graphs; move between word problems, algebraic representations, tables, and graphical representations ## 5. Measurement · Measuring - [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 - [Unit Conversions](https://ai.page/c/unit-conversions/index.md): Convert freely between related standard units of measurement (time, length, area, volume/capacity, mass) using decimal notation to up to three decimal places where appropriate ## 6. Measurement · Perimeter, area, volume - [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 ## 7. Geometry · Shapes - [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 - [Parts of a circle](https://ai.page/c/parts-of-a-circle/index.md): Illustrate and name parts of circles, including radius, diameter, and circumference; know that the diameter is twice the radius ## 8. Geometry · Angles - [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 ## 9. Geometry · Spatial reasoning - [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 - [Angle sums in triangles and polygons](https://ai.page/c/angle-sums-in-triangles-and-polygons/index.md): Derive and use the angle sum in a triangle (180°), use it to deduce the angle sum in any polygon ((n−2) × 180°), and calculate interior and exterior angles of regular polygons ## 10. Statistics · Problem - [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 ## 11. Statistics · Analysis - [Pictograms and tally charts (age 11+)](https://ai.page/c/pictograms-and-tally-charts-age-11/index.md): Construct and interpret frequency tables, bar charts, pie charts, pictograms, and vertical line charts for both categorical and grouped numerical data, choosing appropriate representations for the data type - [Statistical Analysis Vocabulary](https://ai.page/c/statistical-analysis-vocabulary/index.md): Read, write, and use the vocabulary of statistical analysis — mean, median, mode, range, frequency, data, sample, average, chart, table, graph, pie chart, scatter graph, correlation — with understanding of what each term describes ## 12. Probability - [Tree diagrams](https://ai.page/c/tree-diagrams/index.md): Generate theoretical sample spaces for single and combined events using listing, tables, and tree diagrams, and calculate theoretical probabilities as the number of favourable outcomes divided by the total number of equally likely outcomes ## 13. Number · Number structure - [Fractions on a number line](https://ai.page/c/fractions-on-a-number-line-3/index.md): Understand and use place value for decimals, measures, and integers of any size; extend the number system to include all positive and negative integers, decimals, and fractions on a single number line - [Factors, multiples, and primes (age 11+)](https://ai.page/c/factors-multiples-and-primes-age-11/index.md): Use the concepts and vocabulary of prime numbers, factors, multiples, common factors, common multiples, highest common factor (HCF), lowest common multiple (LCM), and prime factorisation including product notation and the unique factorisation property - [Prime numbers](https://ai.page/c/prime-numbers/index.md): Know and use the vocabulary of prime numbers, prime factors, and composite numbers; establish whether a number up to 100 is prime; recall prime numbers up to 19 ## 14. Number · Operations - [Dividing by two-digit numbers](https://ai.page/c/dividing-by-two-digit-numbers/index.md): Divide numbers up to 4 digits by a two-digit number using formal written short division where appropriate, interpreting remainders according to context - [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 - [Estimating by rounding](https://ai.page/c/estimating-by-rounding-maths/index.md): Use approximation through rounding to estimate answers and calculate possible resulting errors expressed using inequality notation a < x ≤ b; understand upper and lower bounds of rounded values - [Decimal place value](https://ai.page/c/decimal-place-value-3/index.md): Round decimals to any place using place-value understanding; round any whole number to a required degree of accuracy - [Positive and Negative Numbers](https://ai.page/c/positive-and-negative-numbers/index.md): Understand positive and negative numbers as describing quantities with opposite directions or values; use them in context such as temperature, floors in a building, and bank balances - [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 ## 15. Number · Number structures and operations - [Square and cube numbers](https://ai.page/c/square-and-cube-numbers-maths/index.md): Use integer powers and associated real roots (square, cube, and higher); recognise powers of 2, 3, 4, and 5; distinguish between exact representations of roots and their decimal approximations - [Powers of Ten Notation](https://ai.page/c/powers-of-ten-notation/index.md): Interpret and compare numbers in standard form A × 10ⁿ where 1 ≤ A < 10 and n is an integer; convert between ordinary numbers and standard form ## 16. Number · Fractions, decimals, percentages and ratios - [Ratio Notation](https://ai.page/c/ratio-notation/index.md): Use ratio notation to describe the relationship between two or more quantities, simplify ratios to their simplest form, and convert between ratio and fraction representations ## 17. Algebra · Algebraic expressions and notation - [Algebraic Notation](https://ai.page/c/algebraic-notation/index.md): Use and interpret algebraic notation including: ab for a × b, 3y for y + y + y, a² for a × a, a/b for a ÷ b, coefficients as fractions, and brackets for grouping; read and write algebraic expressions fluently - [Factorising Expressions](https://ai.page/c/factorising-expressions/index.md): Factorise algebraic expressions by taking out common factors — identify the highest common factor of all terms and write the expression as a product, e.g., 6x + 9 = 3(2x + 3) - [Simple formulae](https://ai.page/c/simple-formulae/index.md): Understand and use standard mathematical formulae; rearrange formulae to change the subject, performing inverse operations to isolate a different variable - [Collecting Like Terms](https://ai.page/c/collecting-like-terms/index.md): Simplify algebraic expressions by collecting like terms — combine terms with the same variable and power (e.g., 3a + 2b + 5a = 8a + 2b) while maintaining equivalence ## 18. Measurement · Area, perimeter and volume - [Area of Triangles & Parallelograms](https://ai.page/c/area-of-triangles-and-parallelograms/index.md): Calculate the area of parallelograms and triangles using formulae (A = b × h for parallelograms, A = ½ × b × h for triangles) - [Circles: Circumference & Area](https://ai.page/c/circles-circumference-and-area/index.md): Calculate the circumference and area of circles using the formulae C = πd (or 2πr) and A = πr², and solve problems involving perimeters and areas of composite shapes that include circular parts - [Volume as additive](https://ai.page/c/volume-as-additive/index.md): Recognise volume as additive; find volumes of composite solid figures made of two or more non-overlapping right rectangular prisms ## 19. Measurement · Duration - [Reading tables](https://ai.page/c/reading-tables/index.md): Complete, read, and interpret information in tables, including timetables ## 20. Statistics · Developing knowledge from data - [Comparing measurements](https://ai.page/c/comparing-measurements/index.md): Describe, interpret, and compare distributions of a single variable using appropriate measures of central tendency (mean, median, mode) and spread (range), including the effect of outliers ## 21. Probability · Experimental probability - [Experimental vs Theoretical](https://ai.page/c/experimental-vs-theoretical/index.md): Run repeated probability experiments and compare experimental (relative frequency) results with theoretical predictions; understand and demonstrate that as the number of trials increases, the experimental probability tends towards the theoretical probability — and that short runs can give very different results ## Health: 0 of 100 Of its 46 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): - Dividing Quantities by Ratio comes before Ratio Notation, which it needs - Dividing Quantities by Ratio has no explanation yet - Number Sets & Infinity comes before Square and cube numbers, which it needs - Number Sets & Infinity has no explanation yet - Adding fractions (different denominators) has no explanation yet - Percentages as Fractions comes before Calculating Percentages, which it needs - Percentages as Fractions has no explanation yet - Ratio (age 11+) comes before Order of operations, which it needs - Ratio (age 11+) has no explanation yet - Compound Units comes before Unit Conversions, which it needs - Compound Units has no explanation yet - Calculating Percentages has no explanation yet - Expanding Single Brackets comes before Collecting Like Terms, which it needs - Expanding Single Brackets has no explanation yet - Number Pattern Relationships has no explanation yet - Substituting into Formulae comes before Algebraic Notation, which it needs - Substituting into Formulae has no explanation yet - Solving Linear Equations has no explanation yet - Algebraic Transformations comes before Algebraic Notation, which it needs - Algebraic Transformations has no explanation yet - Measurement Conversions has no explanation yet - Unit Conversions has no explanation yet - Angles in triangles (age 11+) comes before Area of Triangles & Parallelograms, which it needs - Angles in triangles (age 11+) has no explanation yet - Properties of triangles and quadrilaterals has no explanation yet - Parts of a circle has no explanation yet - Understanding angles (age 11+) has no explanation yet - Coordinate Transformations has no explanation yet - Angle sums in triangles and polygons has no explanation yet - Experimental probability comes before Experimental vs Theoretical, which it needs - Experimental probability has no explanation yet - Pictograms and tally charts (age 11+) comes before Reading tables, which it needs - Pictograms and tally charts (age 11+) has no explanation yet - Statistical Analysis Vocabulary has no explanation yet - Tree diagrams has no explanation yet - Fractions on a number line has no explanation yet - Factors, multiples, and primes (age 11+) has no explanation yet - Prime numbers has no explanation yet - Dividing by two-digit numbers has no explanation yet - Order of operations has no explanation yet - Estimating by rounding has no explanation yet - Decimal place value has no explanation yet - Positive and Negative Numbers has no explanation yet - Numbers on a number line has no explanation yet - Square and cube numbers has no explanation yet - Powers of Ten Notation has no explanation yet - Ratio Notation has no explanation yet - Algebraic Notation has no explanation yet - Factorising Expressions has no explanation yet - Simple formulae 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.