# Year 7: Mathematics A course roadmap (maths). Language: en. By @si. Licence: CC BY-SA 4.0. 0 of 73 concepts ready. In the app: https://ai.page/roadmap/nz-moe-year-7 Part of: [New Zealand Curriculum: Mathematics](https://ai.page/roadmap/nz-moe.md) Goal: The New Zealand Curriculum (Ministry of Education): Mathematics, Year 7 ## 1. Number · Operations - [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 - [Division with remainders (age 10+)](https://ai.page/c/division-with-remainders-age-10/index.md): Divide numbers up to 4 digits by a two-digit divisor using formal written long division, interpreting remainders as whole numbers, fractions, or by rounding as appropriate - [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 ## 2. Number · Rational numbers - [Decimal & Percent Notation](https://ai.page/c/decimal-and-percent-notation/index.md): Read, write, and use decimal and percentage notation correctly — decimal, decimal point, tenths, hundredths, thousandths, percentage, per cent, % symbol, convert, terminating decimal — and understand the relationships between fractions, decimals, and percentages as three ways of expressing the same value - [Fractions on a number line (age 11+)](https://ai.page/c/fractions-on-a-number-line-age-11/index.md): Order positive and negative integers, decimals, and fractions on a number line; use the symbols =, ≠, <, >, ≤, ≥ to compare values including negative numbers and mixed representations - [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% - [Proportional Reasoning Vocabulary](https://ai.page/c/proportional-reasoning-vocabulary/index.md): Know and use advanced vocabulary of multiplicative reasoning — direct proportion, inverse proportion, ratio, rate, unit rate, compound unit, scale factor — accurately in problem-solving contexts - [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 - [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 ## 3. Number · Financial mathematics - [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 - [Rounding Answers](https://ai.page/c/rounding-answers/index.md): Solve problems which require answers to be rounded to specified degrees of accuracy ## 4. Algebra · Equations and relationships - [Writing Algebraic Equations](https://ai.page/c/writing-algebraic-equations/index.md): Express missing number problems algebraically using letters for unknowns; translate word problems into equations - [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 - [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 - [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 - [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) - [Equations with Two Unknowns](https://ai.page/c/equations-with-two-unknowns/index.md): Find pairs of numbers that satisfy an equation with two unknowns (e.g. find pairs (a, b) where a + b = 10 or 2a + b = 15) - [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. 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 - [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 - [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 ## 6. Measurement · Perimeter, area, volume - [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 ## 7. Measurement · Timetables and charts - [Reading tables](https://ai.page/c/reading-tables/index.md): Complete, read, and interpret information in tables, including timetables ## 8. Geometry · Shapes - [Classifying shapes by line properties](https://ai.page/c/classifying-shapes-by-line-properties/index.md): Classify two-dimensional figures based on the presence or absence of parallel or perpendicular lines, or angles of a specified size; recognise right triangles as a category - [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 - [Scale and similar shapes](https://ai.page/c/scale-and-similar-shapes/index.md): Solve problems involving similar shapes where the scale factor is known or can be found - [Angles in triangles (age 10+)](https://ai.page/c/angles-in-triangles-age-10/index.md): Find unknown angles in triangles, quadrilaterals, and regular polygons using angle sum properties ## 9. Geometry · Angles - [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 ## 10. Geometry · Spatial reasoning - [3-D shapes (age 11+)](https://ai.page/c/3-d-shapes-age-11/index.md): Use the properties of faces, surfaces, edges, and vertices of 3-D shapes (cubes, cuboids, prisms, cylinders, pyramids, cones, and spheres) to solve problems, including visualising cross-sections - [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 - [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 - [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 - [Nets of 3-D Shapes](https://ai.page/c/nets-of-3-d-shapes/index.md): Identify, draw, and interpret nets of common 3-D shapes — cubes, cuboids, triangular prisms, and square-based pyramids — by predicting which 3-D shape a given flat arrangement of faces will fold into, checking whether a net will close completely, and sketching a net from a description or 3-D model; understand the relationship between the number of faces and the structure of the net - [Angles with parallel lines](https://ai.page/c/angles-with-parallel-lines/index.md): Understand and use the relationship between parallel lines cut by a transversal: corresponding angles, alternate interior angles, and co-interior (same-side interior) angles; use these to find unknown angles ## 11. Geometry · Pathways - [Scale and similar shapes (age 11+)](https://ai.page/c/scale-and-similar-shapes-age-11/index.md): Use scale factors to interpret and create scale diagrams and maps, calculating real-life distances from map measurements and vice versa ## 12. 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 ## 13. Statistics · Analysis - [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 ## 14. Number · Number structure - [Reading and writing numbers to 10,000,000](https://ai.page/c/reading-and-writing-numbers-to-10-000-000/index.md): Read, write, order, and compare numbers up to 10,000,000 and determine the value of each digit - [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 - [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 ## 15. Number · Number structures and operations - [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 - [Patterns with Powers of Ten](https://ai.page/c/patterns-with-powers-of-ten/index.md): Explain patterns in zeros when multiplying by powers of 10 and in decimal-point placement when multiplying/dividing by a power of 10; use whole-number exponents to denote powers of 10 (e.g. 10³ = 1000) - [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 - [Mixed & Improper Fractions](https://ai.page/c/mixed-and-improper-fractions/index.md): Use the four operations with formal written methods applied to integers, decimals, proper and improper fractions, and mixed numbers, all both positive and negative - [Using inverse operations](https://ai.page/c/using-inverse-operations/index.md): Recognise and use relationships between operations including inverse operations; use these relationships to check answers and simplify calculations - [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 ## 16. Number · Fractions, decimals, percentages and ratios - [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 and fractions (age 11+)](https://ai.page/c/decimals-and-fractions-age-11/index.md): Work interchangeably with terminating decimals and their corresponding fractions (such as 3.5 and 7/2 or 0.375 and 3/8); convert fluently between the two forms - [Fractions, Decimals & Percentages](https://ai.page/c/fractions-decimals-and-percentages/index.md): Look for and use mathematical structure: exploit the relationship between fractions, decimals, and percentages; use factor pairs to simplify multiplication; apply angle facts to find unknowns; use properties of regular polygons systematically - [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 - [Ratio Notation and Relationships](https://ai.page/c/ratio-notation-and-relationships/index.md): Understand that a multiplicative relationship between two quantities can be expressed as a ratio; use ratio notation; simplify ratios - [Ratio Problems](https://ai.page/c/ratio-problems/index.md): Solve problems involving the relative sizes of two quantities where missing values can be found by using integer multiplication and division facts ## 17. Algebra · Algebraic expressions and notation - [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. Algebra · Coordinate plane and linear patterns - [Plotting points in the first quadrant](https://ai.page/c/plotting-points-in-the-first-quadrant/index.md): Plot and read ordered pairs in the first quadrant of the coordinate plane; represent real-world and mathematical problems by graphing points and interpreting coordinate values in context ## 19. Measurement · Area, perimeter and volume - [Measuring length (age 10+)](https://ai.page/c/measuring-length-age-10/index.md): Recognise volume as an attribute of solid figures; understand that a unit cube (side length 1 unit) has 'one cubic unit' of volume and can be used to measure volume; a solid packed with n unit cubes has volume n cubic units - [Using Simple Formulae](https://ai.page/c/using-simple-formulae/index.md): Use simple formulae expressed in words or symbols to calculate values (e.g. perimeter = 2 × (length + width)) - [Estimating answers (age 10+)](https://ai.page/c/estimating-answers-age-10/index.md): Find the volume of right rectangular prisms by packing with unit cubes and show it equals l × w × h (or base area × height); apply V = l × w × h and V = B × h to solve real-world problems; calculate, estimate, and compare volumes of cubes and cuboids in standard units (cm³, m³) - [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 ## 20. Measurement · Duration - [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) ## 21. Statistics · Developing knowledge from data - [Calculating the Mean](https://ai.page/c/calculating-the-mean/index.md): Calculate and interpret the mean as an average of a data set - [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 ## 22. Statistics · Visualisation of data - [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 ## 23. Probability · Experimental probability - [Simple Chance Experiments](https://ai.page/c/simple-chance-experiments/index.md): Conduct simple probability experiments — flipping a coin, rolling a die, pulling coloured counters from a bag — record results, and compare experimental outcomes with expected theoretical outcomes ## 24. Probability · Theoretical 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 - [The 0-to-1 Probability Scale](https://ai.page/c/the-0-to-1-probability-scale/index.md): Understand probability as a measure expressed as a number between 0 (impossible) and 1 (certain); place events on the probability scale; express probabilities as fractions, decimals, and percentages - [Calculating Simple Probability](https://ai.page/c/calculating-simple-probability/index.md): Calculate the probability of a simple event with equally likely outcomes using the formula: probability = number of favourable outcomes ÷ total number of possible outcomes; express the result as a fraction in its simplest form; apply to rolling dice, drawing from bags, and other simple chance situations - [Complementary events](https://ai.page/c/complementary-events/index.md): Understand and apply the rule that probabilities of all mutually exclusive outcomes sum to one; use this to find the probability of a complementary event (P(not A) = 1 − P(A)) ## Health: 0 of 100 Of its 73 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): - Positive and Negative Numbers has no explanation yet - Division with remainders (age 10+) 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 - Decimal & Percent Notation has no explanation yet - Fractions on a number line (age 11+) comes before Fractions on a number line, which it needs - Fractions on a number line (age 11+) has no explanation yet - Percentages as Fractions comes before Calculating Percentages, which it needs - Percentages as Fractions has no explanation yet - Proportional Reasoning Vocabulary has no explanation yet - Ratio Notation has no explanation yet - Multiplying and dividing has no explanation yet - Calculating Percentages comes before Decimals and fractions (age 10+), which it needs - Calculating Percentages has no explanation yet - Rounding Answers has no explanation yet - Writing Algebraic Equations has no explanation yet - Substituting into Formulae comes before Algebraic Notation, which it needs - Substituting into Formulae has no explanation yet - Solving Linear Equations comes before Using inverse operations, which it needs - Solving Linear Equations has no explanation yet - Algebraic Transformations comes before Algebraic Notation, which it needs - Algebraic Transformations has no explanation yet - Number Pattern Relationships has no explanation yet - Expressions & Equations Vocabulary comes before Algebraic Notation, which it needs - Expressions & Equations Vocabulary has no explanation yet - Equations with Two Unknowns has no explanation yet - Numbers on a number line has no explanation yet - Measurement Conversions has no explanation yet - Unit Conversions has no explanation yet - Compound Units has no explanation yet - Counting Unit Cubes comes before Measuring length (age 10+), which it needs - Counting Unit Cubes has no explanation yet - Circles: Circumference & Area has no explanation yet - Reading tables has no explanation yet - Classifying shapes by line properties has no explanation yet - Classifying shapes by properties has no explanation yet - Properties of triangles and quadrilaterals has no explanation yet - Scale and similar shapes comes before Ratio Problems, which it needs - Scale and similar shapes has no explanation yet - Angles in triangles (age 10+) has no explanation yet - Understanding angles (age 10+) has no explanation yet - 3-D shapes (age 11+) has no explanation yet - Coordinate Transformations has no explanation yet - Understanding angles (age 11+) has no explanation yet - Angle sums in triangles and polygons has no explanation yet - Nets of 3-D Shapes has no explanation yet - Angles with parallel lines has no explanation yet - Scale and similar shapes (age 11+) 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.