# Middle Stage (Classes 6–8): Mathematics

A course roadmap (maths). Language: en. By @si. Licence: CC BY-SA 4.0. 0 of 17 concepts ready. In the app: https://ai.page/roadmap/in-ncf-math-middle-stage-classes-6-8

Part of: [NCF-SE 2023: Mathematics](https://ai.page/roadmap/in-ncf-math.md)

Goal: National Curriculum Framework for School Education 2023 (NCERT): Mathematics, curricular goals and competencies, Middle Stage (Classes 6–8)

## 1. Middle Stage (Classes 6–8)

- [Adding and subtracting (age 10+)](https://ai.page/c/adding-and-subtracting-age-10/index.md): Solve addition and subtraction multi-step problems in contexts, deciding which operations and methods to use and why, with numbers up to 10,000,000 and decimals
- [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
- [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
- [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
- [Percentages (age 12+)](https://ai.page/c/percentages-age-12/index.md): Solve problems involving percentage increase, percentage decrease, finding the original value after a percentage change, and calculating simple interest
- [Understanding fractions (age 10+)](https://ai.page/c/understanding-fractions-age-10/index.md): Move fluently between real-world situations, diagrams, coordinate grids, algebraic expressions, tables, and symbolic equations involving fractions, ratio, and algebra, explaining connections between representations
- [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
- [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
- [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
- [Types of angles (age 11+)](https://ai.page/c/types-of-angles-age-11/index.md): Use conventional geometric terms and notation to describe, sketch, and draw points, lines, parallel and perpendicular lines, right angles, regular polygons, and reflectively/rotationally symmetric polygons
- [Types of angles (age 8+)](https://ai.page/c/types-of-angles-age-8/index.md): Use and interpret standard geometric diagram conventions: mark right angles with a small square, equal lengths with single or double tick marks, and equal angles with arc marks; label angles in three-letter notation (∠ABC) and individual angles with a single letter or number; draw diagrams showing angles at a point, angles on a straight line, and angles inside polygons with these conventions; read diagrams with these marks to identify given information and find unknown values
- [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
- [Types of angles (age 13+)](https://ai.page/c/types-of-angles-age-13/index.md): Apply Pythagoras’ Theorem (a² + b² = c²) to calculate unknown side lengths in right-angled triangles, including in real-world and coordinate-geometry contexts
- [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
- [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
- [Constructing mathematical arguments](https://ai.page/c/constructing-mathematical-arguments/index.md): Construct and present logical mathematical arguments involving multiple steps and formal reasoning; critique others' reasoning about fractions, algebra, ratio, or geometry and clearly explain errors or alternative approaches
- [Multi-step problems: choosing operations](https://ai.page/c/multi-step-problems-choosing-operations/index.md): Solve problems involving addition, subtraction, multiplication, and division, deciding which operations and methods to use and why; solve multi-step problems in contexts

## Health: 0 of 100

Of its 17 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):

- Adding and subtracting (age 10+) has no explanation yet
- Number Pattern Relationships has no explanation yet
- Number Sets & Infinity has no explanation yet
- Decimals and fractions (age 10+) has no explanation yet
- Percentages (age 12+) has no explanation yet
- Understanding fractions (age 10+) has no explanation yet
- Algebraic Transformations has no explanation yet
- Understanding angles (age 11+) has no explanation yet
- 3-D shapes (age 11+) has no explanation yet
- Types of angles (age 11+) has no explanation yet
- Types of angles (age 8+) has no explanation yet
- Angles in triangles (age 11+) has no explanation yet
- Types of angles (age 13+) has no explanation yet
- Pictograms and tally charts (age 11+) has no explanation yet
- Comparing measurements has no explanation yet
- Constructing mathematical arguments has no explanation yet
- Multi-step problems: choosing operations has no explanation yet

Credit: The structure of National Curriculum Framework for School Education 2023 (NCERT): Mathematics, curricular goals and competencies (https://ncert.nic.in/pdf/NCFSE-2023-August_2023.pdf); 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.