# Grade 6: Mathematics A course roadmap (maths). Language: en. By @si. Licence: CC BY-SA 4.0. 0 of 15 concepts ready. In the app: https://ai.page/roadmap/jp-mext-grade-6 Part of: [Japan MEXT: Mathematics](https://ai.page/roadmap/jp-mext.md) Goal: Japan Course of Study (MEXT), elementary school: Mathematics, Grade 6 ## 1. Numbers and Calculations · To help students deepen their understanding of the meaning of multiplication and division of fractions, and use the calculations. - [Dividing fractions (unit fractions)](https://ai.page/c/dividing-fractions-unit-fractions/index.md): Interpret and compute division of a unit fraction by a non-zero whole number (e.g. 1/3 ÷ 4 = 1/12); use visual models and the relationship between multiplication and division to explain the result ## 2. Numbers and Calculations - [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 ## 3. Quantity and Measurements - [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 - [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 - [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 ## 4. Quantity and Measurements · To help pupils determine the area of geometrical figures by calculation. - [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 ## 5. Quantity and Measurements · To help pupils determine the volume of geometrical figures by calculation. - [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 ## 6. Geometrical Figures · Through activities such as observing and composing geometrical figures, to help pupils deepen their understanding of plane geometrical figures. - [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 - [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 ## 7. Mathematical Relations - [Percentages (age 9+)](https://ai.page/c/percentages-age-9/index.md): Know and use the vocabulary of ratio and proportion — ratio, proportion, percentage, scale, equivalent, unequal, relative size, part-to-part, part-to-whole, and out of — and understand the difference between ratio (comparing parts to parts) and proportion (comparing a part to the whole) ## 8. Mathematical Relations · To help pupils explore the relationships of two numbers/quantities as they vary simultaneously. - [Proportion Graphs](https://ai.page/c/proportion-graphs/index.md): Represent proportional relationships using double number lines (two parallel number lines aligned at 0) and ratio tables; recognise that equivalent ratios generate straight lines through the origin when graphed - [Proportion](https://ai.page/c/proportion/index.md): Recognise and solve problems involving direct proportion (as one quantity increases, the other increases at a constant rate) and inverse proportion (as one increases, the other decreases), including graphical and algebraic representations ## 9. Mathematical Relations · To help pupils deepen their understanding of algebraic expressions that represent the relationships of two numbers/quantities, and to use the algebraic expressions. - [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 ## 10. Mathematical Relations · To help pupils determine the average of data and the distribution of data, and to explore and represent the data statistically. - [Calculating the Mean](https://ai.page/c/calculating-the-mean/index.md): Calculate and interpret the mean as an average of a data set - [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 ## Health: 0 of 100 Of its 15 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 fractions (unit fractions) has no explanation yet - Decimals and fractions (age 10+) has no explanation yet - Perimeter (age 10+) has no explanation yet - Compound Units comes before Proportion, which it needs - Compound Units has no explanation yet - Measuring length (age 10+) has no explanation yet - Circles: Circumference & Area has no explanation yet - Volume as additive has no explanation yet - Coordinate Transformations has no explanation yet - Types of angles (age 11+) has no explanation yet - Percentages (age 9+) has no explanation yet - Proportion Graphs has no explanation yet - Proportion has no explanation yet - Algebraic Transformations has no explanation yet - Calculating the Mean has no explanation yet - Pictograms and tally charts (age 11+) has no explanation yet Credit: The structure of Japan Course of Study (MEXT), elementary school: Mathematics (https://www.mext.go.jp/component/english/__icsFiles/afieldfile/2011/03/17/1303755_004.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.