# Grade 5: Mathematics A course roadmap (maths). Language: en. By @si. Licence: CC BY-SA 4.0. 0 of 19 concepts ready. In the app: https://ai.page/roadmap/jp-mext-grade-5 Part of: [Japan MEXT: Mathematics](https://ai.page/roadmap/jp-mext.md) Goal: Japan Course of Study (MEXT), elementary school: Mathematics, Grade 5 ## 1. Numbers and Calculations · To help pupils deepen their understanding of the properties of integers. - [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 - [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 · To help pupils deepen their understanding of integers and decimal numbers based on the concept of the numeration system, and to use the understanding efficiently in calculat - [Tenths (age 9+)](https://ai.page/c/tenths-age-9/index.md): Recognise and use thousandths; relate them to tenths, hundredths, and their decimal equivalents (e.g. 1/1000 = 0.001, 35/1000 = 0.035) ## 3. Numbers and Calculations · To help pupils deepen their understanding of the meaning of multiplication and division in decimal numbers, and use the calculations. - [Division with Decimals](https://ai.page/c/division-with-decimals/index.md): Use written division methods in cases where the answer has up to two decimal places; divide decimals to hundredths by whole numbers ## 4. Numbers and Calculations · To help pupils deepen their understanding of fractions, understand the meaning of addition and subtraction of fractions with different denominators, and to use the calculati - [Fraction Addition Concepts](https://ai.page/c/fraction-addition-concepts/index.md): Understand addition and subtraction of fractions as joining and separating parts; decompose a fraction into a sum of fractions with the same denominator in more than one way - [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 ## 5. Quantities and Measurements · To help pupils determine the area of geometrical figures by calculation. - [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) - [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 ## 6. Quantities and Measurements · To help pupils understand the meaning of units and measurements of volume, and determine the volume by calculation. - [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 - [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 ## 7. Quantities and Measurements · To help pupils understand the measured value of quantities. - [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 ## 8. Quantities and Measurements · To help pupils understand how to represent and compare quantities that are obtained as a ratio of two quantities of different types. - [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) ## 9. Geometrical Figures · Through activities such as observing and composing geometrical figures, to help pupils deepen their understanding of plane geometrical figures. - [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 - [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 - [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 ## 10. Geometrical Figures · Through activities such as observing and composing geometrical figures, to help pupils understand solid geometrical figures. - [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 ## 11. Mathematical Relations · To help pupils use tables to explore the relationships between two 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 ## 12. Mathematical Relations - [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 - [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 ## Health: 0 of 100 Of its 19 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 - Dividing fractions (unit fractions) has no explanation yet - Tenths (age 9+) has no explanation yet - Division with Decimals has no explanation yet - Fraction Addition Concepts has no explanation yet - Adding fractions (different denominators) has no explanation yet - Area of Triangles & Parallelograms has no explanation yet - Angles in triangles (age 11+) has no explanation yet - Measuring length (age 10+) has no explanation yet - Counting Unit Cubes has no explanation yet - Measurement Conversions has no explanation yet - Percentages (age 9+) has no explanation yet - Classifying shapes by properties has no explanation yet - Types of angles (age 11+) has no explanation yet - Parts of a circle has no explanation yet - Volume as additive has no explanation yet - Proportion Graphs has no explanation yet - Algebraic Transformations has no explanation yet - Line graphs (age 10+) 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.