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How to learn Grade 5: Mathematics

Japan Course of Study (MEXT), elementary school: Mathematics, Grade 5

0 of 19 concepts ready to learn · Markdown, for your AI

1. Numbers and Calculations · To help pupils deepen their understanding of the properties of integers.

  1. Positive and Negative Numbers: 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
  2. Dividing fractions (unit fractions): 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

  1. Tenths (age 9+): 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.

  1. Division with Decimals: 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

  1. Fraction Addition Concepts: 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
  2. Adding fractions (different denominators): 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.

  1. Area of Triangles & Parallelograms: Calculate the area of parallelograms and triangles using formulae (A = b × h for parallelograms, A = ½ × b × h for triangles)
  2. Angles in triangles (age 11+): 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.

  1. Measuring length (age 10+): 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
  2. Counting Unit Cubes: 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.

  1. Measurement Conversions: 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.

  1. Percentages (age 9+): 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.

  1. Classifying shapes by properties: 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
  2. Types of angles (age 11+): 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
  3. Parts of a circle: 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.

  1. Volume as additive: 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.

  1. Proportion Graphs: 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

  1. Algebraic Transformations: 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
  2. Line graphs (age 10+): Interpret and construct pie charts and line graphs; use these to solve problems