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How to learn Grade 4: Mathematics

Japan Course of Study (MEXT), elementary school: Mathematics, Grade 4

0 of 24 concepts ready to learn · Markdown, for your AI

1. Numbers and Calculations · To help pupils deepen their understanding that integers are represented by the decimal positional numeration system.

  1. Comparing Decimals: Compare two decimals to hundredths (or up to three decimal places) by reasoning about size using place-value understanding; record with >, =, <

2. Numbers and Calculations · To help pupils understand round numbers and use them according to their purposes.

  1. Rounding Answers: Solve problems which require answers to be rounded to specified degrees of accuracy
  2. Estimating by rounding: Estimate the answer to a calculation and use inverse operations to check answers; apply to increasingly large numbers using rounding and inverse reasoning

3. Numbers and Calculations · To help pupils deepen their understanding of division of integers, divide accurately, and extend their ability to use the calculation appropriately.

  1. Division with remainders (age 10+): 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
  2. 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
  3. Dividing by two-digit numbers: Divide numbers up to 4 digits by a two-digit number using formal written short division where appropriate, interpreting remainders according to context
  4. Dividing by Fractions: Interpret and compute division of a whole number by a unit fraction (e.g. 4 ÷ 1/5 = 20); use visual models and the relationship between multiplication and division to explain why the quotient is larger than the dividend
  5. 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

4. Numbers and Calculations

  1. Adding and subtracting (age 9+): Solve addition and subtraction multi-step problems in contexts, deciding which operations and methods to use and why
  2. Adding and subtracting (age 8+): Add and subtract numbers with up to four digits using formal written methods of columnar addition and subtraction

5. Numbers and Calculations · To help pupils deepen their understanding of decimal numbers as well as their understanding of addition and subtraction of decimal numbers, and to help them understand the m

  1. Decimals for Tenths & Hundredths: Use decimal notation for fractions with denominators 10 or 100; read and write decimal numbers as fractions (e.g. 0.62 = 62/100, 0.71 = 71/100)
  2. Adding and subtracting (age 10+): 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

6. Numbers and Calculations · To help pupils deepen their understanding of fractions, and to help them understand the meaning of addition and subtraction of fractions with the same denominators, and use

  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
  3. Fraction Notation: Read, write, and use fraction notation correctly — fraction, numerator, denominator, unit fraction, non-unit fraction, proper fraction, improper fraction, mixed number, equivalent fraction, simplest form — and understand what each term describes, including the roles of the numerator and denominator in expressing parts of a whole

7. Quantities and Measurements · To help pupils understand the meaning of units and measurements of area, and determine the area by calculation.

  1. Area (age 8+): Measure areas by counting unit squares (square cm, square m, square in, square ft)

8. Quantities and Measurements · To help pupils understand the meaning of unit and measurements of angle, and measure angles.

  1. Degrees and turns: Know that angles are measured in degrees, where one degree is 1/360 of a full turn; understand that an angle turning through n one-degree angles has a measure of n degrees
  2. Measuring angles: Measure angles in whole-number degrees using a protractor; draw given angles and sketch angles of specified measure

9. Geometrical Figures · Through activities such as observing and composing geometrical figures, to help pupils pay attention to the elements that compose geometrical figures as well as their positional

  1. Classifying shapes by line properties: 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
  2. 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

10. Geometrical Figures · Through activities such as observing and composing geometrical figures, to help pupils understand solid geometrical figures.

  1. Lines, Rays & Angles: Draw and identify points, lines, line segments, rays, angles (right, acute, obtuse), and perpendicular and parallel lines; identify these in two-dimensional figures

11. Mathematical Relations · To help pupils represent and explore the relationships between two numbers/quantities as they vary simultaneously.

  1. Number Pattern Relationships: Generate two numerical patterns using two given rules; identify relationships between corresponding terms; form ordered pairs and graph them on a coordinate plane

12. Mathematical Relations · To help pupils understand the algebraic expressions that represent the relationships between numbers/quantities, and use these expressions.

  1. Understanding fractions (age 10+): Move fluently between real-world situations, diagrams, coordinate grids, algebraic expressions, tables, and symbolic equations involving fractions, ratio, and algebra, explaining connections between representations

13. Mathematical Relations · To help pupils deepen their understanding of the properties of the four basic operations.

  1. Properties of Operations: Apply properties of operations (commutative, associative, distributive) as strategies to multiply and divide