How to learn Preparatory Stage (Classes 3–5): Mathematics

National Curriculum Framework for School Education 2023 (NCERT): Mathematics, curricular goals and competencies, Preparatory Stage (Classes 3–5)

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1. Preparatory Stage (Classes 3–5)

Reading and writing numbers (age 9+): Read, write, order, and compare whole numbers up to at least 1,000,000 using base-ten numerals, number names, expanded form, and place-value understanding
Fractions of a whole (age 8+): Express whole numbers as fractions (e.g. 3 = 3/1) and recognise fractions equivalent to whole numbers (e.g. 4/4 = 1, 6/1 = 6)
Fractions of a whole (age 10+): Interpret a fraction as division of the numerator by the denominator (a/b = a ÷ b); solve word problems involving division of whole numbers leading to fractional or mixed-number answers
Adding and subtracting (age 9+): Solve addition and subtraction multi-step problems in contexts, deciding which operations and methods to use and why
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
3-D shapes (age 5+): Analyse and compare 2-D and 3-D shapes using informal language to describe sides, vertices, and other attributes
2-D shapes (age 7+): Draw 2-D shapes and make 3-D shapes using modelling materials; recognise 3-D shapes in different orientations and describe them
Measuring length (age 7+): Measure the length of an object by selecting and using appropriate tools such as rulers, yardsticks, metre sticks, and measuring tapes
Converting measurement units (age 9+): Know relative sizes of measurement units within one system (km/m/cm/mm, kg/g, l/ml, hr/min/sec); convert between different metric units and express measurements in terms of a smaller unit; record equivalents in conversion tables
Estimating answers (age 9+): Apply the area formula (l × w) and perimeter formula (2l + 2w) for rectangles including squares in real-world and mathematical problems; calculate and compare areas using standard units (cm², m²) and estimate areas of irregular shapes
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
Perimeter (age 10+): Recognise that shapes with the same area can have different perimeters and vice versa; explore this relationship systematically
Choosing mathematical tools: Select and use appropriate tools and representations strategically: choose between mental, written, and diagrammatic methods; use calculators for checking; select fraction models suited to the task