How to learn Class 2: Mathematics

NCERT syllabus (National Council of Educational Research and Training): Mathematics, Class 2

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1. Geometry · SHAPES & SPATIAL UNDERSTANDING

Understanding angles: Recognise angles as a property of shape or a description of a turn

3-D shapes: Recognise and name common 3-D shapes (cubes, cuboids, pyramids, spheres, cylinders, cones)
2-D shapes: Recognise and name common 2-D shapes (circles, triangles, rectangles including squares)
2-D shapes (age 6+): Identify and describe properties of 2-D shapes including the number of sides and line symmetry in a vertical line
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
2-D faces on 3-D shapes: Identify 2-D shapes on the surface of 3-D shapes (e.g. a circle on a cylinder, a triangle on a pyramid)

Number Words to 100: Read and write numbers to at least 100 in words
Place Value Problem-Solving: Solve number and practical problems involving place value with increasingly large positive numbers
Tenths: Count up and down in tenths; recognise that tenths arise from dividing an object into 10 equal parts and from dividing one-digit numbers or quantities by 10
Counting in 2s: Count in multiples of 2, 5, and 10 (skip counting)
Ordering Numbers to 1000: Compare and order numbers up to 1000 using >, =, and < symbols, based on place-value understanding
The two digits of a two-digit number: Understand that the two digits of a two-digit number represent amounts of tens and ones
Numbers on a number line: Represent whole numbers as lengths on a number line and represent sums and differences within 100 on a number line diagram

Adding two two-digit numbers: Add and subtract two two-digit numbers using concrete objects, pictorial representations, and mental methods
Adding and subtracting: Add and subtract one-digit and two-digit numbers to 20, including zero
Addition as combining or putting together two: Understand addition as combining or putting together two groups to find the total
Addition in any order: Understand and apply the commutative property of addition: addends can be added in any order
Representing Addition and Subtraction: Represent addition and subtraction using objects, drawings, and mental images
Addition and subtraction word problems: Solve addition and subtraction word problems within 10 using objects or drawings
Mental and written addition and subtraction: Solve addition and subtraction problems using mental and written methods, including problems involving numbers, quantities, and measures
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

Multiplication as repeated addition (age 6+): Solve problems involving multiplication and division using arrays, repeated addition, mental methods, and known facts
Division as equal sharing: Understand division as sharing equally into groups or as grouping (how many groups of a given size can be made)

Mentally adding hundreds to 3-digit numbers: Mentally add and subtract a three-digit number and hundreds
Mental addition and subtraction (age 7+): Mentally add and subtract a three-digit number and ones
Adding and subtracting tens mentally: Add and subtract a two-digit number and tens mentally and using concrete/pictorial representations

Measuring with different units: Measure the length of an object using two different length units and describe how the measurements relate to the size of the unit chosen
Comparing lengths by measuring: Measure to determine how much longer one object is than another, expressing the length difference in terms of a standard length unit
Measuring & Plotting Lengths: Generate measurement data by measuring lengths to the nearest whole unit and display the data on a line plot

Measuring mass and weight (age 4+): Compare two objects directly by mass or weight and describe the difference using language such as heavy, light, heavier than, lighter than

Comparing and ordering measurements: Compare and order lengths, mass, and capacity and record results using >, <, and =

Days, Weeks, Months & Years: Recognise and use language relating to dates, including days of the week, weeks, months, and years
Sequence intervals of time: Compare and sequence intervals of time

Representing numbers with objects (age 8+): Draw a scaled picture graph and a scaled bar graph to represent a data set; solve one- and two-step comparison, sum, and difference problems using bar charts, pictograms, and tables

Patterns & Sequences: Order and arrange combinations of mathematical objects in patterns and sequences
Shape patterns: Look for and use mathematical structure: apply properties of operations, place-value patterns, and relationships between shapes to solve problems efficiently