How to learn Class 3: Mathematics

NCERT syllabus (National Council of Educational Research and Training): Mathematics, Class 3

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1. Geometry · SHAPES & SPATIAL UNDERSTANDING

Composing Shapes: Compose two-dimensional shapes (rectangles, squares, trapezoids, triangles, half-circles, quarter-circles) to create composite shapes, and compose new shapes from the composite shape
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
Understanding angles: Recognise angles as a property of shape or a description of a turn
Transformations on a grid: Represent and carry out geometric transformations on squared paper or a coordinate grid: reflections (in horizontal, vertical, and diagonal mirror lines, including the axes), translations (described as a vector or as left/right/up/down moves), and rotations (90° or 180° about a stated centre point); describe each transformation precisely using the correct language; identify which transformation maps one shape onto its image by comparing position, orientation, and size
Area by Tiling: Find the area of a rectangle by tiling it with unit squares and show that the result equals the product of the side lengths

Reading and writing numbers to 1000: Read and write numbers to 1000 in numerals, number names, and expanded form
Place Value to 1000: Solve number problems and practical problems involving place value of numbers up to 1000
Counting Within 1,000: Count within 1000, including skip-counting by 5s, 10s, and 100s

Comparing Large Numbers: Order and compare numbers beyond 1000
Working with Large Numbers: Solve number and practical problems involving reading, writing, ordering, comparing, and rounding whole numbers up to 1,000,000

Adding and subtracting mixed numbers: Add and subtract mixed numbers with like denominators, including by converting to improper fractions or using properties of operations
Adding numbers: Add up to four two-digit numbers using strategies based on place value and properties of operations
Representing Addition and Subtraction: Represent addition and subtraction using objects, drawings, and mental images
Addition and subtraction word problems: Solve word problems involving addition and subtraction of fractions with like denominators, using visual models and equations
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

Multiplication as repeated addition: Understand multiplication as repeated addition and grouping equal sets
What Multiplication Means: Interpret products of whole numbers (e.g. 5 × 7 as the total number of objects in 5 groups of 7)
Times tables: Recall and use multiplication and division facts for the 2, 5, and 10 multiplication tables
Written Multiplication: Multiply two-digit and three-digit numbers by a one-digit number using formal written layout

What Division Means: Interpret whole-number quotients (e.g. 56 ÷ 8 as the number of objects in each share or the number of equal groups)
All times tables to 12×12: Recall multiplication and division facts for multiplication tables up to 12 × 12

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

Fractions of amounts: Recognise, find, name, and write fractions 1/3, 1/4, 2/4, and 3/4 of a length, shape, set of objects, or quantity
Fractions of a whole: Understand a fraction 1/b as the quantity formed by 1 part when a whole is partitioned into b equal parts; understand a/b as a parts of size 1/b
Fraction-Decimal Equivalents: Recognise and write decimal equivalents of 1/4, 1/2, and 3/4

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

Estimating Lengths: Estimate lengths using units of inches, feet, centimetres, and metres

Measuring mass and weight: Measure and begin to record mass/weight using non-standard and standard units

Capacity and volume: Measure and begin to record capacity and volume using non-standard and standard units

Sequence intervals of time: Compare and sequence intervals of time
Estimating answers (age 7+): Estimate and read time with increasing accuracy to the nearest minute; record and compare time in terms of seconds, minutes, and hours

Pictograms and tally charts: Interpret and construct simple pictograms, tally charts, block diagrams, and simple tables

Shape patterns: Generate a number or shape pattern that follows a given rule; identify apparent features of the pattern not explicit in the rule and explain informally why they occur
Patterns & Sequences: Order and arrange combinations of mathematical objects in patterns and sequences