How to learn Class 5: Mathematics

NCERT syllabus (National Council of Educational Research and Training): Mathematics, Class 5

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1. Geometry · SHAPES & SPATIAL UNDERSTANDING

Nets of 3-D Shapes: Identify, draw, and interpret nets of common 3-D shapes — cubes, cuboids, triangular prisms, and square-based pyramids — by predicting which 3-D shape a given flat arrangement of faces will fold into, checking whether a net will close completely, and sketching a net from a description or 3-D model; understand the relationship between the number of faces and the structure of the net
3-D shapes (age 9+): Identify 3-D shapes, including cubes and other cuboids, from 2-D representations
Types of angles: Identify acute and obtuse angles; compare and order angles up to two right angles by size
What Is an Angle?: Understand that an angle is a geometric shape formed by two rays sharing a common endpoint (vertex); recognise angles in real-life contexts and 2-D shapes
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
Coordinate Transformations: Identify properties of translations, rotations, and reflections; describe and perform these transformations on given figures, and understand that the image is congruent to the original
2-D shapes (age 8+): Identify lines of symmetry in 2-D shapes presented in different orientations; recognise line-symmetric figures and draw lines of symmetry

Place Value Problem-Solving: Solve number and practical problems involving place value with increasingly large positive numbers
Addition and subtraction strategies (age 10+): Add and subtract decimals to hundredths using strategies based on place value, properties of operations, and the relationship between addition and subtraction; relate strategies to written methods and explain reasoning

Mixed & Improper Fractions: Use the four operations with formal written methods applied to integers, decimals, proper and improper fractions, and mixed numbers, all both positive and negative
Factors, multiples, and primes: Find all factor pairs for a whole number in the range 1–100; identify common factors and common multiples of two numbers; use these concepts to solve problems

Estimation to check answers to calculations: Use estimation to check answers to calculations and determine, in the context of a problem, an appropriate degree of accuracy

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
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)

Multi-step problems: choosing operations: Solve problems involving addition, subtraction, multiplication, and division, deciding which operations and methods to use and why; solve multi-step problems in contexts
Compound Units: Use compound units such as speed (distance ÷ time), unit pricing (cost ÷ quantity), and density (mass ÷ volume); solve problems involving compound units
Estimating and comparing money: Estimate, compare, and calculate different measures including money in pounds and pence

Measurement Conversions: Solve problems involving the calculation and conversion of units of measure, using decimal notation and multi-step reasoning in real-world contexts
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
Simplifying Fractions: Use common factors to simplify fractions to their simplest form; use common multiples to express fractions with a common denominator

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

Picture & Bar Graphs: Draw a picture graph and a bar graph (with single-unit scale) to represent a data set with up to four categories; solve put-together, take-apart, and compare problems using information presented in a bar graph

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
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