ai.page · roadmaps

How to learn Class 4: Mathematics

NCERT syllabus (National Council of Educational Research and Training): Mathematics, Class 4

0 of 37 concepts ready to learn · Markdown, for your AI

1. Geometry · SHAPES & SPATIAL UNDERSTANDING

  1. Parts of a circle: Illustrate and name parts of circles, including radius, diameter, and circumference; know that the diameter is twice the radius
  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
  3. 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
  4. Perimeter (age 10+): Recognise that shapes with the same area can have different perimeters and vice versa; explore this relationship systematically
  5. 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
  6. 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
  7. 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. Numbers · NUMBERS AND OPERATIONS

  1. Written Multiplication: Multiply two-digit and three-digit numbers by a one-digit number using formal written layout

3. Numbers

  1. Adding and subtracting mixed numbers: Add and subtract mixed numbers with like denominators, including by converting to improper fractions or using properties of operations
  2. Adding fractions (different denominators): Add and subtract fractions with denominators that are multiples of the same number by finding a common denominator
  3. 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
  4. Properties of Operations: Apply properties of operations (commutative, associative, distributive) as strategies to multiply and divide
  5. 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

4. MENTAL ARITHMETIC

  1. Mental addition and subtraction (age 9+): Add and subtract numbers mentally with increasingly large numbers, using place-value knowledge and derived facts
  2. Mental multiplication and division (age 9+): Multiply and divide numbers mentally drawing upon known facts, including related facts and place-value adjustments

5. FRACTIONAL NUMBERS

  1. 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
  2. Comparing fractions (age 8+): Compare two fractions with the same numerator or the same denominator by reasoning about size; record comparisons with >, =, or < symbols
  3. Equivalent fractions: Recognise and show, using diagrams, equivalent fractions with small denominators
  4. 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)

6. Measurement · LENGTH

  1. 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
  2. Calculating with measurements: Measure, compare, add, and subtract lengths (m/cm/mm), mass (kg/g), and volume/capacity (l/ml) using standard units
  3. 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

7. Measurement · Length

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

8. Measurement · Weight

  1. Measuring Liquids & Masses: Measure and estimate liquid volumes and masses of objects using grams, kilograms, and litres; solve one-step word problems involving mass or volume

9. Measurement · Volume

  1. 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
  2. Counting Unit Cubes: Measure volumes by counting unit cubes using cubic cm, cubic in, cubic ft, and other units

10. Measurement · Time

  1. Telling time to the minute (age 9+): Solve problems involving converting between units of time (hours↔minutes, minutes↔seconds, years↔months, weeks↔days)
  2. Time Units and Calendar Facts: Know the number of seconds in a minute and the number of days in each month, year, and leap year
  3. Telling time to the minute (age 7+): Tell and write time from analogue and digital clocks to the nearest five minutes, using a.m., p.m., and 12-hour and 24-hour notation
  4. Telling time to the minute (age 8+): Tell and write time to the nearest minute using analogue and digital clocks
  5. 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
  6. Comparing Time Durations: Compare durations of events and calculate the time taken by particular events or tasks

11. Data Handling

  1. Pictograms and tally charts (age 6+): Read, write, and use the vocabulary of data collection and display — data, tally, tally chart, frequency, frequency table, survey, pictogram, bar chart, axis/axes, scale, label, category, discrete data, continuous data, line graph, pie chart — and apply these terms when collecting, organising, and presenting data
  2. 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

12. Patterns

  1. Patterns in Times Tables: Identify arithmetic patterns (including patterns in the addition table or multiplication table) and explain them using properties of operations
  2. Multiplying and dividing: Multiply and divide whole numbers and those involving decimals by 10, 100, and 1000
  3. 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