Class 5 Maths

Here you can find Class 5 Maths Notes. These notes include important revision points, simple explanations of “Maths Mela”.

Chapter 1.  We the Travellers—I 

This chapter strengthens understanding of large numbers up to ten-thousands. Students revise place value, learn to use commas correctly, and practice reading and writing number names accurately.

It covers:

• Comparing and ordering numbers (increasing & decreasing order)

• Identifying and continuing number patterns

• Writing numbers in expanded form

• Digit swapping to create larger or smaller numbers

• Rounding off to the nearest tens, hundreds, and thousands

The chapter also includes fun puzzles and number tricks, helping students develop logical thinking while enjoying mathematics.

Overall, it builds a strong foundation in working confidently with large numbers.

Key Points

• Large Numbers & Place Value – Understanding numbers up to ten-thousands; using commas to write them correctly.

• Number Patterns – Sequences with patterns like adding 111, 1,050, 900, 100, 20, etc., to generate the next number in the sequence.

• Reading & Writing Numbers – Correctly writing names of numbers (e.g., 8,045 as “Eight thousand forty-five”).

• Ordering Numbers – Arranging numbers in increasing or decreasing order.

• Comparing Numbers – A five-digit number (49,014) is always greater than a four-digit number (9,990), regardless of the first digit.

• Digit Swap – Interchanging digits to make numbers larger/smaller (e.g., swap to get numbers >5,500 or between 11,000 & 15,000).

• Rounding Off – Rounding to nearest tens, hundreds, and thousands; finding nearest hundred/thousand for numbers like 2,346.

• Expanded Form – Writing numbers as sum of place values: e.g., 65,342 = 60,000 + 5,000 + 300 + 40 + 2.

• Fun with Numbers – Including puzzles, such as the lion-sheep-grass river crossing, and games with numbers illustrating tricks with digit subtraction (differences always multiples of 9). 

👉 👉Numbers tell stories! From writing large numbers with commas to solving puzzles and patterns, this chapter shows how maths makes numbers come alive. It sharpens thinking, attention to detail, and playful curiosity through travel-themed contexts. 

Chapter 2. Fractions 

This chapter introduces the concept of fractions, which represent a part of a whole. When something is divided into equal parts, a fraction tells us how many parts are taken. For example, ½ means 1 out of 2 equal parts.

Students learn about the two important parts of a fraction:

• Numerator – The top number showing the parts taken.

• Denominator – The bottom number showing the total equal parts.

The chapter explains different types of fractions:

• Proper Fractions (numerator less than denominator)

• Improper Fractions (numerator greater than denominator)

• Mixed Fractions (a whole number and a proper fraction together)

Students also understand equivalent fractions, which look different but have the same value (like ½ = 2/4). They learn about like fractions (same denominator) and unlike fractions (different denominators).

The chapter teaches how to:

• Compare fractions (by checking numerators or finding LCM when needed)

• Add and subtract fractions (same denominator – simple addition/subtraction; different denominators – make them same using LCM first)

Through examples and daily life situations such as sharing food, dividing money, and measuring lengths, students understand how fractions are used in real life.

Overall, this chapter builds a strong foundation in understanding, comparing, and performing basic operations with fractions.

Key Points

• Fraction represents a part of a whole. Example: ½ means 1 part out of 2 equal parts.

• Parts of a Fraction –

• Numerator: The top number (shows parts taken).

• Denominator: The bottom number (shows total equal parts).

• Types of Fractions –

• Proper Fraction: Numerator < Denominator (e.g., 3/4).

• Improper Fraction: Numerator > Denominator (e.g., 7/5).

• Mixed Fraction: Whole number + proper fraction (e.g., 2 ½).
  • Equivalent Fractions: Fractions that look different but are equal (e.g., ½ = 2/4 = 4/8).
  • Like Fractions: Fractions with the same denominator (e.g., 3/7, 5/7).
  • Unlike Fractions: Fractions with different denominators (e.g., 2/3, 3/5).

• Comparison of Fractions:

• If denominators are same → compare numerators.

• If denominators are different → make them same by LCM.

• Addition/Subtraction of Fractions:

• Same denominator → add/subtract numerators.

• Different denominator → find LCM, convert, then add/subtract.

• Fractions are used in daily life: sharing food, dividing money, measuring lengths. 

👉 👉 Fractions help us understand sharing and equal division in daily life. Learning fractions builds strong foundations for higher maths. 

Chapter 3. Angles as Turns 

This chapter explains angles in a simple and practical way by understanding them as turns. An angle is formed when a line rotates or turns around a point, called the vertex. The two lines that form the angle are known as its arms.

Students learn that angles show how much something turns — like the hands of a clock, an opening door, a swing, or a moving wheel. Turns can be clockwise (right turn) or anticlockwise (left turn).

The chapter introduces different types of angles:

• Acute Angle – Less than 90°

• Right Angle – Exactly 90° (quarter turn)

• Obtuse Angle – More than 90° but less than 180°

• Straight Angle – 180° (half turn)

• Complete Angle – 360° (full turn)

Students also learn that angles are measured in degrees (°) using a protractor. Through real-life examples, they understand how angles are everywhere around us.

Overall, this chapter helps students understand angles as turns and recognize different types of angles in daily life.

Key Points

• Angle is made when a line turns around a point.
• Angles show turns – how much a line, hand of a clock, or an object rotates.
• Types of Angles –

• Right Angle (90°): Quarter turn.

• Straight Angle (180°): Half turn.

• Complete Angle (360°): Full turn.

• Acute Angle (< 90°): Less than a right angle.

• Obtuse Angle (> 90° but < 180°): Greater than right angle, smaller than straight angle.

• Measuring Angles – Measured in degrees (°) using a protractor.

• Angles in Daily Life – Clock hands (3 o’clock = right angle), open doors, swings, wheel turns.

• Turns can be clockwise (to the right) or anticlockwise (to the left). 

👉 👉 Angles are everywhere in real life—clocks, doors, wheels, and turns. Understanding angles helps us read directions, measure turns, and connect maths to daily experiences. 

Chapter 4. We the Travellers—II 

This chapter focuses on improving addition and subtraction skills using smart tricks and logical thinking. Students learn quick calculation methods like adding 100 and subtracting 1, and shortcuts for subtracting 9 or 99.

It explains the strong relationship between addition and subtraction and how to check answers using reverse operations. Students also practice:

• Adding large numbers correctly

• Finding missing numbers

• Equalizing sums by swapping numbers

• Understanding patterns in consecutive numbers

• Identifying even and odd numbers

Fun activities like palindromes, number grids, and target-sum puzzles make learning engaging.

Overall, the chapter builds speed, accuracy, and confidence in working with numbers.

Key Points

• Making Sums Equal – You can swap numbers between two groups to equalize their sums with the fewest moves.
• Fuel Arithmetic & Easy Addition – Techniques for quick addition: use tricks like adding 100 and subtracting 1 (e.g., 46 + 99 = 46 + (100 – 1)) for speed and ease
• Addition–Subtraction Relationship – From a sum, you can subtract one addend to find the other (e.g., if 46 + 21 = 67, then 67 – 21 = 46 and 67 – 46 = 21)
• Subtraction & Check by Addition – After subtracting, check by adding back the difference to get the original number (e.g., 82 – 37 = 45, recheck: 37 + 45 = 82)
• Sums of Consecutive Numbers – Sum of two consecutive numbers is always odd; sum of three alternates between even and odd depending on start
• Large Number Addition – Practice addition of large numbers—align digits properly for accurate addition (e.g., 1,234 + 12,345; 46,120 + 12,890)
• Road-Trip Word Problems – Solve real-life route additions (e.g., Delhi → Mumbai → Goa distances added)
• Choose Pairs Closest to a Target – Among given numbers, find two whose sum is closest to a target (e.g., find pair closest to 10,000)
• Estimations & Missing Numbers – Find the number needed to reach totals like 1,000 or 10,000 by subtraction (e.g., 1,000 – 877 = 123)
• Subtracting 9 or 99 Shortcut – Instead of subtracting 9 or 99 directly, subtract 10 or 100 and then add back 1 (e.g., 67 – 9 = (67 – 10) + 1 = 58)
• Palindromes & Grid Patterns – Fascinating puzzles: palindrome numbers (e.g., 363), and arranging numbers 1–9 in increasing/decreasing order in 3×3 grids
• Even & Odd Recognition – Spot even numbers by their last digit; visualize pairing to identify odd or even counts 

👉 👉 This chapter shows how maths is an everyday travel companion—from balancing quantities, shuffling sums, to cracking puzzles and planning trips. It sharpens mental math, logical thinking, and gives creative problem-solving tools. 

Chapter 5. Far and Near

This chapter teaches students about measurement of length using standard units — millimetre (mm), centimetre (cm), metre (m), and kilometre (km). Students learn when to use each unit depending on the size of the object or distance.

The chapter focuses on converting lengths between different units and comparing them by first writing them in the same unit. Tools like the double number line help in understanding conversions clearly.

Students solve real-life problems involving:

• Addition and subtraction of lengths

• Comparing heights and distances

• Measuring and drawing line segments

• Converting between cm, mm, m, and km

Through examples like statue heights, train journeys, races, and daily measurements, students understand how length is used in everyday life.

Overall, this chapter builds practical skills in measuring, converting, and comparing distances accurately.

Key Points

• Standard Units of Length:

• 1 cm = 10 mm

• 100 cm = 1 m

• 1 km = 1,000 m 

• Choosing Units Wisely:

• Use mm for very small lengths (like coin thickness), cm for small-medium (like pencil), m for room or door heights, km for long distances (between cities) 

• Conversion & Comparison:

• Convert measurements to the same unit (e.g., cm to m) before comparing using <, >, = signs 

• Double Number Lines help convert and compare measurements visually (e.g., a sari's length in different units) 

• Practical Examples:

• Example: 456 cm vs 5 m → convert → 456 cm < 500 cm 

• Some lengths are exactly equal (e.g., 2 m 150 cm = 3 m 50 cm = 350 cm) 

• Real-Life Applications:

• Statue Heights: Calculate differences (e.g., Statue of Unity 182 m and Statue of Liberty 93 m → difference 89 m) and identify pairs with least or greatest difference 

• Kilometre Race: 3 km race with water stations every 500 m → stations at 500 m, 1,000 m, etc. 

• Longest Train Journey in India: Dibrugarh to Kanyakumari = 4,187 km; compare distances between stations (e.g., Guwahati–Dimapur vs Bhubaneswar–Jalpaiguri) 

• Measuring & Drawing:

• Draw lines in cm and mm; convert 36 mm = 3 cm 6 mm; use a ruler to measure and convert 

• Conversions across Units:

• Convert between cm, mm, m, km (e.g., 34 km = 34,000 m; 5,792 cm = 57 m 92 cm) 

• Everyday Word Problems:

• Total ribbon length: 3 m 75 cm + 2 m 25 cm = 6 m 

• Difference between distances (e.g., between waterfall and Sanchi): 48 km 700 m – 17 km 900 m = 30 km 800 m 

• Combine segments: 2 km 300 m + 2 km 650 m = 4 km 950 m 

• Shared measurement conversions for daily use

👉 👉Understanding Far and Near teaches us more than numbers—it teaches us about measurement in real life. Knowing the right unit, converting accurately, and comparing properly helps us make sense of the world around us, from planning journeys to measuring objects at home. 

Chapter 6. Dairy Farm

This chapter explains multiplication as repeated addition and shows how it helps calculate totals in equal groups. Students learn about the parts of multiplication — multiplicand, multiplier, and product — and understand that multiplication follows the commutative property (order does not change the product).

Important properties like the zero property and easy methods for multiplying by 10, 100, and 1000 are introduced. The chapter also teaches smart strategies such as doubling and halving, using the nearest multiple method, and solving problems through the expanded form method.

Through real-life dairy farm examples like calculating milk and fodder quantities, students see how multiplication is used in daily life.

Overall, this chapter builds strong multiplication skills using practical methods and real-world applications.

Key Points

• Multiplication as Repeated Addition – Helps compute total when we have equal groups (e.g., 7 × 6 = 42 butter packets)
• Factors, Multiplicand & Multiplier – The numbers multiplied are factors; the multiplicand is the number being multiplied, the multiplier is the number it’s multiplied by, and the result is the product
• Commutative Property – Swapping the numbers doesn’t change the product (e.g., 7 × 6 = 6 × 7 = 42)
• Zero Property of Multiplication – Any number multiplied by zero equals zero (both ways)
• Multiplying by 10, 100, 1000 – Just add zeros: one for ×10, two for ×100, three for ×1000
• Doubling & Halving Strategy – Halve one number and double the other to make multiplication easier (e.g., 3 × 18 = 6 × 9 = 54)
• Nearest Multiple Method – Use nearby round numbers to simplify multiplication and adjust (e.g., 4 × 19 ≈ 4 × 20 – 4 = 76)
• Expanded Form Method – Break numbers into tens, hundreds, etc., multiply each part, then add results (e.g., 268 × 4 = 800 + 240 + 32 = 1,072)
• Real-Life Examples –

• Cows’ milk: 29 cows × 5 litres = 145 litres; 297 cows × 18 kg fodder = 5,346 kg

👉 👉 This chapter gives us multiple tools to multiply smarter—not harder! From handy tricks to breaking numbers down, these strategies make math flexible, fun, and linked to real life—like managing a dairy farm. 

Chapter 7. Shapes and Patterns

This chapter explores patterns and shapes found in daily life. Students learn about weaving patterns using over–under rules and how changing the rule creates new designs. They practice completing grid patterns using repetition and symmetry.

The chapter introduces tessellations, where shapes like squares, triangles, and hexagons cover a surface without gaps or overlaps. Students also discover how combining triangles can form different quadrilaterals such as rectangles, kites, and parallelograms.

Fun activities include solving tangram puzzles, exploring cube nets, and counting cubes in 3D structures using simple formulas.

Overall, this chapter develops creativity and understanding of geometric patterns in both 2D and 3D shapes.

Key Points

• Weaving Patterns – Like basket or mat weaving: follow an “over–under” rule. Change the rule (2 over–1 under, 3 over–3 under) → get new designs.

• Patterns in Grids – Extend the missing parts in given designs. Symmetry and repetition are clues!

• Tessellations (Tile Fitting) – Shapes that cover a surface without gaps or overlaps:

• Squares: 4 meet at a point (90° each).

• Hexagons: 3 meet at a point (120° each).

• Triangles: 6 meet at a point (60° each).

• Everyday examples: honeycombs, tiled floors, brick walls.

• Mixing Shapes – Triangles + hexagons or triangles + squares make repeating floor or wall designs.

• Quadrilaterals from Triangles – Put 2 or more triangles together to make:

• Rectangle (opposite sides equal),

• Kite (two equal adjacent sides),

• Parallelogram (opposite sides parallel).

• Tangram Fun – 7 pieces (triangles, square, parallelogram) → form animals, houses, or letters.

• • Cube Nets & 3D Shapes – A cube can be “unfolded” into 6 squares (its net). Many nets are possible.

• Example: Dice faces are a cube net design.

• Counting Cubes in Frames – For big cubes made of small ones:

• Total cubes = side³ (e.g., 3×3×3 = 27).

• Frame cubes = corner + edge cubes. Removed cubes = Total − Frame.

👉 👉 Patterns are hidden everywhere—on floors, in honeycombs, in quilts, in dice, even in art! By learning how shapes fit, fold, and combine, we train our brain to think creatively, logically, and visually. 

Chapter 8. Weight and Capacity

This chapter teaches students how to measure weight (mass) and capacity using standard units. Weight is measured in milligrams (mg), grams (g), kilograms (kg), quintals, and tonnes, while capacity (mainly for liquids) is measured in millilitres (ml) and litres (l).

Students learn important conversions such as:

• 1 kg = 1,000 g

• 1 g = 1,000 mg

• 1 l = 1,000 ml

The chapter focuses on converting units correctly, reading analog and digital scales, and performing addition and subtraction of weights and capacities by aligning units properly. Through real-life examples like measuring groceries, liquids, and daily usage items, students understand the practical use of weight and capacity in everyday life.

Overall, this chapter builds accuracy in measuring, converting, and calculating weights and capacities confidently.

Key Points

• Weight (Mass): Measures how heavy an object is. Units: grams (g) for light items, kilograms (kg) for heavier ones.

• 1 kg = 1,000 g; 1 g = 1,000 mg

• Larger units: quintal (100 kg), tonne (1,000 kg) 

• Capacity: Measures how much a container can hold—mainly liquids. Units: millilitres (ml) and litres (l).

• 1 l = 1,000 ml 

• Unit Conversions – Weight:

• Convert kg → g by multiplying by 1,000

• Convert g → kg by dividing by 1,000

• Convert between kg, quintals, tonnes by grouping (e.g., 5,000 kg = 50 quintals = 5 tonnes) 

• Unit Conversions – Capacity:

• Convert l → ml or vice versa by using 1,000 factor

• Group litres and millilitres when performing calculations 

• Reading Scales:

• Read both analog and digital scales; pay attention to units and divisions (e.g., 100 g or 10 g per small division) 

• Real-Life Applications:

• Converting weights like 5 kg 50 g = 5,050 g

• Scaling quantities—e.g., total onions used in days, flour used, etc. 

• Working with money or sales where weight/capacity are involved

👉 👉 Knowing Weight and Capacity is about far more than numbers—it’s about understanding how much things weigh or hold in real life. From cooking to transporting goods, accurate measurement helps us plan better, avoid mistakes, and work smarter. 

Chapter 9. Coconut Farm

This chapter introduces division as sharing and grouping into equal parts using real-life farm examples. Students learn how to divide coconuts into equal baskets and understand the parts of a division sentence — dividend, divisor, quotient, and remainder.

The chapter explains the strong inverse relationship between multiplication and division and uses the array method (rows and columns) to connect multiplication and division facts.

Students also explore division patterns, such as the remainder always being smaller than the divisor, and solve practical problems related to coconut oil production and sales.

Overall, this chapter builds a clear understanding of division and its connection to multiplication through real-life applications.

Key Points

• Division as Sharing & Grouping – Splitting coconuts into equal baskets or groups.
• Array Method – Coconuts arranged in rows & columns → helps write 1 multiplication + 2 division facts.
• Division Sentence Parts –

• Dividend = total coconuts

• Divisor = coconuts per basket

• Quotient = number of baskets

• Remainder = leftover coconuts

• Inverse Relation – Multiplication ↔ Division (If 8 × 6 = 48, then 48 ÷ 8 = 6 and 48 ÷ 6 = 8).
• Patterns in Division –

• If Dividend ×10 → Quotient ×10 (when divisor fixed).

• Remainder always smaller than divisor.

• Real-Life Farm Math –

• Oil making: “8 coconuts → 1 litre oil.”

• Husk sales: Divide total husks by price per husk.

• Tender coconut sales: Total money ÷ price per coconut.

👉 👉 Math is not just numbers—it’s in farming, markets, and daily life. Division helps us share fairly, calculate earnings, and use resources wisely. Learning from the coconut farm shows how maths supports real-world problem-solving. 

Chapter 10. Symmetrical Designs

This chapter explores symmetry in shapes, letters, numbers, and designs. Students learn about reflection symmetry, where one half of a shape is the mirror image of the other, divided by a line of symmetry (like a butterfly or the letter A).

The chapter also explains rotational symmetry, where a shape looks the same after being turned around its center. The order of rotation tells how many times a shape matches itself in a full 360° turn (for example, a square has order 4).

Some shapes, such as squares and circles, have both reflection and rotational symmetry. Students also observe symmetry in letters, numbers, rangoli, mandalas, and tile patterns.

Overall, this chapter helps students understand and create beautiful symmetrical designs using reflection and rotation.

Key Points

• Reflection Symmetry (Mirror Magic) – A shape is symmetrical if one side is the mirror image of the other, divided by a line of symmetry.

• Example: Letter A (vertical line), Letter H (vertical + horizontal line).

• Nature Example: Butterfly wings.

• Rotational Symmetry (Spin & Match) – A shape has rotational symmetry if it looks the same after turning around its center.

• Order of Rotation = Number of times it matches in a full 360° turn.

• Example: A square matches at 90°, 180°, 270°, 360° → Order = 4.

• Both Symmetries Together – Some shapes (like a square, circle, or star) have both mirror lines and rotational order.

• Symmetry in Letters & Numbers

• Reflection: 0, 3 (horizontal), 8 (vertical + horizontal).

• Rotational: 0, 8 (180°), 1 (sometimes).

• Both: 0, 8.

• Patterns & Designs

• Mandalas, rangoli, tiles, and quilt patterns all use symmetry.

• For a ¼ turn design, repeat shapes at every 90°.

• For a ½ turn design, place shapes opposite each other. 

👉 👉 Symmetry is everywhere—in nature, art, and design. It makes things look beautiful, balanced, and structured. Learning symmetry helps us in drawing, architecture, crafts, and appreciating patterns around us. 

Chapter 11. Grandmother’s Quilt (Area & Perimeter) 

This chapter explains the concepts of perimeter and area through the example of designing a quilt.

Perimeter means the total distance around a shape — like stitching lace along the edge of a quilt.

• Square = 4 × side

• Rectangle = 2 × (length + breadth)

Area means the space covered inside a shape — measured in square units (cm²).

• Square = side × side

• Rectangle = length × breadth

Students learn that shapes can have the same perimeter but different areas, or the same area but different perimeters. This helps them understand how length and breadth affect measurements.

The chapter also includes patchwork activities, where students count squares and triangles to cover a surface without gaps or overlaps (tiling concept).

Overall, this chapter builds a clear understanding of area and perimeter through practical and creative examples like quilt patchwork.

Key Points

• Perimeter = Boundary 🪡 → Total distance around a shape (like stitching lace on the quilt’s edge).
👉 Formula:

• Square = 4 × side

• Rectangle = 2 × (length + breadth)

• Area = Space Inside 🧵 → How many unit squares (1 cm × 1 cm) can fit inside.
👉 Formula:

• Square = side × side

• Rectangle = length × breadth

• Same Perimeter, Different Area 🤔

• Ex: 6 × 5 rectangle → Perimeter = 22 cm, Area = 30 cm²

• 9 × 2 rectangle → Perimeter = 22 cm, Area = 18 cm²

• Same Area, Different Perimeter 🪢

• 6 × 6 square → Area = 36 cm², Perimeter = 24 cm

• 9 × 4 rectangle → Area = 36 cm², Perimeter = 26 cm

• Patchwork Counting 🟦🟩🔺

• 1 square patch = 2 green triangles

• To cover 54 squares → 108 green triangles

• Red triangle covers 4.5 patches → Need 12 for 54 patches

• 1 blue square patch = 1 square

👉 👉 Grandma’s quilt shows us: Area = how much space, Perimeter = how much border. In real life, we use these for fencing fields, covering tables, tiling floors, and stitching clothes. Knowing both helps in smart design and planning. 

Chapter 12. Racing Seconds 

This chapter helps students understand time and its measurement using seconds, minutes, and hours. They learn important conversions such as:

• 1 minute = 60 seconds

• 1 hour = 60 minutes = 3,600 seconds

• 1 day = 24 hours

Students practice calculating elapsed time by finding the difference between start and end times. The chapter also explains the difference between the 12-hour clock (a.m./p.m.) and the 24-hour clock, including special times like midnight (00:00) and noon (12:00).

In race examples, time is converted into seconds to compare results easily. Tools like the double number line help in converting between hours, minutes, and seconds.

Students also learn that in races, less time means faster speed, and more time means slower speed.

Overall, this chapter builds strong skills in reading clocks, converting time units, and calculating time differences accurately.

Key Points

• Time Units

• 1 min = 60 sec ⏱

• 1 hr = 60 min = 3,600 sec

• 1 day = 24 hr

• Elapsed Time (Time Passed)

• Subtract start time from end time.

• Example: 05:35 a.m. → 05:55 a.m. = 20 min 🧘

• 12-hr vs 24-hr Clock

• 02:30 p.m. = 14:30

• 09:35 p.m. = 21:35

• Midnight = 00:00, Noon = 12:00

• Race Timing in Seconds

• Winner’s time: 1 min 55 sec → 115 sec

• Comparing in seconds makes small differences easy to see.

• Double Number Line

• Helps convert hours ↔ minutes ↔ seconds.

• Example:
  1 hr = 60 min = 3,600 sec
  2 hr = 120 min = 7,200 sec

• Speedy Thinking

• More time taken → slower.

• Less time taken → faster.

👉 👉 ⏳ “Every second counts.” Whether in sports, studies, or daily routines, understanding time helps us manage tasks, plan better, and improve speed. 

Chapter 13. Animal Jumps  

This chapter introduces the concepts of factors and multiples through fun examples of animal jumps.

Factors are numbers that divide another number exactly. For example, the factors of 20 are 1, 2, 4, 5, 10, and 20.
Multiples are numbers obtained by repeated multiplication or skip counting, like multiples of 3: 3, 6, 9, 12, and so on.

Students learn about common factors and common multiples, which are shared by two or more numbers. The chapter also explains the difference between:

• Prime numbers (exactly two factors: 1 and itself)

• Composite numbers (more than two factors)

Helpful divisibility rules are introduced to quickly check if a number is divisible by 2, 3, 5, 9, or 10.

Overall, this chapter builds a strong understanding of number relationships using factors, multiples, and simple divisibility shortcuts.

Key Points

• Factors = Footprints 🐾 – Numbers that fit exactly into another.

• Ex: Factors of 20 → 1, 2, 4, 5, 10, 20.

• Multiples = Jumps 🐇🐸 – Numbers we get when we keep hopping (multiplying).

• Ex: Multiples of 3 → 3, 6, 9, 12, 15… (endless).

• Common Meeting Points –

• Rabbit jumps 4 steps, frog jumps 3 steps → both land at 12, 24, 36… (Common Multiples).

• Factors common to 12 & 18 → 1, 2, 3, 6 (Common Factors).

• Prime vs Composite

• Prime = exactly 2 factors (1 & itself) → 2, 3, 5, 7, 11, 13…

• Composite = more than 2 factors → 4, 6, 8, 9, 10, 12…

• Divisibility Quick Rules

• By 2 → last digit even

• By 3 → sum of digits ÷ 3

• By 5 → last digit 0 or 5

• By 10 → last digit 0

• By 9 → sum of digits ÷ 9

👉 👉 Numbers are like animals jumping on a track—some land together, some apart. Finding these meeting spots (multiples) and footprints (factors) helps us unlock patterns in maths. 

Chapter 14. Maps and Locations   

This chapter introduces maps as drawings of places viewed from above (bird’s-eye view). Students learn the important parts of a map, including the title, legend (key), scale, and directions.

They understand how to identify the cardinal directions — North, South, East, and West — and simple ways to find directions using the position of the sunrise. The chapter also explains how scale helps relate map distances to real-life distances.

Students practice describing routes step by step, finding the shortest path, and locating places using grids and coordinates (x, y).

Overall, this chapter develops map-reading skills and helps students understand directions, distance, and location clearly.

Key Points

• What is a Map? – A drawing of a place seen from above (bird’s-eye view).
• Parts of a Map –

• Title: What the map shows.

• Key/Legend: Symbols for places (🏫 school, 🌳 park, 🚉 station).

• Scale: How distance on map relates to real life (2 cm = 1 km).

• Directions: North, South, East, West.
  • How to Find North? – Face sunrise 🌅 → that’s East. Left hand = North, right hand = South, behind you = West.
  • Routes on Maps – Describes paths step by step (e.g., go 2 km east, then 3 km north).
  • Shortest Route – Always saves time and effort.
  • Grids & Coordinates – Maps often use rows & columns. Location is shown as (x, y). Example: (3, 2) means move 3 across, 2 up.

👉 👉 Maps are guides to the world – they help us find places, save time, and explore safely. Tip to Remember → “T-K-S-D-G” → Title, Key, Scale, Directions, Grid. 

Chapter 15. Data Through Pictures  

This chapter introduces data as information collected about people, objects, or events. Students learn how data can be represented visually using a pictograph, which uses pictures or symbols to show quantities.

A pictograph includes important parts such as a title, a key or scale (showing what each symbol represents), and clear, equal-sized symbols. Sometimes half symbols are used to represent partial values.

Students practice reading and interpreting pictographs by counting symbols and multiplying by the scale to find actual numbers. They also compare categories and understand trends.

The chapter shows how pictographs are useful in real life, such as displaying school attendance, survey results, shop items, or traffic counts.

Overall, this chapter helps students organize, represent, and interpret data clearly using pictures.

Key Points

• Data = Story in Numbers 📊 – Information about things, people, or events.

• Ex: Students’ favourite fruits, number of books read, or hours spent on games.

• Pictograph = Picture Chart 🖼️ – Uses symbols or pictures to represent data quantities.

• Key/Scale: Each symbol represents a certain number (½ icon can represent half-unit).

• Example: 🍎 = 5 apples, 🟦 = 2 books, etc.

• Essential Features of Pictographs

• Title → What the data is about

• Key / Scale → How much each symbol stands for

• Symbols / Icons → All the same size; can use fractions for half/partial units

• Neatness & Clarity → Makes reading and comparing easy

• Reading & Interpreting Data

• Count symbols × scale → actual numbers

• Compare totals, differences, or trends between categories

• Simplifying Large Data

• Use bigger scale (1 icon = 5, 10, or 20 units) to make charts manageable

• Practical Use 🏫

• School attendance, shop stock, traffic counts, survey results—all can be shown using pictographs.

👉 👉 Pictographs turn numbers into pictures, making it easy to spot patterns, compare, and understand data quickly. Great for school surveys, traffic studies, or even daily habits!