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📖 Mathematics

Std 4
Curriculum Book Guide
1 2 3 4 5 6 7 8 9 10 11 12 13 14
Chapters
1 Shapes Around Us 2 Hide and Seek 3 Patterns Around Us 4 Thousands Around Us 5 Sharing and Measuring One Quarter 6 Measuring Length 7 The Cleanest Village 8 Fun at Vegetable Market! Weigh It, Pour It 9 Animal Jumps Equal Groups 10 Elephants, Tigers and Leopards 11 Fun with Symmetry 12 Ticking Clocks and Turning Calendar 13 Mystery Matrix The Transport Museum 14 Data Handling Physical Education
9
Chapter 9
Skill: 30%

Animal Jumps Equal Groups

Animal Jumps Equal Groups

Chapter at a Glance

This chapter introduces students to multiplication and division, focusing on multiples, common multiples, array models, doubling/halving, and division methods like partial quotients. Through activities like animal jump progressions on a number line, cup cake baking arrays, and calculating legs on geese, sheep, cows, and ants, students learn to multiply and divide up to three-digit numbers. They study the patterns of multiplication tables, explore the mathematical distinction between sharing and measuring divisions, and evaluate the truth of logical arithmetic statements.

Key Definitions & Terminology

  • Multiple: The product of a given number multiplied by any integer (e.g. multiples of $3$ are ${3, 6, 9, 12, \dots}$).
  • Common Multiple: A number that is a multiple of two or more distinct numbers (e.g. common multiples of $6$ and $8$ are ${24, 48, 72, \dots}$).
  • Multiplier: The number of equal groups in a multiplication statement.
  • Multiplicand: The size of each group.
  • Remainder: The amount left over after division when a number cannot be split evenly.
  • Share Division: A division context where the number of equal groups is known, and the goal is to find the size of each share.
  • Measure Division: A division context where the size of each group is known, and the goal is to find how many groups can be formed.
  • Partial Quotient Method: A division method where easy multiples of the divisor (like $10$, $5$, $2$) are subtracted step-by-step from the dividend until the remainder is smaller than the divisor.

Formulas, Rules & Properties

  • Doubling Parity Rule:
    Doubling any integer always yields an even number. The ones digit of a doubled number must belong to ${0, 2, 4, 6, 8}$; it can never be odd.
  • Commutative Property of Multiplication:
    $$A \times B = B \times A$$
  • Row $N$ values are identical to Column $N$ values in a multiplication grid.
  • Multiplication Table Parity Rules:
  • Even row numbers contain only even products.
  • Odd row numbers contain alternating even and odd products.
  • Multiples of 10 and 100 Rules:
  • Multiplying by $10$ appends $0$ in the ones place: $A \times 10 = A0$.
  • Multiplying by $100$ appends $00$ to the end: $A \times 100 = A00$.

Core Concepts & Topics

  • Animal Jumps (Visualizing Multiples):
  • Frog (jumps of $3$), squirrel ($4$), rabbit ($6$), and kangaroo ($8$) move along a number line.
  • Finding common landing points by calculating common multiples.
  • Cat (starts at $6$, jumps of $3$) chasing Rat (starts at $12$, jumps of $2$): they land on the same number at $18$ (the cat catches the rat).
  • Multiplication Arrays and Splitting:
  • Calculating quantities in grids (rows and columns) like flower saplings and strawberry boxes.
  • Cupcake trays: 18 cupcakes per tray. To solve $18 \times 4$, split it using multiples of $10$:
    $$18 \times 4 = (10 \times 4) + (8 \times 4) = 40 + 32 = 72$$
  • Animal Leg Tallies (Addition/Multiplication):
  • $25$ geese ($2\text{ legs each}$) and $12$ sheep ($4\text{ legs each}$):
    $$\text{Total legs} = (25 \times 2) + (12 \times 4) = 50 + 48 = 98\text{ legs}$$
  • Division via Partial Quotients:
  • Solving $58 \div 3$ (wheels for $3$-wheeled tempos) by subtracting easy chunks: $10$ tempos ($30$ wheels), $5$ tempos ($15$ wheels), $3$ tempos ($9$ wheels), and $1$ tempo ($3$ wheels) $\rightarrow$ total $19$ tempos with a remainder of $1$ wheel.
  • Boat Capacity Allocation (Share Division):
  • Distributing $108$ people equally among $9$ boats using partial quotients:
    $$108 \div 9 = (45 \div 9) + (45 \div 9) + (18 \div 9) = 5 + 5 + 2 = 12\text{ people per boat}$$
  • Logical Statements (Always, Sometimes, or Never True):
  • Evaluating statements under different arithmetic conditions to build critical thinking.

Worked Examples

  • Animal Jump Progressions:
  • Question: Will a frog jumping $3$ steps at a time land on $67$?
    Solution: No, because $67$ is not a multiple of $3$ ($67 \div 3 = 22\text{ R } 1$).
  • Question: What is the smallest 3-digit number a rabbit (jumping $6$ steps) lands on, and how many jumps does it take?
    Solution: $102$, which takes $102 \div 6 = 17$ jumps.
  • Legs-to-Animals Division (Cows & Octopuses):
  • Question: Chippi the lizard sees $88$ legs of cows in a dairy farm. How many cows are there?
    Solution: $88 \div 4\text{ legs/cow} = 22\text{ cows}$.
  • Question: Jolly fish sees $72$ legs of octopuses. How many octopuses are there?
    Solution: $72 \div 8\text{ legs/octopus} = 9\text{ octopuses}$.
  • Shuttlecock Box Packing:
  • Question: A sports store packs $4$ shuttlecocks per box. They have $50$ shuttlecocks. How many boxes are needed?
    Solution: $50 \div 4 = 12$ boxes, with $2$ shuttlecocks left unpacked.
  • UNESCO Toy Train Weekly Distance:
  • Question: The Darjeeling Toy Train runs $88\text{ km}$ daily. How much distance does it travel in a week?
    Solution: $88\text{ km/day} \times 7\text{ days/week} = 616\text{ km}$.
  • River Rafting in Shivpuri:
  • Question: Rafts take $7$ people each. VentureOut company took $259$ people for rafting. How many rafts did it take?
    Solution: $259 \div 7 = 37$ rafts.
  • Anu's Monthly Piggy Bank Savings:
  • Question: Anu saves $\text{Rs. } 45$ every month. How much does she save in $6$ months, and how much does each friend get if shared among: (a) $6$ friends, (b) $3$ friends?
    Solution: Savings $= 45 \times 6 = \text{Rs. } 270$.
    • Shared among $6$ friends $\rightarrow 270 \div 6 = \text{Rs. } 45$ each.
    • Shared among $3$ friends $\rightarrow 270 \div 3 = \text{Rs. } 90$ each.
  • Always/Sometimes/Never True Check:
  • Multiplying by 10 gives 0 in the ones digit $\rightarrow$ Always True.
  • Multiplying a number by 2 gives an odd number $\rightarrow$ Never True.
  • Multiplying by 5 gives a number ending in 5 $\rightarrow$ Sometimes True (odd numbers only).
  • Halving a number gives an even number $\rightarrow$ Sometimes True (e.g. $8 \div 2 = 4$ is even, but $6 \div 2 = 3$ is odd).

Practical Activities & Experiments

  • Multiples Jump game: Drawing a number line on the playground floor and having students jump in sets of $3, 4, \text{ or } 6$ to identify landing numbers.
  • Cupcake Tray Array Arrangement: Arranging counters representing $36$ mini cupcakes in different grid sizes ($6 \times 6$, $4 \times 9$, $3 \times 12$).
  • Multiplication Table Grid Search: Filling a $10 \times 10$ product chart and coloring common multiples of $2$ and $3$, $4$ and $8$, or $7$ and $9$ to spot patterns.
  • Dosing Cup/Dropper counts: Counting divisions to fill a bottle using $10\text{ ml}$ increments.
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