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📖 Mathematics

Std 3
Curriculum Book Guide
1 2 3 4 5 6 7 8 9 10 11 12 13 14
Chapters
1 What's in a Name? 2 Toy Joy 3 Double Century 4 Seeds on Vacation with My Nani Maa 5 Fun with Shapes 6 House of Hundreds - I 7 Raksha Bandhan 8 Fair Share 9 House of Hundreds - II 10 Fun at Class Party! 11 Filling and Lifting 12 Give and Take 13 Time Goes On 14 The Surajkund Fair
12
Chapter 12
Skill: 30%

Give and Take

Give and Take

Chapter at a Glance

This chapter covers addition and subtraction of three-digit numbers, contextualized through a plant nursery, village markets, and a local general store. Students learn standard algorithms and regrouping methods using Dienes blocks (Hundreds, Tens, Ones) and number lines. The curriculum traces trade history from the ancient Barter System to modern currency, prompting students to use play money (notes of $\text{Rs. } 100$, $\text{Rs. } 10$, and $\text{Rs. } 1$) to model place-value trades. Additionally, children practice rounding to the nearest hundred, analyzing arithmetic inequalities, and playing digit-card optimization games.

Key Definitions & Terminology

  • Barter System: A trade system where people exchange goods directly for other goods (e.g. sacks of onions for sarees) without using money.
  • Regrouping (Carrying/Borrowing): The process of exchanging ten units of one place value for one unit of the next higher place value (e.g., $10\text{ Ones} \leftrightarrow 1\text{ Ten}$, or $10\text{ Tens} \leftrightarrow 1\text{ Hundred}$).
  • Estimation to the Nearest Hundred: Rounding three-digit values to the nearest multiple of $100$ to quickly approximate sums and differences.
  • Play Money: Paper representations of currency notes ($\text{Rs. } 100$, $\text{Rs. } 10$, $\text{Rs. } 1$) used as a physical model for place-value addition and subtraction.

Formulas, Rules & Properties

  • Regrouping in Addition:
    $$\text{If } \text{Ones} \ge 10 \rightarrow \text{Subtract } 10\text{ Ones and Add } 1\text{ Ten to the Tens column.}$$
    $$\text{If } \text{Tens} \ge 10 \rightarrow \text{Subtract } 10\text{ Tens and Add } 1\text{ Hundred to the Hundreds column.}$$
  • Regrouping in Subtraction:
    $$\text{If } \text{minuend Ones} < \text{subtrahend Ones} \rightarrow \text{Convert } 1\text{ Ten from Tens column into } 10\text{ Ones.}$$
    $$\text{If } \text{minuend Tens} < \text{subtrahend Tens} \rightarrow \text{Convert } 1\text{ Hundred from Hundreds column into } 10\text{ Tens.}$$
  • Commutative and Additive Properties:
  • Compounding multiple sales or savings:
    $$\text{Total Earnings} = \text{Sale}_1 + \text{Sale}_2 + \dots$$
  • Exchanging denominations:
    $$1\text{ note of } \text{Rs. } 500 = 5\text{ notes of } \text{Rs. } 100$$

Core Concepts & Topics

  • Visualizing Equations with Box Diagrams:
  • Representing word problems as block rectangles (Parts and Wholes) to clarify whether the problem requires addition or subtraction.
  • Dienes Block & Number Line Calculations:
  • Modelling double and triple-digit equations physically.
  • Rounding addends to estimate the result before formal calculation.
  • Smart Grid Navigations:
  • Executing sums on a grid chart ($450$ to $530$) by moving up, down, left, and right, noting how digits change systematically when adding $100$, $10$, or $1$.
  • Barter Logic vs. Money Trade:
  • Discussing Shamu Kaka and Dariya Didi's exchanges in Jadupur.
  • Analyzing relative value: a $\text{Rs. } 10$ note can buy $1$ cotton candy (hawa mithai) or $10$ toffees, meaning a cotton candy is more expensive than a toffee.
  • Piggy Bank Calculations:
  • Calculating linear accumulation over time (starting amount $+$ recurring additions).
  • Inequality Circle Puzzles:
  • Comparing expression pairs (e.g. $373 + 23$ vs. $373 + 40$) mentally by observing which addend is larger, or which subtrahend is smaller.
  • Digit Slip Optimization Game:
  • Permuting slips ${0, 1, 2, 3, 4, 5}$ to build two $3$-digit numbers that yield either the maximum possible sum or the minimum possible difference.

Worked Examples

  • Nursery Saplings Addition (Carrying):
  • Problem: Kishan has $364$ saplings. He buys $52$ more. How many total?
  • Solution:
    • Ones: $4 + 2 = 6$.
    • Tens: $6\text{ tens} + 5\text{ tens} = 11\text{ tens} = 1\text{ hundred} + 1\text{ ten}$ (carry $1$).
    • Hundreds: $3 + 1\text{ (carry)} = 4$.
    • Total: $416\text{ saplings}$.
  • Saplings Order Subtraction (Borrowing):
  • Problem: Deliver $230$ saplings. $75$ are packed. How many more to pack?
  • Solution: $230 - 75$.
    • Ones: $0 < 5 \rightarrow$ Borrow $1\text{ ten}$ from Tens column to make $10\text{ ones}$. $10 - 5 = 5\text{ ones}$.
    • Tens: Left with $2\text{ tens}$. $2 < 7 \rightarrow$ Borrow $1\text{ hundred}$ to make $12\text{ tens}$. $12 - 7 = 5\text{ tens}$.
    • Hundreds: Left with $1\text{ hundred}$.
    • Total: $155\text{ saplings}$.
  • Box Diagram Word Problems:
  • $456$ saplings, distributed $63$. Remaining: $456 - 63 = 393\text{ saplings}$.
  • $309$ saplings, gets $80$ more. Total: $309 + 80 = 389\text{ saplings}$.
  • Kishan has $270$ herbs, friend has $36$. Kishan has $270 - 36 = 234$ more.
  • Book box diagram: $356 - 138 = 218\text{ books}$.
  • Children diagram: $234\text{ boys} + 156\text{ girls} = 390\text{ children}$.
  • Sacks diagram: $305 - 210 = 95\text{ sacks}$.
  • Grid Solutions:
  • $456 + 10 = 466$
  • $481 + 19 = 500$
  • $489 + 21 + 15 = 525$
  • $405 + 23 = 428$
  • $467 + 51 = 518$
  • $519 - 40 = 479$
  • Peter Uncle's Transactions:
  • Earned since morning: $\text{Rs. } 756\text{ (afternoon)} - \text{Rs. } 465\text{ (morning)} = \text{Rs. } 291$.
  • Sale total: $\text{Rs. } 640\text{ (rice)} + \text{Rs. } 215\text{ (sugar)} = \text{Rs. } 855$.
  • Accumulated earnings: Day 1 $\text{Rs. } 650 +$ Day 2 $\text{Rs. } 250 = \text{Rs. } 900$.
  • Groceries change:
  • Reena buys groceries for $\text{Rs. } 209$, pays with $\text{Rs. } 500$ note. Change returned: $500 - 209 = \text{Rs. } 291$.
  • Weekly Savings:
  • Shireen starts with $\text{Rs. } 150$. She adds $\text{Rs. } 100$ weekly for $4$ weeks. Total $= 150 + (4 \times 100) = \text{Rs. } 550$.
  • Nearest Hundred Estimations:
  • $156 + 34 \approx 200 + 0 = 200$ (actual is $190$).
  • $125 - 15 \approx 100 - 0 = 100$ (actual is $110$).
  • $105 + 195 \approx 100 + 200 = 300$ (actual is $300$).
  • $205 + 215 \approx 200 + 200 = 400$ (actual is $420$).
  • $500 - 395 \approx 500 - 400 = 100$ (actual is $105$).
  • $765 - 567 \approx 800 - 600 = 200$ (actual is $198$).
  • $505 + 405 \approx 500 + 400 = 900$ (actual is $910$).
  • Inequality Comparisons (Circle the larger):
  • $373 + 23$ vs. $\mathbf{373 + 40}$
  • $\mathbf{240 + 10}$ vs. $204 + 10$
  • $900 + 9$ vs. $\mathbf{890 + 60}$ ($950 > 909$)
  • $\mathbf{345 - 45}$ vs. $345 - 54$
  • $\mathbf{800 - 8}$ vs. $700 - 8$
  • Equal Pair Matching:
  • $516 + 100$ equals $816 - 200$ (both equal $616$)
  • $400 + 15$ equals $615 - 200$ (both equal $415$)
  • $450 - 50$ equals $350 + 50$ (both equal $400$)
  • Equation Solutions:
  • $265 + 9 = 274$
  • $405 + 56 = 461$
  • $825 + 175 = 1000$
  • $600 - 82 = 518$
  • $568 - 5 = 563$
  • $653 - 356 = 297$

Practical Activities & Experiments

  • Classroom Barter Simulation: Playing roles of Shamu Kaka and Dariya Didi to trade paper cards of vegetables, onions, and grains.
  • Play Money Regrouping: Exchanging plastic or paper play notes ($\text{Rs. } 100$, $\text{Rs. } 10$, $\text{Rs. } 1$) to solve carry-over addition and borrow subtraction equations.
  • Grid Path Coloring: Finding solutions to equations on a $100$-number grid slice and coloring the tiles.
  • Number Cards Optimization Game: Shuffling cards $0-5$. Players rearrange cards to make two $3$-digit numbers that compete for the greatest sum and the smallest difference.
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