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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
3
Chapter 3
Skill: 30%

Patterns Around Us

Patterns Around Us

Chapter at a Glance

This chapter introduces students to the concepts of pattern-based counting, grouping, and number parity (even vs. odd numbers). Through practical tasks like counting arranged cups and coconuts, grouping play money, and placing coins in triangular shapes, children learn that numbers can be classified into two classes based on pairing. They investigate the properties of even and odd numbers, identify alternating page numbers in textbooks, explore consecutive number progressions, and learn to determine parity instantly by looking at the ones digit.

Key Definitions & Terminology

  • Even Number: A number of objects that can be grouped into pairs with no objects left over. Even numbers end in $0, 2, 4, 6, \text{ or } 8$.
  • Odd Number: A number of objects that cannot be completely paired, always leaving one leftover object. Odd numbers end in $1, 3, 5, 7, \text{ or } 9$.
  • Consecutive Numbers: Whole numbers that follow each other in order without any gaps (e.g. $21, 22, 23, 24$).

Formulas, Rules & Properties

  • The Parity Ending Rule:
    To determine if a whole number is even or odd, examine only its ones (units) digit:
    $$\text{If ones digit } \in {0, 2, 4, 6, 8} \rightarrow \text{Even}$$
    $$\text{If ones digit } \in {1, 3, 5, 7, 9} \rightarrow \text{Odd}$$
  • The Alternation Property:
    In a sequence of consecutive whole numbers, even and odd numbers alternate:
    $$\dots \rightarrow \text{Even} \rightarrow \text{Odd} \rightarrow \text{Even} \rightarrow \text{Odd} \rightarrow \dots$$
  • The number directly before and after any even number is always odd.
  • The number directly before and after any odd number is always even.
  • The Times-2 Rule:
    All numbers in the times-2 multiplication table are even.
  • Interval Parity:
    Between $1$ and $100$, there are exactly $50$ even numbers and $50$ odd numbers.

Core Concepts & Topics

  • Arranged Counting & Grouping:
  • Counting pottery cups and coconut trees in grid arrangements (rows and columns) rather than one-by-one.
  • Finding total quantities using repeated addition or multiplication (e.g., counting tree crops).
  • Counting items in stacked identical trays (laddoos, pedas).
  • Play Money Composition:
  • Arranging and counting currency notes and coins.
  • Representing given amounts (like $\text{Rs. } 36$, $\text{Rs. } 125$, and $\text{Rs. } 183$) using denominations of $\text{Rs. } 1, 2, 5, \text{ and } 10$.
  • Triangular Coin Arrangements (Tactile Parity):
  • Mini and Shiv arrange coins in triangular patterns:
    • Even check: Shiv groups coins in pairs (count: $2, 4, 6, \dots$ with no leftovers).
    • Odd check: Shirley finds a single leftover coin at the apex of her triangles (count: $1, 3, 5, \dots$).
  • Textbook Page Patterns:
  • Observing how even and odd page numbers alternate sequentially on the left and right pages of a textbook.

Worked Examples

  • Gundappa's Coconut Harvest:
  • Problem: Gundappa has $20$ coconut trees. He plucks $5$ coconuts from each tree. How many coconuts has he plucked in total?
  • Solution: $20 \text{ trees} \times 5 \text{ coconuts/tree} = 100 \text{ coconuts}$.
  • Even/Odd Sorting (Crayon Selection):
  • Problem: Classify these numbers: ${5, 51, 30, 43, 38, 52, 22, 37, 8, 36, 69}$.
  • Solution:
    • Odd: $5, 51, 43, 37, 69$ (each ends in $1, 3, 5, 7, \text{ or } 9$).
    • Even: $30, 38, 52, 22, 8, 36$ (each ends in $0, 2, 4, 6, \text{ or } 8$).
  • Large Numbers Parity Check:
  • Problem: Identify if the following numbers are even or odd: $30$, $300$, $78$, $415$, $46$, $154$, $67$, $99$.
  • Solution:
    • $30 \rightarrow$ Even (ends in $0$)
    • $300 \rightarrow$ Even (ends in $0$)
    • $78 \rightarrow$ Even (ends in $8$)
    • $415 \rightarrow$ Odd (ends in $5$)
    • $46 \rightarrow$ Even (ends in $6$)
    • $154 \rightarrow$ Even (ends in $4$)
    • $67 \rightarrow$ Odd (ends in $7$)
    • $99 \rightarrow$ Odd (ends in $9$)
  • Two-Digit Digit Slip Combinations:
  • Problem: Make two-digit numbers using the digits $1$ and $6$ without repetition, and classify them.
  • Solution:
    • Number $16$: Ends in $6 \rightarrow$ Even.
    • Number $61$: Ends in $1 \rightarrow$ Odd.
  • Creating Even Pairs:
  • Problem: Choose any two digits (e.g. $3$ and $8$) and make all possible even two-digit numbers.
  • Solution: To make an even number, the last digit must be even. Using $3$ and $8$:
    • Without repeating digits: $38$ (ends in $8$, so it is even).
    • With repeating digits: $88$.

Practical Activities & Experiments

  • Play Money Layouts: Creating patterns with play notes and coins to match target sums.
  • Coin Triangle Pairs: Laying out rows of coins to build triangles of sizes $3, 4, 5$, checking which configurations leave a single coin unpaired.
  • Textbook Page Audit: Flicking through pages to identify patterns of left-page and right-page numbers.
  • Crayon Grid Sorting: Playing a board game on a $100$-number grid, putting circles around odd numbers and squares around even numbers.
  • Consecutive String Test: Writing down $10$ consecutive numbers in a row and writing "even" or "odd" beneath each to trace the alternating pattern.
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