Review Activity — पुनरावलोकनFruit Garden Simulation
🌳 Animated Fruit Garden — फलफूल बगैंचा
Nirmala has a fruit garden with Oranges and Mangoes. Help her solve the equation!
Drag the Fruits! 🍊🥭
$x + 4 = 12$
where $x$ = number of oranges 🍊
Move $4$ to the other side: $x = 12 - 4 = 8$
तसर्थ $x = 8$ संखुवा छन्! (So there are 8 oranges!)
📊 Complete the Table — तालिका भर्नुहोस्
| $x$ (Value) | $x + 4$ | = 12? ✓ |
|---|---|---|
| 5 | 9 | ❌ |
| 6 | 10 | ❌ |
| 7 | 11 | ❌ |
| 8 | 12 | ✅ |
| 9 | 13 | ❌ |
📈 Plot the Graph
Simultaneous Linear Equations — एकसाथ रैखिक समीकरणIntroduction with Mango Sharing Activity
🥭 Mango Sharing Story — आम बाँड्ने कथा
Nirmala has 6 mangoes 🥭🥭🥭🥭🥭🥭
She wants to share them between Asmi and Anisha.
Asmi has 2 more mangoes than Anisha.
Let: $x$ = Asmi's mangoes, $y$ = Anisha's mangoes
Setting Up Equations
Equation 2: $x - y = 2$ (Difference)
🔢 Fill in the Values Table
| $x$ | $y$ | $x+y$ | $x-y$ | Check |
|---|---|---|---|---|
| 5 | 1 | 6 ✅ | 4 ❌ | — |
| 4 | 2 | 6 ✅ | 2 ✅ | ✅ Solution! |
| 3 | 3 | 6 ✅ | 0 ❌ | — |
| 2 | 4 | 6 ✅ | -2 ❌ | — |
Asmi: 4 mangoes 🥭🥭🥭🥭 | Anisha: 2 mangoes 🥭🥭
📈 Graph of Both Equations
🧠 Solving by Elimination Method — जोड्दिम विधि
$x + y = 6$ ... (i)
$x - y = 2$ ... (ii)
$2x = 8$
$\therefore x = 4$
$4 + y = 6$
$y = 6 - 4 = 2$
🔄 Verification — प्रमाणिकरण
Graphical Method — ग्राफिय विधिInteractive Coordinate Plane & Graph Plotting
Example 1
$x - 2y = -1$
Table for $3x - y = 7$ → $y = 3x - 7$
| $x$ | 0 | 1 | 2 | 3 | 4 |
|---|---|---|---|---|---|
| $y$ | -7 | -4 | -1 | 2 | 5 |
Table for $x - 2y = -1$ → $y = \frac{x+1}{2}$
| $x$ | -1 | 1 | 3 | 5 |
|---|---|---|---|---|
| $y$ | 0 | 1 | 2 | 3 |
Example 2 — Father-Daughter Age Problem 👨👧
A father's age is 10 more than double his daughter's age. The difference of their ages is 25 years.
$x - y = 25$
Table for $x = 2y + 10$
| $y$ | 0 | 5 | 10 | 15 | 20 |
|---|---|---|---|---|---|
| $x$ | 10 | 20 | 30 | 40 | 50 |
Table for $x - y = 25$
| $y$ | 0 | 5 | 10 | 15 | 20 |
|---|---|---|---|---|---|
| $x$ | 25 | 30 | 35 | 40 | 45 |
Daughter's age: $\boxed{y = 15}$ years
🔧 Dynamic Graph Plotter — आफैं समीकरण हाल्नुहोस्!
Graph Investigation Lab — ग्राफ अनुसन्धान प्रयोगशालाExplore slope, intercept, parallel & intersecting lines
Use the sliders to explore how changing $m$ (slope) and $c$ (intercept) affects the graph of $y = mx + c$
📚 Key Concepts:
• Parallel lines (same slope, different intercept): No solution
• Coincident lines (same slope, same intercept): Infinite solutions
• Intersecting lines (different slopes): Unique solution
Practical Life Problems — व्यावहारिक समस्याहरू10 Real-Life Interactive Problems
🎮 Gamified Graph Challenge — ग्राफ खेल प्रतियोगिताCompete, Plot, Win Badges!
📋 Current Challenge
Find the intersection point!
🏆 Achievement Badges
Introduction to Quadratic Equations — द्विघात समीकरण परिचयCompare Linear vs Quadratic, Degree Detector
⚖ Compare: Linear vs Quadratic
📐 General Form of Quadratic Equation
where $a$, $b$, $c$ are real numbers and $a \neq 0$
🔍 Dynamic Degree Detector
Click an equation to detect its degree:
Factorization Method — गुणनखण्ड विधिStep-by-Step Interactive Factorization
Example: Solve $x^2 - 2x - 3 = 0$
Click each step to see the animation:
Numbers: $-3$ and $+1$ (since $-3 \times 1 = -3$ and $-3 + 1 = -2$)
$x^2 - 3x + x - 3 = 0$
$x(x - 3) + 1(x - 3) = 0$
$(x - 3)(x + 1) = 0$
$x - 3 = 0 \Rightarrow x = 3$
$x + 1 = 0 \Rightarrow x = -1$
More Examples — अतिरिक्त उदाहरण
Solve: $x^2 - 5x + 6 = 0$
$x^2 - 2x - 3x + 6 = 0$
$x(x-2) - 3(x-2) = 0$
$(x-2)(x-3) = 0$
✅ $x = 2$ or $x = 3$
Solve: $x^2 - 7x + 12 = 0$
$(x-3)(x-4) = 0$
✅ $x = 3$ or $x = 4$
🔧 Practice Factorizer
Quadratic Root Explorer — द्विघात मूल अन्वेषणDynamic Visualization with Number Line
Example: $x^2 - 25 = 0$
$x^2 = 25$
$(x+5)(x-5) = 0$
✅ $x = 5$ or $x = -5$
🔧 Root Explorer Tool
Enter your quadratic $x^2 + bx + c = 0$:
📊 Number Line Visualization
Build Your Own Quadratic! — आफ्नै द्विघात बनाउनुहोस्Choose roots → system builds the equation!
🎛 Choose Your Roots
🔨 Building Process:
Product of roots: $r_1 \times r_2 = c/a = 6$
Interactive Practice Zone — अभ्यास क्षेत्रAll Chapter Exercises — Easy, Medium, Advanced
🟢 Easy — सजिलो
Solve one-variable equations
🟡 Medium — मध्यम
Simultaneous equations, graphs
🔴 Advanced — उन्नत
Quadratic, factorization
Digital Whiteboard — डिजिटल श्वेतपटInteractive Whiteboard Solution Mode
Find: intersection point of the two lines using graphical or algebraic method.
Project Work Zone — परियोजना कार्य4 Mini Projects for Student Groups
Project 1: Classroom Object Survey
Survey classroom objects, count them, form equations, and draw graphs representing the data.
Project 2: School Canteen Cost Analysis
Analyze canteen items, set up a cost equation system, find the price of each item.
1 samosa + 2 teas = Rs 40
Project 3: Age Comparison Investigation
Survey family ages, form age-comparison equations, solve and verify graphically.
Father = Son + 22 → Solve!
Project 4: Cats and Chickens Puzzle
A farmer has cats and chickens. Total heads: 10, total legs: 26. Find the number of each!
$4x + 2y = 26$ (legs)
Final Assessment — अन्तिम मूल्याङ्कनMCQ, Fill Blanks, Match, Factorization, Word Problems
📌 Part A: Multiple Choice Questions (MCQ) — बहुविकल्पीय प्रश्न
📝 Part B: Fill in the Blanks — रिक्त स्थान भर्नुहोस्
1. The degree of $x^2 - 4x + 3 = 0$ is .
2. The solution of $x + y = 6$ and $x - y = 2$ is $x = $ and $y = $ .
3. If $(x-3)(x+1) = 0$, then $x = $ or $x = $ .
4. The roots of $x^2 - 25 = 0$ are $x = $ and $x = $ .
🔗 Part C: Match the Following — मिलाउनुहोस्
🔢 Part D: Factorize — गुणनखण्ड गर्नुहोस्
📖 Part E: Word Problems — शाब्दिक समस्याहरू
Congratulations! बधाई छ!
You have successfully completed
"समीकरण र ग्राफ (Equation and Graph)"
Grade 8 Mathematics | Creator: R.P. Pandey
👨🏫 Created with ❤ by R.P. Pandey
Smart Classroom Mathematics | Grade 8 | Nepal