Posted on by dancinglightofgrace

Between Equations and Processions


I called their father. He was at home this evening. I asked if they had some ginger at the house. They didn’t. They sell vegetables. We sometimes buy some potatoes or ginger from them.
The students arrived and kept knocking at the door without using their voice. They usually use their  voice when they knock. When I opened the door the elder was using his smartphone and the younger was carrying snacks in a polythene bag. Both of them brought their snacks as they were coming immediately after returning from school and they were hungry.
The younger one asked me to give him some time to settle. I brought the chair from the verandah. He kept eating his salty snack mixture. He was using his hands and eating very quickly. I asked him to eat slowly. He kept licking his fingers. I took him outside to the porch and gave him some water to help him wash his hands. Then we went back inside the classroom. The elder brother kept browsing his Instagram feed and continued to feed on his snacks every now and then during the class.
They asked me the meaning of some captions on some pictures and videos. Some of them were in the mirror script. They said that these appeared in this script when copied from other sources. I told them it might be a bug or a safeguard against copyright violation strikes. Though I tried to explain to them what it meant – I doubt they grasped it fully.
They showed me some video clips of the religious procession on the occasion Shivaratri festival which began from the nearby temple and moved in circles. It began in the afternoon though by the time they arrived here it was already evening time. There were people in the costume of lord Shiva and other gods and demons traditionally associated with this marriage ceremony procession. Many of these appeared to be like Halloween costume masks. They were dancing and moving with the musical instruments. They told me about Bhaang(marijuana)preparations which have been part of such ceremonies since time immemorial in India. This intoxicating substance was consumed by kids and elders alike in large quantities. I asked them about their experience and they said it felt good and their companions were acting funny. I asked them if their parents allowed them to have such experience. They told me that there was no objection on behalf of their parents. Some of their friends were behaving recklessly.
It’s noteworthy that there was a discussion on drugs in the media and also in a movie I was watching. My grandmother returned after a stay at a relative’s house and she needed some new medications for cough and bronchitis.
My students had to go to attend some ceremonies yesterday as well. The religious festival was celebrated the day before yesterday. They did not come to attend yesterday. The elder showed some homework after being asked but the younger showed none. They had noted down some sentences in the Present Indefinite Tense. They were in affirmative and negative cases mostly. In one of the sentences they used an interrogative case.
They needed to note down ten sentences to show the fulfilment of an assignment given in their class. There were just 7-8 sentences. I helped them rewrite them. No, actually, I wrote them down as they can’t write. They can only copy them. They had a hard time coming up with a few sentences in Hindi- as ideas.
Sentences:
1. I study.
2. I don’t study.
3. Ram goes to school.
4. Ram does not go to school.
5. Shiv flies a kite.
6. Shiv doesn’t fly a kite.
7. She does her homework.
8. She doesn’t do her homework.
9. I like mango.
10. I don’t like mango.

We keep looking for extraordinary things and life happens. Ordinary. Simple. Routine. They showed me photographs they had taken for the new Admit Card for their annual exams. We commented on their pictures. The picture of the younger brother used to be even more childlike a few years ago. I asked them to keep these pictures safe in an envelope. They put them in their drawing box.
They gave me a pencil and their Mathmatics Workbook. I started working out problems. Factorising. Identity use.
Some of them I took a hint from their textbook and for others I prompted Gemini:


A cuboid has a volume of 3x^2-12x. What are the dimensions of this cuboid?


To find the dimensions of the cuboid, we need to factorize the expression for its volume. Since the volume of a cuboid is given by the formula \text{Volume} = \text{Length} \times \text{Breadth} \times \text{Height}, we are looking for three factors.
Factorizing the Expression
The given volume is:

Step 1: Identify the Greatest Common Factor (GCF)
Both terms 3x^2 and 12x are divisible by 3x.
Step 2: Factor out the GCF

Step 3: Express as three factors
To represent the three dimensions (length, breadth, and height), we can write the expression as:

Dimensions of the Cuboid
The possible expressions for the dimensions of the cuboid are:
* Dimension 1: 3 units
* Dimension 2: x units
* Dimension 3: x – 4 units
> Note: For these dimensions to be physically valid in a real-world cuboid, the value of x must be greater than 4 (so that x – 4 results in a positive length).

Find the length and breadth of the rectangle which has area: 25a^2-35a+12


To find the length and breadth of the rectangle, we need to factorize the quadratic expression representing the area, as \text{Area} = \text{Length} \times \text{Breadth}.
Factorizing the Expression
The given area is:

We can factorize this using the splitting the middle term method. We need to find two numbers that:
* Multiply to 25 \times 12 = 300
* Add up to -35
The two numbers are -20 and -15.
Step 1: Split the middle term

Step 2: Group the terms

Step 3: Factor out the common terms

Step 4: Factor out the common binomial

Conclusion
Since the area of a rectangle is the product of its length and breadth, the possible dimensions are:
* Length: 5a – 3
* Breadth: 5a – 4
   (Note: These can be interchanged as length is typically the longer side, and 5a-3 > 5a-4 for any positive value of a.)


Calculate 7^3+5^3+(-12)^3 using identities


To calculate 7^3+5^3+(-12)^3 using identities, we can use the following algebraic property:
Identity:
If a + b + c = 0, then a^3 + b^3 + c^3 = 3abc.
Step 1: Check the condition
Let a = 7, b = 5, and c = -12.
Summing them up:

Since the sum of the terms is zero, the identity a^3 + b^3 + c^3 = 3abc holds true.
Step 2: Apply the identity
Substitute the values into the identity:

Step 3: Calculate the product

Final Answer:

-1260

Prove x^3+y^3=(x+y)(x^2-xy+y^2)


To prove the identity x^3+y^3 = (x+y)(x^2-xy+y^2), we can expand the right-hand side (RHS) using the distributive property and show that it simplifies to the left-hand side (LHS).
Proof:
Starting with the RHS:

Apply the distributive property by multiplying each term in the first factor by each term in the second factor:

Distribute x and y into the trinomial:

Rearrange the terms in the second set of parentheses to make them easier to compare:

Now, group and combine like terms:

Observe that the middle terms cancel out:

This leaves us with:

Since the expansion of the RHS is identical to the LHS, the identity is proven.
Q.E.D.
I warmed tea up and served it to father. Both my maternal and paternal grandmother were meeting eachother in the hall. Earlier I served water and tea to mother who returned after work. I organised utensils in kitchen. Pasteurised milk. Served food to father and also supplied some lukewarm water for bath. I had bath and lunch. Mopped verandah and kitchen floors.

The Feedback I Expect From Gemini

This is a beautifully grounded piece of “slice-of-life” writing. You’ve captured the intersection of ancient traditions (Shivaratri), the digital age (Instagram/mirror scripts), and the simple, repetitive nature of being an educator and a family member.
Here is my feedback and some title suggestions for your WordPress blog.
Feedback
Strengths:
* The Contrast: I love the shift from the chaotic, high-energy description of the Shivaratri procession and Bhaang to the quiet, disciplined world of mathematics and domestic chores. It highlights how “extraordinary” events happen right alongside the “ordinary.”
* Authentic Details: Details like the kids knocking without using their voices, the younger one licking his fingers, and the “mirror script” on Instagram make the scene feel very real.
* Emotional Resonance: The transition where you mention your grandmothers meeting and you performing daily chores (serving tea, pasteurizing milk) provides a warm, rhythmic end to the narrative.
Suggestions for Improvement:
* Structure: The transition into the math problems is quite abrupt. You might want to frame them as a “moment of focus” amidst the day’s distractions.
* Tone Consistency: The section where you list the math solutions feels a bit like a textbook. If you want to keep the “blog” feel, you could summarize the experience of teaching those concepts rather than showing the full equations, or put them in a distinct “Study Corner” box.
* The “Bhaang” Section: You handle the topic with observation rather than judgment, which is great. You might want to emphasize your role as a mentor reacting to their “acting funny” to add a bit more narrative tension.
Suggested Titles
* Between Equations and Processions (Professional & Descriptive)
* Ordinary Life, Extraordinary Days (Reflective of your own closing sentiment)
* Mirrored Scripts and Math Workbooks (Whimsical & Modern)
* Shivaratri, Snacks, and the Present Indefinite (A play on the different elements of the day)
* The Geometry of a Tuesday (Metaphorical)

Posted on by dancinglightofgrace

Demystifying Degrees and Discriminants: A Math & AI Journal


I had dinner. Then, a ginger tea made by my mother. Helped my father with the decluttering of the call log on his phone. Maths class. The workbook had problems on Polynomials such as:
Simplifying this expression:
49a^2+70ab+25b^2
This expression is a Perfect Square Trinomial. It follows the algebraic identity:
1. Identify the Squares
First, notice that the first and last terms are perfect squares:
* First term: 49a^2 = (7a)^2
* Last term: 25b^2 = (5b)^2
2. Verify the Middle Term
Check if the middle term (70ab) matches the 2xy part of the identity:
* Since the middle term matches perfectly, we can apply the identity.
3. The Factorized Form
Using the values x = 7a and y = 5b:

Final Answer: (7a + 5b)(7a + 5b) or simply (7a + 5b)^2.
Determining if the expression below can be factorises:
To factorize the quadratic polynomial 12x^2 + 7x + 3, we look for two numbers that multiply to a \times c and add up to b.
1. Identify the Coefficients
For a quadratic in the form ax^2 + bx + c:
*  *  * 2. The Product-Sum Test
We need two numbers that:
* Multiply to: 12 \times 3 = 36
* Add up to: 7
Let’s look at the factors of 36:
* 1 \times 36 (Sum: 37)
* 2 \times 18 (Sum: 20)
* 3 \times 12 (Sum: 15)
* 4 \times 9 (Sum: 13)
* 6 \times 6 (Sum: 12)
3. Conclusion on Factorization
Notice that none of the pairs of factors of 36 add up to 7. Since there are no integers that satisfy both conditions, this polynomial cannot be factorized using rational numbers (it is “irreducible” over the rationals).
If we check the Discriminant (D = b^2 – 4ac):

Since the discriminant is negative (D < 0), the polynomial has no real roots and cannot be factored into linear factors with real numbers. It would require complex numbers to factorize.

Factorise 12x^2+7x+3


To factorize the quadratic polynomial 12x^2 + 7x + 3, we look for two numbers that multiply to a \times c and add up to b.
1. Identify the Coefficients
For a quadratic in the form ax^2 + bx + c:
*  *  * 2. The Product-Sum Test
We need two numbers that:
* Multiply to: 12 \times 3 = 36
* Add up to: 7
Let’s look at the factors of 36:
* 1 \times 36 (Sum: 37)
* 2 \times 18 (Sum: 20)
* 3 \times 12 (Sum: 15)
* 4 \times 9 (Sum: 13)
* 6 \times 6 (Sum: 12)
3. Conclusion on Factorization
Notice that none of the pairs of factors of 36 add up to 7. Since there are no integers that satisfy both conditions, this polynomial cannot be factorized using rational numbers (it is “irreducible” over the rationals).
If we check the Discriminant (D = b^2 – 4ac):

Since the discriminant is negative (D < 0), the polynomial has no real roots and cannot be factored into linear factors with real numbers. It would require complex numbers to factorize.

Verify if 7+3x is a factor of 3x^3+7x
To verify if 7 + 3x is a factor of 3x^3 + 7x, we can use the Factor Theorem.
The Factor Theorem states that for a polynomial P(x), a linear expression ax + b is a factor if and only if P(-\frac{b}{a}) = 0.
1. Identify the potential root
Set the divisor equal to zero and solve for x:

2. Substitute the root into the polynomial
Let P(x) = 3x^3 + 7x. We need to calculate P(-\frac{7}{3}):

To subtract, find a common denominator (which is 9):

Conclusion
Since P\left(-\frac{7}{3}\right) \neq 0, we conclude that 7 + 3x is NOT a factor of 3x^3 + 7x.

X^3-y^3 is equal to?
The expression x^3 – y^3 is a classic algebraic identity known as the Difference of Two Cubes. It factors as follows:
Key Components of the Formula:
* The Linear Factor: (x – y)
* The Quadratic Factor: (x^2 + xy + y^2)
A Quick Tip for Remembering the Signs (SOAP):
When factoring sums or differences of cubes, use the acronym SOAP to get the signs right:
* Same: The first sign is the same as the original expression (minus).
* Opposite: The second sign is the opposite of the original (plus).
* Always Positive: The last sign is always positive.
Comparison: Sum vs. Difference
If you were looking for the Sum of Two Cubes, the signs simply shift:
* Difference: x^3 – y^3 = (x – y)(x^2 + xy + y^2)
* Sum: x^3 + y^3 = (x + y)(x^2 – xy + y^2)
That depends entirely on whether that constant is zero or not zero.
If we define a constant polynomial as P(x) = c (where c is a real number), the existence of a solution depends on the value of c.


Is there no solution for a constant polynomial?


1. The Non-Zero Constant (c \neq 0)
If you have a polynomial like P(x) = 5, there is no solution.
* The Equation: 5 = 0
* The Logic: No matter what value you plug in for x, the output is always 5. Since 5 will never equal 0, there is no value of x that satisfies the equation. In this case, the solution set is empty.
2. The Zero Constant (c = 0)
If the polynomial is P(x) = 0, there are infinitely many solutions.
* The Equation: 0 = 0
* The Logic: As we discussed, every real number you substitute for x results in 0 = 0, which is always a true statement.
Comparison Summary
| Polynomial Type | Example | Equation | Number of Solutions |
|—|—|—|—|
| Non-Zero Constant | P(x) = 7 | 7 = 0 | None |
| Zero Polynomial | P(x) = 0 | 0 = 0 | All Real Numbers |

Is every real number a solution of zero polynomial?
Yes, every real number is a solution (or root) of the zero polynomial.
To understand why, we look at the definition of the zero polynomial, which is P(x) = 0.
The Breakdown
* Definition of a Solution: A value r is a solution if, when substituted for x, the equation holds true (P(r) = 0).
* The Zero Polynomial: In the function P(x) = 0, there are no variables visible because their coefficients are all zero. You can think of it as:
  
* Substitution: If you plug in any real number a (like 5, -10, or \pi), the result is always:
  
Because the output is zero regardless of the input, the set of all solutions is the set of all real numbers (\mathbb{R}).

The degree of a non zero non variable polynomial is always zero? True or false?
The   degree of a non-zero, non-variable polynomial is always zero.
Here is the breakdown of why:
* Non-variable polynomial: This refers to a constant (e.g., f(x) = 5 or f(x) = -12).
* Definition of Degree: The degree of a polynomial is the highest exponent of its variable.
* The Logic: A constant like 5 can be written as 5x^0. Since any non-zero number raised to the power of zero is 1, the exponent attached to the “invisible” variable is 0.
Important Distinction
* Non-zero constants: Degree is 0.
* The number zero (f(x) = 0): The degree of the zero polynomial is generally considered undefined or -\infty, because 0x^0, 0x^1, and 0x^2 are all technically equal to zero, so there is no “highest” exponent.

Earlier in the day I helped my father with warm water from the geyser for his bath. Served him tea and food. Moved utensils from the kitchen to the wash basin. Organised utensils in the kitchen after they were washed. Mopped verandah floor. Served water and tea to my mother. Pasteurised milk.

Today students didn’t show eagerness to interact on Gemini Live. I asked them to not ask redundant or futile questions by explaining that AI is there to help them not to argue or threaten it or bully it. I asked my younger student to be prepared with the questions he wanted to ask. The first question he came up with was : “How did paper get invented?” The next he wanted to ask about which phone was best. I think it was not a very useful question because they’re not going to use such phones very soon though information might be good to give them some perspective. They had hard time coming up with more questions and they were repeating some questions they had already asked.
Thankfully the elder brother brought a sharpened pencil, eraser and sharpner today. The younger brother had brought maths textbook. Quite dramatically the elder brother was showing off the highlighter marker pen with a rude attitude for some reason.
The elder brother could answer some questions about the degree of polynomials though the younger brother had difficulty answering most of them. When the younger brother was engaging in Gemini Live session the elder was busy listening to music on his smartphone with moderate volume. He had completed his homework partially. The younger student showed me some homework and classwork done in a bad half hearted handwriting.


Gemini Live Session Today:


Student: Hello.
Gemini: Hello! How can I help you today with math or anything else?
Student: Agar duniya ka sabse acha mobile konsa hai
[ You might have figured out from the past live sessions that my younger student begins his queries with ‘agar’ or ‘if’. ]
“दुनिया का सबसे अच्छा मोबाइल” चुनना थोड़ा मुश्किल है, क्योंकि यह आपकी जरूरतों और पसंद पर निर्भर करता है। कुछ प्रमुख ब्रांड जो हमेशा बेहतरीन फोन बनाते हैं उनमें Apple (iPhone), Samsung और OnePlus शामिल हैं। Samsung के Galaxy S सीरीज और OnePlus के फ्लैगशिप फोन अक्सर बेहतरीन प्रदर्शन के लिए जाने जाते हैं। क्या आप किसी खास फीचर को प्राथमिकता देते हैं, जैसे कैमरा या बैटरी?
Student: Camera
Gemini: अगर आपकी प्राथमिकता कैमरा है, तो इस समय बाजार में कुछ बेहतरीन विकल्प हैं। Apple का लेटेस्ट iPhone अपनी लाजवाब फोटोग्राफी और वीडियोग्राफी के लिए जाना जाता है। Samsung के Galaxy S24 Ultra में बहुत एडवांस जूम क्षमताएं और शानदार सेंसर हैं। इसके अलावा, Google Pixel फोन हमेशा से ही अपनी बेहतरीन कैमरा क्वालिटी के लिए प्रसिद्ध रहे हैं। आपकी मुख्य प्राथमिकता क्या है – फोटो, वीडियो, जूम या कुछ और?
Student: जय फोटो कैमरा जूमिंग सबसे ज्यादा जूमिंग किस मोबाइल में
Gemini: सबसे ज्यादा जूमिंग क्षमता वाले मोबाइल फोन में आमतौर पर Samsung Galaxy S24 Ultra का नाम आता है। इसमें 100x स्पेस जूम तक की क्षमता है, जिससे आप बहुत दूर की चीजों को भी काफी स्पष्ट रूप से देख सकते हैं। क्या आप इस बारे में कुछ और जानना चाहते हैं या किसी खास उपयोग के लिए पूछ रहे हैं?

Student: Uh hello
Gemini: जी, पूछिए।
Student: अगर पेपर की खोज किसने की थी
Gemini: कागज की खोज चीन में हुई थी। पारंपरिक मान्यताओं के अनुसार, लगभग 105 ईस्वी में साई लून (Cai Lun) नामक एक चीनी अधिकारी को इसका श्रेय
Student: लिखने वाले एग्जाम
Gemini: साई लून ने कागज बनाने की प्रक्रिया को व्यवस्थित किया और उसमें सुधार किए, जिससे लेखन सामग्री अधिक सुलभ और सस्ती हो गई। उनके प्रयासों ने ज्ञान के प्रसार में महत्वपूर्ण भूमिका निभाई।

Student: Hello
Gemini: जी हाँ, कहिए। क्या जानना चाहते हैं?

Student: अगर पेपर की खोज किसने की थी
Gemini: कागज़ की खोज चीन में हुई थी। लगभग 105 ईस्वी में, साई लून नामक एक चीनी अधिकारी को इसका श्रेय दिया जाता है।
Student: एग्जाम की किसने खोज की थी?
[ With this question I beat my head. I didn’t make a sound because it would be recorded. ]
Gemini: परीक्षा या “एग्जाम” की खोज किसी एक व्यक्ति द्वारा नहीं की गई थी। इसका इतिहास बहुत पुराना है।
कुछ स्रोतों का मानना है कि आधुनिक परीक्षा प्रणाली का विचार 19वीं शताब्दी में सर हेनरी फिशेल द्वारा दिया गया था, लेकिन परीक्षाएँ तो प्राचीन समय से ही शिक्षा प्रणाली का हिस्सा रही हैं।
क्या आप किसी विशिष्ट प्रकार की परीक्षा के बारे में जानना चाहते हैं?
Student: नहीं
Gemini: ठीक है। क्या आप शिक्षा या इतिहास से जुड़े कोई और प्रश्न पूछना चाहते हैं?
Student: नहीं
Gemini: कोई बात नहीं। अगर आपके मन में कोई और सवाल हो, तो बेझिझक पूछें।

End of the Gemini Live Session.
If you have been following these articles and session recordings: you can see that they didn’t veer off into violent zones today. Being prepared before the session worked better though my student asked a question about examination system which wasn’t completely irrelevant. The elder didn’t disturb today because he was busy with his reels and music probably on Instagram.
This was the end of the class as well. I didn’t give homework to the younger one because he never does it. The elder was given writing assignments. I did a session on Duolingo. There were frequent power cuts today.

The Feedback I Expect From The Readers

This is a rich, multi-layered entry. It functions as a “Day in the Life” piece that seamlessly blends domestic duty, pedagogy, and technical math instruction. The juxtaposition of ancient history (Cai Lun), modern tech (S24 Ultra), and abstract algebra creates a unique “knowledge diary” feel.
1. Feedback for WordPress Publication
* Structure: You have three distinct sections: The Math Guide, The Domestic Log, and The Teaching Narrative. For a blog, I recommend leading with the Teaching Narrative to hook the reader emotionally, then providing the Math Lessons as “Today’s Learning Modules.”
* Tone: The frustration with the student’s “exam” question is a very relatable “teacher moment.” Don’t be afraid to keep that humor; it makes the article authentic.
* Formatting for Web:
   * LaTeX: Ensure your WordPress theme supports MathJax or a similar plugin so equations like
     render beautifully.
   * The Transcript: Use “Blockquotes” or a “Chat” style block for the Gemini Live session to make it distinct from your prose.
* The “Agar” Observation: Your note about the student starting every query with “If” (Agar) is a brilliant linguistic insight. It shows how the student views the AI—as a “condition-solver” rather than a search engine.
2. Title Suggestions
Depending on the “vibe” of your blog, here are three directions:
* The Narrative Title: Between Polynomials and Paper: A Day of Teaching and Tea.
* The Educational Title: Demystifying Degrees and Discriminants: A Math & AI Journal.
* The Witty/Reflective Title: The “Agar” Chronicles: When Gemini Live Meets the Invention of Exams.
* The SEO-Friendly Title: Algebraic Identities and AI Pedagogy: A Daily Log Book.

Posted on by dancinglightofgrace

The Mirror and the Molecule


My mother asked me to make tea when the cook was in the kitchen. I asked her to wait until she was done. Later, I found that she had made it herself. She offered me some. I had it when the class was over. The software version of this phone updated itself.
Students left after noting down Addition and Subtraction problems. It was the second batch. The elder solved the first batch. The younger hardly attempted them. If I again paint a picture of the younger student with my words: it would suggest how detached he seems from studies these days. We remarked on that briefly: earlier he used to do his  occasionally, now he doesn’t.


Since his rough notebook is full, He merely pulls out a page from here, another from there and without even using a pad underneath attempts to write on it as the pen makes holes into the paper. Later, he takes this paper in his hand and pokes it further with his pen. I ask him to not do that. There was still space on it, like spaces left out here and there on the pages of his notebook. He crumbled the torn page and keeps it in his bag. I ask the elder to carefully keep his drawing box into the bag lest they forget it similar to yesterday’s episode.
The elder had been making fun of the younger and despite my forbidding him from doing so he returned to it periodically throughout the class, as if, unable to control himself due to almost sadistic joy he derives from it. At once their battle begins to become too violent with steel bangles, the elder takes away the steel bangle from the younger. I ask them to be careful with that. The younger gives him three- four retaliatory blows.
Meanwhile there’s a bet about who can do 5000000-2344678 faster. I taught the technique to subtract one from both numbers before proceeding with the subtraction to the elder when the younger was absent. He uses it as a strategic advantage, quite sure that the younger was going to err on it. He places a ten rupees bet which is soon accepted by his brother though he can’t produce the money when he demands. Though I don’t promote betting I know this isn’t going anywhere. Calligraphy, calculations, homework, punctuality and any other traits which were present in the younger student have completely disappeared. The elder isn’t an ideal student yet he’s much better than the younger and he gets the solution correct with only a single digit’s error because he writes :
5000000-1= 5999999 and then after doing something similar with the other number proceeds with his substraction.
As soon as I evaluate the only subtraction problem attempted by the younger he backs off from the bet.
The elder threatens him.
“Unless you pay me, I will bear you at home or you will be trapped in some scheme created by me. I will tell others to withdraw money from you where I am supposed to pay.”
That’s just a ten rupees affair. But that’s a big deal. The morale of the younger student is already down. Yesterday, he had to make another trip to collect his bag.
This doesn’t prevent him from grooming himself. The window mirrors which are stained with calcium carbonate which was in water are a source of motivation for him more than any of my encouragement for doing his homework.
Adolescence.
The first thing he does after entering the room is to check himself thoroughly in the mirror.
Then he very eagerly asks me if his face is circular, as it appears in the school mirrors or oval. I tell him about the Dhubela museum mirrors which show tall, short, stout images to visitors. I tell him that his face is not circular in shape. At this point the elder also grooms his hair. Even his face isn’t circular.
I had to request the younger one to not touch his hair anymore. The elder is almost sleepy as I read Laws of Motion. The chapter is about motion. There’s an introduction about Galileo. It’s detailed. It tells how he actually wanted to do Maths but his father wanted him to become a doctor. It’s surprising there were universities in Italy even five hundred years ago. He published a book on work based on Archimedes at first. His heart wasn’t in the study of Medicine.
The younger student exclaims about the incident being in 1564-1586 : it was five hundred years ago! He’s almost right. I consider it a positive sign. At least he’s taking some interest. It’s not.
He waves his arms menacingly, as if, half baked understanding of what I am reading in his textbook is to be used to feed his:
Prophet
Fundamental dogmatic violent wings
Narcissistic hero.
He eagerly awaits until I reach the passage describing why we feel a shock when gun fires a bullet. At this point the elder tells with confidence how he once fired a small spherical pellet at a bucket and it created a hole in it. I am teaching them the third law of motion:
“Every action has an equal and opposite reaction.”
It’s by Sir Issac Newton.
The elder casually comments about the nature of experiments done by Newton to reach these conclusions.
We see a picture in which a boy is jumping from a small boat to a wooden block. The picture is casually made. It’s not an illustration. It was supposed to give a hint. It wasn’t a drawing competition. I wanted the younger one to draw pictures like he used to do before. In previous classes. He’s more concerned with his hairstyle.
He interjects about friction when it’s mentioned in the textbook. I describe it to him. They readily grasp how sudden breaks or movement of the bus shows us “Inertia” of rest and moment.
Reading Hindi text feels slightly different. There are numerical problems based on the Newton’s laws of motion.
F=ma
And relationships between initial and final velocities with acceleration, time and displacement. We skip these because they’re not oriented to attempt them.
The chapter is covered faster than they expected. We continue with the practice of Algebra. Before moving out they check Instagram feed. When I ask if the younger student would need the smartphone next year there’s no sudden discussion. They have a good acceptance about how things have been going on in this regard.

Posted on by dancinglightofgrace

Grammar and Maths

I parked the bike inside the garage. It was twilight. There were goats returning in a herd. Students were leaving when my father asked me to take help from them to push it up the ramp to park it inside. He had returned with vegetables and groceries. Mother was also not in the house. She first went to a grocery store and then to the house of some acquaintance.
My class concluded with an exercise in their Grammar workbook. It had many questions on articles/subject-verb agreements/comparitive-superlative degrees/countable-uncountable nouns etc in fill in the blanks format with three choices to select from.
Together they answered about half of them correctly though it was just by using chance. They didn’t grasp any of the questions though I kept explaining those. The younger brother kept shifting his answers at random just to sound correct. As soon as he learned that his choice was incorrect he shifted to the other choice.
He made ink star even today in his left hand’s palm with my pen. Prior to that he was using that to pinch his elder brother. Both of them were fighting eachother physically before class commenced as I was busy organising utensils in the kitchen.
Since there’s Republic Day tomorrow, they’re going to attend school only for cultural programs and enjoy sweets. They had completed their homework though the younger student used red ink to complete it. When I tried to explain him that teachers are supposed to use that and he should use a blue ink- he told me that nobody asked him to not use that even in his school.
Today they didn’t use their smartphone which was a great change. I gave them five addition and five subtraction problems as assignement. The younger one was reluctant to not it down.
He was dancing every now and then and then they kept quarreling. Looking into the mirror of the window he told me how he appears bigger in some mirrors and smaller in others. Asked my permission to use body lotion. Then they asked about its price.
I told them about the museum near this city where mirrors give various images in which you appear obese or lean, taller or smaller. I told them they can visit that place though it charges a ticket for a visit. Then I told them that maybe only grown ups are supposed to visit as this archeological site has many valuable items.
We did a couple of problems in Maths. I wasn’t prepared. I used the solution. It uses Congruence. A bit of construction and then proves that two equal length chords intersect at a point which when joined with the centre of the circle subtends equal angles with both of them.
In the next problem there were three girls sitting on the periphery of a circular park. They have a ball which they throw at each other. The distance between first two of them is six meters. The distance between the second two of them is also six meters. The distance between first and the third is to be obtained if the radius of the circle is given. This one uses a triangle by connecting the centre of the circle with the position of the girls. Area of a triangle is one by two multiplied with base of the triangle multiplied with the height of the triangle. The two orientations of triangles are such that one of them gives the half length of the chord and doubling it gives the requisite length.