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.