Give possible reasons for wrong result?

A class 2 child adds 141 and 41 as follows:

A class 2 child adds 141 and 41 as follows:

 What is a tiling (tessellation)? Give an example of a tiling using two different shapes. 

Give an example of a mathematical conjecture.

We have a hypothesis: “Class V girls perform better in mathematics than boys of the same class”. What data would children need to gather to test this hypothesis? How would they analyse the data?

What do ássimilation’ and áccommodation’ mean? Explain, the terms in the context of learning measurement of time.

) Deepa had to introduce the concept of ‘half’ to her class of 7-yar olds. She began by asking children if they could show half of anything. Most children came up with examples by breaking a chalk piece or tearing a sheet of paper into two. Deepa allowed children to talk to each other and share their examples with the whole class. More examples emerged, such as half of a glass of water. Deepa did not emphasize that the size of the two pieces must be equal for each to be one-half of the whole. Through the entire class she did not introduce the symbol ½.

i) Do you think Deepa should have started by giving examples of ‘half’ herself? Justify your answer.

ii) Was Deepa justified in not introducing the symbol? Explain why? 

iii) Suggest an activity to carry this forward on the following day.

 If E is a measurable set and f is a simple function such that , show that

Give an example of an algebra which is not a -algebra. Justify your choice of examples

 Let (X, d) be a metric space and A be a subset of X. Show that  if and only if A is both open and closed.

 Verify the hypothesis and conclusions of the Fatou’s lemma for the sequence  given by

Give an example of a family f_i of subsets of a set X which has finite intersection property. Justify your choice of example.

Find  in  where d is the metric given by .

Based on the image provided, here is the transcription of the final questions:

Suppose that  is given by  and  is given by

. Compute the derivative of .

 Find the directional derivative of the function  defined by

at the point (1, 2, -1, -2) in the direction .

 Is the continuous image of a Cauchy sequence a Cauchy sequence? Justify.

) Show that the function f defined by

is not differentiable at (0,0). Do the partial derivatives of f exist at (0,0)? or at any other point in ? Justify your answer.

 Let F be the function from  to  defined by

Show that F is differentiable at (1, 2). Find the differential matrix of F.

Find the interior and closure of the set  of rationals in  with standard metric.