# Classroom Resources

## Problems for the Middle School March 2019

Pure geometry or Euclidean geometry is a body of theorems and corollaries logically derived from certain axioms and postulates as presented in Euclid’s Elements. Later geometers, both Greek and others, have added to this. Occasionally some algebra is brought in but not trigonometry. Abraham Lincoln is said to have read the Elements just for the reasoning.

## Problems for the Senior School - March 2019

Some problems for the Senior School.

## Taking a Chance with a Graphics Calculator

Graphics calculators have been available to students in secondary school in some countries now for more than thirty years, although of course their capabilities have been developed in various ways to support the school curriculum over that time. The most frequent use of these devices seems to be concerned with the representation of functions, including in particular their graphical representation, which was an important component of a previous paper in this magazine (Kissane, 2016).

## QUILTING Explorations by a Mathematics Teacher

I must confess that it was the top layer that attracted me to quilting. This was clearly a case of the whole being greater than the sum of its parts- I was wonderstruck at how scraps of material could be pieced together to make beautiful patterns that were all at once eye-catching and pleasing.

## Two Striking Number Patterns

Sums of squares of the natural numbers from the Pascal triangle.

## Squaring the Dots Think into the Box

A square dot sheet has equally spaced dots aligned vertically and horizontally. Many interesting investigations can be devised with this simple learning material.

## Playing with Tiles Beginning to Tessellate

Many people are of the opinion that mathematics is only about numbers and number operations, and thus myths related to who can do mathematics and who cannot, abound. It is possible that children may struggle with numbers, but it is hard to believe that there could be a child who doesn’t recognize patterns. We see children creating patterns all the time using stones, sticks, leaves, flowers, finger prints, vegetable carvings, rubber stamp impressions and also mathematical shapes.

## Finding the Number of Ordered Tuples Having a Given LCM

Counting is one of the first skills that a student of mathematics learns. Here we feature an article that observes patterns while counting and generalises this pattern. While the actual combinatorics and use of the binomial theorem may be appreciated only by students of classes 11 and 12, students of High School will certainly be able to follow the reasoning in the two examples given. It is important for students to have such gentle introductions to mathematical notation and theorems used at a more senior level.

## Development of Teacher Education in Meghalaya

Teacher Education Institutions were established in a gradual manner to cater to the needs of teachers in the state. The first Teacher Education Institution under the Theological College was started by the Welsh Mission at Cherrapunjee for training of teachers at the primary level. In 1861, the Government decided to amalgamate the Training School section of the Cherrapunjee Normal School from Nongsawlia to Shillong and attached to the Welsh Mission High School at Mawkhar Shillong. By 1946, the Training School functioned in the same building.

## Climate of India

India is home to an extraordinary variety of climatic regions, ranging from tropical in the south to temperate in the Himalayan north, where elevated regions receive sustained winter snowfall. The nation's climate is strongly influenced by the Himalayas and The Thar Desert.Though the Tropic of Cancer—the boundary between the tropics and subtropics—passes through the middle of India, the bulk of the country can be regarded as climatically tropical.

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