Are certain individuals born to be teachers and can only those be truly competent? Or can people without such aspirations develop to become ‘great teachers’? Are there certain conditions, the presence of which foster such development?

# place value

Arrow cards are a simple manipulative to grasp place value or more generally the base-ten number-writing system that we use. Dr. Maria Montessori invented the static cards shown in Figure 1. These cards are used along with proportional material like static beads (unit = single bead, ten = 10 beads strung together forming a line, hundred = 10 tens strung together to form a square and thousand = 10 hundreds strung to form a cube) to gain a sense of numbers – the quantities they indicate and the numerals that represent them and how they are linked.

Arrow cards originated as static cards in Montessori and were adopted in mainstream with the addition of arrow - an extension that can be used to hold the cards up (together) to display for an entire class.

These arrow cards can be extended for decimal numbers. To ensure that the numbers can be extended on either side (i.e. to thousands etc. on the left and to ten-thousandths etc. on the right), the arrow has been replaced by a groove at the decimal point.

In this edition of ‘Adventures’ we study a few miscellaneous problems, mostly from the Pre-Regional Mathematics Olympiad (PRMO; this year’s PRMO was conducted on August 19 in centres all over the country). As usual, we pose the problems first and present solutions later.

We have often seen that what we think happens the way we wanted it to happen but at times the results are much better than what we expected.

This article deals with a simple test for divisibility by 7 for natural numbers having a minimum of four digits. Here, a case of a six-digit number is proved initially and similar proofs follow for other higher-digit numbers.

Invite your middle school students to this set of problems.

Bharat Learn (BL) is a NGO that works with the aim of empowering teachers and students to enhance the learning outcomes of the students. BL uses its Film Based Teaching Methodology (FBTM®) to convert existing school curriculum into video based teaching-learning content and makes it available to the teachers and students free and freely.

There is a well-known test for divisibility by powers of 2: to check the divisibility of a number M by 2^{n}, we form a new number M' using only the last n digits of M and then examine the divisibility of *that* number (i.e., M') by 2^{n}. The test works because of the easily-proved fact that M is divisible by 2 if and only if M' is divisible by 2^{n}.

Here are more examples of multiplication for your students to strengthen their learning of the concept.