Question

here an activity !

⚫Aim of the activity -

develop the concept of inverse variation by activity method.

please explain !

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Answer 1

Aim - To develop the concept of inverse variation by activity method .

Materials Required -

1. 4 sets of congruent circles , where each set has a dozen congruent circles .

2. 10 plain sheets of paper

Procedure -

considered the number of sheets of a paper as x and the number of circles pasted on it as y.

1. Take 1 sheet and paste the first set on the dozen circles on it.

Number of sheets × Number of circle pasted on it = 1 × 12 = 12

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Here , x × y = 1 × 12 = 12

2. take 2 sheets and paste the second set of the dozen circle equally on them .

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○○○⠀⠀|⠀○○○

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Here , x × y = 2 × 6 = 12

3. take 3 sheets and paste the third set on one dozen circle equally on them

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○○⠀⠀|⠀○○⠀⠀|⠀○○

○○⠀⠀|⠀○○⠀⠀|⠀○○

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Here , x × y = 3 × 4 = 12

4. take 4 sheets and paste fourth set of one dozen circles equally on them.

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⠀⠀○⠀⠀|⠀⠀○⠀⠀⠀|⠀⠀○⠀⠀⠀|⠀⠀⠀○⠀

○⠀⠀○⠀|⠀○⠀⠀○⠀|⠀○⠀⠀○⠀|⠀⠀○⠀⠀○

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Here , x × y = 4 × 3 = 12

Observations -

$\begin{gathered}\begin{gathered}\begin{gathered}\begin{gathered}\boxed{\begin{array}{cccc}\sf no. \: of \: sheets(x) &\sf no. \: of \: circles \: stick \: on \: it(y)&\sf total \: no. \: of \: circles(k)\\\frac{\qquad \qquad \qquad \qquad}{}&\frac{\qquad \qquad \qquad \qquad}{}&\frac{\qquad \qquad \qquad \qquad\qquad}{}\\\sf 1&\sf 12 &\sf 12 \\\\\sf 2 &\sf 6 &\sf 12 \\\\\sf 3&\sf 4&\sf 12 \\\\\sf 4&\sf \ 3&\sf 12\\\frac{\qquad \qquad \qquad \qquad}{}&\frac{\qquad \qquad \qquad \qquad}{\bf{}}&\frac{\qquad \qquad \qquad \qquad\qquad}{}\end{array}}\end{gathered}\end{gathered}\end{gathered} \end{gathered}$

When the number of circles based on each sheet become less , than the more number of sheets are used .

In each case product x × y = constant

this mean X increases , y decreases and vice versa.

this shows that the value of x and y are inversely proportional

Result -

The number of sheet required in inversely proportional to the number of circular cuts out pasted on each sheet.

Answer 2

Answer:

When the number of circles based on each sheet become less , than the more number of sheets are used .

In each case product x × y = constant

this mean X increases , y decreases and vice versa.

this shows that the value of x and y are inversely proportional

Result -

The number of sheet required in inversely proportional to the number of circular cuts out pasted on each sheet.