<h3>Integers and the rules of signs</h3><p><strong>Integers</strong> are the counting numbers, their negatives and zero: …, -3, -2, -1, 0, 1, 2, 3, … We use a <strong>number line</strong> to picture them. Moving right increases a value; moving left decreases it.</p><ul><li>Adding a negative is the same as subtracting: <code>5 + (-3) = 2</code>.</li><li>Subtracting a negative is the same as adding: <code>5 - (-3) = 8</code>.</li><li>Multiplying or dividing two numbers with the <strong>same sign</strong> gives a positive; with <strong>different signs</strong> gives a negative.</li></ul><h3>Cubes and cube roots</h3><p>The <strong>cube</strong> of a number raises it to the power three: <code>4^3 = 4 x 4 x 4 = 64</code>. The <strong>cube root</strong> (written <code>∛</code>) undoes this. Using the <strong>factor method</strong>, write 343 as <code>7 x 7 x 7</code>, group the factors in threes, and read off one seven, so <code>∛343 = 7</code>.</p><div class="callout"><strong>Kenyan context:</strong> A cubic water tank on a Kiambu farm holds 27 cubic metres. To find the length of one side, take the cube root: <code>∛27 = 3</code> metres. At dawn the temperature on the Aberdares was -2 degrees Celsius and by noon it rose by 9 degrees. The new temperature is <code>-2 + 9 = 7</code> degrees Celsius.</div>