<h3>The Main Idea</h3> <p><strong>Area is the space inside a shape — measured in square units.</strong></p> <p>When you see "area," immediately ask: <em>What shape?</em> The shape tells you which formula to use.</p> <h3>The 3-Step Approach</h3> <ol> <li><strong>What do you want?</strong> — Read the question sentence. Look for "area" or "square units" (ft², m², cm²).</li> <li><strong>What do you have?</strong> — Identify dimensions with their labels (length, width, base, height, side).</li> <li><strong>What's the connection?</strong> — Pick the formula that matches your shape, plug in, solve.</li> </ol> <h3>Key Word Clues</h3> <ul> <li><strong>Square units</strong> (ft², m², yd²) → You're dealing with area</li> <li><strong>"Covers," "surface," "inside"</strong> → Area</li> <li><strong>"Tiles," "carpet," "paving"</strong> → Area (covering a surface)</li> </ul> <h3>Working Backwards</h3> <p>Sometimes you're given the area and asked to find a missing dimension:</p> <ul> <li><strong>Rectangle:</strong> If Area = L × W, then L = Area ÷ W</li> <li><strong>Square:</strong> If Area = s², then s = √Area</li> <li><strong>Triangle:</strong> If Area = ½ × b × h, then h = 2 × Area ÷ b</li> </ul>
Practice This Goal<h3>The Main Idea</h3> <p><strong>Perimeter is the distance around the outside of a shape.</strong></p> <p>Think of it as walking along the edges — how far do you walk to get back to where you started?</p> <h3>The 3-Step Approach</h3> <ol> <li><strong>What do you want?</strong> — Read the question sentence. Look for "perimeter," "around," "edge," "outline," or "fence/frame."</li> <li><strong>What do you have?</strong> — Identify dimensions. Note which ones are given and which is missing.</li> <li><strong>What's the connection?</strong> — Pick the formula, plug in, solve.</li> </ol> <h3>Key Word Clues</h3> <ul> <li><strong>"Perimeter," "around," "edge," "outline"</strong> → Add up all sides</li> <li><strong>"Fence," "frame," "border," "string of lights"</strong> → Perimeter (going around something)</li> <li><strong>Units are NOT squared</strong> (ft, m, in — not ft², m²) → Perimeter, not area</li> </ul> <h3>Working Backwards</h3> <p>When you're given the perimeter and need to find a side:</p> <ol> <li><strong>Shortcut for rectangles:</strong> Divide the perimeter by 2 first → gives you (L + W)</li> <li>Then subtract the known dimension to find the unknown</li> </ol> <p><em>Example: P = 62, L = 20 → 62 ÷ 2 = 31 → 31 - 20 = 11 (width)</em></p>
Practice This Goal<h3>The Main Idea</h3> <p><strong>These problems require more than just plugging into a formula — you need to reason through the relationship.</strong></p> <p>The key word "fit" often signals division. Combined shapes require you to think about what happens when shapes are joined.</p> <h3>The 3-Step Approach (Extended)</h3> <ol> <li><strong>What do you want?</strong> — Read the question sentence. Is it asking for area, perimeter, or something else (how many, how far, etc.)?</li> <li><strong>What do you have?</strong> — Identify all given values. Look for clues about shape combinations or repeated operations.</li> <li><strong>What's the connection?</strong> — This usually involves TWO steps: calculate an area/perimeter first, THEN do an additional operation.</li> </ol> <h3>Common Reasoning Patterns</h3> <ul> <li><strong>"How many fit?"</strong> → Calculate total area, then <em>divide</em> by area per item</li> <li><strong>"How many steps/laps?"</strong> → Calculate perimeter, then <em>divide</em> by step length (or multiply by laps)</li> <li><strong>"Two shapes joined"</strong> → Think about which sides are hidden (shared edge) vs. exposed</li> <li><strong>"Border/frame/deck"</strong> → Big area <em>minus</em> small area</li> </ul> <h3>The "Fit" Rule</h3> <p>Anytime a problem asks "how many X fit into Y" — that's <strong>division</strong>.</p> <p><em>How many 5-dollar bills fit into 20 dollars? → 20 ÷ 5 = 4</em></p> <p><em>How many 4 ft² crates fit on a 96 ft² shelf? → 96 ÷ 4 = 24</em></p> <h3>Combined Shapes — What Changes?</h3> <p>When two squares are joined edge-to-edge:</p> <ul> <li><strong>Area:</strong> Just add them (the touching edge doesn't affect inside space)</li> <li><strong>Perimeter:</strong> The shared edge is no longer on the outside — subtract those sides</li> </ul>
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