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<h3>Warm Up (5 minutes)</h3>
<p>In this warm up, students practice writing an inequality to represent a constraint, reasoning about its solutions, and interpreting the solutions.</p>
<p>To write an inequality, students need to attend carefully to verbal clues so they can appropriately model the situation. The word “budget,” for instance, implies that the exact amount given or any amount less than it meets a certain constraint, without explicitly stating this. Discuss how budgets can be useful as a way to measure spending in a household, at a company, or even as a government. Using budgets to measure the amount that can be spent is a useful tool for financial responsibility.</p>
<p>When thinking about how many pounds of food Kiran can buy, students should also recognize that the answer involves a range, rather than a single value.</p>
<h4>Student Activity</h4>
<p>Kiran is getting dinner for his drama club on the evening of their final rehearsal. He plans to buy some prepared dishes from a supermarket.</p>
<ul>
<li>The budget for the dinner is $60.</li>
<li>The prepared dishes are sold by the pound, at $5.29 per pound. </li>
<li>He also plans to buy two large bottles of sparkling water at $2.49 each.</li>
</ul>
<p>1. Represent the constraints in the situation mathematically. If you use variables, specify what each one means.</p>
<p><strong>Answer: </strong>\(5.29p\;+\;2(2.49)\;\leq\;60\) or \(5.29p\;+\;4.98\;\leq\;60\). \(p\) is the pounds of prepared foods Kiran could buy without going over budget.</p>
<P>2. How many pounds of prepared dishes can Kiran buy? Be prepared to show your reasoning.</p>
<p><strong>Answer: </strong>Up to 10.4 pounds, or \(p\leq10.4\). For example: After removing the cost of sparkling water, Kiran still has $55.02. Dividing that amount by 5.29 gives 10.4.</p>
<h4>Activity Synthesis</h4>
<p>Make sure students see one or more inequalities that appropriately model the situation. Then, focus the discussion on the solution set. Discuss questions such as:</p>
<ul>
<li>“What strategy did you use to find the number of pounds of dishes Kiran could buy?”</li>
<li>“Does Kiran have to buy exactly 10.4 pounds of dishes?” (No.) “Can he buy less? Why or why not?” (Yes. He can buy any amount as long as the cost of the food doesn’t exceed $55.02. This means he can buy up to 10.4 pounds.)</li>
<li>“What is the minimum amount he could buy?” (He could buy 0 pounds of food, but it wouldn’t make sense if his goal is to feed the club members.)</li>
</ul>