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<!DOCTYPE html>
<html data-require="math spin word-problems">
<head>
<meta http-equiv="Content-Type" content="text/html; charset=UTF-8">
<title>Counting 1</title>
<script src="../khan-exercise.js"></script>
</head>
<body>
<div class="exercise">
<div class="problems">
<div id="page-numbers">
<div class="vars">
<var id="START">randRange( 20, 50 )</var>
<var id="ANSWER">randRange( 20, 40 )</var>
<var id="END">START + ANSWER - 1</var>
<var id="DO, DID, PROBLEMS">spin( "{do,did,problems|read,read,{pages|papers|articles}}" ).split( "," )</var>
</div>
<p class="spin">
<var>person( 1 )</var> {had to <var>DO</var>|was assigned} <var>PROBLEMS</var> <var>START</var> through <var>END</var> for homework {{last {week|night}}|tonight}.
</p>
<p class="question spin">
If <var>person( 1 )</var> <var>DID</var> all of the <var>PROBLEMS</var> <var>he( 1 )</var> was assigned, how many <var>PROBLEMS</var> did <var>he( 1 )</var> <var>DO</var>?
</p>
<div class="solution" data-type="multiple">
<p><span class="sol" data-forms="integer"><var>ANSWER</var></span> <var>PROBLEMS</var></p>
</div>
<div class="hints">
<p>Instead of counting <var>PROBLEMS</var> <var>START</var> through <var>END</var>, we can subtract <var>START - 1</var> from each number so we instead consider <var>PROBLEMS</var> 1 through <var>ANSWER</var>.</p>
<p>We see that <var>person( 1 )</var> <var>DID</var> <var>ANSWER</var> <var>PROBLEMS</var>.</p>
<p>Notice that <var>he( 1 )</var> <var>DID</var> <var>ANSWER</var> and not <var>ANSWER - 1</var> <var>PROBLEMS</var>.</p>
</div>
</div>
<div id="slices">
<div class="vars">
<var id="NUM">randRange( 5, 15 )</var>
</div>
<p class="spin">A baker has a whole {baguette|loaf of bread}.</p>
<p class="question spin">How many cuts must {he|she} make to have exactly <var>NUM</var> even slices?</p>
<div class="solution" data-type="multiple">
<p><span class="sol" data-forms="integer"><var>NUM -1</var></span> cuts</p>
</div>
<div class="hints">
<p>One cut will make two slices, two cuts will make three slices, and so on.</p>
<p>Therefore, we need <var>NUM - 1</var> cuts to make <var>NUM</var> slices.</p>
</div>
</div>
<div id="fences">
<div class="vars">
<var id="LENGTH">randRange( 10, 20 )</var>
</div>
<p><var>person( 1 )</var> is building a straight fence, with posts one meter apart.</p>
<p class="question">If the fence is <var>LENGTH</var> meters long, how many fence posts does <var>he( 1 )</var> need?</p>
<div class="solution" data-type="multiple">
<p><span class="sol" data-forms="integer"><var>LENGTH + 1</var></span> fence posts</p>
</div>
<div class="hints">
<p>If the fence is one meter long, <var>he( 1 )</var> needs two posts (one for each end).</p>
<p>If the fence is two meters long, then <var>he( 1 )</var> needs three posts, and so on.</p>
<p>Therefore, <var>he( 1 )</var> needs <var>LENGTH + 1</var> posts for a <var>LENGTH</var> meter fence.</p>
</div>
</div>
</div>
</div>
</body>
</html>
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