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74 lines
2.5 KiB
Markdown
74 lines
2.5 KiB
Markdown
+++
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title = "Integer foundations"
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description = "Model directed magnitude on number lines; use the zero principle and tiles to add and subtract integers, and see subtraction as adding an opposite."
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template = "chapter.html"
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weight = 8
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[extra]
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subject = "math"
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chapter_id = "integer-foundations"
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strand = "Number & Algebra"
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+++
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<div class="book-prose">
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<p>
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Integers extend whole numbers to include values below zero. They are useful for temperature,
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elevation, and money balances.
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</p>
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<h2 id="number-line" class="book-prose__heading">Directed numbers on a number line</h2>
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<p>
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Positive numbers are to the right of zero, negative numbers are to the left. Moving right
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increases value; moving left decreases value.
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</p>
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<div class="book-callout book-callout--formula" role="note">
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<p class="book-callout__label">Compare quickly</p>
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<p class="book-formula">\(a > b\) means \(a\) is to the right of \(b\) on the number line.</p>
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</div>
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<h2 id="absolute-value" class="book-prose__heading">Absolute value and opposites</h2>
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<p>
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Absolute value is distance from zero: \(|-7|=7\). Opposites have equal distance from zero and
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opposite signs, such as \(+5\) and \(-5\).
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</p>
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<h2 id="add-subtract" class="book-prose__heading">Adding and subtracting integers</h2>
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<p>
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You can think of addition and subtraction as movement on the number line.
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</p>
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<ul>
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<li>\(a+b\): start at \(a\), move by \(b\).</li>
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<li>\(a-b = a+(-b)\): subtracting is adding the opposite.</li>
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</ul>
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<p>
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Example: \(6-(-4)=6+4=10\).
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</p>
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<h2 id="zero-principle" class="book-prose__heading">Zero principle with tiles</h2>
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<p>
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A positive tile and a negative tile form a zero pair. Add or remove zero pairs to simplify
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without changing value.
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</p>
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<details class="book-question">
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<summary class="book-question__prompt">Checkpoint: evaluate \(-3 + 8\)</summary>
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<div class="book-question__solution">
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<p>\(-3 + 8 = 5\). Start at \(-3\), move 8 units right.</p>
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</div>
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</details>
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<details class="book-question">
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<summary class="book-question__prompt">Checkpoint: evaluate \(4 - 9\)</summary>
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<div class="book-question__solution">
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<p>\(4 - 9 = -5\). Equivalent to \(4 + (-9)\).</p>
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</div>
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</details>
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<details class="book-question">
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<summary class="book-question__prompt">Checkpoint: explain why \(2-(-2)=4\)</summary>
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<div class="book-question__solution">
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<p>
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Subtracting \(-2\) means adding its opposite \(+2\), so \(2-(-2)=2+2=4\).
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</p>
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</div>
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</details>
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</div>
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