<h2>Modeling Addition of Whole Numbers</h2>
<p><a href="https://data.ulearngo.com/assets/fa0ac528-2ad8-4d85-8971-2709b2750e09"><img alt="model-addition" class="size-full wp-image-101867 alignnone" height="537" src="https://data.ulearngo.com/assets/fa0ac528-2ad8-4d85-8971-2709b2750e09" width="800"/></a></p>
<p id="fs-id1484984">Addition is really just counting. We will model addition with \(\text{base}\)-\(10\) blocks. Remember, a block represents \(1\) and a rod represents \(10.\) Let’s start by modeling the addition expression we just considered, \(3 + 4.\)</p>
<p id="fs-id1567091">Each addend is less than \(10,\) so we can use ones blocks.</p>
<table class="unnumbered unstyled" id="eip-167" summary="This image consists of two columns: the left column are annotations and the right column are base blocks. The first line in the left column states “we start modeling the first number with three blocks”, followed by 3 individual blocks with the number 3 labeled under them. The next line is “then we model the second number with four blocks” followed by three individual blocks, a space, and then 4 individual blocks. The three blocks are labeled with the number 3 underneath and the four blocks are labeled with the number 4 underneath. The last line is “count the total number of blocks” followed by 7 individual blocks labeled with the number 7 underneath.">
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<td>We start by modeling the first number with 3 blocks.</td>
<td><a href="https://data.ulearngo.com/assets/1d16007b-387d-4eae-a0fa-194e3bafab37"><img alt="" class="size-full wp-image-99724 alignnone" height="51" src="https://data.ulearngo.com/assets/1d16007b-387d-4eae-a0fa-194e3bafab37" width="186"/></a></td>
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<td>Then we model the second number with 4 blocks.</td>
<td><a href="https://data.ulearngo.com/assets/ac564980-1125-438a-a21e-e68985552b18"><img alt="" class="size-full wp-image-99725 alignnone" height="51" src="https://data.ulearngo.com/assets/ac564980-1125-438a-a21e-e68985552b18" width="186"/></a></td>
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<td>Count the total number of blocks.</td>
<td><a href="https://data.ulearngo.com/assets/08f417c0-ff3a-4b81-a415-f37edcc317a5"><img alt="" class="size-full wp-image-99726 alignnone" height="51" src="https://data.ulearngo.com/assets/08f417c0-ff3a-4b81-a415-f37edcc317a5" width="186"/></a></td>
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<p id="fs-id1607848">There are \(7\) blocks in all. We use an equal sign \((=)\) to show the sum. A math sentence that shows that two expressions are equal is called an equation. We have shown that \(3 + 4 = 7.\)</p>
<div class="ns-school-emp">
<h3>Example</h3>
<div class="ns-school-defn">
<p id="fs-id1738612">Model the addition \(2 + 6.\)</p>
<h4>Solution</h4>
<p>\(2 + 6\) means the sum of \(2\) and \(6\)</p>
<p id="eip-id1170195494564">Each addend is less than 10, so we can use ones blocks.</p>
<table class="unnumbered unstyled" id="eip-951" summary="This image consists of two columns: the left column are annotations and the right column are base blocks. The first line in the left column states “model the first number with 2 blocks” followed by two individual blocks labeled 2 underneath them. The second line states “model the second number with 6 blocks” followed by 2 individual blocks labeled with the number 2 underneath, separated from a row of six individual blocks which is labeled six underneath. The last line states “count the total number of blocks” and shows eight individual blocks labeled with the number 8 underneath.">
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<td>Model the first number with 2 blocks.</td>
<td><a href="https://data.ulearngo.com/assets/cfd8833b-65fb-47a2-9fc9-b81dd9ed014a"><img alt="" class="size-full wp-image-99728 alignnone" height="41" src="https://data.ulearngo.com/assets/cfd8833b-65fb-47a2-9fc9-b81dd9ed014a" width="204"/></a></td>
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<td>Model the second number with 6 blocks.</td>
<td><a href="https://data.ulearngo.com/assets/43e9ea51-9aa9-4cd6-91fa-d91309671976"><img alt="" class="size-full wp-image-99729 alignnone" height="45" src="https://data.ulearngo.com/assets/43e9ea51-9aa9-4cd6-91fa-d91309671976" width="204"/></a></td>
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<td>Count the total number of blocks</td>
<td>
<div data-type="newline"><a href="https://data.ulearngo.com/assets/fe8b3870-e54d-4854-ae3f-4c77a26157fe"><img alt="" class="size-full wp-image-99730 alignnone" height="46" src="https://data.ulearngo.com/assets/fe8b3870-e54d-4854-ae3f-4c77a26157fe" width="204"/></a></div>

There are \(8\) blocks in all, so \(2 + 6 = 8.\)</td>
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<p class="example" data-type="example" id="fs-id1891091">When the result is \(10\)or more ones blocks, we will exchange the \(10\) blocks for one rod.</p>
<div class="ns-school-emp">
<h3>Example</h3>
<div class="ns-school-defn">
<p id="fs-id1738612">Model the addition \(5 + 8.\)</p>
<h4>Solution</h4>
<p>\(5 + 8\) means the sum of \(5\) and \(8.\)</p>
<div class="example" data-type="example" id="fs-id998472">
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<div class="exercise" data-type="exercise" id="fs-id1792383">
<section>
<div class="solution ui-solution-visible" data-type="solution" id="fs-id1471782">
<section class="ui-body">
<table class="unnumbered unstyled" id="eip-555" summary="This image is two columns. The left column is annotations and the right column are base blocks. The first line on the left says “model the first number with five blocks, followed by five individual blocks. The five blocks are labeled with the number 5 underneath. The second line says “model the second number with 8 blocks, followed by 5 individual blocks and 8 individual blocks separated as separate groups. Each set of blocks are labeled 5 and 8 respectively. The next line syays count the result. there are more than 10 blocks so we exchange 10 ones blocks for 1 tens block, followed by 5 individual blocks, then another five individual blocks then three individual blocks. The first ten blocks are circled and point downward to a set of red base ten blocks, followed by a set of three blue blocks. The last line says “now we have 1 ten and 3 ones, which is 13.">
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<td>Each addend is less than 10, se we can use ones blocks.</td>
<td> </td>
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<td>Model the first number with 5 blocks.</td>
<td><a href="https://data.ulearngo.com/assets/28007c05-d577-4211-a9f5-951fe441b2b5"><img alt="" class="size-full wp-image-99792 alignnone" height="40" src="https://data.ulearngo.com/assets/28007c05-d577-4211-a9f5-951fe441b2b5" width="324"/></a></td>
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<td>Model the second number with 8 blocks.</td>
<td><a href="https://data.ulearngo.com/assets/705351e6-45a0-4b7c-a70a-73c49ef8a3b6"><img alt="" class="size-full wp-image-99793 alignnone" height="43" src="https://data.ulearngo.com/assets/705351e6-45a0-4b7c-a70a-73c49ef8a3b6" width="324"/></a></td>
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<td>Count the result. There are more than 10 blocks so we exchange 10 ones blocks for 1 tens rod.</td>
<td><a href="https://data.ulearngo.com/assets/a01c6c08-8052-4902-bc54-f9f48d66fe8c"><img alt="" class="size-full wp-image-99794 alignnone" height="97" src="https://data.ulearngo.com/assets/a01c6c08-8052-4902-bc54-f9f48d66fe8c" width="324"/></a></td>
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<td>Now we have 1 ten and 3 ones, which is 13.</td>
<td>5 + 8 = 13</td>
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<p id="eip-571">Notice that we can describe the models as ones blocks and tens rods, or we can simply say <em data-effect="italics">ones</em> and <em data-effect="italics">tens</em>. From now on, we will use the shorter version but keep in mind that they mean the same thing.</p>
</section>
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</section>
</div>
</section>
</div>
<div class="note try" data-type="note" id="fs-id1762424"> </div>
</div>
</div>
<p class="example" data-type="example" id="fs-id1891091">Next we will model adding two digit numbers.</p>
<div class="ns-school-emp">
<h3>Example</h3>
<div class="ns-school-defn">
<p id="fs-id1738612">Model the addition: \(17 + 26.\)</p>
<h4>Solution</h4>
<p>\(17 + 26\)means the sum of 17 and 26.</p>
<table class="unnumbered unstyled" data-label="" id="eip-93" summary="This is an image with three columns: the left column states “model 17.” The middle column states “1 ten and 7 ones” and the right column shows one row of 10 base blocks and 7 individual base blocks. The next line says “model the 26.” The middle column states 2 tens and 6 ones followed by 2 stacked base ten blocks and six individual blocks. The next line is “combine.” The middle column states 3 tens and 13 ones, followed by 3 stacked base ten blocks, and 7 individual blocks stacked above 6 individual blocks. The next line says “exchange 10 ones for 1 ten” then, 4 tens and 3 ones, followed by 4 rows of base ten blocks, and three individual blocks.">
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<td>Model the 17.</td>
<td>1 ten and 7 ones</td>
<td><a href="https://data.ulearngo.com/assets/decef418-daf3-4fda-bd12-28a5fe1f35df"><img alt="" class="size-full wp-image-99803 alignnone" height="45" src="https://data.ulearngo.com/assets/decef418-daf3-4fda-bd12-28a5fe1f35df" width="315"/></a></td>
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<td>Model the 26.</td>
<td>2 tens and 6 ones</td>
<td><a href="https://data.ulearngo.com/assets/60776b82-29b5-4f55-b98a-8e619c8b485e"><img alt="" class="size-full wp-image-99804 alignnone" height="46" src="https://data.ulearngo.com/assets/60776b82-29b5-4f55-b98a-8e619c8b485e" width="315"/></a></td>
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<td>Combine.</td>
<td>3 tens and 13 ones</td>
<td><a href="https://data.ulearngo.com/assets/69aa4223-acbb-4f97-bf23-7af59e33f8db"><img alt="" class="size-full wp-image-99805 alignnone" height="71" src="https://data.ulearngo.com/assets/69aa4223-acbb-4f97-bf23-7af59e33f8db" width="315"/></a></td>
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<td>Exchange 10 ones for 1 ten.</td>
<td>
<p>4 tens and 3 ones</p>
<p>\(40 + 3 = 43\)</p>
</td>
<td><a href="https://data.ulearngo.com/assets/9482ebdd-232e-4632-8202-68b831dab5d0"><img alt="" class="size-full wp-image-99806 alignnone" height="97" src="https://data.ulearngo.com/assets/9482ebdd-232e-4632-8202-68b831dab5d0" width="315"/></a></td>
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<td>We have shown that \(17 + 26 = 43\)</td>
<td> </td>
<td> </td>
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</tbody>
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<h2>Optional Video: Adding Three-Digit Numbers With Base-10</h2>
<p>This video below by <a href="http://www.mathispower4u.com/">Mathispower4u</a> explains addition of three digit whole numbers by using base ten blocks.</p>
<p><iframe allowfullscreen="allowfullscreen" frameborder="0" height="360" src="https://www.youtube.com/embed/-NRUc2Kxu10?rel=0&amp;modestbranding=1&amp;cc_lang_pref=en&amp;cc_load_policy=1" width="640"></iframe></p>

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Model Addition

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