3rd grade
https://edboost.org/index.php/
enDivision Facts
https://edboost.org/index.php/node/30
<span>Division Facts</span>
<div class="field field--name-body field--type-text-with-summary field--label-hidden field-item"><div class="tex2jax_process"><p>Division facts are the opposite of times tables. For some students, the process of learning the times tables automatically means that they know the division facts. Other students need to learn the division facts more explicitly. Knowing division facts makes long division much easier. It's worth it for students to learn these facts.</p><p>As you practice them, make sure to highlight the relationship between times tables and division facts. Once the pattern sinks in, students should be able to draw upon their times tables knowledge and learn these division facts quickly.</p><p>If, as you practice division facts, you find that students do not know their times tables, go back to the <a href="4476">Times Tables</a> lesson for practice there. </p></div></div>
<span><span>edboost</span></span>
<span><time datetime="2024-05-29T21:01:27-07:00" title="Wednesday, May 29, 2024 - 21:01">Wed, 05/29/2024 - 21:01</time>
</span>
<div class="node-taxonomy-container field--name-field-skill field--type-entity-reference field--label-inline">
<h4><i class="icon-bookmark"></i> Skill:</h4>
<ul class="taxonomy-terms">
<li><a href="https://edboost.org/index.php/taxonomy/term/33" hreflang="en">Division (whole numbers)</a></li>
</ul>
</div>
<div class="node-taxonomy-container field--name-field-common-core-grade-level-su field--type-entity-reference field--label-inline">
<h4><i class="icon-bookmark"></i> Common Core Grade Level/Subject</h4>
<ul class="taxonomy-terms">
<li><a href="https://edboost.org/index.php/taxonomy/term/10" hreflang="en">3rd grade</a></li>
</ul>
</div>
<div class="node-taxonomy-container field--name-field-edboost-test field--type-entity-reference field--label-inline">
<h4><i class="icon-bookmark"></i> EdBoost Test:</h4>
<ul class="taxonomy-terms">
<li><a href="https://edboost.org/index.php/taxonomy/term/2" hreflang="en">Middle Computation</a></li>
</ul>
</div>
Thu, 30 May 2024 04:01:27 +0000edboost30 at https://edboost.orgMultiplication (2 by 1 digit)
https://edboost.org/index.php/node/27
<span>Multiplication (2 by 1 digit)</span>
<div class="field field--name-body field--type-text-with-summary field--label-hidden field-item"><div class="tex2jax_process"><p>Times tables are great for multiplying one-digit (and select two-digit) numbers. But, once we get into larger numbers, it's important to understand how multiplication works when numbers have multiple digits. We typically use a number of algorithms for doing multiplication -- namely we multiply all digits of multipliers by all digits of multiplicands. The processes become automatic, but it's very helpful for students to understand why we have to multiply each digit by each each digit.</p><p><em>First, think about a typical multiplication problem in which we multiply a one-digit multiplier times a two digit multiplicand:</em></p><p>$$\begin{array}{r} &21\\\times\!\!\!\!\!\!&3\\ \hline \end{array}$$</p><p>We put the two digit number on the top (remember, in multiplication, it doesn't matter what order you multiply in, so it's usually more efficient to put the number with more digits on top) and the one-digit number on the bottom.</p><p>Then, we multiply the 3 times 1:</p><p>$$\begin{array}{r} &21\\\times\!\!\!\!\!\!&3\\ \hline &\quad 3 \end{array}$$</p><p>Then we multiply 3 times 2:</p><p>$$\begin{array}{r} &21\\\times\!\!\!\!\!\!&3\\ \hline & 63 \end{array}$$</p><p>We get a final answer of 63.</p><p> </p><p>We go through this process because each digit in a two-digit number represents a separate value. In the case of 21, the two represents 2 tens (or 20) and the 1 represents 1 one (or 1). We multiply the 3 times both 20 and 1, in a vertical format as a short cut.</p><p>Think about it the long way:</p><p>$$\eqalign{21 \times 3 & = (20 \times 3)+ (1 \times 3)\\&=60 + 3\\&=63}$$</p><p>When we multiply in a vertical format, we bring the 6 (of the 60) down in the tens column, eliminating the need to write out 60. We know that the 6 represents 60 because it is in the tens column.</p><p> </p><p>Essentially, we use vertical formats in multiplication to keep our place values in order. These processes become even more important (and a little more complicated) as we move into multiplying two multi-digit numbers!</p></div></div>
<span><span>edboost</span></span>
<span><time datetime="2024-05-29T20:58:31-07:00" title="Wednesday, May 29, 2024 - 20:58">Wed, 05/29/2024 - 20:58</time>
</span>
<div class="node-taxonomy-container field--name-field-skill field--type-entity-reference field--label-inline">
<h4><i class="icon-bookmark"></i> Skill:</h4>
<ul class="taxonomy-terms">
<li><a href="https://edboost.org/index.php/taxonomy/term/32" hreflang="en">Multiplication (whole numbers)</a></li>
</ul>
</div>
<div class="node-taxonomy-container field--name-field-common-core-grade-level-su field--type-entity-reference field--label-inline">
<h4><i class="icon-bookmark"></i> Common Core Grade Level/Subject</h4>
<ul class="taxonomy-terms">
<li><a href="https://edboost.org/index.php/taxonomy/term/10" hreflang="en">3rd grade</a></li>
</ul>
</div>
<div class="node-taxonomy-container field--name-field-edboost-test field--type-entity-reference field--label-inline">
<h4><i class="icon-bookmark"></i> EdBoost Test:</h4>
<ul class="taxonomy-terms">
<li><a href="https://edboost.org/index.php/taxonomy/term/2" hreflang="en">Middle Computation</a></li>
</ul>
</div>
Thu, 30 May 2024 03:58:31 +0000edboost27 at https://edboost.orgMultiplication (Times tables)
https://edboost.org/index.php/node/26
<span>Multiplication (Times tables)</span>
<div class="field field--name-body field--type-text-with-summary field--label-hidden field-item"><div class="tex2jax_process"><p>**<strong>Note</strong>: A huge part of learning times tables is practice. Scroll down for a <strong>blank times table chart</strong>, <strong>worksheets</strong> (40 and 100 problem sets), times table <strong>sprints</strong> (for competitive practice), and times table <strong>tesselations</strong> (for artistic practice).**</p><p>Multiplication is the process of adding groups, multiple times. It's a streamlined and faster way to add, if you need to add the same number repeatedly.</p><p>$4+4+4+4+4=5 \times 4$</p><p>Learning multiplication often involves a lot of adding. When a student who is just learning to multiply tries to do the problem $5\times4$, the student will often draw (or use fingers) to count up 5 groups of 4 (or 4 groups of 5 -- there is a commutative property of multiplication, so it does not matter what order you multiply numbers).</p><p>In the very early stages of learning to multiply, it's helpful to draw groups and count or add them. This process helps students to understand what multiplication is. But, once they understand the concept, students want to work towards doing multiplication more quickly and fluidly (after all, it's meant to be a more efficient way of doing a lot of addition).</p><p>The best tool that students can acquire to speed their math work is memorization of the times tables. Most students find that, once they memorize the times tables (at least 1 - 10, though 1 - 12 is even better!), all of their math goes faster.</p><p>But, there are some intermediary steps that can help memorizing times tables go faster.</p><p><strong>First, start by skip counting.</strong></p><p>Adding up is time consuming, but skip counting makes that process go faster. Start with easy numbers to skip count: 2, 10, 5. </p><p>Have the student count by 2s, 5s, and 10s. </p><p>Then, when the student has mastered skip counting, ask the student a basic question: What is $2\times3$? Have the student count by 2 three times: 2, 4, 6 = 6!</p><p>Once the student sees the benefit in skip counting, he or she might want to learn to skip count other numbers, like 3s, 4s, and 6s. Other students will jump right to times tables. Either way, a student who is fluid in skip counting will find times tables easy. And, a student who knows his or her times tables should be able to skip count.</p><p><strong>Second, do the easy times tables first:</strong></p><p>Multiplication is intimidating. Start with the easy ones:</p><ul><li>0s</li><li>1s</li><li>2s</li><li>10s</li><li>5s</li><li>11s</li></ul><p>The best part about starting with these easy multipliers, is that they include a lot of harder multipliers. Sixes are hard. But a student who has mastered the easy times tables already knows $6\times0$, $6\times1$, $6\times2$, $6\times5$, $6\times10$, and $6\times11$. That student already knows half of the 6 times tables. </p><p><strong>Third, learn the fun times tables:</strong></p><p>Find some times tables that you like (or that your student likes). We like to teach:</p><ul><li>Doubles ($4\times4$, $9\times9$)</li><li>Their favorite number</li><li>9s (many students already have a trick for 9s, so they like this one-- see alternate method below for one way to teach 9s)</li></ul><p><strong>Fourth, remember to remind them of the commutative property. </strong></p><p>Once they learn $7\times8$, they know $8\times7$. Essentially, every time they learn a full set of times tables, they cut down the problems that remain in each subsequent set!</p><p><br> </p><p><strong>Finally, drill. </strong></p><p>There is really only one effective way to learn times tables, that's to do them over and over again. We find that writing out the answers on worksheets is often more effective than quizzing orally, but do what works for the student (often a combination of both).</p><p><strong>Drill in sets.</strong> It's very overwhelming, when you're first learning times tables, to find a mixed set of problems, 1-12. Have students master a set of times tables at a time. Have them do all of the easy ones. Then when you give them a set of 3s, they will find that they know a lot of them already. Not only does that give them confidence, but it gives them benchmarks to count up from when they encounter problems they don't know.</p><p>For example:</p><p>If you teach a student 1s, 2s, 5s, 10s, and 11s, first, the next obvious set is 3s. </p><p>Give the student a worksheet of 3 times tables. Let the student fill in the problems he or she knows.</p><p>Then, think about what's left: $3\times3$ is a double. The student probably already knows that that's 9.</p><p>$3\times4$ is just 3 more than 9: 12.</p><p>$3\times6$ is just 3 more than $3\times5=15$ so: 18</p><p>You can see the pattern. Soon, the student will know all of the threes (including $3\times4$, which means that the student already knows one more problem when he or she starts the 4s). By the time you get to 12s, the only "new" problem that students have to learn is $12\times12$. </p><p> </p><p>Overall, learning times tables can be arduous -- but it's worth it in time and aggravation saved over 10 (or more!) more years of math! Push students to learn them and learn them well. </p></div></div>
<span><span>edboost</span></span>
<span><time datetime="2024-05-29T20:56:45-07:00" title="Wednesday, May 29, 2024 - 20:56">Wed, 05/29/2024 - 20:56</time>
</span>
<div class="field field--name-field-alternate-method field--type-text-long field--label-above">
<div class="field__label">Alternate Method:</div>
<div class="field-item"><div class="tex2jax_process"><p>There's a common trick used to teach 9s. We don't emphasize it, because we try not to push students to rely on their hands. But it can come in handy.</p><p>Here's how it works:</p><ul><li>Put both of your hands out in front of you, palms up, fingers extended. You have fingers 1-10 in front of you (starting with your left thumb, ending with your right thumb).</li><li>Take a 9s times table: $9\times8$ </li><li>Take the multiplier that is not a 9: 8 (REMEMBER: THIS TRICK ONLY WORKS FOR 9s.)</li><li>Fold your 8th finger over (the middle finger on your right hand).</li><li>The number of fingers standing to the left of that folder finger is your 10s digit: 7</li><li>The number of fingers standing to the right of that folded finger is your 1s digit: 2</li><li>You have the answer to $9\times8$: 72</li></ul></div></div>
</div>
<div class="node-taxonomy-container field--name-field-skill field--type-entity-reference field--label-inline">
<h4><i class="icon-bookmark"></i> Skill:</h4>
<ul class="taxonomy-terms">
<li><a href="https://edboost.org/index.php/taxonomy/term/32" hreflang="en">Multiplication (whole numbers)</a></li>
</ul>
</div>
<div class="node-taxonomy-container field--name-field-common-core-grade-level-su field--type-entity-reference field--label-inline">
<h4><i class="icon-bookmark"></i> Common Core Grade Level/Subject</h4>
<ul class="taxonomy-terms">
<li><a href="https://edboost.org/index.php/taxonomy/term/10" hreflang="en">3rd grade</a></li>
</ul>
</div>
<div class="node-taxonomy-container field--name-field-edboost-test field--type-entity-reference field--label-inline">
<h4><i class="icon-bookmark"></i> EdBoost Test:</h4>
<ul class="taxonomy-terms">
<li><a href="https://edboost.org/index.php/taxonomy/term/2" hreflang="en">Middle Computation</a></li>
</ul>
</div>
Thu, 30 May 2024 03:56:45 +0000edboost26 at https://edboost.org