Explore A - Lesson 4.4 Division on a Number Line

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For this lesson you will need the open number line mat found in the lesson materials. Part 1 How do you show 4 x 5 on a number line? Answer: 4 jumps of 5 <img src="/courses/1101090/files/84730252/preview" alt="4 x 5 on a number line.png" width="660" height="69" data-api-endpoint="https://dsd.instructure.com/api/v1/courses/1112554/files/77874812" data-api-returntype="File"> <iframe style="width: 320px; height: 14.25rem; display: inline-block;" title="Audio player for [Untitled Tue Oct 27 2020 09:02:13 GMT-0600 (Mountain Daylight Time)]" data-media-type="audio" src="/media_objects_iframe/m-6dBK9vjaDLeE5pA8bv7wMTeNBJgVgmfa?type=audio" data-media-id="m-6dBK9vjaDLeE5pA8bv7wMTeNBJgVgmfa"/> Part 2 <img class="equation_image" title="12\div3=?" src="https://dsd.instructure.com/equation_images/12%255Cdiv3%253D%253F" alt="LaTeX: 12\div3=?" data-equation-content="12\div3=?"> How would we represent this on a number line? 12 represents our total. So mark 12 on the right of your number line. 3 represents how many are in each group. So this will be our "jump" size. We will jump backward in lengths of 3. So mark 12 and take 1 jump backward of 3. <img src="/courses/1101090/files/84730261/preview" alt="1 jump of 3 backwards from 12" width="321" height="239" data-api-endpoint="https://dsd.instructure.com/api/v1/courses/1112554/files/82972823" data-api-returntype="File"> The label of "1" represents 1 group. <iframe style="width: 320px; height: 14.25rem; display: inline-block;" title="Audio player for [Untitled Tue Oct 27 2020 09:03:34 GMT-0600 (Mountain Daylight Time)]" data-media-type="audio" src="/media_objects_iframe/m-6dCg6b2Ye8vchBqN4VZhp2rPe8y88iUb?type=audio" data-media-id="m-6dCg6b2Ye8vchBqN4VZhp2rPe8y88iUb"/> Continue jumping backward in groups of 3, until no more groups of 3 can be taken. How many jumps did it take? <img src="/courses/1101090/files/84730257/preview" alt="12 ÷3=4" data-api-endpoint="https://dsd.instructure.com/api/v1/courses/1112554/files/82972785" data-api-returntype="File"> This took 4 jumps of 3. This means <img class="equation_image" title="12\div3=4\:or\:4\times3=12" src="https://dsd.instructure.com/equation_images/12%255Cdiv3%253D4%255C%253Aor%255C%253A4%255Ctimes3%253D12" alt="LaTeX: 12\div3=4\:or\:4\times3=12" data-equation-content="12\div3=4\:or\:4\times3=12">. <iframe style="width: 400px; height: 225px; display: inline-block;" title="Video player for [Untitled Tue Oct 27 2020 09:05:35 GMT-0600 (Mountain Daylight Time)]" data-media-type="video" src="/media_objects_iframe/m-6dCKWKXJFL6rd6FDaSHj7DiD5CuVbiH6?type=video" allowfullscreen="allowfullscreen" allow="fullscreen" data-media-id="m-6dCKWKXJFL6rd6FDaSHj7DiD5CuVbiH6"/> Part 3 <img class="equation_image" title="42\div6=?" src="https://dsd.instructure.com/equation_images/42%255Cdiv6%253D%253F" alt="LaTeX: 42\div6=?" data-equation-content="42\div6=?"> Let's model this on the number line. We start at 42 on the right side of the number line. Then we will take jumps of 6 until we cannot take anymore. <img src="/courses/1101090/files/84730254/preview" alt="42 counting back 6" data-api-endpoint="https://dsd.instructure.com/api/v1/courses/1112554/files/82972866" data-api-returntype="File"> How does this number line example look like multiplication? What would the multiplication equation be? <iframe style="width: 400px; height: 225px; display: inline-block;" title="Video player for [Untitled Tue Oct 27 2020 09:07:54 GMT-0600 (Mountain Daylight Time)]" data-media-type="video" src="/media_objects_iframe/m-6dDegReyJAxFFgnbqLqMHmqRTSpXMX9J?type=video" allowfullscreen="allowfullscreen" allow="fullscreen" data-media-id="m-6dDegReyJAxFFgnbqLqMHmqRTSpXMX9J"/> Part 4 Another way to divide using a number line is by counting up or repeated addition. Because multiplication is the inverse of division, the division equation <img class="equation_image" title="42\div6=?" src="https://dsd.instructure.com/equation_images/42%255Cdiv6%253D%253F" alt="LaTeX: 42\div6=?" data-equation-content="42\div6=?"> can be thought of as ? X 6 = 42 or "How many jumps of 6 is 42?". This would look like: <img src="/courses/1101090/files/84730256/preview" alt="Counting up by six to 42" data-api-endpoint="https://dsd.instructure.com/api/v1/courses/1112554/files/82972877" data-api-returntype="File"> <ul> </ul>