{"id":824,"date":"2018-01-05T23:15:27","date_gmt":"2018-01-06T04:15:27","guid":{"rendered":"https:\/\/mathisvisual.com\/?p=824"},"modified":"2018-05-21T06:48:42","modified_gmt":"2018-05-21T11:48:42","slug":"integer-addition-symbolic","status":"publish","type":"post","link":"https:\/\/mathisvisual.com\/integer-addition-symbolic\/","title":{"rendered":"Integer Addition Using Number Lines and Symbolic Notation"},"content":{"rendered":"<p><iframe loading=\"lazy\" width=\"1104\" height=\"621\" src=\"https:\/\/www.youtube.com\/embed\/0cmpKYIh30o?wmode=transparent&amp;rel=0&amp;feature=oembed\" frameborder=\"0\" gesture=\"media\" allow=\"encrypted-media\" allowfullscreen><\/iframe><\/p>\n<p>In the previous posts, we have primarily used colour to differentiate between <strong>positive<\/strong> and <strong>negative<\/strong> values. In this second last video of the <strong>adding and subtracting integers<\/strong> series, we look to explicitly introduce the symbolic notation used to represent <strong>negative integers<\/strong>.<\/p>\n<p>The video shown at the top of the post has the entire <strong>visual progression of integer addition using symbolic notation<\/strong>.<\/p>\n<p>See the instructional guide below aimed to help teachers and\/or parents use this activity with their own students\/children.<\/p>\n<h2>Visual Prompts:\u00a0Question 1, Act 1<\/h2>\n<p>Watch the first 52 seconds of\u00a0<a href=\"https:\/\/youtu.be\/0cmpKYIh30o\">the video<\/a>\u00a0above before pausing.<\/p>\n<p>The video shows the following integer situation which should be familiar if the <a href=\"https:\/\/mathisvisual.com\/tag\/integers\/\">previous integer posts<\/a> have been explored already:<\/p>\n<p><img loading=\"lazy\" decoding=\"async\" class=\"alignnone size-large wp-image-826\" src=\"https:\/\/mathisvisual.com\/wp-content\/uploads\/2018\/01\/Integer-Addition-Using-a-Number-Line-and-Symbolic-Notation-01-Q1-3-plus-4-1024x576.jpeg\" alt=\"Integer Addition Using a Number Line and Symbolic Notation 01 - Q1 3 plus 4\" width=\"1024\" height=\"576\" srcset=\"https:\/\/mathisvisual.com\/wp-content\/uploads\/2018\/01\/Integer-Addition-Using-a-Number-Line-and-Symbolic-Notation-01-Q1-3-plus-4-1024x576.jpeg 1024w, https:\/\/mathisvisual.com\/wp-content\/uploads\/2018\/01\/Integer-Addition-Using-a-Number-Line-and-Symbolic-Notation-01-Q1-3-plus-4-300x169.jpeg 300w, https:\/\/mathisvisual.com\/wp-content\/uploads\/2018\/01\/Integer-Addition-Using-a-Number-Line-and-Symbolic-Notation-01-Q1-3-plus-4-768x432.jpeg 768w, https:\/\/mathisvisual.com\/wp-content\/uploads\/2018\/01\/Integer-Addition-Using-a-Number-Line-and-Symbolic-Notation-01-Q1-3-plus-4-1104x621.jpeg 1104w, https:\/\/mathisvisual.com\/wp-content\/uploads\/2018\/01\/Integer-Addition-Using-a-Number-Line-and-Symbolic-Notation-01-Q1-3-plus-4-366x205.jpeg 366w, https:\/\/mathisvisual.com\/wp-content\/uploads\/2018\/01\/Integer-Addition-Using-a-Number-Line-and-Symbolic-Notation-01-Q1-3-plus-4-534x300.jpeg 534w, https:\/\/mathisvisual.com\/wp-content\/uploads\/2018\/01\/Integer-Addition-Using-a-Number-Line-and-Symbolic-Notation-01-Q1-3-plus-4-165x92.jpeg 165w, https:\/\/mathisvisual.com\/wp-content\/uploads\/2018\/01\/Integer-Addition-Using-a-Number-Line-and-Symbolic-Notation-01-Q1-3-plus-4-249x140.jpeg 249w, https:\/\/mathisvisual.com\/wp-content\/uploads\/2018\/01\/Integer-Addition-Using-a-Number-Line-and-Symbolic-Notation-01-Q1-3-plus-4-232x130.jpeg 232w, https:\/\/mathisvisual.com\/wp-content\/uploads\/2018\/01\/Integer-Addition-Using-a-Number-Line-and-Symbolic-Notation-01-Q1-3-plus-4-344x193.jpeg 344w, https:\/\/mathisvisual.com\/wp-content\/uploads\/2018\/01\/Integer-Addition-Using-a-Number-Line-and-Symbolic-Notation-01-Q1-3-plus-4-533x300.jpeg 533w, https:\/\/mathisvisual.com\/wp-content\/uploads\/2018\/01\/Integer-Addition-Using-a-Number-Line-and-Symbolic-Notation-01-Q1-3-plus-4.jpeg 1920w\" sizes=\"auto, (max-width: 1024px) 100vw, 1024px\" \/><\/p>\n<p>For most students, this first prompt will be a fairly easy warm-up with or without the number line with a result of 7.<\/p>\n<p>&nbsp;<\/p>\n<p><img loading=\"lazy\" decoding=\"async\" class=\"alignnone size-large wp-image-827\" src=\"https:\/\/mathisvisual.com\/wp-content\/uploads\/2018\/01\/Integer-Addition-Using-a-Number-Line-and-Symbolic-Notation-02-Q1-Act-3-1024x576.jpeg\" alt=\"Integer Addition Using a Number Line and Symbolic Notation 02 - Q1 Act 3\" width=\"1024\" height=\"576\" srcset=\"https:\/\/mathisvisual.com\/wp-content\/uploads\/2018\/01\/Integer-Addition-Using-a-Number-Line-and-Symbolic-Notation-02-Q1-Act-3-1024x576.jpeg 1024w, https:\/\/mathisvisual.com\/wp-content\/uploads\/2018\/01\/Integer-Addition-Using-a-Number-Line-and-Symbolic-Notation-02-Q1-Act-3-300x169.jpeg 300w, https:\/\/mathisvisual.com\/wp-content\/uploads\/2018\/01\/Integer-Addition-Using-a-Number-Line-and-Symbolic-Notation-02-Q1-Act-3-768x432.jpeg 768w, https:\/\/mathisvisual.com\/wp-content\/uploads\/2018\/01\/Integer-Addition-Using-a-Number-Line-and-Symbolic-Notation-02-Q1-Act-3-1104x621.jpeg 1104w, https:\/\/mathisvisual.com\/wp-content\/uploads\/2018\/01\/Integer-Addition-Using-a-Number-Line-and-Symbolic-Notation-02-Q1-Act-3-366x205.jpeg 366w, https:\/\/mathisvisual.com\/wp-content\/uploads\/2018\/01\/Integer-Addition-Using-a-Number-Line-and-Symbolic-Notation-02-Q1-Act-3-534x300.jpeg 534w, https:\/\/mathisvisual.com\/wp-content\/uploads\/2018\/01\/Integer-Addition-Using-a-Number-Line-and-Symbolic-Notation-02-Q1-Act-3-165x92.jpeg 165w, https:\/\/mathisvisual.com\/wp-content\/uploads\/2018\/01\/Integer-Addition-Using-a-Number-Line-and-Symbolic-Notation-02-Q1-Act-3-249x140.jpeg 249w, https:\/\/mathisvisual.com\/wp-content\/uploads\/2018\/01\/Integer-Addition-Using-a-Number-Line-and-Symbolic-Notation-02-Q1-Act-3-232x130.jpeg 232w, https:\/\/mathisvisual.com\/wp-content\/uploads\/2018\/01\/Integer-Addition-Using-a-Number-Line-and-Symbolic-Notation-02-Q1-Act-3-344x193.jpeg 344w, https:\/\/mathisvisual.com\/wp-content\/uploads\/2018\/01\/Integer-Addition-Using-a-Number-Line-and-Symbolic-Notation-02-Q1-Act-3-533x300.jpeg 533w, https:\/\/mathisvisual.com\/wp-content\/uploads\/2018\/01\/Integer-Addition-Using-a-Number-Line-and-Symbolic-Notation-02-Q1-Act-3.jpeg 1920w\" sizes=\"auto, (max-width: 1024px) 100vw, 1024px\" \/><\/p>\n<p>Then, students are given a visual of 4 red squares added with 6 black squares.<\/p>\n<p><img loading=\"lazy\" decoding=\"async\" class=\"alignnone size-large wp-image-828\" src=\"https:\/\/mathisvisual.com\/wp-content\/uploads\/2018\/01\/Integer-Addition-Using-a-Number-Line-and-Symbolic-Notation-03-Q2-4-red-plus-6-black-1024x576.jpeg\" alt=\"Integer Addition Using a Number Line and Symbolic Notation 03 - Q2 4 red plus 6 black\" width=\"1024\" height=\"576\" srcset=\"https:\/\/mathisvisual.com\/wp-content\/uploads\/2018\/01\/Integer-Addition-Using-a-Number-Line-and-Symbolic-Notation-03-Q2-4-red-plus-6-black-1024x576.jpeg 1024w, https:\/\/mathisvisual.com\/wp-content\/uploads\/2018\/01\/Integer-Addition-Using-a-Number-Line-and-Symbolic-Notation-03-Q2-4-red-plus-6-black-300x169.jpeg 300w, https:\/\/mathisvisual.com\/wp-content\/uploads\/2018\/01\/Integer-Addition-Using-a-Number-Line-and-Symbolic-Notation-03-Q2-4-red-plus-6-black-768x432.jpeg 768w, https:\/\/mathisvisual.com\/wp-content\/uploads\/2018\/01\/Integer-Addition-Using-a-Number-Line-and-Symbolic-Notation-03-Q2-4-red-plus-6-black-1104x621.jpeg 1104w, https:\/\/mathisvisual.com\/wp-content\/uploads\/2018\/01\/Integer-Addition-Using-a-Number-Line-and-Symbolic-Notation-03-Q2-4-red-plus-6-black-366x205.jpeg 366w, https:\/\/mathisvisual.com\/wp-content\/uploads\/2018\/01\/Integer-Addition-Using-a-Number-Line-and-Symbolic-Notation-03-Q2-4-red-plus-6-black-534x300.jpeg 534w, https:\/\/mathisvisual.com\/wp-content\/uploads\/2018\/01\/Integer-Addition-Using-a-Number-Line-and-Symbolic-Notation-03-Q2-4-red-plus-6-black-165x92.jpeg 165w, https:\/\/mathisvisual.com\/wp-content\/uploads\/2018\/01\/Integer-Addition-Using-a-Number-Line-and-Symbolic-Notation-03-Q2-4-red-plus-6-black-249x140.jpeg 249w, https:\/\/mathisvisual.com\/wp-content\/uploads\/2018\/01\/Integer-Addition-Using-a-Number-Line-and-Symbolic-Notation-03-Q2-4-red-plus-6-black-232x130.jpeg 232w, https:\/\/mathisvisual.com\/wp-content\/uploads\/2018\/01\/Integer-Addition-Using-a-Number-Line-and-Symbolic-Notation-03-Q2-4-red-plus-6-black-344x193.jpeg 344w, https:\/\/mathisvisual.com\/wp-content\/uploads\/2018\/01\/Integer-Addition-Using-a-Number-Line-and-Symbolic-Notation-03-Q2-4-red-plus-6-black-533x300.jpeg 533w, https:\/\/mathisvisual.com\/wp-content\/uploads\/2018\/01\/Integer-Addition-Using-a-Number-Line-and-Symbolic-Notation-03-Q2-4-red-plus-6-black.jpeg 1920w\" sizes=\"auto, (max-width: 1024px) 100vw, 1024px\" \/><\/p>\n<p>Students will recall from the <a href=\"https:\/\/mathisvisual.com\/tag\/integers\/\">previous integer posts<\/a> that combining a red and black square will make them disappear. This is the visual representation of the zero principle, which is very important for students to understand conceptually what is happening when we work with integers.<\/p>\n<p>In the video, the red and black squares are laid out on the number line as we see below.<\/p>\n<p><img loading=\"lazy\" decoding=\"async\" class=\"alignnone size-large wp-image-829\" src=\"https:\/\/mathisvisual.com\/wp-content\/uploads\/2018\/01\/Integer-Addition-Using-a-Number-Line-and-Symbolic-Notation-04-4-red-plus-6-black-on-number-line-1024x576.jpeg\" alt=\"Integer Addition Using a Number Line and Symbolic Notation 04 - 4 red plus 6 black on number line\" width=\"1024\" height=\"576\" srcset=\"https:\/\/mathisvisual.com\/wp-content\/uploads\/2018\/01\/Integer-Addition-Using-a-Number-Line-and-Symbolic-Notation-04-4-red-plus-6-black-on-number-line-1024x576.jpeg 1024w, https:\/\/mathisvisual.com\/wp-content\/uploads\/2018\/01\/Integer-Addition-Using-a-Number-Line-and-Symbolic-Notation-04-4-red-plus-6-black-on-number-line-300x169.jpeg 300w, https:\/\/mathisvisual.com\/wp-content\/uploads\/2018\/01\/Integer-Addition-Using-a-Number-Line-and-Symbolic-Notation-04-4-red-plus-6-black-on-number-line-768x432.jpeg 768w, https:\/\/mathisvisual.com\/wp-content\/uploads\/2018\/01\/Integer-Addition-Using-a-Number-Line-and-Symbolic-Notation-04-4-red-plus-6-black-on-number-line-1104x621.jpeg 1104w, https:\/\/mathisvisual.com\/wp-content\/uploads\/2018\/01\/Integer-Addition-Using-a-Number-Line-and-Symbolic-Notation-04-4-red-plus-6-black-on-number-line-366x205.jpeg 366w, https:\/\/mathisvisual.com\/wp-content\/uploads\/2018\/01\/Integer-Addition-Using-a-Number-Line-and-Symbolic-Notation-04-4-red-plus-6-black-on-number-line-534x300.jpeg 534w, https:\/\/mathisvisual.com\/wp-content\/uploads\/2018\/01\/Integer-Addition-Using-a-Number-Line-and-Symbolic-Notation-04-4-red-plus-6-black-on-number-line-165x92.jpeg 165w, https:\/\/mathisvisual.com\/wp-content\/uploads\/2018\/01\/Integer-Addition-Using-a-Number-Line-and-Symbolic-Notation-04-4-red-plus-6-black-on-number-line-249x140.jpeg 249w, https:\/\/mathisvisual.com\/wp-content\/uploads\/2018\/01\/Integer-Addition-Using-a-Number-Line-and-Symbolic-Notation-04-4-red-plus-6-black-on-number-line-232x130.jpeg 232w, https:\/\/mathisvisual.com\/wp-content\/uploads\/2018\/01\/Integer-Addition-Using-a-Number-Line-and-Symbolic-Notation-04-4-red-plus-6-black-on-number-line-344x193.jpeg 344w, https:\/\/mathisvisual.com\/wp-content\/uploads\/2018\/01\/Integer-Addition-Using-a-Number-Line-and-Symbolic-Notation-04-4-red-plus-6-black-on-number-line-533x300.jpeg 533w, https:\/\/mathisvisual.com\/wp-content\/uploads\/2018\/01\/Integer-Addition-Using-a-Number-Line-and-Symbolic-Notation-04-4-red-plus-6-black-on-number-line.jpeg 1920w\" sizes=\"auto, (max-width: 1024px) 100vw, 1024px\" \/><\/p>\n<p>At this point, I would recommend that you pause the video and allow your students or your children attempt coming up with the solution.<\/p>\n<p>After they have been given a chance to work through this problem, you can resume the video.<\/p>\n<p>The Math Is Visual animation will show that 4 red squares combine with 4 black squares and disappear leaving only 2 black squares remaining.<\/p>\n<p><img loading=\"lazy\" decoding=\"async\" class=\"alignnone size-large wp-image-830\" src=\"https:\/\/mathisvisual.com\/wp-content\/uploads\/2018\/01\/Integer-Addition-Using-a-Number-Line-and-Symbolic-Notation-05-4-red-plus-6-black-equals-2-black-1024x576.jpeg\" alt=\"Integer Addition Using a Number Line and Symbolic Notation 05 - 4 red plus 6 black equals 2 black\" width=\"1024\" height=\"576\" srcset=\"https:\/\/mathisvisual.com\/wp-content\/uploads\/2018\/01\/Integer-Addition-Using-a-Number-Line-and-Symbolic-Notation-05-4-red-plus-6-black-equals-2-black-1024x576.jpeg 1024w, https:\/\/mathisvisual.com\/wp-content\/uploads\/2018\/01\/Integer-Addition-Using-a-Number-Line-and-Symbolic-Notation-05-4-red-plus-6-black-equals-2-black-300x169.jpeg 300w, https:\/\/mathisvisual.com\/wp-content\/uploads\/2018\/01\/Integer-Addition-Using-a-Number-Line-and-Symbolic-Notation-05-4-red-plus-6-black-equals-2-black-768x432.jpeg 768w, https:\/\/mathisvisual.com\/wp-content\/uploads\/2018\/01\/Integer-Addition-Using-a-Number-Line-and-Symbolic-Notation-05-4-red-plus-6-black-equals-2-black-1104x621.jpeg 1104w, https:\/\/mathisvisual.com\/wp-content\/uploads\/2018\/01\/Integer-Addition-Using-a-Number-Line-and-Symbolic-Notation-05-4-red-plus-6-black-equals-2-black-366x205.jpeg 366w, https:\/\/mathisvisual.com\/wp-content\/uploads\/2018\/01\/Integer-Addition-Using-a-Number-Line-and-Symbolic-Notation-05-4-red-plus-6-black-equals-2-black-534x300.jpeg 534w, https:\/\/mathisvisual.com\/wp-content\/uploads\/2018\/01\/Integer-Addition-Using-a-Number-Line-and-Symbolic-Notation-05-4-red-plus-6-black-equals-2-black-165x92.jpeg 165w, https:\/\/mathisvisual.com\/wp-content\/uploads\/2018\/01\/Integer-Addition-Using-a-Number-Line-and-Symbolic-Notation-05-4-red-plus-6-black-equals-2-black-249x140.jpeg 249w, https:\/\/mathisvisual.com\/wp-content\/uploads\/2018\/01\/Integer-Addition-Using-a-Number-Line-and-Symbolic-Notation-05-4-red-plus-6-black-equals-2-black-232x130.jpeg 232w, https:\/\/mathisvisual.com\/wp-content\/uploads\/2018\/01\/Integer-Addition-Using-a-Number-Line-and-Symbolic-Notation-05-4-red-plus-6-black-equals-2-black-344x193.jpeg 344w, https:\/\/mathisvisual.com\/wp-content\/uploads\/2018\/01\/Integer-Addition-Using-a-Number-Line-and-Symbolic-Notation-05-4-red-plus-6-black-equals-2-black-533x300.jpeg 533w, https:\/\/mathisvisual.com\/wp-content\/uploads\/2018\/01\/Integer-Addition-Using-a-Number-Line-and-Symbolic-Notation-05-4-red-plus-6-black-equals-2-black.jpeg 1920w\" sizes=\"auto, (max-width: 1024px) 100vw, 1024px\" \/><\/p>\n<p>This is where we finally formally introduce the symbolic notation used to represent the red squares. Instead of using the colour red, we are going to replace the colour red with a hyphen or a &#8220;negative&#8221; sign.<\/p>\n<p><img loading=\"lazy\" decoding=\"async\" class=\"alignnone size-large wp-image-831\" src=\"https:\/\/mathisvisual.com\/wp-content\/uploads\/2018\/01\/Integer-Addition-Using-a-Number-Line-and-Symbolic-Notation-06-4-red-plus-6-black-symbolically-1024x576.jpeg\" alt=\"Integer Addition Using a Number Line and Symbolic Notation 06 - 4 red plus 6 black symbolically\" width=\"1024\" height=\"576\" srcset=\"https:\/\/mathisvisual.com\/wp-content\/uploads\/2018\/01\/Integer-Addition-Using-a-Number-Line-and-Symbolic-Notation-06-4-red-plus-6-black-symbolically-1024x576.jpeg 1024w, https:\/\/mathisvisual.com\/wp-content\/uploads\/2018\/01\/Integer-Addition-Using-a-Number-Line-and-Symbolic-Notation-06-4-red-plus-6-black-symbolically-300x169.jpeg 300w, https:\/\/mathisvisual.com\/wp-content\/uploads\/2018\/01\/Integer-Addition-Using-a-Number-Line-and-Symbolic-Notation-06-4-red-plus-6-black-symbolically-768x432.jpeg 768w, https:\/\/mathisvisual.com\/wp-content\/uploads\/2018\/01\/Integer-Addition-Using-a-Number-Line-and-Symbolic-Notation-06-4-red-plus-6-black-symbolically-1104x621.jpeg 1104w, https:\/\/mathisvisual.com\/wp-content\/uploads\/2018\/01\/Integer-Addition-Using-a-Number-Line-and-Symbolic-Notation-06-4-red-plus-6-black-symbolically-366x205.jpeg 366w, https:\/\/mathisvisual.com\/wp-content\/uploads\/2018\/01\/Integer-Addition-Using-a-Number-Line-and-Symbolic-Notation-06-4-red-plus-6-black-symbolically-534x300.jpeg 534w, https:\/\/mathisvisual.com\/wp-content\/uploads\/2018\/01\/Integer-Addition-Using-a-Number-Line-and-Symbolic-Notation-06-4-red-plus-6-black-symbolically-165x92.jpeg 165w, https:\/\/mathisvisual.com\/wp-content\/uploads\/2018\/01\/Integer-Addition-Using-a-Number-Line-and-Symbolic-Notation-06-4-red-plus-6-black-symbolically-249x140.jpeg 249w, https:\/\/mathisvisual.com\/wp-content\/uploads\/2018\/01\/Integer-Addition-Using-a-Number-Line-and-Symbolic-Notation-06-4-red-plus-6-black-symbolically-232x130.jpeg 232w, https:\/\/mathisvisual.com\/wp-content\/uploads\/2018\/01\/Integer-Addition-Using-a-Number-Line-and-Symbolic-Notation-06-4-red-plus-6-black-symbolically-344x193.jpeg 344w, https:\/\/mathisvisual.com\/wp-content\/uploads\/2018\/01\/Integer-Addition-Using-a-Number-Line-and-Symbolic-Notation-06-4-red-plus-6-black-symbolically-533x300.jpeg 533w, https:\/\/mathisvisual.com\/wp-content\/uploads\/2018\/01\/Integer-Addition-Using-a-Number-Line-and-Symbolic-Notation-06-4-red-plus-6-black-symbolically.jpeg 1920w\" sizes=\"auto, (max-width: 1024px) 100vw, 1024px\" \/><\/p>\n<p>It is important for the teacher or parent to clarify to the participant that the hyphen can be used to represent the operation of subtraction, but also to represent a negative value algebraically. This is very heavy and complex for students to understand initially, so that is why I believe in doing a lot of work visually to ensure they build their fluency with this idea.<\/p>\n<p>Next up in the video, we let students wrestle with some symbolic notation for the first time. Pause the video at the 1 minute, 45 second mark when you see the following:<\/p>\n<p><img loading=\"lazy\" decoding=\"async\" class=\"alignnone size-large wp-image-832\" src=\"https:\/\/mathisvisual.com\/wp-content\/uploads\/2018\/01\/Integer-Addition-Using-a-Number-Line-and-Symbolic-Notation-07-5-plus-3-1024x576.jpeg\" alt=\"Integer Addition Using a Number Line and Symbolic Notation 07 - -5 plus -3\" width=\"1024\" height=\"576\" srcset=\"https:\/\/mathisvisual.com\/wp-content\/uploads\/2018\/01\/Integer-Addition-Using-a-Number-Line-and-Symbolic-Notation-07-5-plus-3-1024x576.jpeg 1024w, https:\/\/mathisvisual.com\/wp-content\/uploads\/2018\/01\/Integer-Addition-Using-a-Number-Line-and-Symbolic-Notation-07-5-plus-3-300x169.jpeg 300w, https:\/\/mathisvisual.com\/wp-content\/uploads\/2018\/01\/Integer-Addition-Using-a-Number-Line-and-Symbolic-Notation-07-5-plus-3-768x432.jpeg 768w, https:\/\/mathisvisual.com\/wp-content\/uploads\/2018\/01\/Integer-Addition-Using-a-Number-Line-and-Symbolic-Notation-07-5-plus-3-1104x621.jpeg 1104w, https:\/\/mathisvisual.com\/wp-content\/uploads\/2018\/01\/Integer-Addition-Using-a-Number-Line-and-Symbolic-Notation-07-5-plus-3-366x205.jpeg 366w, https:\/\/mathisvisual.com\/wp-content\/uploads\/2018\/01\/Integer-Addition-Using-a-Number-Line-and-Symbolic-Notation-07-5-plus-3-534x300.jpeg 534w, https:\/\/mathisvisual.com\/wp-content\/uploads\/2018\/01\/Integer-Addition-Using-a-Number-Line-and-Symbolic-Notation-07-5-plus-3-165x92.jpeg 165w, https:\/\/mathisvisual.com\/wp-content\/uploads\/2018\/01\/Integer-Addition-Using-a-Number-Line-and-Symbolic-Notation-07-5-plus-3-249x140.jpeg 249w, https:\/\/mathisvisual.com\/wp-content\/uploads\/2018\/01\/Integer-Addition-Using-a-Number-Line-and-Symbolic-Notation-07-5-plus-3-232x130.jpeg 232w, https:\/\/mathisvisual.com\/wp-content\/uploads\/2018\/01\/Integer-Addition-Using-a-Number-Line-and-Symbolic-Notation-07-5-plus-3-344x193.jpeg 344w, https:\/\/mathisvisual.com\/wp-content\/uploads\/2018\/01\/Integer-Addition-Using-a-Number-Line-and-Symbolic-Notation-07-5-plus-3-533x300.jpeg 533w, https:\/\/mathisvisual.com\/wp-content\/uploads\/2018\/01\/Integer-Addition-Using-a-Number-Line-and-Symbolic-Notation-07-5-plus-3.jpeg 1920w\" sizes=\"auto, (max-width: 1024px) 100vw, 1024px\" \/><\/p>\n<p>By this point, I would be anticipating that students will be able to see that 5 red plus 3 red results in 8 red. While I&#8217;d likely continue speak in terms of colour at least initially, I would want to make the connection that this is the same as saying -5 + (-3) will result in -8 total.<\/p>\n<p>While I would expect some students to struggle with the new symbolic notation we have just introduced, I would hope that they could come up with &#8220;8 red&#8221; as a result. If they are still struggling to identify how many squares in terms of colour will result, then you probably want to back up the bus and do more work there prior to introducing the symbolic notation.<\/p>\n<p>After giving you students an opportunity to solve this problem, you can resume the video and see the 8 red squares or -8 on the number line.<\/p>\n<p><img loading=\"lazy\" decoding=\"async\" class=\"alignnone size-large wp-image-833\" src=\"https:\/\/mathisvisual.com\/wp-content\/uploads\/2018\/01\/Integer-Addition-Using-a-Number-Line-and-Symbolic-Notation-08-5-plus-3-equals-8-1024x576.jpeg\" alt=\"Integer Addition Using a Number Line and Symbolic Notation 08 - -5 plus -3 equals -8\" width=\"1024\" height=\"576\" srcset=\"https:\/\/mathisvisual.com\/wp-content\/uploads\/2018\/01\/Integer-Addition-Using-a-Number-Line-and-Symbolic-Notation-08-5-plus-3-equals-8-1024x576.jpeg 1024w, https:\/\/mathisvisual.com\/wp-content\/uploads\/2018\/01\/Integer-Addition-Using-a-Number-Line-and-Symbolic-Notation-08-5-plus-3-equals-8-300x169.jpeg 300w, https:\/\/mathisvisual.com\/wp-content\/uploads\/2018\/01\/Integer-Addition-Using-a-Number-Line-and-Symbolic-Notation-08-5-plus-3-equals-8-768x432.jpeg 768w, https:\/\/mathisvisual.com\/wp-content\/uploads\/2018\/01\/Integer-Addition-Using-a-Number-Line-and-Symbolic-Notation-08-5-plus-3-equals-8-1104x621.jpeg 1104w, https:\/\/mathisvisual.com\/wp-content\/uploads\/2018\/01\/Integer-Addition-Using-a-Number-Line-and-Symbolic-Notation-08-5-plus-3-equals-8-366x205.jpeg 366w, https:\/\/mathisvisual.com\/wp-content\/uploads\/2018\/01\/Integer-Addition-Using-a-Number-Line-and-Symbolic-Notation-08-5-plus-3-equals-8-534x300.jpeg 534w, https:\/\/mathisvisual.com\/wp-content\/uploads\/2018\/01\/Integer-Addition-Using-a-Number-Line-and-Symbolic-Notation-08-5-plus-3-equals-8-165x92.jpeg 165w, https:\/\/mathisvisual.com\/wp-content\/uploads\/2018\/01\/Integer-Addition-Using-a-Number-Line-and-Symbolic-Notation-08-5-plus-3-equals-8-249x140.jpeg 249w, https:\/\/mathisvisual.com\/wp-content\/uploads\/2018\/01\/Integer-Addition-Using-a-Number-Line-and-Symbolic-Notation-08-5-plus-3-equals-8-232x130.jpeg 232w, https:\/\/mathisvisual.com\/wp-content\/uploads\/2018\/01\/Integer-Addition-Using-a-Number-Line-and-Symbolic-Notation-08-5-plus-3-equals-8-344x193.jpeg 344w, https:\/\/mathisvisual.com\/wp-content\/uploads\/2018\/01\/Integer-Addition-Using-a-Number-Line-and-Symbolic-Notation-08-5-plus-3-equals-8-533x300.jpeg 533w, https:\/\/mathisvisual.com\/wp-content\/uploads\/2018\/01\/Integer-Addition-Using-a-Number-Line-and-Symbolic-Notation-08-5-plus-3-equals-8.jpeg 1920w\" sizes=\"auto, (max-width: 1024px) 100vw, 1024px\" \/><\/p>\n<p>Finally, we will give students one more problem to wrestle with.<\/p>\n<p>Pause the video at the 2 minutes, 22 second mark when you see the following:<\/p>\n<p><img loading=\"lazy\" decoding=\"async\" class=\"alignnone size-large wp-image-834\" src=\"https:\/\/mathisvisual.com\/wp-content\/uploads\/2018\/01\/Integer-Addition-Using-a-Number-Line-and-Symbolic-Notation-09-2-plus-6-1024x576.jpeg\" alt=\"Integer Addition Using a Number Line and Symbolic Notation 09 - 2 plus -6\" width=\"1024\" height=\"576\" srcset=\"https:\/\/mathisvisual.com\/wp-content\/uploads\/2018\/01\/Integer-Addition-Using-a-Number-Line-and-Symbolic-Notation-09-2-plus-6-1024x576.jpeg 1024w, https:\/\/mathisvisual.com\/wp-content\/uploads\/2018\/01\/Integer-Addition-Using-a-Number-Line-and-Symbolic-Notation-09-2-plus-6-300x169.jpeg 300w, https:\/\/mathisvisual.com\/wp-content\/uploads\/2018\/01\/Integer-Addition-Using-a-Number-Line-and-Symbolic-Notation-09-2-plus-6-768x432.jpeg 768w, https:\/\/mathisvisual.com\/wp-content\/uploads\/2018\/01\/Integer-Addition-Using-a-Number-Line-and-Symbolic-Notation-09-2-plus-6-1104x621.jpeg 1104w, https:\/\/mathisvisual.com\/wp-content\/uploads\/2018\/01\/Integer-Addition-Using-a-Number-Line-and-Symbolic-Notation-09-2-plus-6-366x205.jpeg 366w, https:\/\/mathisvisual.com\/wp-content\/uploads\/2018\/01\/Integer-Addition-Using-a-Number-Line-and-Symbolic-Notation-09-2-plus-6-534x300.jpeg 534w, https:\/\/mathisvisual.com\/wp-content\/uploads\/2018\/01\/Integer-Addition-Using-a-Number-Line-and-Symbolic-Notation-09-2-plus-6-165x92.jpeg 165w, https:\/\/mathisvisual.com\/wp-content\/uploads\/2018\/01\/Integer-Addition-Using-a-Number-Line-and-Symbolic-Notation-09-2-plus-6-249x140.jpeg 249w, https:\/\/mathisvisual.com\/wp-content\/uploads\/2018\/01\/Integer-Addition-Using-a-Number-Line-and-Symbolic-Notation-09-2-plus-6-232x130.jpeg 232w, https:\/\/mathisvisual.com\/wp-content\/uploads\/2018\/01\/Integer-Addition-Using-a-Number-Line-and-Symbolic-Notation-09-2-plus-6-344x193.jpeg 344w, https:\/\/mathisvisual.com\/wp-content\/uploads\/2018\/01\/Integer-Addition-Using-a-Number-Line-and-Symbolic-Notation-09-2-plus-6-533x300.jpeg 533w, https:\/\/mathisvisual.com\/wp-content\/uploads\/2018\/01\/Integer-Addition-Using-a-Number-Line-and-Symbolic-Notation-09-2-plus-6.jpeg 1920w\" sizes=\"auto, (max-width: 1024px) 100vw, 1024px\" \/><\/p>\n<p>Giving your children an opportunity to use physical square tiles or counters would be beneficial here and even drawing out their own number line would be useful.<\/p>\n<p>Have them line up the tiles like we see here:<\/p>\n<p><img loading=\"lazy\" decoding=\"async\" class=\"alignnone size-large wp-image-835\" src=\"https:\/\/mathisvisual.com\/wp-content\/uploads\/2018\/01\/Integer-Addition-Using-a-Number-Line-and-Symbolic-Notation-10-2-plus-6-on-numberline-1024x576.jpeg\" alt=\"Integer Addition Using a Number Line and Symbolic Notation 10 - 2 plus -6 on numberline\" width=\"1024\" height=\"576\" srcset=\"https:\/\/mathisvisual.com\/wp-content\/uploads\/2018\/01\/Integer-Addition-Using-a-Number-Line-and-Symbolic-Notation-10-2-plus-6-on-numberline-1024x576.jpeg 1024w, https:\/\/mathisvisual.com\/wp-content\/uploads\/2018\/01\/Integer-Addition-Using-a-Number-Line-and-Symbolic-Notation-10-2-plus-6-on-numberline-300x169.jpeg 300w, https:\/\/mathisvisual.com\/wp-content\/uploads\/2018\/01\/Integer-Addition-Using-a-Number-Line-and-Symbolic-Notation-10-2-plus-6-on-numberline-768x432.jpeg 768w, https:\/\/mathisvisual.com\/wp-content\/uploads\/2018\/01\/Integer-Addition-Using-a-Number-Line-and-Symbolic-Notation-10-2-plus-6-on-numberline-1104x621.jpeg 1104w, https:\/\/mathisvisual.com\/wp-content\/uploads\/2018\/01\/Integer-Addition-Using-a-Number-Line-and-Symbolic-Notation-10-2-plus-6-on-numberline-366x205.jpeg 366w, https:\/\/mathisvisual.com\/wp-content\/uploads\/2018\/01\/Integer-Addition-Using-a-Number-Line-and-Symbolic-Notation-10-2-plus-6-on-numberline-534x300.jpeg 534w, https:\/\/mathisvisual.com\/wp-content\/uploads\/2018\/01\/Integer-Addition-Using-a-Number-Line-and-Symbolic-Notation-10-2-plus-6-on-numberline-165x92.jpeg 165w, https:\/\/mathisvisual.com\/wp-content\/uploads\/2018\/01\/Integer-Addition-Using-a-Number-Line-and-Symbolic-Notation-10-2-plus-6-on-numberline-249x140.jpeg 249w, https:\/\/mathisvisual.com\/wp-content\/uploads\/2018\/01\/Integer-Addition-Using-a-Number-Line-and-Symbolic-Notation-10-2-plus-6-on-numberline-232x130.jpeg 232w, https:\/\/mathisvisual.com\/wp-content\/uploads\/2018\/01\/Integer-Addition-Using-a-Number-Line-and-Symbolic-Notation-10-2-plus-6-on-numberline-344x193.jpeg 344w, https:\/\/mathisvisual.com\/wp-content\/uploads\/2018\/01\/Integer-Addition-Using-a-Number-Line-and-Symbolic-Notation-10-2-plus-6-on-numberline-533x300.jpeg 533w, https:\/\/mathisvisual.com\/wp-content\/uploads\/2018\/01\/Integer-Addition-Using-a-Number-Line-and-Symbolic-Notation-10-2-plus-6-on-numberline.jpeg 1920w\" sizes=\"auto, (max-width: 1024px) 100vw, 1024px\" \/><\/p>\n<p>Then, have them use the zero principle to make two black and two red tiles go away.<\/p>\n<p><img loading=\"lazy\" decoding=\"async\" class=\"alignnone size-large wp-image-836\" src=\"https:\/\/mathisvisual.com\/wp-content\/uploads\/2018\/01\/Integer-Addition-Using-a-Number-Line-and-Symbolic-Notation-11-2-plus-6-equals-4-1024x576.jpeg\" alt=\"Integer Addition Using a Number Line and Symbolic Notation 11 - 2 plus - 6 equals -4\" width=\"1024\" height=\"576\" srcset=\"https:\/\/mathisvisual.com\/wp-content\/uploads\/2018\/01\/Integer-Addition-Using-a-Number-Line-and-Symbolic-Notation-11-2-plus-6-equals-4-1024x576.jpeg 1024w, https:\/\/mathisvisual.com\/wp-content\/uploads\/2018\/01\/Integer-Addition-Using-a-Number-Line-and-Symbolic-Notation-11-2-plus-6-equals-4-300x169.jpeg 300w, https:\/\/mathisvisual.com\/wp-content\/uploads\/2018\/01\/Integer-Addition-Using-a-Number-Line-and-Symbolic-Notation-11-2-plus-6-equals-4-768x432.jpeg 768w, https:\/\/mathisvisual.com\/wp-content\/uploads\/2018\/01\/Integer-Addition-Using-a-Number-Line-and-Symbolic-Notation-11-2-plus-6-equals-4-1104x621.jpeg 1104w, https:\/\/mathisvisual.com\/wp-content\/uploads\/2018\/01\/Integer-Addition-Using-a-Number-Line-and-Symbolic-Notation-11-2-plus-6-equals-4-366x205.jpeg 366w, https:\/\/mathisvisual.com\/wp-content\/uploads\/2018\/01\/Integer-Addition-Using-a-Number-Line-and-Symbolic-Notation-11-2-plus-6-equals-4-534x300.jpeg 534w, https:\/\/mathisvisual.com\/wp-content\/uploads\/2018\/01\/Integer-Addition-Using-a-Number-Line-and-Symbolic-Notation-11-2-plus-6-equals-4-165x92.jpeg 165w, https:\/\/mathisvisual.com\/wp-content\/uploads\/2018\/01\/Integer-Addition-Using-a-Number-Line-and-Symbolic-Notation-11-2-plus-6-equals-4-249x140.jpeg 249w, https:\/\/mathisvisual.com\/wp-content\/uploads\/2018\/01\/Integer-Addition-Using-a-Number-Line-and-Symbolic-Notation-11-2-plus-6-equals-4-232x130.jpeg 232w, https:\/\/mathisvisual.com\/wp-content\/uploads\/2018\/01\/Integer-Addition-Using-a-Number-Line-and-Symbolic-Notation-11-2-plus-6-equals-4-344x193.jpeg 344w, https:\/\/mathisvisual.com\/wp-content\/uploads\/2018\/01\/Integer-Addition-Using-a-Number-Line-and-Symbolic-Notation-11-2-plus-6-equals-4-533x300.jpeg 533w, https:\/\/mathisvisual.com\/wp-content\/uploads\/2018\/01\/Integer-Addition-Using-a-Number-Line-and-Symbolic-Notation-11-2-plus-6-equals-4.jpeg 1920w\" sizes=\"auto, (max-width: 1024px) 100vw, 1024px\" \/><\/p>\n<p>In other words, we had 4 and subtracted 4.<\/p>\n<p>Or, 4 &#8211; 4.<\/p>\n<p>Or, 4 + (-4).<\/p>\n<p>Or, -4 + 4.<\/p>\n<p>In any case, we end up with 4 of each &#8220;type&#8221; cancelling out because of the zero principle.<\/p>\n<p>Watch in the next few days for the final video that will use symbolic notation for integer subtraction.<\/p>\n<p>Let me know in the comments how you used this activity!<\/p>\n<p>&nbsp;<\/p>\n","protected":false},"excerpt":{"rendered":"<p>Let&#8217;s continue exploring integer addition, but this time we will progress from using colour alone to represent the opposite signs of positive and negative values and explicitly write out these expressions and equations mathematically!<\/p>\n","protected":false},"author":1,"featured_media":834,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"video","meta":{"footnotes":""},"categories":[23],"tags":[32,33,34,30,31],"series":[44,45,35],"class_list":["post-824","post","type-post","status-publish","format-video","has-post-thumbnail","hentry","category-number","tag-grade-7","tag-grade-8","tag-grade-9","tag-integers","tag-intermediate","post_format-post-format-video","series-addition","series-integer-addition","series-integers"],"yoast_head":"<!-- This site is optimized with the Yoast SEO plugin v27.1.1 - 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