Math.7.NS.A.1b

Common core State Standards

  • Math:  Math
  • 7:  Grade 7
  • NS:  The Number System
  • A:  Apply and extend previous understandings of operations with fractions
  • 1b: 
    Apply and extend previous understandings of addition and subtraction to add and subtract rational numbers; represent addition and subtraction on a horizontal or vertical number line diagram.


    a. Describe situations in which opposite quantities combine to make 0. For example, a hydrogen atom has 0 charge because its two constituents are oppositely charged.


    b. Understand p + q as the number located a distance |q| from p, in the positive or negative direction depending on whether q is positive or negative. Show that a number and its opposite have a sum of 0 (are additive inverses). Interpret sums of rational numbers by describing real-world contexts.


    c. Understand subtraction of rational numbers as adding the additive inverse, p – q = p + (–q). Show that the distance between two rational numbers on the number line is the absolute value of their difference, and apply this principle in real-world contexts.


    d. Apply properties of operations as strategies to add and subtract rational numbers.

Download Common Core State Standards (PDF 1.2 MB)

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Math.7.NS.A.1d

Common core State Standards

  • Math:  Math
  • 7:  Grade 7
  • NS:  The Number System
  • A:  Apply and extend previous understandings of operations with fractions
  • 1d: 
    Apply and extend previous understandings of addition and subtraction to add and subtract rational numbers; represent addition and subtraction on a horizontal or vertical number line diagram.


    a. Describe situations in which opposite quantities combine to make 0. For example, a hydrogen atom has 0 charge because its two constituents are oppositely charged.


    b. Understand p + q as the number located a distance |q| from p, in the positive or negative direction depending on whether q is positive or negative. Show that a number and its opposite have a sum of 0 (are additive inverses). Interpret sums of rational numbers by describing real-world contexts.


    c. Understand subtraction of rational numbers as adding the additive inverse, p – q = p + (–q). Show that the distance between two rational numbers on the number line is the absolute value of their difference, and apply this principle in real-world contexts.


    d. Apply properties of operations as strategies to add and subtract rational numbers.

Download Common Core State Standards (PDF 1.2 MB)

What's Your Sign: Integer Addition
Lesson Objective: Students master integer addition using number lines as a visual tool
Grade 7 / Math / Number Sense
Math.7.NS.A.1b | Math.7.NS.A.1d

Thought starters

  1. How does the use of number lines help students visualize integer operations?
  2. How does this approach support long-term conceptual understanding as compared to rote memorization of rules?
  3. Why is it important to use both horizontal and vertical number lines?
24 Comments
I thought the combination of using color and hand signals was a good idea for all students to be involved. The idea of using the stickers as an initial method for see who knows the sign (allowing students to check their answers with others) in the class was a good way to take a quick poll and get all students to interact with the lesson.
Recommended (0)
Great strategy to take the abstract concept of adding integers and make it visual and hands-on. The strategy demonstrated in this video was engaging and memorable. Excellent. Thank you.
Recommended (1)
This method could be a great refresher for my students! Even when I was in school, the idea of subtracting a negative just didn't make sense to me, but once I visualized it, I never forgot it. Thank you for this helpful lesson!
Recommended (0)
I loved this lesson. This hits the first common core standard I will be teaching this 9 weeks . Thank you so much for this awesome idea.
Recommended (0)
It helped me explain the neg/pos relationship in a better way! Thanks!
Recommended (0)

Transcripts

  • Luna Productions for Teaching Channel
    Great Lesson Ideas: What's Your Sign: Integer Addition
    Allison Krasnow
    C0203-004003

    [01:00:10;07]
    Allison: I'm Allison Krasnow.

    Luna Productions for Teaching Channel
    Great Lesson Ideas: What's Your Sign: Integer Addition
    Allison Krasnow
    C0203-004003

    [01:00:10;07]
    Allison: I'm Allison Krasnow. I teach 8th grade pre-Algebra and today we are going big, in a lesson entitled:

    Students: Hey baby, what’s your sign?!

    [Title]

    Allison: "Today we're going big."

    I designed this class around what are the big stumbling blocks that kids who struggle in algebra face.

    Allison: "By the end of today I should be able to give you any number, i don’t care how big it is positive or how little it is negative, I should be able to give you any number, two numbers, that you can add together."

    You can't be successful in algebra if you don't have a real mastery of integers.

    Allison: "You were at negative 21, how much takes you back to zero?"

    Student: uhh, 7?

    Allison: "7? But I'm at negative 21.

    Student: "Oh!"

    Allison: "What's my jump going to be to go to zero?"

    Is it going to be positive? Is it going to be negative? Is it going to be zero? And I think a lot of kids come in with a limited model where they're able to do negative 5 plus 3. They can draw 5 negatives they can draw 3 positives, they can cancel things out and that's great but how do you do negative 375 plus positive 204?

    Allison: "So, look at this problem. My number line could not solve this problem for me. If I make a jump that’s negative 45 I'd be around the corner somewhere right around President Obama. But I don't know exactly where, because the number line runs out. But I want you to visualize for a minute, if you make a jump of negative 45 and how make another jump of negative 75, will you have an answer that's positive or negative? Hold up your stickers. Green is positive, red is negative. What's the sign of the answer going to be?

    I think the color-coding helps tremendously with visual learners but just with everyone to sort of have a little hook of when are you adding the values when are you subtracting the values.

    Allison: "The first thing I want you to do, is take your orange stickers, and this is going to remind you to do your positive and negatives, is put a sticker down. The reason we are doing this is because a lot of you know how to do this but you mess up the sign of the answer.

    Student: "Is the orange negative or is it..."

    Allison: "The orange is like neutral the orange is just to put is it positive or is it negative. A plus or a minus.

    Today I wanted to add that color element to it.

    Allison: "So, we're going to use these stickers. The green is going to be positive. Red is going to be negative for rest of today.

    On any given day, kids are now trained to put a key at the top of their paper. So this color is positive, this color is negative.

    Allison: Draw a number line, and we're going to actually do the math problem. So I’m just going to write 45 and 75. Negative 45 and then one that's a little bigger for negative 75. The answer is going to be positive or negative?

    Student: Negative.

    Allison: Negative! OK, so on your orange sticker make a big old negative sign.

    Writing that down somewhere so you don't lose that piece, the sign, helps tremendously.

    Allison: So I have my 45, I'm going to add it to my 75, red tells me they're negative, so I don't have to add the negatives and now I just add them up.

    And the third piece is doing to calculations. Are you adding these absolute values, are you finding the difference and subtracting the absolute values?

    Allison: 5 plus 5 is?

    Students: 10.

    Allison: Ok so put the zero down, carry the one. 1 plus 4?

    Students: Twelve.

    Allison: Well, 1 plus 4?

    Students: Five.

    Allison: Five plus Seven?

    Students: Twelve.

    Allison: I'm done right its 120?

    Students: negative 120.

    Allison: Oh! What?

    Student: negative 120.

    Allison: Yes. It is not 120. But many of you have gotten things wrong on quizzes, because you did something like this, and then you forgot to go back and look at the original problem. That orange sticker now helps me not forget.

    I feel like the most important thing is conceptual understanding that's going to last. They actually have a system in their head that's going to stick with them.

    TEXT:
    The System:
    - number line
    - color coding
    - intuitive understanding of positive and negative

    We started with really small numbers and now we are in a place where we should be able to do it with any numbers.

    Allison: So, today we went big.

    They very last piece of the class was just, I should be able to throw any numbers up there. It was just a quick, look at these two. Is the answer positive, is the answer negative?

    Allison: What's the sign of the answer? Positive or negative? I want to see everybody's hands. Positive or negative?

    What you're going for is automaticity. You wants to just look and automatically know.

    Student: "The answer would be negative."

    Allison: "Yeah! Why did you know that so fast?"

    Student: Because 4 thousand is bigger than 2 thousand.

    Allison: Because 4 thousand and something is bigger than 2 thousand and something. Good!

    Most kids now feel really successful with the small numbers but didn't realize they could do anything with integers now and I think today gave them the confidence to know that could have any problem in front of them and now they have the skills to do it.

    CREDITS

School Details

Willard Middle School
2425 Stuart Street
Berkeley CA 94705
Population: 561

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Allison Krasnow
Math / 8 / Teacher

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