No Series: Adding Integers

Math.7.NS.A.1c

Common core State Standards

  • Math:  Math
  • 7:  Grade 7
  • NS:  The Number System
  • A:  Apply and extend previous understandings of operations with fractions
  • 1c: 
    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)

Adding Integers

Lesson Objective: Add and subtract integers using a number line and a song with motions
Grade 7 / Math / Engagement
14 MIN
Math.7.NS.A.1c

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Discussion and Supporting Materials

Thought starters

  1. How does Mr. Kajitani use rap music to reinforce math concepts and build class culture?
  2. What specific strategies does Mr. K use to refocus students' attention?
  3. How does the real life context help make mathematical concepts approachable for students?

30 Comments

  • Private message to Tracy Youngberg

1. Using students' interests to achieve engagement.

2. Think outside the box:

    Learn/ integrate culture during lessons

3. Motivation, creating a safe, respectful environment where the staff feels valued.   Include teachers' own interests to create PD sessions

4. Incorporate it to walk through's, observations, SLO's.   Indicators: student egagement, decrease in discipline issues, grade increase

5. Morning announcements, Award ceremonies, Patronage from community (ice cream, pizza)

Recommended (0)
  • Private message to Cory Crossett

One last thing that really struck me.... the addition of asking them to figure out how to express the rule clearly.  I do the same thing with my students.  It's true.  If they can figure out how to express the rule verbally and in writing, then they truly have it.  

 

Recommended (0)
  • Private message to Cory Crossett

I love the use of the body to remember concepts.  This really works and I look to use it and pick up more methods everytime I get a chance.  I also really appreciate the connection to the real world applications. 

 

Recommended (0)
  • Private message to karla guardiola
I thought I loved teaching... but you are other level Mister!! Way to go!! Congratulations and thanks for inspiring me!!
Recommended (0)
  • Private message to Cynthia Slaton
Mr K, You are amazing. This was a great lesson. Thanks for sharing!
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Transcripts

  • Transcript for Tough to Teach – Adding Integers
    01:00:00 TV video of kids dancing to Mathematician rap MUSIC

    01:00:05 TOUGH TO

    Transcript for Tough to Teach – Adding Integers
    01:00:00 TV video of kids dancing to Mathematician rap MUSIC

    01:00:05 TOUGH TO TEACH MUSIC
    01:00:08 ADDING INTEGERS MUSIC
    01:00:10 Traffic
    Mission Middle School
    Teacher
    Classroom MUSIC
    01:00:16 Classroom ALEX:
    The reason why math is tough to teach is that for some reason in our society it’s become okay to have been bad at math.
    01:00:23 ALEX KAJITANI
    Math Teacher
    Mission Middle School ALEX:
    Not only is there the challenge of actually teaching the numbers and the operations …
    01:00:31 Today’s Objective:
    We will understand
    And add integers ALEX:
    … but a lot of times as math teachers we’re working to undo a stereotype that which really sort of preexists in society.
    01:00:37 Advanced
    Pre-Algebra
    We will add integers ALEX:
    The most challenging part is finding a way to connect with the students who may come to us with very low academic skills but keep the advanced students inspired and pushing them to reach new heights.
    01:00:52 Cedar St & Mission Ave SCHOOL BELL RINGING
    01:00:55 Mission Middle School KIRSTEN:
    At Mission Middle School we have three grade levels, sixth, seventh and eighth.
    01:00:58 KIRSTEN JOSEPHSON
    Technology/ELD Coach
    Mission Middle School KIRSTEN:
    The population is 93 percent Latino, mostly immigrant communities.
    01:01:03 Neighborhood ALEX:
    And we’re actually one of the fastest growing high poverty neighborhoods in all of San Diego.
    01:01:08 Alex ALEX:
    So our students come to us with issues well beyond whether or not they did their homework last night.
    01:01:14 Students KIRSTEN:
    Especially in this kind of community you need to have outlets for these students, not just focusing on the books you have to have a way to pull them in and interest them.
    01:01:23 Students
    Alex ALEX:
    What I noticed is that a, a rap song would come out on the radio on Monday and by Tuesday they seemed to have every single word memorized. So I wrote a rap song called The Itty Bitty Dot, just line up the dot and give it all you’ve got.
    01:01:35 Alex with Students ALEX
    And I went home and I practiced it all night and I came in the next morning and I performed it for my students and then at the end of the week my test scores shot through the roof and so, I like to say I’ve been math rappin’ ever since.
    01:01:48 3.14 + 99.4 = 102.54
    6.2 + 0.029 = 6.229 LINE UP THE DOTS RAP
    ALEX (RAPPING):
    Just line up the dots, give it all you’ve got I said, line up the dots, give it all you got.
    01:01:53 Alex ALEX:
    Not only am I teaching math but at the same time I’m really working to combat these stereotypes of mathematicians as nerdy and as boring.
    01:02:01 Alex with students ALEX:
    All right if you can hear me, clap once. If you can hear me clap twice, if you can hear me give me a two clap, two snap.
    01:02:09 Alex with students ALEX:
    All right very nice, today we are talking about adding integers, so today’s objective is, by the end of the day you will walk out of here knowing, understanding integers and knowing how to add them.
    01:02:21 Students ALEX:
    For a lot of students it’s a tough concept to grasp that there are numbers less than zero and that you can add them with numbers greater than zero.
    01:02:31 Alex with students
    Temperature worksheet ALEX:
    So you have a warm-up today that we’re going to get started with on temperature, it’s about the temperature getting colder so it’s the only warm-up we’ll ever do that’s actually a cool-down.
    CLASS:
    [LAUGH]
    01:02:41 Alex with students STUDENT:
    Bad Joke.
    ALEX:
    All right, all right.
    ALEX:
    We always start the same way we start with some sort of a warm-up and I usually try to make sure that it’s either something that we need to work on a little bit more from some of the previous days or that it’s going to reinforce some skills that they’re going to need in order to be successful in today’s lesson.
    01:03:00 Alex with students ALEX:
    All right just take a moment, you’re going to discuss with your seat partner the answers that you got and I should hear you saying things like, hey what did you get for the first one? Or how did you figure this out? Don’t just talk about the answers, talk about how you actually got some of the answers. Go ahead you have one minute to discuss the answers with your seat partner.
    01:03:07 Students discussing answers STUDENTS:
    [ALL TALKING]
    01:03:31 Alex with students ALEX:
    The students can’t just be listening to me the whole time. They have to be talking to each other, they have to be learning from each other, working in small and large groups and not just learning the math but learning how to be good learners.
    01:03:42 Alex with students ALEX:
    What you did was you actually were adding integers. You started at eight but then we fell and normally we think of that as subtraction except that once we got to zero we had to go into ah negative numbers and that’s exactly what we’re talking about today but right now I just want to take some time and I want to talk a little bit about positive and negative numbers and where they actually are in our lives, so …
    01:04:05 Students ALEX:
    Get to know the students, get to know their interests, get to know what drives them and what really interests them and bring in every single them that applies.
    01:04:14 Alex with students
    Manuel ALEX:
    Anybody here like football? Anybody here like the Chargers? All right why are positive and negative numbers extremely important to the Chargers and anybody that they play or anybody who likes football, Manuel?
    MANUEL:
    They need to know how far away they are from the touchdown?
    01:04:30 Alex and students ALEX:
    Exactly, exactly and that’s all football is. The teams start, usually at the twenty yard line and they just go back and forth along a big number line so without that number line the teams don’t really know where they are on the field, that’s all football really is, it’s a game of number lines.
    01:04:44 Alex with students ALEX:
    All right, raise your hand if somebody owes you money right now.
    STUDENTS:
    [RAISE HANDS]
    MICHAEL:
    Andy!
    ALEX:
    Andy do you owe Michael money?
    ANDY:
    Yeah.
    ALEX:
    How much?
    ANDY:
    Ah, seven bucks.
    ALEX:
    Seven bucks, for what?
    ANDY:
    Um the dance ticket.
    ALEX:
    Ah the dance ticket, you paid for his dance ticket?
    MICHAEL:
    Yeah.
    01:05:04 Alex with students ALEX:
    Okay so who is positive? Who is positive and who is negative in this situation?
    FEMALE STUDENT:
    Andy’s negative.
    ALEX:
    Angie, what were you going to say?
    ANGIE:
    Michael is positive?
    ALEX:
    Michael is positive how come?
    ANGIE:
    Because he needs to get the money?
    ALEX:
    Okay and what about Andy?
    ANGIE:
    Well, he needs to give the money.

    01:05:20 Alex with students ALEX:
    Okay so is Andy positive or negative?
    ANGIE:
    Well actually he’s positive.
    ALEX:
    Well right now Andy has the money right?
    ANGIE:
    Yeah.
    ALEX:
    But the fact that he owes the money, he’s actually negative seven dollars.
    01:05:31 Alex with students ALEX:
    Today what we’re going to do is we’re going to focus on adding and subtracting positive and negative numbers and I want to start by showing you a very famous video called the Number Line Dance that was made by some of our students about eight years ago about the simple process of what happens when you start by borrowing just a little bit of money from a friend, let’s watch.
    01:05:50 Number Line Dance Video RAPPER:
    So I borrowed five dollars from a friend of mine. Yo, I’ll pay you back and my friend said, fine. So I ate up all my tacos now I’m negative five and we got into the car and oh we did drive but on the way home we stopped for ice cream you should have seen all those flavors, oh I thought it was a dream …
    01:06:07 Number Line Dance Video ALEX:
    And so I try to play the music or show the video first and then I’ll explain the movements.
    01:06:13 Alex and students ALEX:
    All right so you can’t watch the Number Line Dance without learning the Number Line Dance now we’ve made it very simple for you. All you have to do is, everybody take your left hand and you’re going to make a negative sign across your heart. Right, you’re going to make a negative sign across your heart and you’re going to say negative to the left, try it.
    STUDENTS:
    Negative to the left.
    ALEX:
    Again.
    STUDENTS:
    Negative to the left.
    01:06:36 Alex with students ALEX:
    Then you take your right hand and you put it up in front of your left hand like this and make a positive sign and say, positive to the right.
    01:06:45 Alex with students ALEX:
    Now the students will do the moves themselves really internalizing it so they’re internalizing the math not only by hearing it and seeing it but also by acting it out.
    01:06:54 Alex with students ALEX:
    So stand up let’s do this!
    ALEX AND STUDENTS:
    Negative to the left, positive to the right.
    ALEX:
    It’s the number line dance.
    STUDENTS:
    I could dance all night.
    ALEX:
    Well forget the Macarena, forget the Funky Chicken ‘cause I got a new dance and a beat that’s kickin’. Yeah the number line dance is my finest creation, in every math class it is sweeping the nation.
    01:07:15 Alex with students ALEX:
    First of all what I do is I, I look at the concept that the students are having trouble with and so I try to explain the concept as absolutely simply as possible, I break it up into just a few sentences and then I, I kind of play with the words and, and see what rhymes.
    01:07:29 Alex with students ALEX:
    Last time.
    ALEX AND STUDENTS:
    Negative to the left, positive to the right it’s the number line dance, I could dance all night.
    ALEX:
    Yeah give yourself some applause ladies and gentlemen!
    STUDENTS:
    [APPLAUD]
    01:07:42 Alex and students ALEX:
    Then we move into sort of the, the more paper and pencil math that ah, the standards based math that the students need to know. So the music is there again, not in place of great teaching the music and the movements are there as a supplement to great teaching.
    01:07:59 Alex and students ALEX:
    All right, today by the time you leave here you will understand and be able to add integers. So now we’ve got to take it, the Number Line Dance and how we do it standing in class to what it actually means with regards to adding positive and negative numbers. So you pretty much already were doing the Number Line Dance when you were working with the thermometer in our warm-up, right?
    01:08:21 Alex with students ALEX:
    It’s just that you were going up and down for positive and negative instead of to the left and right. So let’s do the first one together and then, the first few together and then we’ll see if we can start to do these on our own. So start by ah, let’s go ahead and start with number one.

    01:08:38 Integer worksheet ALEX:
    We’ve got nine plus negative four. Where does the Number Line Dance always start?
    STUDENTS:
    Zero?
    ALEX:
    Absolutely, the Number Line Dance it starts at zero and when you do this dance you’re the neighborhood hero.
    01:08;50 Alex with students ALEX:
    So at that point we’ll really get into the bulk of the lesson. We’re taking notes, we’re doing answers and you know I’ll pick one or two class members to show the class how to do something and then hopefully they can start to do it on their own.
    01:09:01 Alex with students ALEX:
    I just explained how to do one, now who can explain to us how to do one? George you want to give it a try?
    GEORGE:
    Yeah.
    ALEX:
    Nice and loud.
    01:09:12 Integer worksheet GEORGE:
    So …
    ALEX:
    Take us through number two.
    GEORGE:
    So you start at zero and you go to negative seven.
    ALEX:
    Okay why to negative or which direction is that?
    GEORGE:
    To the left.
    ALEX:
    Okay, let’s go ahead. Okay question for you, do we have to do every single step or can we start to skip steps yet? Can we just go all the way to negative seven?
    STUDENTS:
    Yeah.
    ALEX:
    We don’t need to make every step, okay.

    01:09:33 Alex with students ALEX:
    Don’t teach alone you know don’t be the only one standing up there delivering instruction. Call on the students to help you teach.
    ALEX:
    How’d you get that?
    MALE STUDENT:
    Um because I went to the negative twelve to the left and then I went eight spaces back to the right and then I landed on negative four.
    ALEX:
    Okay so you started by going negative twelve okay, so that’s a great point, does it matter which one we do first?
    STUDENTS:
    No.
    ALEX:
    What property tells us that as long as we’re adding two numbers we can add them in any order, who remembers what property that is? Jesus?
    01:10:09 Alex with students JESUS:
    Ah the commutative property of addition.
    ALEX:
    Very nice remember the commutative property of addition? We are using things we learned all the way back to like the first week of school. So what we’re going to do now is we’re going to actually take this and we’re going to start writing our own rules because I think that what happened was you guys started to figure out how to do this without actually having a number line, of course you’ll never forget the Number Line Dance and I expect to see you all perform that together at the next school dance.
    01:10:39 Alex with students ALEX:
    It’s a good idea, no, but what I want you to do is I want you to be able to come up with and be able to articulate and be able to write the actual rules for adding positive, two positive numbers, two negative numbers and a positive and a negative number because I know you know how to do it but do you know how to express it clearly? If you know how to express it clearly then I know you’ve truly learned it, okay? Here we go.
    STUDENTS:
    [ALL TALKING]
    01:11:13 Students talking FEMALE STUDENT:
    I put when having the same number and keeping the sign, oh I forgot to add.
    MALE STUDENT:
    Add the numbers and keep the sign.
    FEMALE STUDENT 2:
    That’s always going to be positive and that’s always going to be negative.
    MALE STUDENT:
    Yeah so add the numbers and keep the sign.
    MALE STUDENT 2:
    Negative signs add them and then add on.
    01:11:27 Students working ALEX:
    Sometimes it only takes one or two problems, sometimes with harder concepts it takes four or five problems sometimes even a couple of days where they can actually start to tell me how to do it.
    01:11:38 Alex with students ALEX:
    Okay so what’s the rule for adding two positive integers? Who thinks that they could say the rule really, really clearly? Janelle?
    JANELLE:
    You just add it?
    ALEX:
    You just add it, okay that makes sense okay so when you’re adding two positive integers we can just say, we add the numbers and the number is … ?
    JANELLE:
    A positive.
    ALEX:
    Positive good. So why don’t we just say that? And if you said it a different way that’s fine I want you to, to use what works for you.
    01:12:02 Alex and students ALEX:
    Ah and then I always try to leave a few minutes at the end of class for ah for some wrap up.
    ALEX:
    Raise your hand if you can confidently say that you know how to add integers now.
    STUDENTS:
    [RAISE HANDS]
    ALEX:
    Okay rate yourself on a scale of one to five. One means I don’t know it, five means I got this and I’m ready for Monday two, three or four or anywhere in between.
    01:12:25 JANELLE
    JESUS
    JOSE JANELLE:
    My Kajitani is really nice and he makes math fun.
    JESUS:
    He’s funny because like he wakes us up because like half of us are still asleep and he, when he tells us jokes he makes us pay attention to what he’s saying.
    JOSE:
    He’s a really, really nice man because he actually explains math the way my other teachers that I’ve had in elementary could not explain.
    01:12:44 Alex ALEX:
    Teachers come to me all of the time and they say, my students want to know how come I don’t rap like you do? And you know I say, it’s not about rapping, it’s about finding out who you are as a teacher, being comfortable with yourself and letting that spill out into your classroom instruction. You take what you’re all about and you really think about what drives you and what makes you passionate as a person and, and what kind of activities you love to do and teach through that.
    01:13:13 Alex and students ALEX:
    Okay let’s give ourselves a two clap, two snap, two stomp, happy Friday. On the count of three, one, two three!
    STUDENTS:
    [CLAP, SNAP AND STOMP]
    Happy Friday.
    ALEX:
    See you on Monday.
    01:13:24 Alex ALEX:
    I love teaching, I absolutely love teaching. I truly believe that when we teach we live forever. Every time I teach a new concept and the students are able to learn it and grasp it and go on with their lives, I really feel like I, I’m going to go on living forever.
    01:13:43 Fade to black [MUSIC]
    01:13:44 END CREDITS [MUSIC]
    01:14:04 Fade to black

School Details

Mission Middle School
939 East Mission Avenue
Escondido CA 92026
Population: 919

Data Provided By:

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Teachers

Alex Kajitani
Math / 7 / Teacher

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