Co-Teaching Classroom

Those green sheets can go away. Once we see that your math notebook. Looking for a group who's ready. They're ready because they'll just have their math notebook and are writing you. Right here, number five. Histogram. Histogram. Everybody say histogram. Histogram. Okay, now start over. I can. Put data into a histogram. So just like yesterday we were looking.

That's a way to display data in an organized way. Today we're going to talk about histograms. This is another way that you're going to look at... Raise your hand if you've ever heard of a histogram before. Raise your hand if you've heard of a bar graph before. It's really similar to bar graphs, okay? And if you notice, histogram is another one of our words. It's on the math focus wall. That's another thing that you might see in the Iowa assessment. So it's a really important thing that we're going to talk about.

The definition that we are going to use for histogram that I want you guys to record in your notebooks is a bar graph that shows the frequency of data values in equal intervals. And each part of that definition is important, so please record it just how it is up there. Then as I walk around, I see some people underlining that word, putting a star by it, because they know it's a definition, and it's a really good way to keep their notes organized.

We will know that you are ready to continue when your pencils are down and your eyes are back up on the board. You guys are being so quiet. Your classmates appreciate that. A bar graph that shows the frequency of data in equal intervals. I know that back table is ready because their pencils are down and their eyes are back up on the board. I think we're just waiting for a couple seconds. Okay, together let's add these two pictures. First, on the left, we have a histogram. On the right, we have a bar graph.

We're going to pose this question to you. How are they different? We want you guys to talk in your teams for about a minute. Talk about some similarities that they might have and some differences that they might have.

What are some similarities or differences?

Alright, seven, two, one. We heard some really good things as we walked around. Does anyone want to share what their groups talked about? What's one way that you can see that they're different? At the bottom. What is that axis called? Do you guys remember? The X axis. Very good. Did you notice? I know there are

Another idea is, you know, there's like three categories and like one. Explain that to me. Like it says one through two and all the... It is called an interval. That one to two books is called an interval. That is another difference that we're going to see with histograms. They are going to have intervals on your x-axis. A little range of data, okay? Specific. I might have actually just cut it off. That one probably should have had it too. It probably just got cut off. That's a

because a lot of seventh graders forget to label their x and y axis and when you create graphs for us you need to label your x and your y axis, okay? It's very important otherwise we have no idea what the data means if we don't know what those numbers stand for. I heard a couple groups talking about something to do with the comparison between the bars. Becca, what did you say? Yeah, they're touching in the histogram.

going to be touching. Unlike a bar graph, you see that little gap between there? That kind of goes along with the interval, the fact that we have intervals on the bottom. That's why they're going to be touching. So as an adult, the easiest way for me to look when I see something that looks like this, and I'm not sure if it's a bar graph or a histogram, the easiest way for me to do is just look and see if they're touching. See if there's ranges at the bottom? It's a histogram.

Any other things that you notice from these two graphs? I think you guys hit the key points, okay? So we have two graphs here. Can someone come up here and label for us which one is the histogram and which one is the bar graph? Who feels real confident? And you can, those words at the top move. You can drag them down. Can you tell us how you know that?

Which one are they connected in? Yeah, they're touching in the histogram. Raise your hand if you agree with Nick's assessment of these two graphs. Bar graph and histogram. Besides for the fact that they're touching, what other clues are we given that the last one is a bar graph and the other is a histogram? The histogram has intervals. Yes, exactly. Our intervals along the bottom, you see those numbers?

Range, one to 20, 21 to 40, 41 to 60. That's a range, that's an interval. At the bottom here again, it's words, okay? It's a bunch of different words, okay? Seventh graders, I want you to write this in your notes right now. Histograms have, I have to unlock that real quick, I'm sorry. Draw a little bar graph and a histogram so that way you know what the difference is. She says draw a little bar, draw a little histogram to show how they're different. Just a quick one, doesn't have to be like,

These things under your histogram. Histograms have equal intervals along the x-axis. They have bars that touch and the frequency. Those are some of the things that we talked about, the differences or the similarities between the bar graph and the histogram. Those are the key parts. When you're drawing the two graphs in your notes, make sure you're labeling. And they don't have to be a perfect drawing. They can just be a quick sketch. That way you can see some of the differences.

I like how in Dina's drawing, her big differences in her picture is that the bars aren't touching and she wrote in the words on the bottom. For right now in your notes, I don't care if you write in all those numbers and that stuff, okay? What I really like about Dina is that she has those key differences in her notes. Those are the important things to have for now. I can tell that Nick is ready because his pencil's down and his eyes are back up on the board.

So if you're still working on your drawings, would you kind of wrap up your drawings and make sure we get these three important pieces about histograms written? Again, thank you guys for being so quiet while we're writing. Example of what you might see on your Iowa assessment. Okay, they give you a histogram and they ask you a couple questions and we're going to answer these questions together.

The first question says, which interval has the fewest number of students, and how do you know? Whenever I approach a graph, before I can even begin to answer the question, I need to see what's even going on. So first I look at the title, my labels, and try to figure out what the heck does this graph mean. So who can read the title of this graph for me? How many books did you read this year? OK. And then who can read my label on the y-axis? Manuel? Number sign of students. Number sign of students. Number of students, yep.

Number of books. People read one or two books this year. How many people read one or two books this year? Two. How many people read three or four books this year? Six. Okay, so you get the idea? Now let's go back to the question. Which interval had the fewest number of students? I think that's supposed to be most number of students. Oh, sorry. I apologize for that. I know. It's a really great, hard question. Okay, so which one? Let's change this. Which one had the most number of students? Four. And how did you know that, Nick? Six.

The bar is up to six, right? The tallest one. There you go. Any of those. How about the second question? Between to eight books. Incorporates a couple different skills. A little bit since we've talked about percents. What do you know about percents? Sometimes. If you were trying to find, say you got a nine out of ten on your homework assignment. How could you find the percent you got? Break that word down again. When we did percent before.

Does anyone remember what number always goes on the bottom because of this part of the word? Cent. Percent. That's where we get the word percent from. It's per 100. So if we set up a proportion like this with a missing variable, how could we solve this? Do you remember? And how come? You're right. 100 divided by 10. Yep, so you worked this way. You said 100 divided by 10 equals 10.

is divided by 10 is going to equal 10. So if I work the opposite way and I go times 10, I can go times 10 across. So 10 times 10 is 100. 9 times 10 would give me 1. So what percent did I get on the test? 90%. Quick question before we get started. What does 10 mean? If we're talking about a test that you took, what would that 10 represent? Yeah, so that's like your total. Oh, you said how many you got. Out of 10 is like your total. Yes. 10 is the total number of questions on the test, right? What does 10 represent?

Yes. Okay. Apply that now to our histogram. What's the number going to be and how are we going to find it? So we need a total for that bottom number. How are we going to find how many total students are on this graph? What do we need to do? Becca, what are you thinking? Up to seven up here? How high our histogram goes, does it have seven students in them? No. How do you guys think we could find the total number of students that were surveyed in this data collection?

Okay. So how many are in this bar? Two. Two. Everybody can answer. How many are in the next bar? Three. The next bar? Two. And the next bar? Two. We need a total. What are we going to do with these numbers? Add them all up. Add them all up. What do we get when we add two plus six plus three plus two plus two? Fifteen. Fifteen. Fifteen. That is my bottom number. What are we trying to find out the out of? What percent of the students have read between

What do you think, Sally? Five. How do you know that? We did three plus two. So where did you look on the graph to find five through eight? Five, six, seven. Yeah, she looked right down here. This is the number of people who read five through six books. This is the number of people who read seven through eight books. So what Sally did is she added them together. Okay, and got. Okay, are we done? We have a percentage for our answer. A ratio. And now we want to turn it into a proportion.

A proportion. A proportion has two ratios that are equal. Percent. What hundreds? Mrs. Peterson, I'm sorry. There's actually an easier way that we could do this. When there's an easier way. Does anyone know what the easier way is? Talk with your teams right now about an easier way that there might be. What if the method is for when we add a fraction? What do we do?

7th graders, 3, 2, 1. Good idea. A lot of you had the same. Does anyone want to share what they talked about with their team? Someone besides for Dina. We heard from Dina a lot. Divide. Divide. So which number is going to go on the inside? 5. What number is going to go on the outside? 15. 7th graders, do you remember how to do this?

A clock?

When you get an answer, compare with your teammates and see if you all get the same answer. How do you know? Do you remember that? That's one of our words in our word box. It's a small little word.

Give us a hand if your team has an answer. Waiting for a couple teams maybe. Does anyone feel confident that they could come up here maybe and show us how to do this? Volunteer to come up here and show us how to divide these. You gotta stretch your brains back to the beginning of the year when we talked about turning fractions into decimals. Apparently Ms. Peterson has to stretch her brain too. The cool thing about math, there's lots of ways to solve the problems.

All eyes need to be on the board right now. Sally is going to show us how she would divide two numbers. Be looking at your work and make sure that your work looks like what Sally is going to put up on the board right now. So right away Sally put in her decimal because she knows that 15 doesn't count.