Series: Coding in the Classroom

Math.Practice.MP1

Common core State Standards

  • Math:  Math
  • Practice:  Mathematical Practice Standards
  • MP1:  Make sense of problems and persevere in solving them.

    Mathematically proficient students start by explaining to themselves the meaning of a problem and looking for entry points to its solution. They analyze givens, constraints, relationships, and goals. They make conjectures about the form and meaning of the solution and plan a solution pathway rather than simply jumping into a solution attempt. They consider analogous problems, and try special cases and simpler forms of the original problem in order to gain insight into its solution. They monitor and evaluate their progress and change course if necessary. Older students might, depending on the context of the problem, transform algebraic expressions or change the viewing window on their graphing calculator to get the information they need. Mathematically proficient students can explain correspondences between equations, verbal descriptions, tables, and graphs or draw diagrams of important features and relationships, graph data, and search for regularity or trends. Younger students might rely on using concrete objects or pictures to help conceptualize and solve a problem. Mathematically proficient students check their answers to problems using a different method, and they continually ask themselves, \"Does this make sense?\" They can understand the approaches of others to solving complex problems and identify correspondences between different approaches.

Download Common Core State Standards (PDF 1.2 MB)

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Math.Practice.MP4

Common core State Standards

  • Math:  Math
  • Practice:  Mathematical Practice Standards
  • MP4:  Model with mathematics.

    Mathematically proficient students can apply the mathematics they know to solve problems arising in everyday life, society, and the workplace. In early grades, this might be as simple as writing an addition equation to describe a situation. In middle grades, a student might apply proportional reasoning to plan a school event or analyze a problem in the community. By high school, a student might use geometry to solve a design problem or use a function to describe how one quantity of interest depends on another. Mathematically proficient students who can apply what they know are comfortable making assumptions and approximations to simplify a complicated situation, realizing that these may need revision later. They are able to identify important quantities in a practical situation and map their relationships using such tools as diagrams, two-way tables, graphs, flowcharts and formulas. They can analyze those relationships mathematically to draw conclusions. They routinely interpret their mathematical results in the context of the situation and reflect on whether the results make sense, possibly improving the model if it has not served its purpose.

Download Common Core State Standards (PDF 1.2 MB)

Coding in the Algebra Classroom
Lesson Objective: Integrate computer science into math lessons
Grades 9-12 / Math / Technology
Math.Practice.MP1 | Math.Practice.MP4

Thought starters

  1. Why does Mr. Kwon believe it is important to integrate technology into his algebra support classes?
  2. How does coding help students deepen their understanding of algebra?
  3. How does Mr. Kwon formatively assess his students?
9 Comments
Inspiring
Recommended (0)
A=2I + C Action Interesting, Inspiring Challenging Has the possibility of moving from linear to non-linear and thereby promoting complex thought processes. Thanks
Recommended (0)
Because students are engaged and playful with technology, this teacher's hope is that computer science will be integrated into Algebra. Using technology, these students are creating an animation and learning at the same time the ratio between distance and time. He is "peaking their curiosity". I like this as a warm up! Great idea.
Recommended (0)
I found Mr. Kwon’s teaching methods very refreshing. It allows students to ponder on the question, “How can I apply algebra?” A lot of the times students who struggle with math just see a bunch of serial numbers that need to be solved and are not seeing the outcomes of these equations. Thank you for this great resource. It is definitely something that I will share with our math department.
Recommended (0)
It is very interesting. It is connecting math concept in such as contextual learning. I just find out about this. Excellent..Actually I am not a math teacher, but I find out that I can use them for myself to develop my ideas about math.
Recommended (0)

Transcripts

  • Coding in the Algebra Classroom Transcript

    Teacher: Students these days are immersed in a world full of technology, it surrounds them.

    Coding in the Algebra Classroom Transcript

    Teacher: Students these days are immersed in a world full of technology, it surrounds them. We have students basically spending most of their time looking at their own cell phones. I don't want students just to be able to play with the technology they have in their hands, but I also want them to build something out of it.

    My getting [inaudible 00:00:23] together plan is hoping for students to integrate what they learn in algebra classes and apply it to a completely new setting, and in this case computer science. I wanted to get better at integrating computer science like coding in high school algebra class.

    Today I was looking for students to make a table or make a graph from a given scenario, and then with that scenario I want them to apply what they learn from tables and graphs and create an animation, in this case make a rocket blast off in different speeds.

    By the end of class I want students to be able to tell me what is the rate of change in context and explicitly tell me the ratio between distance and time.

    The first thing that we're going to do today is I want you guys to warm up with a little bit of curiosities, wonders, and questions you might have.

    I want kids to wonder and be curious about something so I show them a video.

    A lot of you guys probably played some racing kind of games. The thing I want you guys to be curious about is what you see on the screen. What questions you might have and what do you wonder? If you have something, go ahead and write something down on your screen.

    Sonia said, "Can you really go that fast and still have control over the car?" It looks like looking at your wonders and questions, all of you guys have to do something with speed.

    The second thing I did in this lesson is I created a Desmos activity for students to do. Kids can actually physically manipulate objects on the screen. They can also plot points physically on the graph and the table and see that multiple representations, equations, graph, and tables, they all actually represent the same thing.

    What we're going to be doing today is we're going to play with the rocket animation we created a couple days ago, but I want you guys to change the speed of the rocket and make the rocket look more interesting like the game we just saw. I might have you guys create a rocket that goes maybe 20 feet per second or 20 meters per second or 50. Maybe it starts at a different amount in the very beginning, maybe has a different initial value. Go ahead and start on page seven ...

    Within the Desmos activity, I want students to create multiple representations, so equations, graphs, and tables, and then take that and apply into coding.

    Good. You said -20 right? What does that mean? If it's -20, what's happening to the rocket here?

    Student: It's decreasing.

    Teacher: It's decreasing. Cool. Looks good. I agree. Now I want you guys to go ahead and go to your code and I want you to match your animation to match the situation.

    In algebra when we were making a linear equation, we have something like y=mx+b and we also again have a times and a plus. When they're building a code, they also have to create some sort of operators that allows them to add to different parameters or multiply. Now as they create a representation, so whether it's equation, table, or graph, they now have to match that representation and create a rocket that animates for that particular situation.

    Yeah. Your rocket looks like it starts at 300 and it's going down 20, just like what we want. Looks good.

    At each part of the lesson, I have students ask me to come over and check to see if their table and their graph and their equation matches the animation.

    Good. Tell me what's happening to this rocket?

    Student: It starts at 100 feet and goes up by 15 every second.

    Teacher: Good. All right. Can I check your Desmos? Let me see your Desmos. All right. Let me see your equation. What does your equation say? What does that mean?

    Student: It starts at 100 so it's 100 plus 15 every second.

    Teacher: Okay. Looks good. I see everything matches up and you're line and your table and your points and your equation matches all up. It looks great.

    One of the reasons I like to use code.org to enhance students' understanding of rate of change is that students can actually physically see the rocket going up at different speeds. I want them to see the animation and tie that with what in the world is 20 meters per second mean and what does that 20x mean in the context. Code.org helps them to see what is abstract in a more contextual situation.

    These right here represent your input. Plug in five, what do I do [crosstalk 00:04:40]

    The purpose of taking this class is for all students to be successful in their high school algebra classes. We want all students to really understand the Common Core. We developed this class so that we can create not just a math lesson but also some sort of enrichment for our students. We do a lot of projects, we do coding for example.

    Right here on this graph, you see how the points and the line doesn't match up, so what do you think about that?

    Student: That it's not exact.

    Teacher: It's not exact. Okay. Does your equation here say that I'm starting at 15?

    Student: No.

    Teacher: Okay, so what should we change as your table?

    Student: Should that be zero?

    Teacher: What do you think?

    Student: Yeah.

    Teacher: Yeah. Let's see if it matches with your line.

    Student: Yeah.

    Teacher: Yeah. Okay. Cool.

    One of the mathematical practice standards is modeling with mathematics. In a Desmos activity, we had students create a model, which in this case will be a [formative 00:05:32] equation, from a context of a situation.

    If I choose any seconds, let's say x, all right, any seconds, what do I do with that number?

    Student: You have to multiply it by 15.

    Teacher: Right. That's what the result is with your code. Let's run that and see how your animation matches. Yeah. What's happened to your animation?

    Student: He's going up by 15 every second.

    Teacher: Does that match your Desmos graph? Let's go check.

    Student: Yeah.

    Teacher: Mm-hmm (affirmative)

    I was looking for students to manipulate some blocks of code and maybe changing some parameters so that the rocket can either possibly start at a different part of the air or have the rocket maybe just descending or ascending at different rates.

    Okay, now I want you guys to do a little challenge for me. I want you guys to go to code. So far everything we've been doing is linear stuff, constant rate of change, but I want you to create a rocket that's not going constant rate of change.

    Student: That changes every time?

    Teacher: Kids were just having a fun time experimenting with the codes and that's what code should be, in fact that's what math should be. We should experiment and see what's happens in our graphs and our tables and be curious about it.

    I told you to create a rate of change that's not necessarily constant. How'd you know to do this? What is it saying right here?

    Student: The x could be anything and if you multiplied x by x, you'd always have a different x than if it would be something else so it'd change every time.

    Teacher: Let me see your rocket. Let's see if that's true. Yeah. It's not going constant at all. In fact it looks like it's going, is it slower or faster?

    Student: I think it's going faster.

    Teacher: Another mathematical practice standards that students were working on was persevering on the task. One of the things I really appreciate about coding is that students not only were engaged but they actually had to persevere in coding. For example, when students make a mistake, they automatically don't just give up, but because they actually will want to see a rocket blast off, they actually have to find their mistake in their plethora of code. They actually have to persevere on finding where that mistake is and troubleshoot on that.

    After this lesson, I want now to work on the next mathematical practice which is critiquing the reasoning of others, where they're going to build their own game and now they're going to share it with their peers and talk about how can I improve my code.

    Explain to me how you got 100. Where's the 100 come from in your equation?

    Student: Because [inaudible 00:07:45] 100 meters.

    Teacher: It starts 100. And then let's see [crosstalk 00:07:49]

    Towards the end of the lesson I wanted to measure how much students learned or what students learned from today's lesson. I had students try out two different questions, one from finding a rate of change from tables and also finding the rate of change from a graph.

    Let's see. Who can share with me what the rate of change is for this table? Let's see. Jose.

    Student: At zero seconds it starts at 700 and at one second it's at 660 so it's descending at 40 meters per second.

    Teacher: Okay. Let's give Jose a clap. That was a really good explanation. One, two, three.

    I saw that students were able to find the rate of change easily from a table. They saw that from a list of numbers going down the line from a table they saw that there is some sort of constant amount happening. From a graph, I purposely given them a graph with an interesting scale and I wanted to see if students were able to find a rate of change from a graph with a completely different scale that they haven't seen before.

    If I gave you even more complicated graph, how can I find the speed of this car or this rocket? That's something we're going to learn tomorrow.

    Now I want students in the future to able to create their own game that has different cars or different objects moving at different speeds and we want kids to actually share their games with their peers and just play and also comment on how to improve their games.

    50. 50 miles. Good. 50 miles. Then at two hours-

    I think coding helps students to not only learn the math concepts but also apply what they learn in algebra classes. I think application is really essential in order to have a broader understanding of mathematics. When students are animating a rocket, they actually got to physically see what they built out of an equation or something out of abstract code. That gets kids to be engaged in what they're learning.

    All right. I guess we're good then. All right. Go ahead and log out and I'll see some of you guys third period.

    As a second year teacher and trying something completely new is definitely difficult, but at the same time it's really fun. When I see the kids reaction to these lessons it keeps me going, it keeps me motivated to do more with these students.

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School Details

Mariner High School
200 120th St Sw
Everett WA 98204
Population: 2172

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Joshua Kwon
Math / 9 10 11 12 / Teacher

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