Magnificent Mathematician Awards
Before beginning today's lesson, I reviewed the Magnificent Mathematician Poster inspired by the 8 Mathematical Practices. I also showed students the Magnificent Mathematician Awards on the board, created using this document: Blackbird Mathematician Awards. I explained: Today, I'd like for a student to watch for and celebrate a student who is being magnificent! If you are celebrated, you get a picture of my all-time favorite plane, the Lockheed SR-71 Blackbird, which happens to be the highest flying, fastest plane in the entire world!
As students were celebrated throughout today's math time, I always pointed to the poster and asked: Why is this student magnificent? What was he/she doing?
During multiple subjects throughout the day, I use awards to celebrate students meeting expectations. In Social Studies, the award might be a labeled diagram and in science, the award might be amazing facts about the solar system. Other times, I simply give away classroom money. I simply want to provide students with a way to recognize one another.
Today's Number Talk
For a detailed description of the Number Talk procedure, please refer to the Number Talk Explanation. For this Number Talk, I am encouraging students to represent their thinking using an Open Number Line model.
Task 1: 589 + 204
For the first task, students showed a variety of strategies on their open number line models. Most students started at 589 and took a jump of 200 and then a jump of 4, landing on 793.
Task 2: 793 - 204
Before even starting the next task, several students proclaimed, "We already know the answer! Since 589 + 204 = 793, then 793 - 204 will equal 589. This was great! I always try to create opportunities for students to practice Math Practice 8: Look for and express regularity in repeated reasoning. To solve, many students started on the right side of their number lines at 793, took away 200, and then took away 4. Others "added to subtract" by starting at 204, jumping 500 to 704, then jumping 6 to 710 (landmark number), and a final jump of 83 to 793 (minuend). Then, these students added the jumps: 500 + 6 + 83 = 589.
Task 3: 12,589 + 4,204
For this task, most students started with the larger addend, 12,589 and took jumps of 4000, 200, and 4 to get to 16,793. Others started at 4,204 and took jumps of 10,000, 2,000, 500, 80, and 9.
Task 4: 12,589 - 8385
Unfortunately, we ran of time for this final task, however, I did take the opportunity to ask students to provide the difference simply by referring to the previous problem. Many students said, "4,204!"
Reasoning for Teaching Multiple Strategies
During this Addition and Subtraction Unit, I truly wanted to focus on Math Practice 2: Reason abstractly and quantitatively. I knew that if students learned multiple strategies of adding and subtracting numbers, I wouldn’t only be providing them with multiple pathways to learning, but I would also be encouraging students to engage in “quantitative reasoning” by “making sense of quantities and their relationships in problem situations.” By teaching students how to use a variety of strategies, such as using number lines, bar diagrams, decomposing, compensating, transformation, and subtracting from nines, I hoped students would begin to see numbers as units and quantities that can be computed with flexibility.
Number Line Rationale
Even though the 4th grade standards don't specifically address the use of a number line, the number line model allows students to see the addition and subtraction processes. In addition, working with a number line with whole numbers is a foundational skill that will help with identifying fractions on number lines later on.
I began this lesson by reviewing the meaning of an open number. By teaching math vocabulary, students will have the tools to truly practice MP 3 (Constructing Viable Arguments).
Presentation & Goal
In order to continue teaching students how to take jumps left and right on an open number to model the addition and subtraction process, I created a Google Presentation using Google Drive Documents called Flying on a Number Line prior to the lesson. Here are specific directions explaining How to Create a Google Presentation for Student Practice. Next, I was able to share this presentation with students using their student Google email accounts.
Students then copied the shared presentation and saved it in their math folders under the Google Drive. Once all students were successful at copying the presentation and making it their own,we discussed the first slide together, which was the Goal of the lesson: I can add and subtract multi-digit numbers using a number line model.
Real-World Application: The Life of a Pilot
One of my goal's this year as a math teacher is to make as many lessons relevant as possible. Before jumping into the lesson, I wanted students to truly understand how addition and subtraction of multi-digit numbers happens in everyday life (Math Practice 4: Model with Mathematics).
I began by explaining: Today, I want you to imagine what it would be like to be a pilot. Turn and talk: What would you like most about being a pilot? What would you like least? After students shared their conversations with the rest of the class, I said: Today you will be flying all across America, solving addition and subtraction problems! Before you can truly imagine yourself as a pilot, I think you should watch a video of a plane taking of from a pilot's view, don't you agree?! Students couldn't wait! At this point, I played a 30 second clip of a plane taking off:
To add even more context to the lesson, I showed short clips of the following videos as well:
United States Flight Patterns Map
World Flight Patterns Map
We then moved on to first problem in the Group Practice section of the shared presentation: Modeling Part-Part-Whole Problem. I explained: Today, as a pilot, you're going to be solving problems that have to do with flight distances. Let's look at this first problem together. Imagine that you flew from Seattle to Denver and then you flew on to Phoenix. If you know that your WHOLE flight is 1,588 miles and that PART of the flight (Seattle to Denver is 1,006), what would you do to find the other PART of the flight? Before we begin, let's highlight important words. Please do this on your computer as well. I then modeled how to begin with the starting point of 1006 miles (the larger added). Then, we took jumps of 500, 80, and 2 in order to land on the goal miles traveled, 1,588 miles. Students completed their number lines on this slide in their presentation right along side of me. At this point, I also asked students to check their work on each problem today using the standard algorithm.
We moved on to another problem structure: Modeling Comparison Problem. I explained: Let's say that this time you are comparing two flights. One flight, Minneapolis to Chicago, is 132 miles longer than the other flight, New York to Washington D.C. If you know that Minneapolis to Chicago is 343 miles, what would you do to find the distance between New York and Washington D.C? Again, I modeled as the students completed their own number lines. This time, we started at 343 and took jumps of 100, 30, and 2 to land on 475 miles. Finally, to check our work, students completed the standard algorithm on their number line boards: Student Number Line.
At this time, I knew students were ready to try solving problems in a partner setting so we moved on to the Partner Practice section of the presentation and began working collaboratively!
Assigning partners is always quick and easy as I already have students strategically placed in groups of 4-5 students throughout the room (based on abilities, behavior, communication skills, etc.). I simply divided these larger groups into smaller groups of 2-3 students. For this lesson, I asked students to continue working with the same math partners as yesterday.
Right to Work!
Most students understood what to do and got to work right away. Others needed a little more guided practice (in the areas of technology and math). During this time, I conferenced with students and provided scaffolding to support struggling students.
To begin with, I was so pleased to see students using the standard algorithm to check their work: Checking Work and Checking Work 2. To encourage this expectation, I celebrated these students for being "magnificent!"
This video shows a student making sense of a comparison problem:Flight from Seattle to Miami. Throughout this conference, I keep asking questions to check understanding.
Here, I provide this student with support understanding the bar diagram: Flight from New York to Houston.
This student explains how she calculated the Flight from Atlanta to St. Louis. It was great when I first walked up to this student because she is from Georgia. She certainly connected with this problem right away. As I conferenced with her, I loved how she explained each little strategy she used in detail.
Few students were able to complete their projects. However, many students were able to finish this project either when finished with other assignments throughout the day or by accessing the project from home. Here's a Student Example.