STELLAR PBL MATH
Arizona, United States
About the store
Hi! My name is Milton Johnson. I have taught high school math, physics and engineering classes for 25+ years in a Title 1 STEM school in Phoenix, Az. Integrating these STEM topics into my daily curriculum has been a mainstay in my classroom. My calculus class emphasizes an authentic, real-world context in helping students to develop a mathematical mindset, not just mastery of procedural algorithms. I want students to learn how we use math as a tool to address real-world questions. My students are 12th grade college-bound, who primarily choose STEM majors in college, such as engineering and medical/health related majors.
The store contains problem-based math lessons that I have developed for my honors calculus class over the years. I have chosen to emphasize PBL learning instead AP Calculus curriculum to support the learning experiences that I want my students to have.
Since this curriculum is relatively newly formatted for use outside my classroom, please report and questions or issues to me as soon as possible.
Thank you for visiting my page.
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00. Modeling Our World: PBL-Calc Entire Curriculum
This master page contains links to all (~35) PBL lessons, notes and curriculum for the year. The lessons are all listed on a spreadsheet sheet with links to each lesson. Each lesson also contains links to necessary resources (including answer keys when appropriate). Many of the lessons use spreadsheets (i.e. Google Sheets) and/or Desmos. The spreadsheet also contains links to helpful videos that provide overviews for the curriculum. This curriculum has been newly formatted for use outside my cl
11th - 12th
Calculus
29. Annual Daylight Hours- Accumulation with Riemann Sums
[Lesson 29 from the 'MOW PBL-Calc Curriculum' Set] This lesson has students building sunlight hour models for Phoenix, Arizona and Nome, Alaska. They then use Riemann Sums to find the total amount of sunlight hours for both locations and compare and contrast the findings. This activity is also used in the upcoming assessment for the MOW Unit 5. This lesson will run about 2 to 3 days as classwork and/or homework.
11th - 12th
Calculus
13. Optimization- Small Business Cost Function
[Lesson 13 from the 'MOW PBL-Calc Curriculum' Set] In this lesson, students use data from a 'fictional' small coffee roasting business. Using the data, students will create cost and product functions for the business. From here they will use optimizing techniques to find the optimal productivity level to produce the maximum profit for the business. This lesson will run 2 to 3 days.
11th - 12th
Calculus
14. Related Rates & Euler's Method
[Lesson 14 from the 'MOW PBL-Calc Curriculum' Set] Building off of traditional related rates problems, in this lesson students can go beyond just finding rates of change at a particular instances. Using the rate of change and the differential equation, students can then use Euler's Method (via spreadsheet) to solve more authentic problems, such as when will a growing puddle reach a certain size. Part two of this lesson comes up toward the end of the school year after students have learned integr
11th - 12th
Calculus
01. How Fast Is Bob? : Introduction to Derivatives
[Lesson 1 from the 'MOW PBL-Calc Curriculum' Set] This lessons runs like a physics lab. Students will create math models and slope graphs in a spreadsheet in order to study how the motion of the bobbing mass (Bob) is changing. This will begin the introduction of derivatives (with trig functions). Students will: watch a short video of a bobbing mass collect position-time datagraphcreate a math model (equation) to match the dataFrom here they will create data columns in a spreadsheet to create vel
11th - 12th
Calculus
22. Carrying Capacity- Logistic Growth
[Lesson 22 from the 'MOW PBL-Calc Curriculum' Set] In this lesson students observe and collect logistic growth data for a colony of paramecium. Once the data has been collected students create a math model (equation) for the growth model and proceed to find the greatest rate of growth of the colony. This lesson will run about 2 days.
11th - 12th
Calculus
30. Area Under Irregular Curves- Velocity & Power Examples
[Lesson 30 from the 'MOW PBL-Calc Curriculum' Set] Here student use simple hand drawn techniques to estimate the area of under irregular shaped curves with no known models (using Riemann Sums). One graph deals with an object with irregular velocity, and the other with non-constant power product throughout a day. This lesson will run about a day as classwork and/or homework.
11th - 12th
Calculus
28. First $1 Million- Income Accumulation with Riemann Sums
[Lesson 28 from the 'MOW PBL-Calc Curriculum' Set] In this short, fun activity students create a potential income model for their future career. After creating the model, they use the Riemann Sum technique to predict when they will have made their first $1 million. This lesson will run about a day
11th - 12th
Calculus
10. How Quickly Is The Ball Speeding Up?-Power Rule
[Lesson 10 from the 'MOW PBL-Calc Curriculum' Set] In this lesson, students will collect data from a video of a ball rolling down a ramp. Students will produce position-time, velocity-time and accelation-time graphs for the data. From here they will explore the relationships between a polynomial function and it's 1st and 2nd derivatives. This leads to the development of the Power Rule. This lesson can be completed in 1 to 2 days.
11th - 12th
Calculus
08. Projecting City Population Growth- Tangent Line Projections
[Lesson 8 from the 'MOW PBL-Calc Curriculum' Set] This lesson comes in two versions. Version 2 is the original and version 1 is a shorter activity. This lesson has students use recent rate of growth data from U.S. cities in order to predict the future population. This uses a tangent line projection and also introduces students to Euler's Method. The lesson(s) can be completed in about 2 days as classwork and/or homework.
11th - 12th
Calculus
02. Limit Calculator- Finding Limits
[Lesson 2 from the 'MOW PBL-Calc Curriculum' Set] This lesson proceeds the How Fast Is Bob lesson. Here students explore the idea of instantaneous velocity, but using a spreadsheet to find the slope between two points with decreasing intervals. In doing so they use the limit concept to find the derivative at a point in time.
11th - 12th
Calculus
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About the store
Experience
Hi! My name is Milton Johnson. I have taught high school math, physics and engineering classes for 25+ years in a Title 1 STEM school in Phoenix, Az. Integrating these STEM topics into my daily curriculum has been a mainstay in my classroom. My calculus class emphasizes an authentic, real-world context in helping students to develop a mathematical mindset, not just mastery of procedural algorithms. I want students to learn how we use math as a tool to address real-world questions. My students are 12th grade college-bound, who primarily choose STEM majors in college, such as engineering and medical/health related majors.
The store contains problem-based math lessons that I have developed for my honors calculus class over the years. I have chosen to emphasize PBL learning instead AP Calculus curriculum to support the learning experiences that I want my students to have.
Since this curriculum is relatively newly formatted for use outside my classroom, please report and questions or issues to me as soon as possible.
Thank you for visiting my page.
Teaching style
In my science and engineering classes I try to implement project based learning as much as possible. In calculus class I emphasize problem-based learning. This includes constructivism and inquiry-based learning. Rather than just skill building and mastery of text book problem solving. This approach helps to foster strong problem solving, critical thinking and differential learning in students.
My own education history
I was always 'good' at math through high school. But I found it to be boring much of the time. Too much rote memorizing and emphasize on skills mastery. There was very little application and understanding of how I might use what I was learning.
College math was much more challenging. In addition to being more difficult, it felt taught out of context. As a physics major, it was difficult to connect what I was learning in math classes to what I needed to use in physics classes.
Now as a teacher, I want to help my students see how these math tools might be used in real-world situations. We address the question- "How can we use math to address real questions"? We model real situations mathematically and then apply math tools in order to answer relevant questions.
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