![](https://learnx.ca/wp-content/uploads/2021/10/Screen-Shot-2021-10-03-at-4.37.09-PM.jpg)
Grade 9 Math + Coding Workshop
5 October 2021, (c) George Gadanidis
![](https://learnx.ca/wp-content/uploads/2021/03/math-code-sketch-v2-300-1-3.png)
A. WHAT’S NEW?
GRADES 1-9
- Coding across all grades, in algebra (and beyond).
- Some more sophisticated mathematics.
- A focus on the beauty, aesthetics and wonder of mathematics.
- Social-emotional learning skills.
GRADE 9
- De-streamed classes.
- Research and tell a mathematics story.
B. BIG PICTURE #1
![](https://learnx.ca/wp-content/uploads/2021/10/neural-network.jpeg)
START WITH CODE THAT WORKS
- Have students execute the code to see its output
- Ask them to alter the code to model the different intervals in the table
- Ask: how does the code do what the table does?
- Ask them to share what they understand and what they have questions about
- Have students try to answer one another’s questions
- Don’t be in a hurry to explain
YOU DON’T HAVE TO BE THE EXPERT
- Make “understanding” their “problem”
- For example:
- Print and post the code on a whiteboard
- Draw arrows to the parts that students are unsure about
- Students may use sticky notes to write/post descriptions of what the code sections do
- The more you explain the less they will think about it
GET READY TO BE SURPRISED
- I’ve spend many, many days in grades 1-10 classrooms co-teaching with math + coding
- A common event is teachers telling me to look at a student whose engagement and understanding surprises them
C. INEQUALITIES
![](https://learnx.ca/wp-content/uploads/2021/10/Screen-Shot-2021-10-04-at-3.47.37-PM.jpg)
1. PUZZLE #1
- Go to https://scratch.mit.edu/projects/540216861/editor/
- Run the code. The output is shown below.
![](https://learnx.ca/wp-content/uploads/2021/10/Screen-Shot-2021-10-03-at-5.29.28-PM-971x1024.jpg)
1.1
A. Alter the code to get the following output.
![](https://learnx.ca/wp-content/uploads/2021/06/Screen-Shot-2021-06-03-at-7.28.27-PM.jpg)
B. Alter the code to get the following output.
![](https://learnx.ca/wp-content/uploads/2021/06/Screen-Shot-2021-06-03-at-7.29.46-PM.jpg)
1.2
Alter the code in other ways and notice the effect.
- What part of the code do you understand?
- What part of the code do you have questions about?
2. PUZZLE #2
- Go to https://scratch.mit.edu/projects/540229313/editor/
- Run the code. The output is shown below.
![](https://learnx.ca/wp-content/uploads/2021/10/Screen-Shot-2021-10-03-at-5.33.04-PM-911x1024.jpg)
2.1
A. Alter the code as shown below.
![](https://learnx.ca/wp-content/uploads/2021/06/Screen-Shot-2021-06-03-at-8.10.32-PM.jpg)
- Predict how the output will change.
- Run the code to test your prediction.
- Explain the result.
B. Alter the code as shown below.
![](https://learnx.ca/wp-content/uploads/2021/06/Screen-Shot-2021-06-03-at-8.13.27-PM.jpg)
- Predict how the output will change.
- Run the code to test your prediction.
- Explain the result.
C. Alter the code to get the output shown below.
![](https://learnx.ca/wp-content/uploads/2021/06/Screen-Shot-2021-06-03-at-8.15.48-PM.jpg)
D. Alter the code as shown below. [Notice that “and” changed to “or”]
![](https://learnx.ca/wp-content/uploads/2021/06/Screen-Shot-2021-06-03-at-8.19.12-PM.jpg)
- Predict how the output will change.
- Run the code to test your prediction.
- Explain the result.
2.2
Alter the code in other ways to get similar results.
- What have you learned about about inequalities and their graphs?
- What else do you want to know?
3. PUZZLE #3 – grades 7/8
- Go to https://scratch.mit.edu/projects/507100358/editor
- The code and the output as shown below.
- Run the code.
![](https://learnx.ca/wp-content/uploads/2021/06/Screen-Shot-2021-06-03-at-7.08.41-PM.jpg)
3.1
A. Alter the code to get the output shown below.
![](https://learnx.ca/wp-content/uploads/2021/06/Screen-Shot-2021-06-03-at-7.16.36-PM-1.jpg)
B. Alter the code to get the output shown below.
![](https://learnx.ca/wp-content/uploads/2021/06/Screen-Shot-2021-06-03-at-7.18.09-PM.jpg)
3.2
Alter the code in other ways and notice the effect.
- What more have you learned about about inequalities and their graphs?
- What else do you want to know?
4. PUZZLE #4 – grades 7/8
- Go to https://scratch.mit.edu/projects/540225499/editor/
- Run the code.
- The output is shown below.
![](https://learnx.ca/wp-content/uploads/2021/10/Screen-Shot-2021-10-03-at-5.38.50-PM-903x1024.jpg)
4.1
A. Alter the code as shown below.
![](https://learnx.ca/wp-content/uploads/2021/06/Screen-Shot-2021-06-03-at-7.49.54-PM.jpg)
- Predict how the output will change.
- Run the code to test your prediction.
- Explain the result.
B. Alter the code as shown below.
![](https://learnx.ca/wp-content/uploads/2021/06/Screen-Shot-2021-06-03-at-7.50.42-PM.jpg)
- Predict how the output will change.
- Run the code to test your prediction.
- Explain the result.
C. Alter the code as shown below.
![](https://learnx.ca/wp-content/uploads/2021/06/Screen-Shot-2021-06-03-at-8.00.14-PM.jpg)
- Predict how the output will change.
- Run the code to test your prediction.
- Explain the result.
4.2
Alter the code in other ways to get similar results.
- What more have you learned about inequalities and their graphs?
- What else do you want to know?
Grades 5-6 WORKSHOP
![](https://learnx.ca/wp-content/uploads/2021/07/Screen-Shot-2021-07-12-at-12.58.49-PM.jpg)
D. BIG PICTURE #2
![](https://learnx.ca/wp-content/uploads/2021/10/neural-network.jpeg)
CODING OFFERS ADVANTAGES
- Coding models mathematics concepts & relationships dynamically
- It makes abstract ideas feel tangible
- It affords agency
- It offers a low floor and a high ceiling
- Coding has the potential to change what mathematics can be done and who can do it.
DON’T TEACH CODING, TEACH MATH
- The pressure around us is to teach all kids how to code
- Mathematics education is about offering all students access to the structure, beauty and wonder of mathematics
- Coding is a great tool to think with, especially when we have good conceptual structure of the mathematics
![](https://learnx.ca/wp-content/uploads/2019/08/infinity-in-hand-1019x1024.jpg)
E. EVAPORATION RATES
![](https://learnx.ca/wp-content/uploads/2021/10/Screen-Shot-2021-10-04-at-3.44.45-PM-1.jpg)
![](https://learnx.ca/wp-content/uploads/2021/10/Screen-Shot-2021-10-04-at-3.44.53-PM-1.jpg)
![](https://learnx.ca/wp-content/uploads/2021/10/Screen-Shot-2021-10-04-at-3.45.05-PM.jpg)
Let’s model this with Python –https://colab.research.google.com/drive/1I_AHVoWqFgWBZU7eEMMgBUK0pkJzlRPx?usp=sharing
![](https://learnx.ca/wp-content/uploads/2021/10/Screen-Shot-2021-10-04-at-4.41.12-PM.jpg)
![](https://learnx.ca/wp-content/uploads/2021/10/Screen-Shot-2021-10-04-at-4.41.35-PM.jpg)
![](https://learnx.ca/wp-content/uploads/2021/10/Screen-Shot-2021-10-04-at-4.41.25-PM.jpg)
F. NATURAL DENSITY
Examples
![](https://learnx.ca/wp-content/uploads/2021/09/Screen-Shot-2021-09-01-at-8.40.17-PM.jpg)
- d(even numbers) = 0.5
- what is the probability that a random natural number is odd?
- d(multiples of 5) = 0.2
- what is the probability that a random natural number is a multiple of 5?
- d(multiples 0f 10) = 0.1
- what is the probability that a random natural number is a multiple of 10?
![](https://learnx.ca/wp-content/uploads/2021/09/Screen-Shot-2021-09-01-at-8.19.17-PM.jpg)
NATURAL DENSITY OF SQUARE NUMBERS
A SURPRISE
- d(square numbers) = 0
- what is the probability that a random natural number is a square number?
How do we make sense of d(square numbers) = 0 ?
Here is one way …
page 38
![](https://learnx.ca/wp-content/uploads/2021/09/Screen-Shot-2021-09-01-at-8.24.01-PM.jpg)
Here is the completed table.
![](https://learnx.ca/wp-content/uploads/2021/09/Screen-Shot-2021-09-02-at-4.48.31-AM-copy.jpg)
page 39
![](https://learnx.ca/wp-content/uploads/2021/09/Screen-Shot-2021-09-01-at-8.25.09-PM.jpg)
The Scratch code shown above is available at https://scratch.mit.edu/projects/565845359/editor
algebraically
![](https://learnx.ca/wp-content/uploads/2021/09/Screen-Shot-2021-09-02-at-9.54.19-AM.jpg)
G. +/-/x RELATIONS
![](https://learnx.ca/wp-content/uploads/2021/10/Screen-Shot-2021-10-04-at-4.53.06-PM.jpg)
Adding relations … Try the code at https://scratch.mit.edu/projects/557365154/editor
Multiplying relations … Try the code at https://scratch.mit.edu/projects/557347523/editor/
H. READINGS
Integrated Mathematics + Computer Science – Grade 10: Reforming Secondary School Mathematics Education (April 2018). Read the White Paper by CT CoP members, George Gadanidis (Western University) and Jeff Cummings (Wellington Catholic DSB). See the Grades 1-3 lesson studies.
![](https://learnx.ca/wp-content/uploads/2021/10/Screen-Shot-2021-10-04-at-8.37.29-AM.jpg)
Coding in the Ontario Mathematics Curriculum, 1-8: Might it be transformational? Read the March 2021 report at http://mkn-rcm.ca/wp-content/uploads/2021/03/CL-mkn-v3.pdf
![](https://learnx.ca/wp-content/uploads/2021/10/Screen-Shot-2021-03-24-at-7.48.02-AM-768x261-1.jpg)