# Grade 9 Math + Coding Workshop

26 October 2021, (c) George Gadanidis

# 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

#### 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

## 1. CHALLENGE #1

- Go to https://scratch.mit.edu/projects/540216861/editor/
- Run the code. The output is shown below.

#### 1.1

**A. **Can you alter the code to make the following graph?

**B.** Can you alter the code to make the following graph?

#### 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. CHALLENGE #2

- Go to https://scratch.mit.edu/projects/540229313/editor/
- Run the code. The output is shown below.

#### 2.1

**A. **Alter the code as shown below.

- Can you predict how the output will change?
- Run the code to test your prediction.
- Explain the result.

**B.** Alter the code as shown below.

- Can you predict how the output will change?
- Run the code to test your prediction.
- Explain the result.

**C.** Can you alter the code to make the following graph?

**D.** Alter the code as shown below. [Notice that “and” changed to “or”]

- Can you 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. CHALLENGE #3 – grades 7/8

- Go to https://scratch.mit.edu/projects/507100358/editor
- The code and the output as shown below.
- Run the code.

#### 3.1

**A. **Can you alter the code to make the following graph?

**B.**Can you alter the code to make the following graph?

#### 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. CHALLENGE #4 – grades 7/8

- Go to https://scratch.mit.edu/projects/540225499/editor/
- Run the code.
- The output is shown below.

#### 4.1

**A. **Alter the code as shown below.

- Can you predict how the output will change?
- Run the code to test your prediction.
- Explain the result.

**B.** Alter the code as shown below.

- Can you predict how the output will change?
- Run the code to test your prediction.
- Explain the result.

**C.** Alter the code as shown below.

- Can you 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

# D. BIG PICTURE #2

#### 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

# E. +/-/x RELATIONS

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/

# F. NATURAL DENSITY

#### Examples

*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?

*d*(1) = 0- what is the probability that a random natural number has the value of 1?

#### 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

Here is the completed table.

###### page 39

The Scratch code shown above is available at https://scratch.mit.edu/projects/565845359/editor

#### algebraically

# G. 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.

**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