# Grade 9 Math + Coding Workshop

5 October 2021, (c) George Gadanidis

# A. WHAT’S NEW?

• 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.

• De-streamed classes.
• Research and tell a mathematics story.

# B. BIG PICTURE #1

• 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. PUZZLE #1

#### 1.1

A. Alter the code to get the following output.

B. Alter the code to get the following output.

#### 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

#### 2.1

A. Alter the code as shown below.

• Predict how the output will change.
• Run the code to test your prediction.
• Explain the result.

B. Alter the code as shown below.

• 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.

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

• 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

#### 3.1

A. Alter the code to get the output shown below.

B. Alter the code to get the output shown below.

#### 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

#### 4.1

A. Alter the code as shown below.

• Predict how the output will change.
• Run the code to test your prediction.
• Explain the result.

B. Alter the code as shown below.

• Predict how the output will change.
• Run the code to test your prediction.
• Explain the result.

C. Alter the code as shown below.

• 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?

# 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 conceptual structure of the mathematics

# E. EVAPORATION RATES

Let’s model this with Python –https://colab.research.google.com/drive/1I_AHVoWqFgWBZU7eEMMgBUK0pkJzlRPx?usp=sharing

# 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?

#### 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

# G. +/-/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/