# Grade 9 Math + Coding Workshop

13 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.

##### BOOK A: Teaching Support
• Curriculum expectations
• Trajectories, surprises, insights
• Success criteria
• Act 1 …
• Act 2 …
• Solutions
##### BOOK B: Number
• Sets & subsets of numbers
• Infinity, limit & density
• Powers
• Integers
• Fractions
• Ratios, proportions & rates
##### BOOK C: Algebra
• Expressions & equations
• Linear & non-linear relations
• Applications of linear relations
##### BOOK D: Data
• Data representation & analysis
• Data correlations
• Mathematical modelling
##### BOOK E: Geometry & measurement [ready October 18]
• Geometry & measurement
• Change relationships

# C. INEQUALITIES

C4.2 graph relations represented as algebraic equations of the forms x = k, y = k, x + y = k, x y = k, ax + by = k, and xy = k, and their associated inequalities, where a, b, and k are constants, to identify the points and/or regions defined by these equations and inequalities

#### 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?

#### 2.1

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 else do you want to know?

# D. PLAYING WITH RELATIONS

C4. demonstrate an understanding of the characteristics of various representations of linear and non-linear relations, using tools, including coding when appropriate

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/

# E. NATURAL DENSITY

B1.3 use patterns and number relationships to explain density, infinity, and limit as they relate to number sets

#### 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?

#### 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

• Have students execute the code to see its output
• Ask them to alter the code to model the different intervals in the table
• 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 AN 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

• You will be surprised by who can do what and how
• 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

• 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