# Grade 9 Math + Coding Workshop

13 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. MATHEMATICS GRADE 9

**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: D**ata

- Data representation & analysis
- Data correlations
- Mathematical modelling

**BOOK E: Geometry & measurement [ready October 18]**

- Geometry & measurement
- Change relationships

**BOOK F: Financial literacy [ready early November]**

# C. INEQUALITIES

#### GRADE 9 EXPECTATIONS

**C4.2 **graph relations represented as algebraic equations of the forms *x *= k, *y *= k, *x *+ *y *= k, *x *– *y *= k, a*x *+ b*y *= 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. 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?

#### INEQUALITIES in 1D, 2D & 3D

# 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?

#### 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

# F. ABOUT CODING

#### 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 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 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

# 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