(c) George Gadanidis, 2 September 2021

# What’s new in Grade 9?

- destreamed
- some new big ideas of mathematics (infinity & limit in the context of natural density)
- coding as a tool
- students research & tell a mathematics story

# An example from Number

## 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?

## 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 …

#### 2 PAGES FROM *MATHEMATICS GRADE 9*

###### 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

# Infinity & limit in grade 9?

The short answer is: *Mathematics is big but kids’ minds are bigger!*

If you visit St. Matthew the Evangelist Catholic School in Whitby, Ontario, you will see this large painting in the front foyer, depicting the work of grade 3 students (over 10 years ago), as they learned to hold infinity in their hands.

See also a workshop on infinity & limit at https://learnx.ca/infinity.

# How to approach 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: 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
- Print and post the code on a whiteboard
- Draw arrows to the parts that students are unsure about
- Students can use sticky notes to write/post description 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 math + coding
- A common event is teachers telling me to look at a student whose engagement and understanding surprises them

#### CODING OFFERS ADVANTAGES

- Models mathematics concepts & relationships dynamically
- Makes abstract ideas feel tangible
- Offers agency
- Offers a low floor and a high ceiling

#### DON’T TEACH CODING, TEACH MATH

- The fad around us is to teach all kids how to code
- Our job is to teach all kids about the structure, beauty and wonder of mathematics
- Coding is a great tool, in some mathematics contexts

# The *Mathematics Grade 9* resource

**BOOK A – Teaching support**- Curriculum expectations
- Trajectories, surprises & insights
- Success criteria
- Teaching suggestions
- Solutions

**BOOK B – Number**- for teachers & students

**BOOK C – Algebra**- for teachers & students

… more coming soon