**Key Concepts**

Relationships

**Related Concepts**

Representation, simplification

**Statement of Inquiry**

The evolution of numerical representations are used to express and simplify relationships.

**Careers**

- Bricklayer
- Chef
- Conservation scientist

**Inquiry Questions**

**Factual Questions**

- What is base 10?
- What is an integer?
- What is a quotient/ dividend/ divisor/ remainder?
- What is base 10?
- What is a term/ expressions/ variable/constant/ coefficient?
- What is the link between the base 10 number system and the conversion of metric units?
- What is the difference between commutative and associative rules?
- What real life examples can we relate expanding brackets to?

**Conceptual Questions**

- How did the base 10 number become a number system?
- How can collecting terms simplify a problem?
- What real life examples can we relate expanding brackets to?

**Debatable Questions**

- How is using the metric system favourable over the existence of the imperial one?
- To what extent are we influenced by events of the past?
- To what extent does the systems and decisions of our ancestors affect the way we live today?
- To what extent do metric and imperial number systems affect the way humans interact with one another?
- How can the generalisations allow solutions to differ?

**Key Concepts**

Form, logic

**Related Concepts**

Measurements, change

**Statement of Inquiry**

Artistry and aesthetics are enhanced by a knowledge of form and measurement.

Puzzles and games require logical thought to change outcomes.

**Careers**

- Architect
- Structural Engineer
- Engineering Construction Technician
- Artist
- Town Planner
- Health and Safety Advisor
- Actuary
- Bodyguard
- Outdoor and Adventurous Activity Leader

**Inquiry Questions**

**Factual Questions**

- What are lines?
- What does the word parallel mean?
- What do angles in a triangle sum to?
- What do angles on a straight line/around a point sum to?
- What are mathematical puzzles and games?
- What is logical thought?
- What is the probability scale?

**Conceptual Questions**

- How do varying angles change structures?
- How does a change in one angle influence others in vertically opposite angles?
- How do measurements affect aesthetics?
- Why do the angles in a triangle and angles on a straight line both sum to 180 degrees? Are there connections?
- How are puzzles developed?
- Why is change often required?

**Debatable Questions**

- To what extent is aesthetics linked with angles?
- Can the perception of angles and lines affect the aesthetics from one person to another?
- To what extent does logic elicit change?
- Is illogical change ever necessary?

**Key Concepts**

Form, relationships

**Related Concepts**

Approximation, simplification, models, patterns

**Statement of Inquiry**

Approximating and simplifying quantities in different forms can help us understand digital life.

Does the process of finding patterns and relationships aid in finding model solutions.

**Careers**

- Structural engineer
- Computer programmer
- Farmer

**Inquiry Questions**

**Factual Questions**

- What does simplify mean?
- What is the difference between an exponent, power and index?
- What is a square root?
- What is a pattern?
- What are the different types of patterns?

**Conceptual Questions**

- Depending on the form, how can powers be simplified?
- How can we use our knowledge of fractions to help simplify powers?
- When is it appropriate to exchange the representation?
- How does simplification give a better form?
- How do approximations lead to accurate representations?
- How do we model patterns?
- How is it possible to model a pattern and make predictions?

**Debatable Questions**

- To what extent does the degree of accuracy impact different forms?
- When do simplifications eradicate details?
- Is there a mathematical order to our natural world?

**Key Concepts**

Relationships

**Related Concepts**

Model, representation

**Statement of Inquiry**

Relationships in demography and populations can be represented through different models.

**Inquiry Questions**

**Factual Questions**

- What characteristics must all bar charts have?
- What do angles around a point add up to?
- What is a variable?
- What does solve mean?
- What is a linear equation?

**Conceptual Questions**

- Does the order of operations must be obeyed in every situation?

**Key Concepts**

Form

**Related Concepts**

Quantity, simplification

**Inquiry Questions**

**Factual Questions**

- What are the types of Measurement?
- What are the Systems of measurement?
- Are all measurements metric?

**Conceptual Questions**

- What is the difference between metric and imperial measurement?
- How do the area conversions of metric measures differ from the length conversions?

**Debatable Questions**

- Which system of measurement is commonly used and why?

**Key Concepts**

Logic

**Related Concepts**

Justification, measurement

**Statement of Inquiry**

A knowledge of shape allows us to strategically plan infrastructure in a logical way.

**Careers**

- Town planner
- Logistics
- Architecture

**Inquiry Questions**

**Factual Questions**

- What are the properties of a Triangle?
- What are the properties of a quadrilateral?
- What are the properties of a circle?
- What are the differences between similarity and congruence?

**Conceptual Questions**

- How does a knowledge of 2d shapes help you model 3d problems?
- How can a quadrilateral fit into more than one classification of shape?
- Are all similar shapes also congruent?

**Debatable Questions**

- Why do we have shapes which fit into multiple categories and is this helpful?
- Towns should be made in blocks, just like the USA, it’s just easier that way?
- We should only use the metric system, it’s better, isn’t it?