# Shapes and angles ## Midpoints inquiry

Mathematical inquiry processes: Test and classify cases; counter-example; draw conclusions; reason. Conceptual field of inquiry: Types of quadrilaterals; midpoints; coordinates and vectors.

## 2-dimensional shapes inquiry

Mathematical inquiry processes: Explore and test cases; find rules; generalise. Conceptual field of inquiry: Measurement of angles; interior angles of polygons; inscribed shapes inside circles.

## Four pentagons inquiry

Mathematical inquiry processes: Interpret; explore; find rules; generalise. Conceptual field of inquiry: Measurement of angles; angle properties of regular pentagons and rhombuses; interior and exterior angles of polygons.

## 12 equilateral triangles inquiry

Mathematical inquiry processes: Interpret; explore; find rules; generalise. Conceptual field of inquiry: Angle properties of equilateral triangles; tessellation.

## Parallel lines inquiry

Mathematical inquiry processes: Interpret; explore; generate other examples; find rules. Conceptual field of inquiry: Angle properties of straight and parallel lines; independent and dependent angles. ## Tessellation inquiry

Mathematical inquiry processes: Test cases; reason; generalise to other cases; prove. Conceptual field of inquiry: Tessellation; rotation and translation.

## Overlapping shapes inquiry

Mathematical inquiry processes: Explore; generate and classify more examples. Conceptual field of inquiry: Area; describe shapes; fractions and percentages.

# Area and perimeter

## Equal areas inquiry 1

Mathematical inquiry processes: Generate examples; analyse structure; reason. Conceptual field of inquiry: Area and perimeter; formulae; pi (π).

## Equal areas inquiry 2

Mathematical inquiry processes: Explore; test particular cases; change the condition; reason. Conceptual field of inquiry: Area; formulae; √2.

## Inscribed shapes inquiry

Mathematical inquiry processes: Interpret conditions; analyse structure; reason. Conceptual field of inquiry: Area; compound areas; Pythagoras' Theorem; fractions and percentages.

## Fraction of a shape inquiry

Mathematical inquiry processes: Interpret; analyse structure; reason. Conceptual field of inquiry: Area; Pythagoras' Theorem and trigonometry; fractions and percentages.

## 4-by-3 rectangle inquiry

Mathematical inquiry processes: Interpret; define parameters; explore. Conceptual field of inquiry: Area and perimeter; formulae.

# Volume and surface area

## Volume and surface area inquiry

Mathematical inquiry processes: Explore; test particular cases; reason. Conceptual field of inquiry: Surface area; volume; geometrical solids.

## Volume of a cylinder inquiry

Mathematical inquiry processes: Set conditions; generate examples; test particular cases; represent; reason. Conceptual field of inquiry: Volume of geometrical solids; formulae; graphs and turning points.

# Transformations

## Combined transformations inquiry

Mathematical inquiry processes: Generate examples; test particular cases; analyse structure. Conceptual field of inquiry: Reflections, rotations and translations; combined transformations.

## Reflections and coordinates inquiry

Mathematical inquiry processes: Generate examples; test particular cases; analyse structure. Conceptual field of inquiry: Reflections and other transformations; coordinates.

# Enlargement and scale factor

## Enlargement inquiry

Mathematical inquiry processes: Interpret; generate more examples. Conceptual field of inquiry: Enlargements (positive and negative); other transformations.

## Scale factors inquiry

Mathematical inquiry processes: Verify; test particular cases; analyse structure; reason. Conceptual field of inquiry: Surface area and volume; Length, area and volume scale factors of enlargement.

# Pythagoras' Theorem and trigonometry

## Right-angled triangles inquiry

Mathematical inquiry processes: Generate more examples; conjecture; create and test particular cases. Conceptual field of inquiry: Pythagoras' Theorem; trigonometry; sequences; algebraic expressions for the nth term of a sequence; expanding double brackets; area.

## Four scalene triangles inquiry

Mathematical inquiry processes: Generate more examples; conjecture; create and test particular cases. Conceptual field of inquiry: Sine and cosine rules; sequences; algebraic expressions for the nth term of a sequence.

## Area of a triangle inquiry

Mathematical inquiry processes: Explore; test particular cases; analyse structure; reason. Conceptual field of inquiry: Area of a triangle using the sine of an angle.

# Miscellaneous

## Pyramid inquiry

Mathematical inquiry processes: Interpret; explore; test particular cases. Conceptual field of inquiry: Volume of a pyramid; circumference and perimeter.

## Flags inquiry

Mathematical inquiry processes: Identify properties; generate more examples; analyse structure. Conceptual field of inquiry: Area; fractions; ratio.