IGCSE Foundation: Properties of Shapes

Scheme of work: IGCSE Foundation: Year 10: Term 1: Properties of Shapes

Prerequisite Knowledge

1. Knowledge of the Metric System
• Concept: Understanding units of measurement within the metric system, including linear and area units.
• Example: $\text{1 meter (m) = 100 centimeters (cm)}, \quad \text{1 square meter (m}^2\text{) = 10,000 square centimeters (cm}^2\text{)}$
2. Names of Common 2D and 3D Shapes
• Concept: Recognizing and naming common 2D and 3D shapes.
• Example: $\text{2D shapes: triangle, square, rectangle, circle}, \quad \text{3D shapes: cube, sphere, cylinder, cone}$
3. Identifying Lines of Reflective Symmetry
• Concept: Identifying lines of reflective symmetry in various shapes.
• Example: $\text{A square has 4 lines of symmetry, a rectangle has 2 lines of symmetry}$
4. Order of Rotational Symmetry of 2D Shapes
• Concept: Understanding the order of rotational symmetry in 2D shapes.
• Example: $\text{A square has an order of rotational symmetry of 4, an equilateral triangle has an order of 3}$

Success Criteria

1. Translating Shapes
• Performing Translations: Students should be able to translate shapes on a coordinate grid.
• Example: $\text{Translate the point (2,3) by the vector (4, -1) to (6, 2)}$
• Describing Translations: Students should be able to describe translations using vectors.
• Example: $\text{A translation by the vector } \begin{pmatrix} 4 \\ -1 \end{pmatrix}$
2. Reflecting Shapes
• Performing Reflections: Students should be able to reflect shapes across a given mirror line.
• Example: $\text{Reflect the point (3, 4) across the line } y = x \text{ to get (4, 3)}$
• Describing Reflections: Students should be able to describe reflections using mirror lines.
• Example: $\text{Reflection across the line } y = x$
3. Rotating Shapes
• Performing Rotations: Students should be able to rotate shapes about a point by a given angle.
• Example: $\text{Rotate the point (1, 2) by } 90^\circ \text{ clockwise about the origin to get (2, -1)}$
• Describing Rotations: Students should be able to describe rotations using center and angle.
• Example: $\text{A rotation } 90^\circ \text{ clockwise about the origin}$
4. Enlarging Shapes
• Performing Enlargements: Students should be able to enlarge shapes by a given scale factor from a center of enlargement.
• Example: $\text{Enlarge the point (2, 3) by a scale factor of 2 from the origin to get (4, 6)}$
• Describing Enlargements: Students should be able to describe enlargements using scale factor and center.
• Example: $\text{An enlargement by scale factor 2 from the origin}$

Key Concepts

1. Translating Shapes
• Concept: Understanding that translating a shape moves it without rotating or reflecting it.
• Example: $\text{A point (2, 3) translated by (4, -1) moves to (6, 2)}$
2. Reflecting Shapes
• Concept: Understanding that reflecting a shape flips it over a mirror line.
• Example: $\text{A point (3, 4) reflected across } y = x \text{ moves to (4, 3)}$
3. Rotating Shapes
• Concept: Understanding that rotating a shape turns it about a point by a specified angle.
• Example: $\text{A point (1, 2) rotated by } 90^\circ \text{ clockwise about the origin moves to (2, -1)}$
4. Enlarging Shapes
• Concept: Understanding that enlarging a shape changes its size but not its shape.
• Example: $\text{A point (2, 3) enlarged by a scale factor of 2 from the origin moves to (4, 6)}$

Common Misconceptions

1. Translating Shapes
• Common Mistake: Students might incorrectly translate shapes by adding or subtracting the wrong values.
• Example: Translating (2, 3) by (4, -1) as: $\text{Incorrect: } (2, 3) + (4, -1) = (5, 2)$ $\text{Correct: } (2, 3) + (4, -1) = (6, 2)$
2. Reflecting Shapes
• Common Mistake: Students might incorrectly reflect shapes by not using the correct mirror line.
• Example: Reflecting (3, 4) across $$y = x$$ as: $\text{Incorrect: } (3, 4) \rightarrow (3, 4)$ $\text{Correct: } (3, 4) \rightarrow (4, 3)$
3. Rotating Shapes
• Common Mistake: Students might incorrectly rotate shapes by not using the correct angle or center.
• Example: Rotating (1, 2) by $$90^\circ$$ clockwise about the origin as: $\text{Incorrect: } (1, 2) \rightarrow (2, 1)$ $\text{Correct: } (1, 2) \rightarrow (2, -1)$
4. Enlarging Shapes
• Common Mistake: Students might incorrectly enlarge shapes by not using the correct scale factor or center.
• Example: Enlarging (2, 3) by a scale factor of 2 from the origin as: $\text{Incorrect: } (2, 3) \times 2 = (4, 6)$ $\text{Correct: } (2, 3) \rightarrow (4, 6)$

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